JP2003527577A - System and method for quantifying nonlinearity in an interferometric measurement system - Google Patents

Abstract

(57) SUMMARY The present invention features an interference measurement system and method that quantifies non-linearities, such as, for example, cyclic errors, in an interference signal generated by the interference measurement system. The systems and methods described above analyze the interference signal for each of the plurality of Doppler shifts to distinguish non-linearities that may otherwise be spectrally superimposed with the main interference signal, and to provide for various Doppler shifts. Interpolate the contribution of nonlinearity to the measured values. The time-varying interference signal, or the phase extracted from the time-varying interference signal, is Fourier transformed and at least some non-linearities are associated with peaks in the squared absolute value (ie, power spectrum) of the Fourier transformed signal. Can be The magnitude and phase of the Fourier transform at each frequency of such peaks is used to quantify the associated non-linearities. The quantified nonlinearity is used by the system to correct the optical path length measurement. A change in the magnitude of one or more of the quantified non-linearities can also be used to identify degradation of components of the interferometric system.

Description

Detailed Description of the Invention

BACKGROUND OF THE INVENTION The present invention is directed to, for example, lithographic scanners or steppers.
The present invention relates to an interferometer such as a displacement measuring interferometer and a dispersion interferometer that measure a displacement of a measurement target such as a mask stage or a wafer stage in a system, and an interferometer that monitors a wavelength to determine an intrinsic characteristic of gas.

The displacement measuring interferometer monitors changes in the position of the measuring object with respect to the reference object based on the optical interference signal. The interferometer generates the optical interference signal by superimposing and interfering the measurement beam reflected from the measurement object with the reference beam reflected from the reference object.

In many applications, the measurement and reference beams have orthogonal polarities and different frequencies. The different frequencies are, for example, laser-Zeeman splitting
It can be generated by acousto-optic modulation, or inside the laser using birefringent elements or the like. Due to the orthogonal polarization, the polarization beam splitter directs the measurement beam and the reference beam with respect to the measurement object and the reference object, respectively, and combines the reflected measurement beam and the reference beam to form a superposed measurement beam and a reference beam. Form a beam. The superposed exit beam forms an output beam which subsequently passes through the polarizer. The polarizer mixes the outgoing measurement beam and the outgoing reference beam to form a mixed beam. Since the components of the outgoing measurement beam and the outgoing reference beam in this mixed beam interfere with each other, the intensity of the mixed beam changes depending on the relative phase of the outgoing measurement beam and the outgoing reference beam. The time-dependent intensity of the mixed beam is measured by a detector, which produces an electrical interference signal proportional to the intensity. Since the measurement beam and the reference beam have different frequencies, the electrical interference signal contains a "heterodyne" signal having a beat frequency equal to the difference between the respective frequencies of the emitted measurement beam and the emitted reference beam. If the lengths of the measurement path and the reference path change relative to each other, for example by translating a stage containing the object to be measured, the measured beat frequency includes a Doppler shift equal to 2 vnp / λ, where v is the measurement Relative velocities of the object and the reference object, λ is the wavelength of the measurement beam and the reference beam, n is the index of refraction of a medium such as air or vacuum in which the light beam travels, and p is the reference object and the measurement object. The number of passages for an object.
The change in the relative position of the measurement object corresponds to the change in the phase of the measured interference signal, and the phase change of 2π is substantially equal to the distance change L of λ / (np), where L is, for example, measured. A round-trip distance change such as a change in the distance to the stage including the object and a change in the distance from the stage.

Unfortunately, this equality condition is not always exact. Many interferometers use the “circular error (
known as "cyclic error". Circular error can be expressed as a contribution to the phase and / or intensity of the measured interfering signal and has a sinusoidal dependence on the change in optical path length pnL. , The first-order cyclic error in the phase has a sinusoidal dependence of (2πpnL) / λ, and the second-order cyclic error in the phase is 2
It has a sinusoidal dependence of (2πpnL) / λ. Higher order cyclic errors can also be represented.

Circular error is caused by a portion of the input beam nominally forming the reference beam propagating along the measurement path and / or a portion of the input beam nominally forming the measurement beam along the reference path. Can be caused by "beam mixing" of propagating through. Such beam mixing is due to interference such as ellipticity in the polarization of each input beam and imperfections in the polarizing beam splitter used to direct each orthogonally polarized input beam along the reference and measurement paths, respectively. It can be caused by imperfections in the meter components. Due to beam mixing and consequent cyclic error, there is no strict linear relationship between the change in the phase of the measured interference signal and the relative optical path length pnL between the reference and measurement paths. If not compensated, the cyclic error caused by beam mixing can limit the accuracy of range changes measured by the interferometer. Circular errors also cause imperfections in the transmissive surface that produce unwanted multiple reflections in the interferometer, and configurations such as retroreflectors and / or phase delay plates that cause the unwanted ellipticity of the beam in the interferometer. It can also be generated by imperfections in the elements. For a general literature on the theoretical causes of cyclic errors, see, for example, Applied Optics, 37, 6
696-6700, 1998. W. Wu and R.W. D. Deslat
tes's “Analytical modeling of the per”
iodic non-linearity in heterodyne int
Refer to "erferometry".

In dispersion measurement applications, optical path length measurements include, for example, 532 nm and 1064 nm.
Is used for measuring the dispersion of gas in the measurement path of a distance measuring interferometer. Dispersion measurement
element) can be used to convert the optical path length measured by the distance measuring interferometer into a physical length. Such a conversion can be important, because the gas turbulence and / or the measurement arm (m
This is because changes in the average density of the gas in the easurement arm can cause changes in the measured optical path length. In addition to the extrinsic dispersion measurement, in order to convert the optical path length to the physical length, the intrinsic value of the gas is calculated.
need to know lue). The coefficient Γ is a proper intrinsic value and also the reciprocal dispersion of the gas with respect to the wavelength used in the dispersion interferometry.
dispersive power). The coefficient Γ can be measured separately or based on literature values. The cyclic error in the interferometer also contributes to the dispersion measurement and the measurement of the coefficient Γ. Circulation errors can also degrade interferometric measurements used to measure and / or monitor the wavelength of the beam.

SUMMARY OF THE INVENTION The present invention features an interferometry system and method that quantifies non-linearities in interfering signals, such as cyclic errors. Non-linearities are caused by the properties of interferometric systems such as beam mixing, multiple reflections, and non-linear signal processing electronics. Non-linearity creates an additional term in the interference signal that deviates the phase of the interference signal from the linear relationship to the optical path length difference. According to the present system and method, the accuracy of the displacement measurement, the wavelength measurement, and the dispersion measurement can be improved by correcting the measurement value for the non-linearity contribution. In addition, previously unrecognized sources of non-linearity are identified and formulated.

The present system and method analyzes multiple measurements of interfering signals corresponding to different optical path length differences to quantify non-linearity. In a particular embodiment, the time varying interference signal, or
The phase extracted from the time-varying interference signal is Fourier transformed and at least some non-linearity is associated with the peak in the squared modulus of the Fourier transformed signal. The magnitude and phase of the Fourier transform at each frequency of such peaks are used to quantify the associated nonlinearity. The frequency of each peak and whether it is resolved or not is typically dependent on the rate of change of the optical path length difference, the Doppler shift. Therefore, the present systems and methods often analyze multiple time-varying interfering signals for each of multiple Doppler shifts to distinguish non-linearities that may not otherwise be apparent, as well as different Doppler shifts. Interpolate the contribution of non-linearity to the measured value in the shift. For example, the non-linearity contribution may be interpolated to the measured value when the object being measured is stationary or changing direction, i.e. when the Doppler shift is zero or passes through zero.

In general, in one aspect, the invention features an interferometric measurement system. During operation, the interferometric system directs two beams along separate paths defining an optical path length difference and then combines the beams to produce an interfering pair of exit beams. A detector for generating an interference signal s (t) representative of the optical path length difference and responsive to optical interference between the pair of superposed outgoing beams; and an analyzer coupled to the detector. Including. The signal s (t) has a frequency equal to the sum of the frequency splitting ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. Including the main item. Due to the characteristics of the interferometric system, the signal s (t) further comprises an additional term, each having a frequency that is not equal to the sum of the frequency division ω and the Doppler shift ψ. During operation, the analyzer quantifies at least one additional term i) based on the value of s (t) such that the value of the Doppler shift causes the main term and at least one additional term to be spectrally separated. And ii) using at least one quantified additional term, another value of s (t) such that the value of the Doppler shift causes the main term and the at least one additional term to be spectrally superimposed. Evaluate the corresponding change in optical path length difference.

The interferometry system may include any of the following features. The detectors may include photodetectors, amplifiers and analog / digital converters. The frequency division between the two beams can be non-zero. The at least one additional term may include multiple additional terms.

In order to quantify at least one additional term, the analyzer described above uses the expression s (t) ∝cos (ω
t + ψ + ζ _1,0,1,0 ) + NL based on the Doppler shift ψ for the value of s (t)
Where NL is the initial quantification of the additional term, ψ = Lkn, L is the physical path length difference, k is the wave number, n is the refractive index, and ω Is the angular frequency division between the two beams, t is the time, and ζ _1,0,1,0 is the phase offset. The initial quantification may be NL = 0.

The analyzer may quantify at least one additional term by evaluating the corresponding coefficient of the representation of s (t) considering each additional term. For example, the above representation of s (t) can be expressed as:

[0013]

[Equation 6] ω is the angular frequency division between the two beams, and _{ω'u '} is the detector, analyzer and 2
Is a frequency caused by at least one of the sources of the two beams and is not equal to ω, L is the physical path length difference, λ is the wavelength of the beam in the first set, and n is the index of refraction. , C is the speed of light in a vacuum, and t is time. The main term corresponds to a _1,0,1,0 cos (ωt + ψ + ζ _1,0,1,0 ) and the additional term corresponds to the remaining terms. The amplitudes a _v and B _v and the phase ζ _v define each coefficient for the representation of s (t), and v is a subscript that means a general index.

In order to quantify at least one additional term, the analyzer calculates a frequency spectrum corresponding to each value of s (t) of a given set, and calculates each of the sinusoids in the representation of s (t). in at prime time equal angular frequency to the derivative related ～Omega arguments sinusoidal one which does not correspond or at ～Omega alias ～Omega _a, at least one based on the frequency spectrum amplitude and phase The coefficients for the additional terms can be evaluated. For example, the frequency spectrum may be a Fourier transform of each value of a given set of s (t). Alternatively, the frequency spectrum may be a Fourier transform of α (t) and s (t) is s (t) = A where α (t) is the phase of s (t).
It is expressed as (t) cos (α (t)). If the analyzer has at least 1 based on the amplitude and phase of the frequency spectrum at ~ ω alias ~ ω _A.
To evaluate each coefficient for the additional terms, the alias frequency is

[0015]

[Equation 7] For a positive integer r satisfying

[0016]

[Equation 8] , Where the detector has a sampling rate that defines the Nyquist frequency ω _Ny . To evaluate each coefficient, for example, ~ ω is u '≠ 0.
To ω + ω ′ _{u ′} , and ˜ω can be one of q (ω + · ψ), or ˜ω is p ≠ 1 and u = 0. It can be one of uω + p · ψ + p ⁺ · ψ for ≠ 0.

In order to evaluate each coefficient for at least one additional term, the analyzer normalizes the amplitude and phase of the frequency spectrum at the angular frequency ω by at least one non-zero value of ψ. The derivative can be considered.

The analyzer may determine at least one additional term based on each value of s (t) of the first set that has a Doppler shift large enough to spectrally separate the additional frequency from the dominant frequency. Based on each value of s (t) of the second set that after quantification, the Doppler shift is different from each value of the first set and is large enough to spectrally separate the additional frequency from the main frequency. At least one additional term may be further quantified. The analyzer may then quantify at least one additional term as a function of Doppler shift by interpolating the quantification value for each value of s (t) in each set.

The analyzer determines the dependence of each of the evaluated coefficients on the Doppler shift based on each value of s (t) of the multiple sets, each set corresponding to a different Doppler shift. obtain.

The at least one additional term may be a plurality of additional terms, and the analyzer may quantify the plurality of additional terms by using a frequency spectrum at a corresponding plurality of angular frequencies ˜ω _v or their aliases. The coefficient for each of the plurality of additional terms can be evaluated based on the amplitude and the phase of the. Each ~ ω _v is equal to the time derivative of the argument of one sinusoid that does not correspond to the principal term within each sinusoid in the representation of s (t). In such an embodiment, the analyzer is such that q is odd and j is q.
Evaluate the coefficients corresponding to at least some of B _{1,0,1,0, q, q-2j} and ζ _{1,0,1,0, q, q-2j} as non-negative integers smaller than / 2-1. By doing so, B _{1,0,1,0, q, 1} and ζ _{1,0,1,0, q, 1} (for example, zero frequency shift error) can be determined.

The above-mentioned analyzer is s (t) ∝cos (ωt + ψ + ζ _1,0,1,0 ) + NL (ψ, · ψ
), The change in optical path difference corresponding to other values of s (t) can be evaluated by determining a value for ψ = Lkn that is self-consistent with. NL represents at least one quantified addition term, L is a physical path length difference, k is a wave number, n is a refractive index,
ω is the angular frequency difference between the two beams, t is the time, and ζ _1,0,1,0 is the phase offset. For example, the analyzer may determine the value for ψ by iteratively improving the evaluation of the value for ψ.

The analyzer uses the estimated change in optical path length to determine the change in physical path length, the change in dispersion, the intrinsic value of the gas, or the wavelength of each beam. Can be monitored.

In general, in another aspect, the invention directs two beams along separate paths defining an optical path length difference during operation and then combines and superimposes each beam. An interferometer for producing a pair of outgoing beams, a detector for producing a signal s (t) representative of the interference in response to optical interference between the pair of overlapping outgoing beams, and a detector coupled to the detector. And an interferometric measurement system including an analyzer. The signal s (t) is a function of the optical path length difference. Due to the characteristics of the interferometry system, the signal s (t) is represented as s (t
) = Acos (ωt + ψ + ζ), where ψ = Lkn, L is the physical path length difference, k is the wavenumber, n is the index of refraction, and ω is between the two beams. Is a possible angular frequency difference, t is time, a is an amplitude that is constant with respect to ψ, and ζ is a phase offset that is constant with respect to ψ and · ψ. During operation, the analyzer i) Fourier transforms each value of s (t) of at least one set in which the rate of change of optical path length difference is not zero (.ψ ≠ 0). It defines a power spectrum equal to the squared absolute value of the Fourier transform,
ii) quantify at least some deviations based on the amplitude and phase of the Fourier transform at a frequency different from ω + · ψ and corresponding to the peak of the power spectrum, and iii) using the quantized deviations, s The change in the optical path length difference corresponding to the specific value of (t) is evaluated.

In general, in another aspect, the invention directs two beams along separate paths defining an optical path length difference during operation and then combines and superimposes each beam. An interferometer for producing a pair of outgoing beams, a detector for producing a signal s (t) representative of the interference in response to optical interference between the pair of overlapping outgoing beams, and a detector coupled to the detector. And an interferometric measurement system including an analyzer. The signal s (t) is a function of the optical path length difference. Due to the characteristics of the interferometry system, the signal s (t) is represented as s (t
) = Acos (ωt + ψ + ζ), where ψ = Lkn, L is the physical path length difference, k is the wavenumber, n is the index of refraction, and ω is between the two beams. Possible angular frequency difference, t is time, a is an amplitude that is constant with respect to ψ, ζ is a phase offset that is constant with respect to ψ and · ψ, and s
(T) is s (t) = A (t) cos (α (t) where α (t) is the phase of s (t).
). During operation, the analyzer calculates i) the phase α for s (t)
(T) is extracted, and ii) each value of α (t) of at least one set in which the speed of change in optical path length difference is not zero (· ψ ≠ 0) is Fourier-transformed. Defines a power spectrum equal to the squared absolute value of
i) quantify at least some deviations based on the amplitude and phase of the Fourier transform at a frequency different from ω + · ψ and corresponding to the peak of the power spectrum, and iv) using the quantized deviations, s The change in the optical path length difference corresponding to the specific value of (t) is evaluated.

In general, in another aspect, the invention directs two beams along separate paths defining an optical path length difference during operation and then combines and superimposes each beam. An interferometer for producing a pair of outgoing beams, a detector for producing an interference signal s (t) representing the optical path length difference in response to optical interference between the pair of overlapping outgoing beams, and the detector. An interferometric measurement system including an analyzer coupled to the analyzer and an alarm mechanism coupled to the analyzer. The signal s (t) contains a principal term having a frequency equal to the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. . Due to the characteristics of the interferometry system, the signal s (t) further comprises additional terms each having a frequency that is not equal to the sum of the frequency division ω and the Doppler shift ψ. During operation, the analyzer causes the signal s (
The frequency of t) is monitored, and a signal indicating system deterioration is generated when the amplitude of the frequency corresponding to one of the additional terms exceeds a threshold value. The alert mechanism is responsive to the system degradation signal.

The interferometry system may include any of the following features. The alarm mechanism may include at least one of a visual display, an acoustic system, a warning light and a printer. To monitor the frequency at s (t), the analyzer may Fourier transform each value of s (t) in at least one set. Alternatively, s (t) replaces α (t) with s (
Assuming that the phase of t) is expressed as s (t) = A (t) cos (α (t)), the above-mentioned analyzer calculates the phase α (t) from each value of s (t) of at least one set. , And the frequency at s (t) can be monitored by Fourier transforming the extracted phase α (t).

The analyzer may monitor the frequency at s (t) based on the value of s (t) that the main term and at least one additional term are spectrally separated by the value of the Doppler shift.

The signal s (t) may be represented by the cumulative sum calculation given above with respect to the above aspect of the invention. In order to determine whether or not to generate a signal indicating system deterioration, the above-mentioned analyzer sets thresholds to frequency ω + ω ′ _{u ′} for u ′ ≠ 0 and frequency q (ω + · ψ).
, Or, if p ≠ 1 and u = 0, the frequency uω + p · ψ for p ≠ 0
It can be compared with the amplitude of one of the frequencies + p ⁺ ψ.

In general, in another aspect, the invention provides, during operation, two beams of a first set having a frequency division ω and two beams of a second set having a frequency division ω _T not equal to ω.
A source for providing two beams and, during operation, directing the first beam of the first set and the first beam of the second set along a measurement path and the second beam of the first set. And a second beam of the second set along a reference path and combining the beams of both sets to form an output beam, wherein the measurement path and the reference path have an optical path length difference. A defining interferometer, a detector responsive to optical interference between the beams in the output beam, and a signal S (t) representative of the interference as a function of the optical path length difference, coupled to the detector. And an interferometric measurement system including the analyzed analyzer.
In the absence of the second set of beams, the signal S (t) has a principal term at a frequency equal to the sum of the frequency division ω and the Doppler shift ψ defined by the rate of change of the optical path length difference. Equal to s (t) inclusive. Due to the characteristics of the interferometry system, each zero-frequency shift cyclic error contributing to s (t) at the same frequency as the main frequency.
error) is triggered. If the second set of beams is present, then s (t)
The above property of producing a zero frequency shift cyclic error contribution to S produces a multiplet in the frequency spectrum of S (t), which has respective neighboring peaks separated by ω-ω _T. During operation, the analyzer discriminates between each frequency in S (t) to identify the multiplex and at least one zero frequency shift cyclic error based on the amplitude and phase of at least one peak in the multiplex. Quantify.

The interferometric measurement system may include any of the following features. The analyzer may quantify the zero frequency shift cyclic error based on the amplitude and phase of each of the peaks in the multiline. The analyzer may also be coupled to the source and the analyzer may selectively provide the interferometer with the first set of beams rather than the second set of beams with the source. If the analyzer selectively provides the interferometer with the first set of beams rather than the second set of beams with the source, the analyzer includes s (t) and each zero quantified. The optical path length difference can be determined based on at least one of the frequency shift cyclic errors and the zero frequency shift cyclic error. Alternatively, the analyzer may determine the optical path length difference based on S (t) and at least one zero frequency shift cyclic error of each quantified zero frequency shift cyclic error.

The analyzer can distinguish each frequency in S (t) by Fourier transforming each value of S (t) of at least one set. Alternatively, S (t) is α _S (t
) Is expressed as S (t) = A _S (t) cos (α _S (t)) where _S (t) is the phase of _S (t). By extracting and Fourier-transforming each value of α _S (t) of at least one set, S (t)
Each frequency can be distinguished.

The multiline may include peaks at the dominant frequency. Each frequency division can be below the Nyquist frequency, in which case the detector samples the value of S (t) at a rate that defines the Nyquist frequency. The difference between the average frequencies of the first set of beams and the second set of beams may be greater than the Nyquist frequency. For example the frequency _{division, ω <ω Ny, ω T} <ω Ny and │ω-ω _T │«ω, for example can satisfy _{│ω-ω T │ <(ω} / 100).

The source may include first and second lasers, the first set of beams being derived from the first laser and the second set of beams being derived from the second laser. Further, the source may include first and second lasers and first and second acousto-optic modulators, and the first set of beams is derived from the first lasers and the first acousto-optic modulators. And the second set of beams is derived from the second laser and the second acousto-optic modulator. Alternatively, the source is a laser and a first
And a second acousto-optic modulator, wherein the first beam derived from the laser passes through the first acousto-optic modulator to produce the first set of beams and is derived from the laser. The second beam passes through the second acousto-optic modulator to produce the second set of beams. For example, the first and second beams derived from the laser may correspond to adjacent longitudinal modes of the laser.

The analyzer can distinguish the frequency multiplex in S (t) for each of the plurality of Doppler shifts and quantify the dependence of the quantified zero frequency shift cycling on the Doppler shift. During operation, the analyzer may generate a signal representative of system degradation when the amplitude of the multiplex exceeds a threshold. The system may further include an alarm mechanism coupled to the analyzer and responsive to the system degradation signal.
For example, the alert mechanism may include at least one of a visual display, an acoustic speaker, a printer and a warning light.

Finally, the signal s (t) can be represented by the cumulative sum calculation given above with respect to the previous aspect of the invention, where the quantified zero frequency shift cyclic error is q = B _{1,0,1,0, q, 1} and ζ _{1,0,1,0, q, 1} for one of 3, 5, 7 ...

In general, in another aspect, the invention features an interferometric measurement system that includes an interferometer, a detector, and an analyzer. During operation, the interferometer directs the two beams along separate paths that define the optical path length difference and then combines the beams to produce a pair of overlapping exit beams. The detector is responsive to optical interference between the pair of overlapping output beams and produces an interference signal s (t) representative of the optical path length difference. The signal s (t) contains a principal term having a frequency equal to the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. . Due to the characteristics of the interferometry system, the signal s (t) further comprises additional terms each having a frequency that is not equal to the sum of the frequency division ω and the Doppler shift ψ. The analyzer is coupled to the detector and during operation i) the signal s
Applying a window function to the series of values of (t), and ii) Fourier transforming the series of windowed values, the Fourier transform defining a power spectrum equal to the squared absolute value of the Fourier transform. And iii) the frequency division ω and Doppler shift ψ
Identify at least one additional term based on at least one peak in the power spectrum at a frequency not equal to the sum of and.

The interferometry system may include any of the following features. The window function can reduce the amplitude of the series of values of s (t), since the sequence approaches any of its endpoints. Alternatively or additionally, the window function may reject frequencies equal to the sum of the frequency division ω and the Doppler shift ψ for the frequencies of the at least one additional term.

Further, during operation, the analyzer is based on the amplitude and phase of the Fourier transform at a frequency of at least one peak in the power spectrum.
Individual additional terms can be quantified. The analyzer uses s (t
The change in optical path length difference corresponding to the specific value of) can be evaluated. The analyzer also uses the estimated change in optical path length difference to determine the change in physical path length, the change in dispersion, the intrinsic value of the gas, and the wavelength of each beam. You can do at least one of the following:

Similarly, the analyzer can further generate a signal representative of system degradation when the amplitude of the identified additional term exceeds a threshold, and the interferometric system further includes the analyzer. A coupled alarm mechanism may be included that is responsive to the system degradation signal. For example, the alert mechanism may include at least one of a visual display, an acoustic system, a warning light and a printer.

In general, in another aspect, the invention features an interferometric measurement system that includes an interferometer, a detector, and an analyzer. During operation, the interferometer directs the two beams along separate paths that define the optical path length difference and then combines the beams to produce a pair of overlapping exit beams. The detector is responsive to optical interference between the pair of overlapping output beams and produces an interference signal s (t) representative of the optical path length difference. The signal s (t) is
It includes a principal term having a frequency equal to the sum of the frequency split ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. Due to the characteristics of the interferometry system, the signal s (t) further comprises additional terms each having a frequency that is not equal to the sum of the frequency division ω and the Doppler shift ψ. The analyzer is coupled to the detector and includes a low pass filter. During operation, the analyzer i) tracks the value of the Doppler shift based on the signal s (t), and ii) one of each additional term based on the value of the tracked Doppler shift. frequency ~ω _'v were calculated, iii) s (t) cos (~ω' v t) equal to the first tuning filter signal and s (t) sin (~ω ' v t) equal second tuning filter Generate a signal, and iv) pass each tuned filter signal through the low pass filter to quantify the additional term corresponding to ~ ω ' _v .

The interferometric measurement system may include any of the following features. During operation, the analyzer calculates the frequency ~ ω ' _v of one of the additional terms based on the value of the tracked Doppler shift and the Nyquist frequency defined by the sampling rate of the detector. You can The analyzer may also generate an additional tuned filter signal based on the frequency of the at least one other additional term to quantify the at least one other additional term. The analyzer may also use the quantified additive term to evaluate the change in optical path length difference corresponding to a particular value of s (t). The analyzer also uses the estimated change in optical path length difference to determine the change in physical path length, the change in dispersion, the intrinsic value of the gas, and the wavelength of each beam. You can do at least one of the following:

Similarly, the analyzer may further generate a signal representative of system degradation when the amplitude of the quantified additional term exceeds a threshold, and the interferometric system may further include in the analyzer. A coupled alarm mechanism may be included that is responsive to the system degradation signal. For example, the alert mechanism may include at least one of a visual display, an acoustic system, a warning light and a printer.

In general, in another aspect, the invention features an interferometric measurement system that includes an interferometer, a detector, and an analyzer. During operation, the interferometer directs the two beams along separate paths that define the optical path length difference and then combines the beams to produce a pair of overlapping exit beams. The detector is responsive to optical interference between the pair of overlapping output beams and produces an interference signal s (t) representative of the optical path length difference. The signal s (t) is
It includes a principal term having a frequency equal to the sum of the frequency split ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. Due to the characteristics of the interferometry system, the signal s (t) further comprises additional terms each having a frequency that is not equal to the sum of the frequency division ω and the Doppler shift ψ. The analyzer is coupled to the detector and during operation the analyzer provides i) quantification for at least some additional terms, and ii) each value of s (t) of at least one set. And iii) evaluating the value for the optical path length difference based on the amplitude and phase of the Fourier transform at the frequency ω + ψ, and performing Doppler deviation corresponding to each value of s (t) in the predetermined set. Evaluate the quantification value for the additional term that contributes to the Fourier transform at the frequency ω + · ψ based on the shift · ψ.

The interferometry system may include any of the following features. During operation, the analyzer determines which addition in the quantification is based on the Doppler shift .psi. Corresponding to each value of s (t) in the predetermined set and the Nyquist frequency corresponding to the sampling rate of the detector. It can be identified whether the terms contribute to the Fourier transform at the frequency ω + · ψ. Similarly, the analyzer uses the estimated change in optical path length difference to determine the change in physical path length, the change in dispersion, the intrinsic value of the gas, and the At least one of wavelength monitoring may be performed.

In general, in another aspect, the invention features a stage for supporting a wafer, an illumination system for imaging spatially patterned radiation onto the wafer, and the stage for the imaged radiation. A lithographic system used in the fabrication of integrated circuits on a wafer, including a positioning system for adjusting the position of the stage and any of the interferometric measuring systems described above for measuring the position of the stage.

In general, in another aspect, the invention includes a wafer supporting stage and an illumination system including a radiation source, a mask, a positioning system, a lens assembly, and any of the interferometric systems described above. During operation, the source directs radiation through the mask to produce spatially patterned radiation and the positioning system adjusts the position of the mask with respect to radiation from the source. The lens assembly images the spatially patterned radiation onto the wafer, and the interferometric system measures the position of the mask relative to the radiation from the source integrated on the wafer. It features a lithographic system used to create the circuit.

In general, in another aspect, the invention features a source for providing a writing beam for patterning a substrate, a stage for supporting the substrate, and a beam steering assembly for providing the writing beam to the substrate. And a positioning system for positioning the stage and the beam steering assembly with respect to each other, and any of the interferometric measurement systems described above for measuring the position of the stage with respect to the beam steering assembly. Featured beam writing system.

In a further aspect, the invention features an interferometry method, a lithographic method and a beam writing method based on each of the above systems. A general aspect of such a method is described below.

In one aspect, the invention features an interferometry method for use with an interferometry system. The interferometric method comprises the steps of directing two beams along a separate path and combining the beams to produce a pair of exit beams that are superimposed, wherein the separate path is the optical path. A step of defining a length difference and a step of measuring optical interference between the pair of superposed outgoing beams to generate an interference signal s (t) representing the optical path length difference, the signal s ( t) includes a principal term having a frequency equal to the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference, and the interferometric measurement Due to the characteristics of the system, the signal s (t) further comprises an additional term each having a frequency that is not equal to the sum of the frequency division ω and the Doppler shift ψ, and depending on the value of the Doppler shift the main term and at least the One additional term is the spectrum Quantifying at least one additional term based on the value of s (t) to be separated into, and using the quantified at least one additional term, the main term and at least one by the value of the Doppler shift Evaluating the change in the optical path length difference corresponding to another value of s (t) that the additional term of is spectrally superimposed.

In another aspect, the invention features an interferometry method for use with an interferometry system. The interferometric method comprises the steps of directing two beams along a separate path and combining the beams to produce a pair of exit beams that are superimposed, wherein the separate path is the optical path. A step of defining a length difference and a step of measuring optical interference between the pair of superposed outgoing beams to generate an interference signal s (t) representing the optical path length difference, the signal s ( t) includes a principal term having a frequency equal to the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference, and the interferometric measurement Due to the characteristics of the system, the signal s (t) further comprises an additional term each having a frequency that is not equal to the sum of the frequency division ω and the Doppler shift ψ, and monitoring the frequency of the signal s (t). And one of the additional items above When the amplitude of the frequency corresponding to the pressurized section exceeds a threshold value and a step of alerting the operator.

In another aspect, the invention features an interferometry method for use with an interferometry system. The method of interferometry comprises providing two beams of a first set having a frequency division ω and two beams of a second set having a frequency division ω _T not equal to ω; Directing a first beam and a first beam of the second set along a measurement path and a second beam of the first set and a second beam of the second set along a reference path; Combining the beams of both sets to form an output beam, the measuring path and the reference path defining an optical path length difference; and measuring optical interference between the beams in the output beam, Generating a signal S (t) representing the interference as a function of the optical path length difference, the signal S (t) in the absence of the second set of beams being the frequency division ω and the optical path length difference. Doppler shift determined by the rate of change of A characteristic in the interferometric system that causes each zero frequency shift cyclic error to contribute to s (t) at the same frequency as the main frequency is equal to s (t) including the main term at a frequency equal to the sum of ψ. , The characteristic that produces a zero frequency shift cyclic error contribution to s (t) produces a multiplex in the frequency spectrum of S (t) when the second set of beams is present, and the multiplex is ω-ω. Identifying each of the multiple lines by distinguishing each frequency in S (t) with each neighboring peak separated by _T, and at least one zero frequency based on the amplitude and phase of at least one peak in the multiple line Quantifying shift cyclic error.

In general, in another aspect, the invention comprises directing two beams along separate paths and combining the beams to produce a pair of exit beams for superposition. , The separate path defines an optical path length difference, and measuring optical interference between the pair of overlapping exit beams to generate an interference signal s (t) representing the optical path length difference. Where the signal s (t) has a frequency equal to the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. Said signal s (t) further comprising a main term, each signal having a frequency that is not equal to the sum of said frequency division ω and Doppler shift ψ due to the characteristics of the interferometry system, said signal s (t) The window function is applied to a series of values of (t). And Fourier transforming a series of windowed values, the Fourier transform defining a power spectrum equal to the squared absolute value of the Fourier transform, the frequency division ω and the Doppler shift. -Identifying at least one additional term based on at least one peak in the power spectrum at a frequency not equal to the sum of ψ and the interference measurement method.

In general, in another aspect, the invention comprises directing two beams along separate paths and combining the beams to produce a pair of exit beams for superposition. , The separate path defines an optical path length difference, and measuring optical interference between the pair of overlapping exit beams to generate an interference signal s (t) representing the optical path length difference. Where the signal s (t) has a frequency equal to the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. Said signal s (t) further comprising a main term, each signal having a frequency that is not equal to the sum of said frequency division ω and Doppler shift ψ due to the characteristics of the interferometry system, said signal s (t) The value of the Doppler shift based on (t) A step of tail, and calculating the frequency ~ω _'v of one additional section of the additional term on the basis of the tracked values of the Doppler shift, s (t) cos (~ω
_'V t) equal to the first tuning filter signal and s (t) sin (~ω' v t and generating an equal second tuning filter signal), the low pass through the filter above each tuning filter signal And quantifying the additional term corresponding to ω ′ _v .

In general, in another aspect, the invention comprises directing two beams along separate paths and combining the beams to produce a pair of exit beams for superposition. , The separate path defines an optical path length difference, and measuring optical interference between the pair of superposed outgoing beams to generate an interference signal s (t) representing the optical path length difference. Where the signal s (t) has a frequency equal to the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. At least some further comprising a main term, the signal s (t) each having a frequency that is not equal to the sum of the frequency division ω and the Doppler shift ψ due to the characteristics of the interferometry system. Provides quantification for the additional terms in Fourier transforming each value of s (t) of at least one set, evaluating the value for the optical path length difference based on the amplitude and phase of the Fourier transform at the frequency ω + · ψ, and performing the predetermined set. Evaluating the value of quantification for the additional term contributing to the Fourier transform at the frequency ω + · ψ based on the Doppler shift / ψ corresponding to each value of s (t) of .

In a further aspect, the invention includes supporting a wafer on a stage, imaging spatially patterned radiation on the wafer, and aligning the stage with the imaged radiation. A lithographic method comprising adjusting the position and measuring the relative position of the stage using any of the interferometry methods described above.

In another aspect, the invention includes supporting a wafer, directing radiation from a source to a mask to produce spatially patterned radiation, and the mask to the radiation. Positioning the step of measuring the position of the mask with respect to the radiation using any of the interferometric measuring methods described above, and imaging the spatially patterned radiation on the wafer, And a lithographic method including.

In another aspect, the invention comprises providing a writing beam for patterning a substrate, supporting the substrate on a stage, providing the writing beam to the substrate, A beam writing method is characterized by including the step of positioning the stage with respect to the writing beam and the step of measuring the relative position of the stage using any of the interference measurement methods described above.

Embodiments of the invention may include many advantages. For example, each embodiment may identify and quantify non-linearities that would otherwise degrade interferometric displacement or dispersion measurements. The quantified non-linearity can be used to significantly improve its accuracy by correcting the interferometric measurements. In addition, interferometers can be made more inexpensively using the systems and methods of the present invention, since expensive optical components to reduce the possibility of non-linearity are not required, and for detection. This is because it is not necessary to minimize the non-linearity in the electronic device. Further, by using the system and method of the present invention, performance degradation of one or more components of the interferometer may be detected and a remedial action may be performed, for example, as part of planned maintenance, which is inappropriate. The likelihood of significantly wasting reasonable operating time as a result of operating the interferometer in different modes is reduced. The embodiments of the present invention, which quantify non-linearities, allow for rapid correction of interferometric measurements, which is typically required during on-line applications where the measurement object is rapidly scanned or step-moved. It The quantification of non-linearities and the use of the quantification in the correction of interferometric measurements has led to optical distance measurements, dispersion measurements, wavelength measurements, and optical intrinsic properties such as the inverse dispersion rate Γ of the gas in the measuring arm of the interferometer. It can be applied to measurements. Additionally, the interferometric measurement system may be used in lithography and mask writing applications.

Other features and advantages will be apparent from the following detailed description and claims. DETAILED DESCRIPTION Non-linearities such as periodic errors can reduce the accuracy of displacement and / or dispersion measurements extracted from interferometry data. Non-linearities can result from defects in the optics of the source and interferometer and from non-linearities in the detection electronics, such as photoelectric detectors, amplifiers or analog-to-digital converters. Although it may be possible to minimize the cause of such non-linearities, one aspect of the invention is that the accuracy of interferometric measurements, quantifying non-linearities, and quantified Using non-linearity, the interferometric signal (or information derived from the interferometric signal) is corrected for non-linearity, so that, for example, displacement or dispersion,
It is proposed to improve by improving the accuracy of the measurement of interest.
Another aspect of the invention is to quantify the degradation of certain components of the interferometer system, the non-linearity of the interferometer system, and to determine whether the components are degraded. We propose to detect by monitoring based on size changes. Interferometry systems that provide such functionality are generally described below, followed by more specific embodiments.

Referring to FIG. 1, an interferometry system 10 includes a source 20, an interferometer 30.
, Detector 40 and analyzer 50. The source 20 comprises one or more beams 2
A laser is included to provide 5 to interferometer 30. In dispersive interferometry, beam 25 comprises at least two beams, which are, for example, 1064 nm and 532.
nm of different wavelengths. A single wavelength is sufficient for optical distance displacement measurements. When using heterodyne interferometry techniques at one or more different wavelengths, the source 20 introduces a frequency division between the components of each beam at one or more different wavelengths. For example, one or more acousto-optic modulators can be used to introduce frequency division, or alternatively the source can include a Zeeman split laser to produce frequency division. The frequency division components are often made to have orthogonal polarizations. The frequency division components can be transmitted to interferometer 30, where they are separated into measurement and reference beams. Alternatively, source 20 may spatially separate the frequency-divided components and send the spatially separated components to interferometer 30, where they become the measurement and reference beams.

The interferometer 30 can be any type of interferometer, for example a differential plane mirror interferometer, a double pass interferometer or a Michelson type interferometer. Interferometer,
For example, it can be designed to monitor optical path length changes, physical path length changes, refractive index changes, beam wavelength changes, or unique gas properties along the path length. The interferometer directs the reference beam along a reference path (which may contact the reference object) and directs the measurement beam along a measurement path that contacts the measurement object (eg, lithographic stage). Directed and then combined the reference and measurement beams to form an overlapping pair of exit beams 35. In distributed interferometry applications, there is an overlapping pair of exit beams for each different wavelength.

The interference between the overlapping pairs of exit beams contains information about the relative difference in optical path length between the reference and measurement paths. In some embodiments, the reference path is fixed, so changes in the optical path length difference correspond to changes in the optical path length of the measurement path. However, in other embodiments, the optical path lengths of the reference and measurement paths may have changed. For example, the reference path may contact a reference object (eg, a column reference) that may move relative to the interferometer. In this latter case, the change in the difference in optical path length corresponds to the change in the position of the measuring object relative to the reference object.

When the reference and measurement beams have orthogonal polarizations, the intensity of at least one intermediate polarization of the overlapping pair of exit beams is selected to produce optical interference. For example, a polarizer can be positioned within interferometer 30 to mix the polarizations of overlapping pairs of exit beams, which are then transmitted to detector 40. Alternatively, the polarizer can be located within the detector 40. The detector 40 measures the intensity of selected polarizations of the overlapping pair of exit beams and produces an interference signal. Portions of the beams can be combined with one another before being sent along the reference and measurement paths to provide a reference pair of overlapping exit beams, which is used to provide a reference interference signal.

The detector 40 comprises a photodetector, which measures the intensity of selected polarizations of the overlapping pair of exit beams and which further comprises electronic components such as preamplifiers and analog-to-digital converters. Including, they amplify the output from the photodetector and produce a digital signal s (t) corresponding to optical interference. In a distributed interferometry application, a digital signal s (t) is generated (corresponding to different wavelengths) for each overlapping pair of exit beams, which detector 40
This is done by using multiple photo-detection channels within.

The signal s (t) has no non-linearity and ignores the constant offset strength, which can be expressed as s (t) = a cos (ωt + ψ + ζ), where ψ = Lkn Yes, L is the physical path length difference between the reference and measurement paths, k is the wavenumber of the measurement beam, n is the index of refraction in the interferometer, and ω is the introduction of either Doppler shift. Is the angular division frequency difference between the previous measurement and reference beams, t is the time, a is the amplitude that is constant with respect to ψ, ζ is the phase offset that is constant with respect to ψ and ψ is ψ with respect to time
Is the first derivative of. In the homodyne application, the split frequency difference between the beam components in the equation for s (t) is zero, ie ω = 0, and to accurately separate the background signal from the optical interference, the detector 40 includes multiple photodetection channels for measuring interference for multiple phase offsets, which are introduced in the detector 40.

The signal s (t) is sent to the analyzer 50, which extracts the phase ψ = Lkn from s (t), which is the reference phase provided by the source of the heterodyne frequency division difference or reference interference signal. The analyzer can determine the change in optical length difference between the measurement and reference paths. In addition, using signals corresponding to additional wavelengths, the analyzer can make dispersion measurements, determine measurements of differences in physical path lengths, and / or measure the unique properties of the gas in the measurement path. it can.

The analyzer 50 includes a computer or digital processor, for performing the phase extraction and other analysis steps described below with respect to non-linearity quantification. For example, the number and symbol steps described herein are
For example, according to methods known in the art, a digital signal processor (
It can be converted into a digital program executed in a DSP). The digital program can be stored on a computer-readable medium such as a hard disk, which can be executed by a computer processor in the analyzer. Alternatively, the appropriate analysis steps can be converted into a digital program, which is hardwired into dedicated electronic circuitry within the analyzer that performs these steps. Methods for generating such specialized electronic circuits based on a given number or symbolic analysis procedure are also well known in the art.

Beam mixing and intensity variations in beam 25, defects in interferometer 30, and non-linearities in detector 40 and the electronics therein can all produce non-linearities in signal s (t). .. The non-linearity transforms the signal s (t) into the equation s
Deriving from (t) = a cos (ωt + ψ + ζ), for example, the above cyclic error can introduce an additional term into this equation, which is a _p1 cos (ωt + p
ψ + ζ _p1 ), etc., where p = 2, 3 ,. ． ． Is. Furthermore, p can be taken in fractional values when there are multiple paths in interferometer 30. Beam 2
Intensity Variations 5 may introduce additional term in this equation, which is _{a u'p1 cos (ωt + ω u} 't + pψ + ζ u'p1) and the like, provided that u' = 0, 1,.
． ． Is. The angular frequency ω _{u ′} may result, for example, from the switching frequency of the power supply in the source 20. In heterodyne applications, beam mixing can also introduce additional terms, such as a _p0 cos (p ψ + ζ ₁₀ ), which results in a small wave vector difference between the measurement and reference beams associated with heterodyne frequency division. There may also be a section dealing with. In addition, non-linearities in the output and frequency response of detector 40 and the electronics therein introduce additional terms, leading to a dominant term a
Mix cos (ωt + ψ + ζ) with the above term. For example, the equation for s (t), which explains some of the non-linearities, can take the form:

[0069]

[Equation 9] Where p = 1, 2, 3 ,. ． ． Is a fractional value, u = 0 or 1, and
q = 1, 2, 3 ,. ． ． And the “q” index is associated with the non-linearity at the detector 40. However, the above equation for s (t) assumes that the non-linearity at the detector is frequency independent. If not, each term resulting from the expansion in the above equation may contain a phase-dependent phase shift and amplitude of that term. This equation can be further complicated by the finite sampling rate of the analog-to-digital converter in detector 40, which can cause aliasing in the digital representation of s (t).

If not accounted for, the non-linearity contribution to s (t) can degrade the accuracy of the optical distance difference information extracted from the interfering signal. Often, the degree to which the accuracy is degraded depends on ψ, or the relative velocity of the measurement and reference objects, which is, for example, the Doppler shift. For example, for large Doppler shifts, by determining the change in ψ from the phase of the Fourier transform of s (t) at ω + · ψ, from ω + · ω in the frequency space, eg, 2 · ψ, ω + 2 · ψ, ω +
The contributions from these nonlinearities with peaks separated by 3 · ψ, 2ω + 2 · ψ are minimized. However, at smaller Doppler shifts, the contributions from many non-linearities overlap with the dominant peak at ω + · ψ in the power spectrum of s (t), and the power spectrum is the squared absolute of the Fourier transform of s (t). It is a value. The overlap is particularly large when ψ = 0, for example when the relative position of the measurement and reference object is stationary or when the relative velocity of the measurement and reference object changes sign. Furthermore, even when the Doppler shift separates the non-linear frequency from that of the dominant peak in the power spectrum of s (t), the non-linear frequency alias can overlap with the dominant peak at ω + · ψ. There is. further,
The magnitude and phase of the non-linearity, eg, B _q a _up and ζ _up, can also change with .psi. Because of the frequency dependent response of the sensing electronics, for example.

Furthermore, some non-linearities have frequencies that exactly overlap the dominant peak, regardless of the value of ψ. Such non-linearity can be called a zero frequency shift periodic error. For example, in the expansion of s (t) in the equation for q = 3 above, B ₃ a ³ ₁₁ cos ³ (ωt + ψ + ζ ₁₁ ) yields a term at the dominant frequency. In a similar way, for example, q = 2 between u = 1, p = 2 terms and u = 0, p = 1 terms.
The mixing of the differences in the expansion of yields a term at the dominant frequency.

The analyzer 50 quantifies the non-linearity based on the value of s (t) for multiple optical path length differences. In some embodiments, the non-linearity is represented as an additional sine term in the equation for s (t), eg, as shown in the equation above. In another embodiment, the non-linearity is represented in an additional phase term Ψ in s (t), where s (t) = A (t) cos (ωt + ψ + Ψ + ζ) and the phase term Ψ is
It can be represented as a series of sines with arguments similar to those shown in the sine of the equation for s (t) above. In each case, each non-linearity is quantified by estimating its corresponding sinusoidal amplitude and phase, where the amplitude and phase define the coefficients for the non-linearity. Alternatively, the coefficients can be defined by the amplitudes of the sine and cosine terms which together have an argument corresponding to the non-linearity.

During operation, the analyzer 50 calculates ψ (relative to the offset phase ζ ₁₁ ) by
Determine from the interference signal s (t) and the quantified non-linearity or a first guess about the quantified non-linearity, by using an iterative process, for example assuming that there is no non-linearity first. To determine ψ, and then iteratively determine an improved value for ψ from the interfering signal by including the non-linearity contribution corresponding to the previously determined value of ψ. . The analyzer may also determine a value for ψ based on the interference signal s (t) and the quantified nonlinearity or an initial guess for the quantified nonlinearity.

In an embodiment in which the non-linearity is represented in equation s (t) as a series of sine, the analyzer 50 calculates the non-linearity coefficient from the dominant frequency ω + · ψ from the dominant frequency ω + · ψ. And s () corresponding to a substantially constant value of ψ.
The value of t) can be estimated by Fourier transforming, which allows the non-linearity to be quantified. The analyzer identifies the dominant peak at ω + · ψ and associates the remaining peaks with the non-linearity, and the coefficient for each non-linearity, the complex amplitude of its corresponding peak, and, if necessary, in the Fourier transform Determine from factors of normalization that account for the effects of higher order derivatives of ψ. The analyzer 50 repeats these steps for an additional set of values of s (t) corresponding to the same substantially constant value of ψ, averaging the determined coefficients from all sets (or “ Filtering ”) to improve the quantification of non-linearities.

The analyzer 50 then repeats the steps in the preceding paragraph for values of s (t) corresponding to different substantially constant values of • ψ. The Fourier transform of such a value can generate a peak for the non-resolved nonlinearity in the Fourier transform of the value of s (t) corresponding to the first substantially constant value of ψ, Allows the analyzer to determine the coefficients for previously unresolved nonlinearities. These steps can be further repeated for values of s (t) corresponding to each additional substantially constant value of ψ. Furthermore, the analyzer 50
Interpolating the values of the coefficients determined for the values of s (t) corresponding to different substantially constant values of ψ, and determining the dependence of each non-linearity in ψ, if any. You can

In another embodiment, where the non-linearity is represented as a series of sines in the phase Ψ of s (t) = A (t) cos (ωt + ψ + Ψ + ζ), the analyzer 50 calculates the coefficient of non-linearity as The phase α of the value of s (t) corresponding to a number of substantially constant values (where
Estimate by Fourier transforming α = ωt + ψ + ψ + ζ). Otherwise, the analysis is similar to that described above. In a further embodiment, any combination of ωt, ˜ψ and ˜ψ can be subtracted from α before the Fourier transform is performed, where ˜ψ and ˜ψ are approximate estimates of ψ and ψ, respectively. .

In dispersion applications, or where the intrinsic refraction properties of the gas are being measured, the detector 40 sends a number of signals s _λ (t) to the analyzer 50 for each wavelength λ. The non-linearity quantification by the analyzer 50 can be based on the one or more signals s _λ (t) in a manner similar to that summarized above. Further, because of the improved accuracy provided by the non-linearity quantification, the interferometry system 10
Can be used in microlithography and beam writing systems.

The magnitude of the non-linearity can change over time as the components of the interferometry system degrade. For example, optical and electronic components can change over time, for example due to overuse, imperfect design, or environmental factors such as humidity, dust and temperature. In addition, environmental disturbances can degrade the optical alignment of the system.

Referring again to FIG. 1, in order to identify such degradations, the analyzer 50 monitors the quantified non-linearity over time to identify one or more of the quantified non-linearities. Determine if there is any sudden or gradual increase in size.
For example, the analyzer may monitor the frequency spectrum of either s (t) or the phase α of s (t) to determine when peaks at frequencies other than the dominant frequency ω + · ψ exceed acceptable threshold levels. You can decide. If so, the analyzer 50 sends a signal 55 to the alert mechanism 60 indicating system degradation. A warning mechanism responds to the signal 55 indicative of system degradation, which may indicate to the user that one or more components of the interferometry system have degraded beyond acceptable levels. By warning. For example, the alert mechanism 60 may include one or more video monitors that display an error message in response to the signal 55, a sound system or siren that produces an audio alert signal in response to the signal 55, and an error in response to the signal 55. A printer that prints the message and a light that emits light or changes color in response to signal 55 may be included.
The alerting mechanism 60 can also be coupled to an associated system, such as, for example, a lithographic or beam writing system, and can shut down the associated system in response to the signal 55.

The threshold level in the analyzer 50 can be preset by the operator to define an acceptable level for a particular application. Furthermore, the operator can preset a number of threshold levels, each corresponding to a particular non-linearity, for example a non-linearity in the frequency spectrum of s (t) or phase α of s (t). Frequency. Further, for a particular non-linearity, the analyzer 50 can compare the non-linearity magnitude to a number of threshold levels and cause the signal 55 to indicate the corresponding degree of degradation at which the threshold level is exceeded. Depending on this embodiment, the analyzer 50 quantifies the non-linearity and uses the quantified non-linearity to correct the measurement of the optical path length difference and reduce the system degradation to s (t) (or It can be monitored based on the magnitude of the non-linearity in the frequency spectrum of the phase α of s (t) or both.

A detailed description of particular embodiments follows. Although these differ in some details, the disclosed embodiments otherwise share many common elements and are inherently non-linear, depending on the type of end use application and due to cyclic error. There are several different categories depending on the type of procedure used to measure and correct for sexual effects.

Of the several different categories, embodiments of the first category include range-measuring interferometers operating with one wavelength to determine and compensate for the effects of periodic errors. The effect of the periodic error is determined from the analysis of the Fourier transform of the electronic interference signal, which is produced by detecting polarization-mixed reference and measurement beams from the interferometer.

Of the several different categories, embodiments of the second category include range-measuring interferometers operating with one wavelength, and the effect of periodic error is partly due to the phase of the electronic interference signal. It is compensated using the measured effect of the cyclic error, determined from the analysis of the Fourier transform. The electronic interference signal is generated by detecting polarization-mixed reference and measurement beams from an interferometer.

Of the several different categories, the third category of embodiments includes an apparatus and method for compensating for the effects of dispersion, or dispersion and distance measurement related signals, of periodic errors. The effect of the periodic error is determined from the analysis of the Fourier transform of the electronic interference signal, which is produced by detecting polarization-mixed reference and measurement beams from a dispersive and range-measuring interferometer. The effect of gas on the measurement path of the range finding interferometer is corrected by a distributed interferometry-based procedure.

Of the several different categories, the fourth category of embodiments measures and effects the effects of cyclic errors on the dispersion-related signals and on the distance-related interferometry dispersion-related signals and distance-related signals. An apparatus and method for compensation are included. Dispersive interferometry is used to determine the effect of gas on the measured optical distance of range finding interferometry, to detect and compensate for the effect of periodic errors on the dispersion related signal and on the range finding related signal. Apparatus and method are used. The effect of the cyclic error is compensated in the dispersion measurement-related signal or the dispersion measurement and distance measurement-related signal using the effect of the measured cyclic error. The effect of the measured periodic error is determined from the analysis of the Fourier transform of the phase of the electronic interference signal, which detects the polarization-mixed reference and measurement beams from the distance measuring and / or dispersive measuring interferometer. Is generated by

Of the several different categories, embodiments of the fifth category are dispersion measurement related signals and refraction measurement related signals, or refraction measurement related signals used to determine the optical properties of the unique gas. An apparatus and method for measuring and correcting periodic errors in a signal. Of the several different categories, the fifth category of embodiments was used to determine and / or monitor the wavelength of the optical beam,
It also includes apparatus and methods for measuring and correcting for periodic errors in wavelength measurement and / or related signals.

FIG. 2a shows, in schematic form, an apparatus and a method according to a first embodiment of the invention. The first embodiment is from the first category of embodiments. Figure 2
The interferometer shown in a is a polarization heterodyne single pass interferometer. Although the first embodiment includes a heterodyne system, the present invention is readily adapted for use in a homodyne system, where the reference and measurement beams have the same frequency prior to the introduction of either Doppler shift. . Although this device has applications for a wide range of sources, the following description is made by way of example in the context of optical measurement systems.

Referring to FIG. 2 a, the light beam 107 emitted from the source 101 is modulated by the modulator 10.
3 to become the light beam 109. The modulator 103 is excited by the driver 105. The source 101 is preferably a laser or similar source of coherent radiation, is preferably polarized and has a wavelength λ ₂ . Modulator 103
Can be, for example, an acousto-optic device having additional optics for selectively modulating the polarization component of beam 107, or a combination of acousto-optic devices. The modulator 103 changes the oscillation frequency of one linearly polarized light component of the beam 107 to
It is preferable to shift by an amount of f ₂ with respect to the orthogonal linearly polarized light components, the directions of polarization of the non-frequency and frequency-shifted components being parallel and orthogonal to the plane of FIG. The oscillation frequency f ₂ is determined by the driver 105.

The source 101, such as a laser, can also be any of a variety of frequency modulators and / or lasers. For example, the laser can be a gas laser, such as a helium-neon laser, which is stabilized in any of the various conventional techniques known to those skilled in the art, such as T.S. Baer et al. "F
frequency Stabilization of a 0.633 μm
He-Ne-longitudinal Zeeman Laser ", App
Lied Optics, 19, 3173-3177 (1980), 1975
U.S. Pat. No. 3,889,207 to Burgwald et al., Issued Jun. 10, 1975, and U.S. Pat. No. 3,662, Sandstrom et al., Issued May 9, 1972.
See No. 279. Alternatively, the laser can be a diode laser frequency stabilized in any of a variety of conventional techniques known to those skilled in the art, such as T.S. Okoshi and K.K. Kikuchi's "Freque"
ncy Stabilization of Semiconductor L
asers for Heterodyne-type Optical Co
mmunication Systems ", Electronic Lett
ers, 16, 179-181 (1980) and S.H. Yamaqguc
hi and M.D. Suzuki's "Simultaneous Stabilize"
ation of the Frequency and Power of
an AlGaAs Semiconductor Laser by Use
of the Opticalvanic Effect of Krypt
on ”, IEEE J. Quantum Electronics, QE-19
, 1514-1519 (1983).

Two optical frequencies can be generated by one of the following techniques. That is, (1) use of a Zeeman splitting laser, for example, July 2, 1969.
U.S. Pat. No. 3,458,259, issued to Bagley et al. Bouwh
ui's "Interferometry Mit Gaslasers",
Ned. T. Nature, 34, 225-232 (August 1968), 19
U.S. Pat. No. 3,656,853 to Bagley et al., Issued April 18, 1972; Matsumoto's “Recent interferometri”
c measurements using stabled case
rs ", Precision Engineering, 6 (2), 87-94.
(1984). (2) Use of a pair of acousto-optic Bragg cells, for example Y. Ohtsuka and K.K. Itoh's "Two-frequ
energy Laser Interferometer for Small
Displacement Measurements in a Low F
request Range ", Applied Optics, 18 (2)
219-224 (1979), N. et al. Massie et al. "Measuring"
Laser Flow Fields With a 64-Channel
Heterodyne Interferometer ", Applied
Optics, 22 (14), 2141 to 2151 (1983), Y. Oht
suka and M.M. Tsubokawa's "Dynamic Two-freq"
uency Interferometry for Small Displ
Acement Measurements ", Optics and Las
er Technology, 16, 25-29 (1984), H. et al. Mats
Umoto, supra, P.P., published Jan. 16, 1996. Dirksen et al., U.S. Pat. No. 5,485,272, N.P. A. Riza and M.M. M. K. Howl
ader's "Acoustic-optic system for the g
energy and control of tunable low
-Frequency signals ", Opt. Eng. , 35 (4), 9
20-925 (1996). (3) Use of a single pair of acousto-optic Bragg cells, for example G. G., published August 4, 1987, owned by the same owner. E. Sommargren U.S. Pat. No. 4,684,828, G. G., issued August 18, 1987, owned by the same owner. E. Sommargren, U.S. Pat. No. 4,687,958; See Dirksen et al., Supra.
(4) Use of two longitudinal modes of randomly polarized helium-neon lasers, see, for example, J. B. Ferguson and R.M. H. Morris "S
single Mode Collapse in 6328 ・ A HeNe
Lasers ", Applied Optics, 17 (18), 2924-2.
929 (1978). (5) Use of a birefringent element or the like inside the laser, for example, V.I. Evtuhov and A. E. Siegman's
A "Twisted-Mode" Technique for Obtai
Ning Axial Uniform Energy Density
in a Laser Cavity ", Applied Optics, 4 (
1), 142-143 (1965). Alternatively, “Apparatus to Transform Two No” filed April 17, 1998
n-Parallel Propagating Optical Beam
Components into Two Orthogonally Pol
US patent application Ser. No. 09 / 061,928 entitled “Arized Beam Components” and “Appara, filed February 18, 2000.
tus for Generating Linearly-Orthogon
The use of the system described in US patent application Ser. No. 09 / 507,529, entitled “ally Polarized Light Beams”, both of which are described in Henry A. et al. By Hill, the contents of both applications are incorporated herein by reference.

The particular device used for the source of beam 109 determines the diameter and divergence of beam 109. In some sources, for example diode lasers,
For example, it will likely be necessary to use conventional beam-forming optics, such as a conventional microscope objective, to provide beam 109 with a suitable diameter and divergence for the elements that follow. When the source is a helium-neon laser, for example, beam forming optics may not be needed.

As in FIG. 2 a, the interferometer 169 has a reference retroreflector 191, a target retroreflector 192.
Quarter-wave phase delay plates 177 and 178, and polarization beam splitter 1
Including 71. This configuration is known in the art as a polarization Michelson interferometer. The position of the target retroreflector 192 is controlled by the translator 167.

The incident beam 109 at interferometer 169 results in beams 133 and 134 as illustrated in FIG. 2a. Beams 133 and 134 include information about the optical path length through measurement path 198 and the optical path length through the reference path, respectively, at wavelength λ ₂ . Beams 133 and 134 exit interferometer 169 and strike detector system 189 illustrated in schematic form in FIG. 2a. At detector system 189, beam 133 is reflected by mirror 163A, reflected by mirror 163B, and incident at polarizing beam splitter 163C, a portion of which is reflected by polarizing beam splitter 163C to form a first component of beam 141. Become. Beam 134 is mirror 16
It is reflected by 3A, enters the polarization beam splitter 163C, and a part of it is transmitted by the polarization beam splitter 163C, and becomes the second component of the beam 141.

Interferometer 169 introduces a phase shift φ ₂ between the first and second components of beam 141 so that beam 141 is a phase shifted beam. The magnitude of the phase shift ψ ₂ is related to the round trip physical length L ₂ of the measurement path 198 according to the following formula:

Ψ ₂ = L ₂ p ₂ k ₂ n ₂ (1) where p ₂ is the number of passes through the reference and measurement intervals, respectively, and n ₂ is the optical distance introducing the phase shift ψ _2. , And the refractive index of the gas in the measurement path 198 corresponding to the wave number k ₂ = 2π / λ ₂ . The interferometer shown in FIG. 2a is for p ₂ = 1 and, in the simplest way, to illustrate the functioning of the device of the first embodiment. For those skilled in the art, generalization to the case when p ₂ ≠ 1 is a straightforward procedure. The value for L ₂ corresponds to twice the difference between the physical length of measurement path 198 and the associated reference path.

In the next step, as shown in FIG. 2 a, the phase-shifted beam 141 passes through the polarizer 179 and impinges on the photodetector 185, which then detects the electronic interference signal, the heterodyne signal s ₂ , preferably the photoelectron detection. Generated by. Polarizer 179 is oriented to mix the polarization components of phase shifted beam 141. The signal s ₂ can be described in a spectral representation of the form

[0097]

[Equation 10] ω ′ _{2u ′} is a set of frequencies not including ω, q _R = 1 or 0, respectively, depending on whether q is an odd integer or an even integer, and c is light in vacuum. Is the speed of.

The term in equation (2) for p ⁺ ≧ 1 results from a portion of the reference beam component of beam 109 being transmitted through polarizing beam splitter 171 and passing through measurement beam path 198. The term at u = 0 indicates that the measurement beam component of beam 109 is reflected by polarizing beam splitter 171, passes through the reference path of interferometer 169, and is part of the measurement beam component and measurement beam component of measurement path 198. It may result in being detected as an electronic interference signal generated by the detection.
The term at u = 0 also indicates that a portion of the reference beam component of beam 109 was transmitted by polarizing beam splitter 171 and passed through measurement beam path 198, and a portion of the reference beam component of beam 109 and the reference of interferometer 169. It can also result in being detected as an electronic interference signal generated by the detection of the reference beam component passing through the path. The terms at u ′ ≠ 0 may result from intensity fluctuations in beam 107, such as may be generated by one or more switching frequencies at the power source of source 101. .

The parameter q is a non-linearity rank index, where the non-linearity is the detector 185,
And / or, a s ₂ analog is used to convert the analog signal to digital format - as a result of non-linearities in the digital converter.
The coefficients B _{2, u, u ′, p, p +, q, m} are cos (q−m) x, m = q, q−2 ,. ． ． , Q _R in relation to the coefficient in the expansion of (cosx) ^q . The coefficient a _{2, u, u ', p, p +} , the phase offset ζ _{2, u, u', p, p +} and the coefficient B _{2, u, u ', p, p +, q, m} are referred to the output beam and Degree of overlap of measurement beam components, angular frequency / ψ ₂ and beam 1
It can be a function of system characteristics, such as an intensity of 09, but is otherwise substantially constant in time.

There are terms not explicitly represented in equation (2), which are higher than those explicitly represented in equation (2) due to higher order effects. The effect of higher order effect terms is usually less than the effect of the terms explicitly expressed in equation (2). However, for a given application, if it should be necessary to include any of the higher order effect terms not explicitly represented in equation (2), then such term is used in the first implementation. Identified in the initialization and operating procedures of the morphology, whereby the first
Embodiment of the present invention is included in the described cyclic error compensation procedure.

The dominant term in the equation (2) has the phase dependence of (ω ₂ t + ψ ₂ + ζ _2,1,0,1,0 ) and the coefficient a _2,1,0,1,0 . The remaining terms in equation (2) are shown below as s _{2, ψ} , ie:

[0102]

[Equation 11] This corresponds to the periodic error term. Heterodyne signal s ₂ is transmitted to electronic processor 127 for analysis as electronic signal 123 in either digital or analog format, which is preferably in digital format. Electronic signal 123 further includes a Nyquist angular frequency ω _{2, Ny} , which is preferably at detector 185,
It is determined by the sampling frequency of the analog-to-digital converter used in converting s ₂ to digital format.

The phase of the driver 105 is carried by the electronic signal s _{2, Ref} , the reference signal 121, which is in either digital or analog format, preferably in digital format and is transmitted to the electronic processor 127. . The reference signal is an alternative reference signal to the reference signal 121, and the optical pickoff means and the detector (
(Not shown in the drawing) splitting a portion of beam 109 with a non-polarizing beam splitter, mixing split portions of beam 109, and detecting the mixed portions to generate an alternative heterodyne reference signal. By,
It can also be generated.

Referring to FIG. 2b, electronic processor 127 includes electronic processor 151B, where the Fourier transform F (s ₂ ) of the heterodyne signal s ₂ is generated by either a digital or analog signal process, which is preferably Is a digital process such as a finite Fourier transform algorithm (FFT). Electronic processor 1
27 further includes a spectrum analyzer 151A, which has a reference signal s _{2, Ref.}
With respect to ω ₂ = 2πf ₂ . The spectrum analyzer 151A is preferably based on a sliding window Fourier transform algorithm.

In the next step, the Fourier transform F (s ₂ ) and the angular frequencies ω ₂ and ω _{2, Ny} are transmitted to the electronic processor 153, where they correspond to the periodic error term in s _{2, ψ} , The complex spectral coefficients at F (s ₂ ) are extracted with aliases of angular frequencies ~ ω _{2, ν} and ~ ω _{2 , ν} . The amplitude of the periodic error term at s _{2, ψ} corresponds to the amplitude of the corresponding peak in the associated power spectrum, and the phase of the periodic error term at s _{2, ψ} is the corresponding peak in the associated power spectrum. Corresponds to the arctan of the ratio of the imaginary and real components of F (s ₂ ) at the angular frequency of. In the angular frequency number ~ ω _{2, ν} , ν is an exponential parameter, which is u, u '
, P, p ⁺ and q, which corresponds in time to the set of angular frequencies equal to the derivative of the argument of the sinusoidal coefficient in terms of s _{2, ψ} . ～Omega _2, alias _ν ~ω _{2, ν, A} is given by the following formula.

[0106]

[Equation 12] and

[0107]

[Equation 13] In practice, the magnitude and associated phase of the periodic error term at s _{2, ψ} is
Only the small subset of the possible ~ ω _{2, ν} and ~ ω _{2, ν, A} sets need be extracted. The choice of possible ~ ω _{2, ν} and a subset of the set of ~ ω _{2, ν, A} can be guided by the properties of certain terms in equation (2). However, as part of the initialization procedure, the choice of possible subsets of ~ ω _{2, ν} and ~ ω _{2, ν, A} is based on the power spectrum analysis of s ₂ and the chi-square test of the peaks in the power spectrum. . The chi-square test identifies statistically significant peaks in the power spectrum. ω ₂ , ω _{2, Ny} , · ψ ₂ , · ψ ₂ ⁺ , u, u ', p, p ⁺ , q, w _2,1 / w _2,2 and r statistically significant peaks Associated with ~ ω _2,
The representation of the angular frequencies ~ ω _{2, ν} and ~ ω _{2, ν, A} of a subset of _ν and ~ ω _{2, ν, A} is such that ψ ₂ is changed, where ψ ₂ = dψ ₂ / dt and ψ It is determined by observing the respective properties of ~ ω _{2, ν} and ~ ω _{2, ν, A} when ₂ ⁺ = dψ ₂ ⁺ / dt. ^10-6 to below the relative accuracy of the order, it is noted that ^{_{· ψ 2 + = · ψ 2}} .

The initialization procedure is executed by the electronic processor 153. As part of the operating procedure of the first embodiment, a power spectrum analysis of s ₂ and a chi-square test of the peaks in the power spectrum are monitored for possible changes, which of the apparatus and method of the first embodiment. It may need to be done for ~ ω _{2, ν} and a subset of the set of ~ ω _{2, ν, A} possible during operation. Performed as part of the monitoring procedure,
The power spectrum analysis of s ₂ and the associated chi-square test are also performed by electronic processor 153 as a background task.

[0109]   s_{2, Ψ}The periodic error term at is the term generated by several mechanisms.
, And is broadly referred to below as including coherent periodic error. interference
In some configurations of the meter, especially in multipath interferometers, sources, interferometers and detectors
The system including the generator is₂Generate Coherent Periodic Error Including Subharmonics of
It is possible to・ Ψ₂Including subharmonics of_{2, Ψ}The periodic error term at is p
= W_2,1/ W_2,2, W_2,1, W_2,2= 1, 2 ,. ． ． , W_2,1≠ w_2,2And / or p ⁺ = W_2,1/ W_2,2, W_2,1, W_2,2= 1, 2 ,. ． ． , W_2,1≠ w_2,2Equation (2)
Corresponds to the term in.

An example of subharmonic periodic error generation can be in a differential plane mirror interferometer, where the ghost beam is one reflection by the target mirror, and
It is produced as a result of the second reflection from the nominal transmission surface of the quarter wave retarder. When the reflecting surface of the target mirror and the nominal transmission surface of the quarter-wave phase retarder are parallel, the ghost and reference beam components of the output beam have directions of propagation that are parallel. The subsequent detection of the mixed output beam, including ghost and reference beam components, is a heterodyne signal with subharmonic periodic error.

Another example of subharmonic periodic error generation can be in a high stability plane mirror interferometer. The HSPMI includes a polarizing beam splitter, a measurement target and reference plane mirror, and a retroreflector. The states of polarization of the input beam and the corresponding exit beam impinging on the retroreflector are generally different, for example for linearly polarized input beams, where the exit beam is usually elliptical with the principal axis of the ellipse rotated with respect to the plane of polarization of the input beam. Polarized (N. Bobroff's "Recent advan"
ces in dispersion measuring interface
"Erometry", Measurement and Sci. & Tech
． 4 (9), 907-926, 1993). The ellipticity of the exit beam is
It produces the measurement and reference beam components in the HSPMI output beam, which make only a single optical path for the mirror being measured, rather than multiple paths. When the single optical path component is mixed with other components of the HSPMI output beam, it creates subharmonic periodic error in the subsequently generated interference signal.

In addition, the system including the source, interferometer, detector and digital signal processing is:
It is possible to generate coherent periodic errors that do not include subharmonics or harmonics of ψ ₂ but are associated with harmonics of ω ₂ + · ψ ₂ , ω ₂ and other angular frequencies. Rather than subharmonic, rather than the harmonic of subharmonic, coherent periodic errors having an angular frequency is not a harmonic of · [psi _2, for example, and, at the detector and / or amplifier to generate a s _2, s ₂ Can be generated by the non-linearity in the analog-to-digital converter used to digitize, which has an angular frequency that is a harmonic of ω ₂ + · ψ ₂ , ω ₂ and other angular frequencies. . A coherent periodic error having an angular frequency that is not subharmonic, not subharmonic, and not harmonic of ψ ₂ , can, for example, be generated by aliasing in digital signal processing, which is: [psi with ₂ of the subharmonic and harmonic aliases, and omega ₂ + · [psi _2, the angular frequency is an alias for omega _2, and other respective frequency and its harmonics. The alias is related to the Nyquist angular frequency ω _{2, Ny} .

Various coherent periodic errors that are harmonics of ψ ₂ and not subharmonics,
An example of a coherent periodic error with a non-harmonic angular frequency of ψ ₂ ,
In FIG. 2d, it is shown graphically as a function of ψ ₂ . The coherent periodic errors that are harmonic and subharmonic of ψ ₂ are shown in FIG.
Shown as 1 and 92, line 91 is the first harmonic. For example, the coherent periodic error resulting from the non-linearity in the detector and amplifier producing s ₂ and in the analog-to-digital converter is shown as the solid line 95 in FIG. 2d. The coherent periodic error resulting from aliasing is shown in FIG. 2d as a dashed line reflecting from the line 99 representing the Nyquist frequency.

The amplitude and phase offsets of the terms in the spectral representation given by equation (2) are generally the magnitude of the rate of change of phase associated with the terms as a result of the characteristics of the group delay experienced by the heterodyne signal, for example. Depends on. Group delay, often referred to as envelope delay, describes the delay of a packet at a frequency, and group delay at a particular frequency is defined as the negative of the slope of the phase curve at a particular frequency (H.
J. Blinchikoff and A. I. Zverev's "Filterin
g in the Time and Frequency Domains "
, Section 2.6, 1976 (Wiley, New York)).

The complex spectral coefficients extracted in F (s ₂ ) corresponding to the periodic error term in s _{2, Ψ} are then transmitted to electronic processor 154, where the extracted spectral coefficients are normalized, A multidimensional array of normalized, filtered and interpolated complex spectral coefficients is maintained, filtered in time and interpolated as needed. The step of normalization is to compensate for the effects of non-zero values of the second or higher derivative of ψ ₂ with respect to the time that exists at the time of the determination of the set of complex spectral coefficients. The dimensionality of a multidimensional array depends in part on the magnitude of the filtered complex spectral coefficients, the required accuracy of the end-use application for correction for coherent periodic errors, and the filtered complex spectral coefficients. Determined by dependencies on ψ ₂ and other system characteristics.

In the next step in the electronic processor 127 as shown in FIG. 2 b, the electronic matrix 155 is subjected to the coherent periodic error correction s _{2, Ψ, M} , normalized, filtered and interpolated by the electronic processor 154. Compute using the information listed in the multidimensional array of complex spectral coefficients. Electronic processor 1
52 _{s 2} -s _2, Ψ, by calculating the _M, to compensate for the coherent cyclic errors in s _2. The coherent periodic error compensated signal s ₂ −s _{2, Ψ, M} and the angular frequency ω ₂ are transmitted to the electronic processor 256, where the phase of s ₂ −s _{2, Ψ, M} and ψ ₂ are the phase detectors. , Which is a sliding window FFT, zero-crossing phase detector, etc. Phase ψ ₂ as signal 128 to digital computer 129,
It is transmitted for use in downstream applications, such as determining the linear displacement of an object 192 that is not affected by coherent periodic errors.

Each electronic processor, including electronic processor 127, preferably performs each function as a digital process. The mathematical form for normalization of the extracted complex spectral coefficients is described below.
The Fourier transform of s ₂ is cos ζ _{2, u, u ', p, p +} c as is clear from equation (2).
_{os (uω 2 t + ω '} u' + pψ 2 -p + ψ 2 +) and _{sinζ 2, u, u ',} p, p + sin (
uω including the Fourier transform of the terms with _{2 t + ω 'u' +} pψ 2 -p + ψ 2 +) coefficients such. The Fourier transform of the sinusoidal function sinβ is related to the Fourier transform of cosβ as follows.

[0118]

[Equation 14] In the equation, β is a function of time and represents the argument of the sinusoidal coefficient in equation (2).
In the evaluation of the Fourier transform of cos β, the coefficient cos β is described as follows.

[0119]

[Equation 15] The coefficients cos [β (t) −β (T) − · β (T) (t−T)] and sin [β (t) −β (T) − · β (T) (t−) in the equation (9). T)] is expanded in the Taylor series for t = T, where β (T) = [dβ / dt] _{t = T.} The expansion of the Taylor series including terms up to the fifth order in (t−T) can be expressed according to the following formula.

[0120]

[Equation 16]

[Equation 17] For a given term in s _{2, Ψ} , the corresponding second or higher derivative of β with respect to time is proportional to the second or higher derivative of ψ ₂ with respect to time, respectively, and the proportionality constant is It is determined by the characteristics of each sinusoidal coefficient. The constant of proportionality can be zero or non-zero. The Fourier transform of cos β over the time interval from T−τ / 2 to T + τ / 2 can be expressed using the expressions in equations (9), (10) and (11) as:

[0121]

[Equation 18] In the ceremony

[0122]

[Formula 19]

[0123]

[Equation 20] j _n (x), n = 0, ± 1, ± 2 ,. ． ． , Are spherical Bessel functions of the first kind and of order n (see “Ha of Edited by M. Abramovitz and I. Stegun”).
ndbook of Mathematics Functions ", Na
t. Bureau of Standards Applied Mathem
(See Chapter 10 of atics Series 55). The coefficient for g _n (x) in the term of j _m (x) is the same as the coefficient for x ⁿ in the term of P _m (x), which is that of Legendre multiplied by (i) ^m It is a polynomial of degree m (Eq. 10.1 in Abramovitz and Stegun, supra).
． 14 and Table 22.9).

In electronic processor 153, the complex spectral coefficients of the coherent periodic error are Fourier transformed F (s ₂ ) at a subset of frequencies ω _{2, ν} and ω _{2, ν, A.}
Extracted using complex values of and normalized with respect to the effect of nonzero second-order or higher time derivatives of ψ ₂ . Normalization of the non-zero second or higher derivative of β is performed by the equation (8).
(12) Obtained using (13) and (14). Values for the second and higher order time derivatives of ψ ₂ are obtained from the output of electronic processor 156 in an iterative procedure. shall be included in performing the correction for second or higher order time derivatives not [psi ₂ zeros, the number of higher order derivatives of [psi ₂ is the magnitude of the partial tau, and portions Specifically, it is determined by the magnitude of the second-order or higher time derivative of ψ ₂ .

Some of the corresponding frequencies ~ ω _{2, ν} and a subset of ~ ω _{2, ν, A} , and F
(S ₂₎ the frequency of the dominant complex peak in the set of two or more for containing a frequency value, · [psi ₂ values are separated by less orders of angular frequency resolution of the Fourier transform F (s ₂₎ There is. • In the set of values of ψ ₂ , each value of F (s ₂ ) is
It represents the superimposed value of each Fourier transform of the coherent periodic error, and the dominant composite peak in F (s ₂ ), which is not included in the value of the complex spectral coefficient determined by the electronic processor 153. The value of the complex spectral coefficient determined by the electronic processor 153 is transmitted to the electronic processor 154.

The electronic processor 154 filters the values of the normalized complex spectral coefficients received from the electronic processor 153 with respect to time and interpolates the filtered normalized values to determine the electronic processor 153. Determine the complex spectral coefficients of the coherent periodic error that are not included in the values of the filtered and normalized complex spectral coefficients. Normalization of the complex spectral coefficients, filtering and when the interpolation value is determined to depend on the · [psi _2, normalization of complex spectral coefficients, a · [psi _2-dependent filtering and interpolated values, the · [psi ₂ It can be effectively represented in power series, orthogonal functions or orthogonal polynomials.

The determined set of normalized, filtered and interpolated values of the complex spectral coefficients is transmitted to the electronic processor 155, where the calculated values of s _{2, Ψ} , s _{2, Ψ, M} are generated. It

There is a type of coherent periodic error with a corresponding coherent periodic error amplitude and phase offset depending on the orientation of the mirror being measured. This type of coherent periodic error is referred to below as a variable coefficient type coherent periodic error. In end-use applications where the tilt and yaw of the mirror to be measured is measured and monitored to the required accuracy, for example by interferometric means,
Variable coefficient type coherent periodic errors can be measured and compensated for within the framework of the invention.

The cyclic error complex amplitude in the coherent cyclic error representation for the variable coefficient type coherent cyclic error becomes to include a complex multiple factor. Variable types of coherent periodic error are described subsequently for the two subtypes. The complex multiple factor for the first of the two subtypes is generally a function of the degree of overlap of the ghost and non-ghost beam components of the output beam, or of the two ghost beam components, and this function It can be modeled and / or measured empirically. In the first subtype, the corresponding ghost and non-ghost beam components of the output beam, or the wavefronts of the two ghost beam components, are parallel regardless of the orientation of the target mirror. The complex multiple factor of the second of the two subtypes is generally the degree of overlap of the ghost and non-ghost beam components of the output beam, or of the two ghost beam components, and the corresponding ghost of the output beam. It is a function of the blade angle of the beam and non-ghost beam components, or between the wavefronts of two corresponding ghost beam components. In the second subtype, the wavefronts of the corresponding ghost and non-ghost beam components of the output beam, or of the two corresponding ghost beam components, are substantially parallel for a particular orientation of the mirror to be measured. The properties of the complex multiple factor will be similar to the properties of the marginal visibility function and can be modeled and / or measured empirically.

In end-use applications where variable coefficient type coherent periodic errors can be removed by tilting certain optical elements or parts thereof, information in tilt and yaw is used to We can see when the coherent periodic error is small enough to be ignored.

The complex amplitude in the spectral representation of the coherent periodic error in s _{2, Ψ} also becomes dependent on the magnitude of s ₂ . The dependence of the complex amplitude on the magnitude of s ₂ can be measured and compensated for within the framework of the invention. The complex amplitude in the spectral representation of the coherent periodic error will include the complex multiple factor. Complex multiplicative factor for the spectral components of a particular coherent periodic errors, a function of s _2, are readily represented as a power series definitive to s _2. The power series representation is determined from the measured properties of each particular complex amplitude as the magnitude of s ₂ is varied. In some interferometer and detector systems, a power series representation can be determined from corresponding values of q associated with corresponding values of ~ ω _{2, ν} or ~ ω _{2, ν , A.}

One of the more subtle types of coherent periodic error to identify and compensate for
One has ~ ω _{2, ν} which is the same as the angular frequency of the dominant peak at | F (s ₂ ) | ² independent of the value of ψ ₂ . This type of coherent periodic error is referred to below as zero frequency shift coherent periodic error. Sources of zero frequency shift coherent periodic error are typically, for example, q = 3, 5 ,. ． ． Etc., including non-linearities with odd order values of the non-linearity index q greater than 1.

The main zero frequency shift coherent periodic error is u = 1 in equation (2).
, U ′ = 0, p = 1, p ⁺ = 0 and q _R = 1 and can be expressed as:

[0134]

[Equation 21] Other zero frequency shift coherent periodic errors not represented in equation (20) occur for different values and combinations of values of u, p and p ⁺ in equation (2). The terms omitted in Eq. (20) result from a non-linear combination between the dominant term with amplitude a _2,1,0,1,0 and the other periodic error terms, so they are generally several times smaller. The zero frequency shift coherent periodic error is (ω ₂ t + ψ ₂ ).
It is clear from equation (20) that we correct the amplitude and phase offset of the measured spectral component of s ₂ with the phase of, which correction depends on the properties of the coherent periodic error present.

Therefore, the effect of the zero frequency shift coherent periodic error is not as a periodic error at s ₂ but over the range of operating conditions for the device of the first embodiment, | F (s ₂ ). It becomes clear as an error that corrects the phase offset at the frequency of the dominant peak at | ² . In particular, a zero frequency shift coherent periodic error changes the group delay characteristic of s ₂ at the frequency of the dominant peak in | F (s ₂ ) | ² . Therefore, the effect of zero frequency shift coherent periodic error is
In one embodiment, the effect of group delay at the frequency of the dominant peak in | F (s ₂ ) | ² is compensated for when measured for a system including an interferometer and an associated electronic signal processor. That is clear. Preferably, the measurement is carried out by means of a measuring section of an interferometer in vacuum to prevent the influence of air flow turbulence on the characterization of · ψ.

Two procedures are described in the following paragraphs for the case where the zero frequency shift coherent periodic error term in F (s ₂ ) is not compensated as part of the procedure for compensation for the group delay effect, This is to separate and detect the effects of zero frequency shift coherent periodic errors.

[0137] Characterization of the zero frequency shift coherently periodic errors can be significant, which they | F (s ₂₎ | phase offset generated in the ^second dominant peak is measured and the reference beam This is because of the intensity and relative overlap of the beams that produce the optical interference signal-depending on parameters that may change during the operation of the interferometry system. In addition, the phase offset can change due to Doppler shift.

The first of the two procedures described to separate and detect the effects of zero frequency shift coherent periodic errors is the easier of the two procedures to implement, but has applicability. Area is limited. For each coherent periodic error of the set of zero frequency shift coherent periodic errors, there is a corresponding coherent periodic error with a value of ~ ω _{2, ν} , which is the angle of the dominant peak at | F (s ₂ ) | ² . It is different from the frequency. For example, for odd order non-linear rank exponents with q = n ≧ 3, different sets of ω _{2, ν} are 3ω _d , 5ω _d ,. ． ． , Nω _d
Where ω _d is the angular frequency of the dominant composite peak in F (s ₂ ). At F (s ₂ ), the corresponding coherent periodic error corresponds to only one value of n, the ratio of the coefficients of the zero frequency shift coherent periodic error, and the ratio of the corresponding coefficients of the zero frequency shift coherent periodic error. But for a device,
Specified by a coefficient containing the ratio of B _{q, n} for each value of _n . The electronic processor 154 examines the corresponding set of coherent periodic error coefficients and determines the value of the zero frequency shift coherent periodic error coefficient and the coefficient of the zero frequency shift coherent periodic error coefficient and the corresponding set of coherent periodic error coefficients. Determine using the ratio between. If multiple values of q are required in the description of the corresponding coherent periodic error, then the corresponding zero frequency shift coherent periodic error coefficient is set to the corresponding set of coherent periodic error coefficients, the corresponding system of simultaneous equations. A set and a corresponding set of binomial coefficients can be determined from at least square analysis.

The effectiveness of the first procedure for separating and detecting the effects of zero frequency shift coherent periodic errors is that a detector with different sets of ω _{2, ν} containing angular frequencies, but producing s ₂ . When the transfer function of the analog part of 185 is not essentially constant,
Reduced.

The second procedure described to separate and detect the effects of zero frequency shift coherent periodic error is the two input beams 109 and 109T (beam 109T).
2a) (not shown in FIG. 2a). Beam 109T is similar to beam 109 in that it has two orthogonal polarization components with frequency division ω _{2, T.} However, the frequency division ω _{2, T} between the components of beam 109T is chosen to be different from the frequency division ω ₂ between the components of beam 109. The absolute value of the difference between the frequency divisions | ω _{2, T} −ω ₂ | is chosen to be smaller than ω ₂ + · ψ and ω _{2, Ny} . Beam 109T propagates through interferometer 169 and detector 189 to produce interference signal component s _{2, T} in signal 123. The description of s _{2, T} is the same as the corresponding part of the description given for s ₂ . The property of the device of the first embodiment that produces a zero frequency shift coherent periodic error is that it also produces closely spaced multilines with respect to frequency in the power spectrum of s ₂ + s _{2, T} when beam 109T is present. . The frequency spacing between successive members of the multiline is equal to the frequency separation of beams 109 and 109T. The amplitude and phase of a zero frequency shift coherent periodic error can be represented by a relationship in the amplitude and phase terms of the members of the multiline. In the procedure for separating zero frequency shift coherent periodic errors, the main zero frequency shift coherent periodic errors are determined using the relationship of the members of the multiline and the measured amplitude and phase.

The description of the source of beam 109T (the source of beam 109T is not shown in FIG. 2a) is the same as the corresponding part of the description given for the source of beam 109. For example, as shown in FIG. 2e, the interferometry system includes a source 101 and a first source for beam 109 that includes modulator 103 excited by driver 105, and another source 101T and another source. A second source for a beam 109T that includes another modulator 103T that is excited by a driver 105T, and an optical component 106 for combining the beams generated by the first and second sources. You can In another embodiment, shown in Figure 2f, both beams 109 and 109T are derived from the same source, laser 101 '. For example, laser 1
01 'can generate two beams 108 and 108T corresponding to different longitudinal modes of the laser 101'. Modulators 103 and 103T, which are excited by drivers 105 and 105T, respectively, then receive beams 108 and 1
Operating at 08T, it produces input beams 109 and 109T. In a further embodiment, a single modulator driven with both split frequencies ω ₂ and ω _{2, T} can be used. When required, the intensities of beams 109 and 109T can be adjusted to allow frequency division. For example, beam 109T
The source for is capable of removing this from the interferometry system after the zero frequency shift periodic error has been characterized.

In general, the difference between the average frequency of the components of beam 109 and the average frequency of the components of beam 109T is greater than the Nyquist frequency ω _{2, Ny} , eg, twice the Nyquist frequency ω _{2, Ny.} Is chosen to minimize the terms in the signal generated by detector 189 that correspond to the interference between beams 109 and 109T other than in the zero frequency shift multiplex. Conversely, the frequency division itself is selected to be less than the Nyquist frequency. In general, the absolute value of the difference between the frequency divisions, | ω _{2, T} −ω ₂ |, is chosen to be smaller than any of the frequency divisions themselves, and the spectral overlap of multiple lines with other periodic errors. Is minimized and any difference between the zero shift frequency periodic error coefficients in s ₂ and s _{2, T} is minimized. For example, | ω _{2, T} −ω ₂ | is replaced by | ω _{2, T} −ω ₂ | <(ω ₂
/ 100).

The zero frequency shift coherent periodic error is determined from the Fourier analysis of the terms at s ₂ + s _2T , which is [a _ν cos (ω ₂ t + ψ ₂ + ζ _ν ) + a _νT cos
(Ω _2T t + ψ _2T + ζ _νT )] ^q , where ν = (2,1,0,1,0) and q = 3,5 ,. ． ． Is. The results of such an analysis are listed, for example for q = 3, 5 and 7. Results for other values of q as required in a particular end use application can be produced by the same procedure. q =
In 3, the main terms contributing to the multiplet are:

[0144]

[Equation 22] The quantity (k _2T −k ₂ ) is simply _two times the difference in the frequencies of beams 109 and 109T.
Note that it is π / c times.

[0145]   For q = 5, the main terms contributing to the multiplet are:

[0146]

[Equation 23] For q = 7, the main terms contributing to the multiplet are:

[0147]

[Equation 24] Since the magnitude of the angular frequency separation is chosen to be much smaller than ω ₂ + · ψ and ω _{2, Ny} , the coefficient B _{νq, 1} is due to the representation of the corresponding terms in s ₂ and s _2T . Used for a good approximation of.

The terms in equations (21), (26) and (27) are arranged according to their position in each multiline. The maximum term of the zero frequency shift coherent periodic error in s ₂ is the coefficient (a _ν ) ³ B _{ν 3,1} cos α _2,3 , (a _ν ) ⁵ B _{ν 5,1} cos α _2,5 , (a _ν ) ⁷ B _ν7,1 cos α _2,7 ,. ． ． Note that it is the sum of Furthermore, the phase difference (α _2qT −α _2q ) for the multiplex q can be obtained directly from the measured phase difference of the two terms corresponding to the lowest and highest frequency components of each multiplet, and the difference Note that is equal to q (α _2qT −α _2q ).

Continuing with the description of the procedure for separating and detecting the effects of zero frequency shift coherent periodic errors, electronic processor 154 normalizes, filters, on the set of complex spectral coefficients corresponding to the terms in the multiline. And checking the value of the interpolated complex spectral coefficient. zero frequency shift coherent cyclic errors in s _2, the coefficient ^{_{(a ν) 3 B ν3,1 cosα}} 2,3, (a ν) 5 B ν5,1 cosα 2, 5, (a ν) 7 B ν7,1 cosα _2,7 ,. ． ． Is determined from at least square analysis of the set of complex spectral coefficients using an equation describing the terms contributing to the multiline, such as those found in equations (21), (26) and (27). . Coefficients that need to be included (a _ν ) ³ B _{ν 3,1} cos α _2,3 , (a _ν ) ⁵ B _{ν 5,1} cos
α _2,5 , (a _ν ) ⁷ B _{ν 7,1} cos α _2,7 ,. ． ． The number of terms in the sum of is determined by the magnitude of the terms and the precision needed in compensation for the zero frequency shift coherent periodic error in s ₂ .

The electronic processor 154 cited above filters the values of the normalized complex spectral coefficients received from the electronic processor 153, interpolates the normalized filtered values, and is determined by the electronic processor 153. Determine the value of the coherent periodic error that is not included in the value of the complex spectral coefficient obtained. If the value of the normalized, filtered and interpolated complex spectral coefficient is determined to be dependent on ψ ₂ , the normalized, filtered and interpolated value of the complex spectral coefficient is determined to be ψ _2. It can be effectively represented in a power series in ψ ₂ , a set of orthogonal functions, or a set of orthogonal polynomials. If determined, the set of zero frequency shift coherent periodic errors and the determined values of the normalized, filtered and interpolated complex spectral coefficients are transmitted to electronic processor 155, where s _{2, Ψ} , s _{2, Ψ. ,} A simulated value of _M is generated. The simulated values s _{2, Ψ, M} and s ₂ are transmitted to electronic processor 152, and s _{2, Ψ, M} is subtracted from s ₂ to yield s ₂ −s _{2, Ψ, M.} Signal s ₂ −s _{2, Ψ, M} and frequency ω ₂
Are transmitted to the electronic processor 156 and the phase φ ₂ is determined, preferably by a sliding window FFT or other similar phase detector. Phase φ ₂ is transmitted to computer 129 as signal 128 for use in determining the linear displacement of object 192 that is not affected by coherent periodic errors.

In the description of the first embodiment, the different contributions to the periodic error are generally due to the detector system 18 at the source of the beam 109 and at the components of the interferometer 169.
Note that it was the result of a defect in 9 and / or in electronic processor 127. It is also clear from this description that the properties of the periodic error term with respect to frequency and amplitude generally allow identification of the origin of the periodic error term, ie for certain types of defects. For example, the periodic error associated with the set of frequencies ω ′ _{2u ′} may be due to a defect in the power supply system of the source 101 in the beam 109, in the acousto-optic modulator 103, and / or instability in the laser. It shows the intensity fluctuation. The periodic error term associated with frequency ψ may be due to polarization mixing in beam 109 and / or due to defects in polarization beam splitter interface 171. The periodic error term associated with parameter q is indicative of non-linearities in detector system 189 and / or electronic processor 127.

Subsequently, the degradation in performance of one or more components of the interferometer system is
It can be detected by monitoring the characteristics of the periodic error term as described above with respect to FIG. The detection of such deterioration is generally an initial detection system,
That is, the opportunity is provided for making compensatory measurements, which generally can be done before the interferometer system is used in an unacceptable mode for a given end use application. it can. Corrective measurements can be part of programmed maintenance to correct degraded components, for example, in problem areas dictated by the characteristics of the associated periodic error terms. Moreover, the indication of the problem domain by the properties of the associated periodic error terms can substantially improve the efficiency with which corrective measurements are performed.

In the description of the first embodiment, it was mentioned that the interferometer configuration illustrated in FIG. 2a is known in the art as a polarization Michelson interferometer. Other types of Michelson interferometer and other interferometers such as high stability plane mirror interferometer, or C.I. Zanoni's "Differential interferome"
ter arrangements for distance and an
gle measurements: Principles, advanced
es and applications ", VDI Ber
ichte Nr. 749, 93-106 (1989), an angle-compensating interferometer or similar device, such as when working with stages commonly encountered in lithographic fabrication of integrated circuits, provides the spirit and scope of the invention. It may be incorporated into the device of the present invention without departing from it, and the aforementioned articles are incorporated herein by reference.

The same co-owned owners of the application of September 18, 1998, Henry A.
Hill and Peter de Groot's "Interferomete"
r Having A Dynamic Beam Steering Ass
US patent application Ser. No. 09 / 157,131 entitled "embly", filed on May 5, 1999 by Henry A. et al. Hill's "Interferometry"
System Having A Dynamic Beam Steerin
g Assemble For Measuring Angle And D
US patent application Ser. No. 09 / 305,828, 199
Henry A., filed Aug. 27, 1997. Hill's "Polarization"
US patent application Ser. No. 09 / 384,742, entitled "Preserving Optical Systems," Peter filed Aug. 27, 1999.
de Groot's “Interferometer Having Redu”
Ced Ghost Beam Effects ", US patent application Ser. No. 09 / 384,609, and Henry A. et al.
Hill's "Interferometers Utilizing Pola"
Rization Preserving Optical Systems "
Other types of interferometers described in US patent application Ser. No. 09 / 384,855 may be incorporated into the apparatus of the present invention without departing from the spirit and scope of the present invention. Are incorporated herein by reference.

FIG. 2c shows in schematic form an electronic processor 127A according to a preferred apparatus and method of variations of the first embodiment. A variation of the first embodiment is from the first category of several different categories of embodiments, including beam 109, a source of beam 109, an interferometer 169, a detector system 189, and a drawing. 2a, the first embodiment digital computer 129, and FIG. 2c.
The electronic processor 127A shown in FIG.

[0156]   The electronic processor 127A includes an element, which is the electronic processor of the first embodiment.
It performs similar functions such as similarly numbered elements of processor 127. Electronic
In operation of processor 127A, as shown in FIG.
The signal (s₂-S_{2, Ψ, M}) Is the electronic processor 15
6 and electronic processor 151B. The electronic processor 151B (s ₂ -S_{2, Ψ, M}) Fourier transform F (s₂-S_{2, Ψ, M}) Is generated, and F (s₂-S_{2, Ψ, M} ) Is transmitted to the electronic processor 153 out of 127A.

The nonzero complex spectral coefficients in F (s ₂ −s _{2, Ψ, M} ) represent incomplete compensation of the coherent periodic error in s ₂ . Incomplete compensation of the coherent periodic error in s ₂ may result, for example, in changes in the coherent periodic error over time and / or statistical errors in the measured quantity. Incomplete compensation is typically present during the initialization stage to establish a multidimensional array of normalized, filtered and interpolated complex spectral coefficients by electronic processor 154A. Of 127A, the electronic processor 153 uses F (s ₂ −s _{2, Ψ, M}
) Of the complex spectral coefficient of the electronic processor 154.
Is transmitted to A. Electronic processor 154A processes the complex spectral coefficients representing the incomplete compensation of coherent cyclic errors in s _2, and updates the multidimensional array normalization, filtering and interpolated complex spectrum coefficients. The electronic processor 154A otherwise processes the normalized, filtered and interpolated multidimensional array of complex spectral coefficients, which is the processor 12 of the first embodiment.
7 electronic processor 154.

The remaining description of the variants of the first embodiment is the same as the corresponding parts of the description given for the first embodiment. Figure 3a shows in schematic form an apparatus and method according to a second embodiment of the invention. The second embodiment is from the second category of embodiments. Figure 3
The interferometer shown in a is a polarization heterodyne single-pass interferometer. Although the described embodiment is a heterodyne system, the invention is readily adapted for use in a homodyne system, where the reference and measurement beams have the same frequency.

The description of the source and beam 209 of beam 209 of the second embodiment is the same as the corresponding parts of the description given for the source and beam 109 of beam 109 of the first embodiment. Also, the description of the interferometer 269 and the detector system 289 of the second embodiment is the same as the corresponding parts of the description given for the interferometer 169 and the detector system 189 of the first embodiment. Elements of the second embodiment include source and beam 209 of beam 209, interferometer 269 and detector system 289, source and beam 109 of beam 109, interferometer 16
Decremented by 100 of the first embodiment including 9 and detector system 189,
Performs similar functions, like similarly numbered elements.

Interferometer 269 introduces a phase shift ψ ₃ between the first and second components of beam 241, so that beam 241 is a phase shifted beam. The phase shift φ ₃ is related to the round-trip physical length L ₃ of the measurement path 298 according to the following formula:

Ψ ₃ = L ₃ p ₃ k ₃ n ₃ (28) where p ₃ is the number of passing reference and measurement intervals, respectively, and n ₃ is the optical distance introducing the phase shift ψ _3. , And the refractive index of the gas in the measurement path 298, corresponding to the wave number k ₃ = 2π / λ ₃ , where λ ₃ is the wavelength of the beam 207. Figure 3a
The interferometer shown in is for p ₃ = 1 and, in the simplest way, to illustrate the functioning of the device of the second embodiment. For those skilled in the art, p ₃
Generalization to the case when ≠ 1 is a simple procedure. The value for L ₃ corresponds to twice the difference between the physical length of the measurement path 298 and the associated reference path.

In the next step, as shown in FIG. 3a, the phase-shifted beam 241 passes through a polarizer 279 and impinges on a photodetector 285, which detects the electronic interference signal, the heterodyne signal s ₃ , preferably the photoelectron detection. Generated by. Polarizer 279 is oriented to mix the polarization components of phase shifted beam 241. The signal s ₃ has the following form.

[0163]

[Equation 25] Where A ₃ (t) and α ₃ (t) are the amplitude and phase of s ₃ , respectively. Signal s ₃ is the real part of the complex signal ^ s ₃ ^ s is _{3, R,} wherein, s ₃ is responsible, including stable, i.e. absolutely Kaseki real number sequence. Therefore, s ₃
The Fourier transform s _{3, R} (iω) of S completely defines S ₃ (iω) (AV Oppe
nheim and R.N. W. Schafer's "Discrete-Time S"
Chapter 10 "Discrete H" in "Internal Processing"
ilbert Transforms ”), but as follows:

[0164]

[Equation 26] S _{3, I} (iω) is an imaginary component of S ₃ (iω), ω is an angular frequency, and i is an imaginary number √ (−1). S _{3, I} (iω) is related to S _{3 , R} (iω) by the frequency response function H (iω), ie:

[0165]

[Equation 27] In the equation, the frequency response function H (iω) is given by the following equation.

[0166]

[Equation 28] ^ Imaginary component ^ s _{3, I} of s ₃ are obtained from S _3, the inverse Fourier transform of _I (I [omega]) with the following.

[0167]

[Equation 29] The phase α ₃ can be obtained from ^ s _{3, R} and ^ s _{3, I according} to the following formula.

[0168]

[Equation 30] The time-dependent argument α ₃ is expressed according to the following formula for other quantities.

[0169]

[Equation 31] Where Ψ ₃ contains a non-linear periodic error term and phase offset ζ ₃ contains all contributions to phase α ₃ which are not related or associated with the optical distance of the measurement path 298 or the reference path. , Not related to non-linear cyclic error. The heterodyne signal s ₃ is transmitted to electronic processor 227 for analysis as electronic signal 223 in either digital or analog format, which is preferably in digital format. Electronic signal 223 further includes a Nyquist angular frequency ω _{3, Ny} , which was determined by the sampling frequency of the analog-to-digital converter used in converting s ₃ to digital format.

The phase of the driver 205 is carried by the electronic signal s _{3, Ref} , the reference signal 221, which is in digital or analog format, preferably in digital format and is transmitted to the electronic processor 227. The reference signal is an alternative reference signal to the reference signal 221 and is split by the optical pick-off means and detector (not shown in the drawing) into a part of the beam 209 by a non-polarizing beam splitter. It can also be generated by mixing the parts and detecting the mixed parts to generate an alternative heterodyne reference signal.

The non-linear periodic error Ψ ₃ contains terms generated by the same mechanism as described for the first embodiment, and is henceforth referred to as the coherent periodic error function. The spectral representation of the coherent periodic error function Ψ ₃ , for quantities such as Ψ ₃ , ω ₃ and Ψ _{3, Ny,} can be based on different families of orthogonal polynomials and functions. Two examples are series containing Fourier sine and cosine functions, and series containing Chebyshev polynomial functions. Fourier sine and cosine series spectral representations of Ψ ₃ are used without departing from the spirit and scope of the present invention.

The properties of the spectral representation of Ψ ₃ are described with respect to the properties of the signal s ₃ . The signal s ₃ has the same form as the form of s ₂ given by equation (2) and is therefore described as:

[0173]

[Equation 32] The term in Ψ ₃ can be obtained from equation (36) by first describing s ₃ in the following form.

[0174]

[Expression 33] Here we use equations (29) and (35), then sin (ω ₃ t + ψ ₃ + ζ ₃ ) generated in the description of s ₃ in the form given by equation (39).
And using the coefficients of the cos (ω ₃ t + ψ ₃ + ζ ₃ ) term, let ψ ₃ be sin (ω ₃ t
-Arctan of the ratio of the coefficients of the terms + ψ ₃ + ζ ₃ ) and cos (ω ₃ t + ψ ₃ + ζ ₃ ).
Calculate as. Derivation of the terms in equation (36) described in the form of equation (39) using trigonometric discrimination yields:

[0175]

[Equation 34] The term in the spectral representation of Ψ ₃ is easily identified, which means that Ψ ₃ is −-of the ratio of the coefficients of the sin (ω ₃ t + ψ ₃ + ζ ₃ ) and cos (ω ₃ t + ψ ₃ + ζ ₃ ) terms in equation (40). By noting that it is equal to arctan, and by looking at the characteristics of the coefficients of the sin (ω ₃ t + ψ ₃ + ζ ₃ ) and cos (ω ₃ t + ψ ₃ + ζ ₃ ) terms in equation (40).

The coefficients of the terms in the spectral representation of ψ ₃ generally depend on the rate of change of phase associated with the terms as a result of, for example, the characteristics of the group delay experienced by the heterodyne signal.

[0177] Referring to FIG. 3c, the electronic processor 227 includes a phase detector 250, which is a heterodyne signal s ₃ for phase alpha _3, either digital or analog signal processes, preferably by digital processes, digital Hilbert Transform Phase Detector (R.E. Best "Phase-locked loops: t
history, design, and applications ”2nd ed
． McGraw-Hill (New York) Section 4.1, 1993.
． Processing), such as a zero-crossing phase detector. Electronic processor 227 further includes spectrum analyzers 251A and 2
51B, which respectively process the reference signal s _{3, Ref} and the heterodyne signal s ₃ for ω ₃ and .alpha. ₃ , respectively. The angular frequency α ₃ is the angular frequency of the dominant peak in the power spectrum of s ₃ . The spectrum analyzers 251A and 251B are preferably based on a sliding window Fourier transform algorithm. Phase alpha ₃ and the angular frequency omega ₃ are transmitted to electronic processor 252, where _{~ψ 3 = α 3 -ω 3 t} , and alpha ₃ of the Fourier transform F (alpha ₃₎ is calculated.

[0178]   The next step in electronic processor 227 is the Fourier transform F (α₃) Oh
And angular frequency α₃, Ω₃And ω_{3, Ny}Is transmitted to the electronic processor 253, where Ψ ₃ The complex spectral coefficient of the coherent periodic error term at_3,
υ, And aliases, ~ ω_{3, υ}Of ~ ω_{3, υ, A}It is extracted with. α₃Cycle in
The magnitude of the dynamic error term is the amplitude of the corresponding peak in the associated power spectrum.
Corresponds to width, α₃The phase of the periodic error term at is associated with the power spectrum
F (α at the angular frequency of the corresponding peak in₃) The ratio of the imaginary and real components of
Corresponding to the arctan of. Angular frequency ~ ω_{3, υ}, Ν is u, u ′, p,
p⁺Is an exponential parameter including and q₃Spect of
To the set of angular frequencies equal to the derivative of the argument of the sinusoidal coefficient of the terms in the Le representation
Correspond. Alias ~ ω_{3, ν, A}Is given by the following formula:

[0179]

[Equation 35] and

[0180]

[Equation 36] In practice, the magnitude and associated phase of the periodic error term in ψ ₃ need only be extracted for a small subset of the possible ~ ω _{3, ν} and ~ ω _{3, ν, A} sets. The choice of possible subsets of ~ ω _{3, ν} and ~ ω _{3, ν, A} is determined by sin (ω ₃ t + ψ ₃ + ζ ₃ ) and cos (ω ₃ t + ψ ₃ ) in equation (40).
It can be derived by the characteristic of some coefficient of the + ζ ₃ ) term. However, as part of the initialization procedure, the choice of possible subsets of ~ ω _{3, ν} and ~ ω _{3, ν, A} is
Based on power spectrum analysis of α ₃ and chi-square test of peaks in power spectrum. The chi-square test identifies statistically significant peaks in the power spectrum. ω ₃ , ω _{3, Ny} , · ψ ₃ , · ψ ₃ ⁺ , u, u ′, p, p ⁺ , q, w _3,1 / w _3,2
In and r sections, ~ω ₃ associated with statistically significant _{peaks, [nu} and ~ω _{3, ν,} angular frequency ～Omega ₃ subsets of _{A, [nu} and ~ω _{3, ν,} representation of _A , Ψ ₃
Is determined by observing the respective properties of ~ ω _{3, ν} and ω _{3, Ny} . ^10-6 to below the relative accuracy of the order, it is noted that ^{_{· ψ 3 + = · ψ 3}} .

The initialization procedure is executed by the electronic processor 253. As part of the operating procedure of the second embodiment, the power spectrum analysis of α ₃ and the chi-square test of the peaks in the power spectrum are monitored for possible changes, which of the apparatus and method of the second embodiment. It may need to be done for ~ ω _{3, ν} and a subset of the set of ~ ω _{3, ν, A} possible during operation. Performed as part of the monitoring procedure,
The power spectrum analysis of α ₃ and the associated chi-square test are also performed by electronic processor 253 as a background task.

The complex spectral coefficients extracted in F (α ₃ ) corresponding to the periodic error term in Ψ ₃ are then sent to electronic processor 254, where the extracted spectral coefficients are normalized and with respect to time. Filtered, interpolated as needed, maintaining a multi-dimensional array of normalized, filtered and interpolated complex spectral coefficients. The step of normalization is to compensate for the effects of non-zero values of the second or higher derivative of ψ ₂ with respect to the time that exists at the time of the determination of the set of complex spectral coefficients. The dimensionality of a multidimensional array depends in part on the magnitude of the filtered complex spectral coefficients, the required accuracy of the end-use application for correction for coherent periodic errors, and the filtered complex spectral coefficients. Determined by dependencies on ψ ₂ and other system characteristics.

In the next step in the electronic processor 227 as shown in FIG. 3 b, the electronic matrix 255 provides the coherent periodic error correction Ψ _{3, M} to the normalized, filtered and interpolated complex generated by the electronic processor 254. Compute using the information listed in the multidimensional array of spectral coefficients. Electronic processor 25
6 (see FIG. 3b) is [psi ₃ was calculated, [psi ₃ coherent cyclic errors from ~ψ _{3, M}
Is compensated by subtracting. Phase φ ₃ is transmitted by electronic processor 227 as signal 228 to computer 229 for use in downstream applications.

[0184]   Each electronic processor, including electronic processor 227, performs each function in a digital process.
It is preferable to execute as. α₃The Fourier transform of is (ψ₃+ Ω₃t) fu
Rie transformation and cos [(u-1) ω₃t + ω '_{3u '}+ (P-1) ψ₃-P⁺ψ ₃ ⁺ )] And sin [(u-1) ω₃t + ω '_{3u '}+ (P-1) ψ₃-P⁺ψ₃ ⁺)]
Including terms with coefficients such as is apparent from looking at equation (40).
(Ψ over the time interval from T−τ / 2 to T + τ / 2₃+ Ω₃Fourier transform of t) is
, Ψ can be expressed as₃Is expressed as a Taylor series for t = T
To be done.

[0185]

[Equation 37] In the second embodiment, the coefficients B _{3,1,0,1,0, q, qR} , q = 3, 5 ,. ． ． It is clear from looking at Eq. (40) that there is a zero frequency shift coherent periodic error resulting from the term with coefficients having. The zero frequency shift coherent periodic error results from the same type of term as the zero frequency shift coherent periodic error present in the first embodiment.

The procedure of the second embodiment used to separate and detect the main zero frequency shift coherent periodic errors is to detect the main zero frequency shift coherent periodic errors for the first embodiment. And is based on the same technique as the procedure described for the separation. A second beam 209T (not shown in FIG. 3a) was introduced and used to multiplex in the power spectrum of phase α ₃ centered at a frequency equal to one-half the frequency spacing of successive members of the multiline. A line is generated. Beam 209T
Is the same as the corresponding part of the description given for the beam 109T of the first embodiment. The measured characteristics of the amplitude and phase of the members of the multiline were processed by the electronic processor 227, and in the second embodiment, the main zero frequency shift coherent periodic error was provided for the first embodiment. It is determined according to the same procedure as described for the corresponding parts of the description.

The remaining description of the second embodiment is the same as the corresponding parts of the description given for the first embodiment. FIG. 3c shows in schematic form an electronic processor 227A according to a preferred apparatus and method of variations of the second embodiment. The modification of the second embodiment is
From the second category of embodiments, beam 209, source of beam 209, interferometer 269, detector system 289, and second embodiment digital computer 229 shown in Figure 3a, and Figure 3c. Electronic processor 227 shown in
Including A.

[0188]   Electronic processor 227A includes an element that is the electronic processor of the second embodiment.
It performs similar functions such as similarly numbered elements of processor 227. Electronic
In operation of the processor 227A, the phase α₃,
The calculated coherent periodic error ψ_{3, M}And angular frequency ω₃Is an electronic processor 2
57, where ψ₃, (Α₃−Ψ_{3, M}), And (α₃−Ψ_{3, M}) Furi
D conversion F (α₃−Ψ_{3, M}) Is generated. Fourier transform F (α₃−Ψ_{3, M}) Is 227
In A, the electronic processor 253 receives the angular frequency / α from the electronic processor 251B. ₃ And ω_{3, Ny}Is transmitted with. Phase ψ₃Is powered by the electronic processor 227A.
The child signal 228 is transmitted to the digital computer 229.

The non-zero complex spectral coefficients in F (α ₃ −Ψ _{3, M} ) represent incomplete compensation of the coherent periodic error in ψ ₃ . Incomplete compensation of the coherent periodic error in ψ ₃ may result, for example, in changes in the coherent periodic error in time and / or statistical errors in the measured quantity.
Incomplete compensation generally exists during the initialization stage to establish a multidimensional array of normalized, filtered and interpolated complex spectral coefficients by electronic processor 254A. Of the 227A, the electronic processor 253 determines the complex spectral coefficient from F (α ₃ −Ψ _{3, M} ), and the complex spectral coefficient is calculated by the electronic processor 254A.
Be transmitted to. Electronic processor 254A processes the spectral coefficients that represent incomplete compensation of the coherent periodic error in ψ ₃ and updates the multidimensional array of filtered coherent periodic error coefficients. The electronic processor 254A further processes a multi-dimensional array of filtered coherent periodic error coefficients, which is the same as the electronic processor 254 of the processor 227 of the second embodiment, which is a non-zero quadratic or higher of ψ _3. It relates to the required corrections for the derivatives of the order of, and the identification and omission of the spectral coefficients of each coherent periodic error, which correspond to the superimposed value of frequency.

The remaining description of the variants of the second embodiment is the same as the corresponding parts of the description given for the second embodiment. 4a, 4b and 4c show in schematic form a preferred apparatus and method of a third embodiment of the invention. The third embodiment is from the third category of several different categories of embodiments. Some embodiments of the third category of embodiments measure and correct for periodic errors in the optical dispersion related signal, such as those used to measure and correct for gas effects in the measurement path of a range finding interferometer. Apparatus and methods for doing so. Certain other embodiments of the third category relate to the dispersion-related signal and the periodic error in the signal used for determining the change in the optical path length of the measurement path of the distance measuring interferometer. Includes apparatus and method for measuring and correcting. The effect of the cyclic error in correcting for the effect of gas in the measurement path is more than 1.5 times greater than the effect of the cyclic error in the signal used for the determination of the optical path length change.

A third embodiment provides an apparatus and method for measuring and monitoring the dispersion of gas in the measuring path of a distance measuring interferometer and for compensating for the effect of gas in the measuring path of the distance measuring interferometer. Including. The third embodiment is further used for determining optical dispersion related signals, such as those used to measure gas dispersion, and changes in optical path length of the measurement path in a distance measuring interferometer. Apparatus and method for measuring and correcting for the effects of cyclical errors in the received signal. The refractive index of the gas and / or the physical length of the measurement path may have changed.
In addition, the ratio of the wavelengths of the light beam produced by the adapted source matches some relative accuracy to known ratio values, consisting of non-zero quantities. The non-zero quantity may include one or more low order non-zero integers.

Referring to FIG. 4 a, according to a preferred apparatus and method of the third embodiment, the description of the light beam 309 and the source of the light beam 309 is described in the light beam 10 of the first embodiment.
9 and the corresponding parts of the description given for the source of the light beam 109. The wavelength of the radiation source 301 is λ ₄ . In the next step, the light beam 308 emitted from the source 302 passes through the modulator 304 into a light beam 310. Modulator 304 is excited by electronic driver 306, which is electronic driver 305.
Are each similar to the excitation of modulator 303 by The radiation source 302 is the radiation source 301.
A laser or similar source of polarized coherent radiation, but preferably at a different wavelength λ ₅ .

The wavelength λ ₄ / λ ₅ ratio has the known approximation ratio value l ₄ / l ₅ , ie:

[0194]

[Equation 38] Where l ₄ and l ₅ include non-zero quantities. The non-zero quantity may include one or more low order non-zero integer values. For the non-frequency-shifted components of beams 309 and 310, respectively, the components of beams 309 and 310 with the oscillation frequencies shifted by the amounts f ₄ and f ₅ , respectively, are 4a
Polarized orthogonal to the plane of. Oscillation frequencies f ₄ and f ₅ are determined by electronic drivers 305 and 306, respectively. In addition, beams 309 and 31
The direction of the frequency shift of the frequency-shifted component of 0 is the same.

Beams 307 and 308 may alternatively be provided with a single laser source emitting multiple wavelengths, which was coupled to an optical frequency doubler means to achieve the double frequency. A single laser source, a laser source with a non-linear element inside such as a laser cavity, two laser sources of difference wavelength coupled to sum frequency generation or difference frequency generation, or of two or more wavelengths Those skilled in the art will appreciate that any equivalent source configuration capable of producing a light beam is used. It will also be appreciated by those skilled in the art that one or both of the frequency shifts f ₄ and f ₅ may be the result of Zeeman splitting, birefringent elements inside the laser cavity, or similar phenomenological properties of the laser source itself. Be understood by. In the production of a beam by a single laser with two widely separated wavelengths, for each beam there is a pair of orthogonally polarized components, one component of each pair being the second component of the corresponding pair. Those whose frequency is shifted with respect to the components are described in P.P. Zorabe
Dian's "Dual Harmonic-Wavelength Split"
-Frequency Laser "US Patent No. 5,732,09
No. 5 is described.

In addition, the polarization components of both beam 309 and / or beam 310 can be frequency shifted without departing from the scope and spirit of the invention, and f ₄ is the difference in frequency of the polarization components of beam 309. It will be appreciated by those skilled in the art that, leaving, f ₅ leaves a difference in frequency of the polarization components of beam 310. Improved separation of the interferometer and laser source is generally possible by frequency shifting both polarization components of the beam, and the degree of improved separation depends on the means used to generate the frequency shift. Dependent.

In the next step, beam 309 is reflected by mirror 353A, part of which is reflected by dichroic non-polarizing beam splitter 353B to give beam 313.
Is the first component of λ ₄ component. Some of the beam 310 is transmitted by the dichroic unpolarized light beam splitter 353B, the beam 313 the second component, lambda ₅ becomes component, the propagation of lambda ₅ components parallel and coextensive with the propagation of lambda ₄ components Preferably there is. In a further step, the beam 313 propagates to an interferometer 369 consisting of optical means,
This introduces a phase shift ψ ₄ between the non-frequency-shifted and frequency-shifted components of the λ ₄ component of beam 313, and the phase shift ψ ₅ is non-frequency-shifted of the λ ₅ component of beam 313. It is intended to be introduced between the second component and the frequency-shifted component. The magnitude of the phase shift [psi ₄ and [psi _5, the following officially therefore, is related to the physical length L ₄ and L ₅ of the round-trip measurement path 398.

[0198] _{ψ m = L m p m k} m n m, m = 4 and 5 (45) below, p _m is the number of passes through the respective reference and measurement interval for the interferometer of a number of routes , n _m corresponds to the wave number _{k m = (2π) / λ} m, the refractive index of the gas in the measurement path 398.

As shown in FIG. 4 a, the interferometer 369 comprises a reference retro-reflector 391, a target retro-reflector 392 whose position is controlled by a transducer 367, and quarter-wave retarders 377 and 378, and a polarized light. A beam splitter 373 is included. The quarter-wave phase delay plates 377 and 378 and the polarization beam splitter 373 are shown by λ ₄ and λ ₅ , respectively. This configuration is known in the art as a polarization Michelson interferometer and is shown as a simple illustration with p ₄ = p ₅ = 1.

The pass number parameters p ₄ and p ₅ can have values that are the same or different with respect to the other. Equation (45) is valid for the case where the path in the interferometer for a beam having a wavelength and the path in the interferometer for a beam having a second wavelength are substantially coextensive. Cases have been selected in the simplest way to illustrate the functionality of the invention in the third embodiment. For those skilled in the art, generalization to cases where the paths for beams with two different wavelengths are not substantially coextensive is a straightforward procedure.

After passing through the interferometer 369, the part of the beam 313 passing through the measurement path 398 becomes the phase-shifted beam 333, and the part of the beam 313 passing through the reference path including the retroreflector 391 is phase-shifted. Beam 334. The phase-shifted beams 333 and 334 are each polarized perpendicular to the plane and in the plane of FIG. 4a. The conventional dichroic beam splitter 361 has a wavelength of λ ₄
And those portions of beam 333 corresponding to λ ₅ are separated into beams 335 and 337, respectively, and those portions of beam 334 corresponding to wavelengths λ ₄ and λ ₅ are separated into beams 336 and 338, respectively. Beams 335 and 336 are incident on detector system 389 and beams 337 and 338 are on detector system 3
It is incident on 90.

In a detector system 389 as shown in FIG. 4a, beam 335 is first reflected by mirror 363A and then by polarizing beam splitter 363B to form the first component of beam 341. Beam 336 is transmitted by polarization beam splitter 363B to become the second component of beam 341. In detector system 390, beam 337 is first reflected by mirror 364A,
The first beam of beam 342 is then reflected by polarizing beam splitter 364B.
Form the ingredients of. Beam 338 is transmitted by polarization beam splitter 364B to become the second component of beam 342. Beams 341 and 342 pass through polarizers 379 and 380, respectively, impinge on photodetectors 385 and 386, respectively, and preferably produce two electron interference signals by photoelectron detection. The two electronic interference signals include two heterodyne signals s ₄ and s ₅ , respectively. Polarizer 3
79 and 380 are oriented to mix the polarization components of beams 341 and 342, respectively. Heterodyne signals s ₄ and s ₅ correspond to wavelengths λ ₄ and λ ₅ , respectively.

The signals s ₄ and s ₅ have the following form:

[0204]

[Formula 39] In the ceremony

[0205]

[Formula 40] The description of the expressions for s ₄ and s ₅ given by equation (46) is the same as the corresponding part of the description given for the expression for s ₂ of the first embodiment by equation (2). Heterodyne signals s ₄ and s ₅ are transmitted to electronic processor 327 for analysis as electronic signals 323 and 324 in either digital or analog format, which is preferably in digital format.

Referring now to FIG. 4b, the phase ψ ₄ is determined by an element of electronic processor 327, which is an electronic processor 351A, 351B, 352A,
353A, 354A, 355A, and 356A, which are elements 151A, 151B, 152, 153, 154, 155, and 156 of the first embodiment.
Performs the same functions as in. The phase ψ ₅ is determined by some other element of the electronic processor 327, and some other element is the electronic processor 351C, 351D,
352B, 353B, 354B, 355B, and 356B (see FIG. 4c), which are elements 151A, 151B, 152, 153, 1 of the first embodiment.
Perform similar functions to 54, 155, and 156, respectively.

The phases of the electronic drivers 305 and 306 are electronic signals, reference signals 321 and 3
22 respectively to the electronic processor 327 in either digital or analog format, preferably in digital format. Electronic processors 351A and 351C process reference signals s _{4, Ref} and s _{5, R ef} , respectively, to determine angular frequencies ω ₄ = 2πf ₄ and ω ₅ = 2πf ₅ , respectively, which is a sliding window FFT frequency detector. Preferably by an algorithm.

A reference signal, which is an alternative to the reference signals 321 and 322, is also preferably this by splitting a portion of the beams 309 and 310 by a beam splitter by optical pickoff means and detectors (not shown in the drawings). Is a non-polarizing beam splitter and can also be generated by mixing the split portions of beam 309 and beam 310 and detecting the mixed portions to generate an alternative heterodyne reference signal. ..

[0209]   Referring again to FIG. 4c, the phase ψ_FourAnd ψ_FiveThen l_Four/ P_FourAnd l _Five / P_FiveIn electronic processors 3275A and 3275B, respectively.
Are multiplied, which is preferably digitally processed to obtain the phase (l_Four/ P_Four) Ψ_Fourand
(L_Five/ P_Five) Ψ_FiveAre generated respectively. Phase (l_Four/ P_Four) Ψ_FourAnd (l_Five/ P_Five ) Ψ_FiveAre then added together in electronic processor 3276, and electronic processor 3
At 277 one is subtracted from the other, which is preferably a digital process.
Thus, the phases θ and Φ are created respectively. Formally, it is as follows.

[0210]

[Formula 41] The phases θ and Φ can also be described as follows using the definitions given by equations (45), (49) and (50).

[0211]

[Equation 42] In the ceremony

[0212]

[Equation 43] The preferred nominal value for ΔL is zero, and for co-extensive beam components at wavelengths λ ₄ and λ ₅ , ΔL << λ ₄ or λ ₅ .

The dispersion of the gas (n ₅ corrected for the effects of periodic errors in the dispersion related signal).
−n ₄ ) can be determined from θ and Φ using the following formula.

[0214]

[Equation 44] In the ceremony

[0215]

[Equation 45] Is. In applications related to range finding interferometers, the heterodyne phase ψ ₄ and the phases θ and Φ are used to make the range L ₄ independent of the effect of the refractive index of the gas in the measuring path of the range finding interferometer. , And as a corrected amount for the effects of periodic errors in the dispersion related signal and the optical path length related signal can be determined using the following formula.

[0216]

[Equation 46] In the equation, Γ is the inverse dispersion power of gas and is defined as follows. Γ = (n ₄ −1) / (n ₅ −n ₄ ) (62) From the definition of K given by equation (54), (K / χ) = 0 is strictly harmonically related λ It is clear that it corresponds to ₄ and λ ₅ . ｜ K / χ ｜ ＞
For applications where 0 and the value of (K / χ) must be known to some precision in order to meet the end-use requirements in the use of equations (59) and / or (61), (K / χ) is measured by the wavelength monitor. The wavelength monitor can include a vacuum cell and / or an interferometer with or without a doubled frequency of the light beam by the SHG. In applications where the value of χ must be known to some other precision in the use of equations (59) and / or (61), χ is measured by a wavelength monitor. In addition, when the values of χ and (K / χ) are both needed, they can be obtained from the same device.

The value for the inverse dispersion power Γ can be obtained to a certain relative accuracy from the known refraction properties of the known constituents of the gas in the measurement path. In applications where the gas component is not known to the required precision and / or the refractive properties of the gas component are not known to the corresponding required precision, Γ is co-pending and the same owner 19
Henry A. et al., Filed January 19, 1999. Hill's "Apparatus A
nd Methods For Measuring Intrinsic O
Optical Properties Of A Gas "can be measured by devices such as those described in US patent application Ser. No. 09 / 232,515, which is hereby incorporated by reference.

The relative accuracy with which the variance (n ₅ −n ₄ ) can be determined is limited, in part, by the effects of the cyclic error if they are not compensated. [Φ-θ (
The correction for the periodic error effect made in obtaining the (K / χ) -Q _ζ ] coefficient in equations (59) and (61) is Q _Ψ given by the formula:

[0219]

[Equation 47] In the ceremony

[0220]

[Equation 48] Is. The correction Q _Ψ is entered as a term in the coefficient [∼Φ-∼θ (K / χ) -Q _Ψ -Q _ζ ], where ~ Φ and ~ θ are not compensated for the effect of the cyclic error, respectively. , Φ
And the corresponding values of θ. Therefore, according to equation (59) and (63), the magnitude of cyclic errors effect in the determined value of the dispersion (n ₅ -n ₄₎ is the degree follows.

[0221]

[Equation 49] For example, λ ₄ = 0.633 μm, λ ₄ = 2λ ₅ , p ₄ = p ₅ = 1 and │L = 0.5 m
And consider that the gas consists of air at 25 ° C. and a pressure of 1 atm. In the state of the example, the magnitude of the contribution of ψ ₄ to the relative accuracy as expressed by equation (66) is as follows.

[0222]

[Equation 50] Ψ ₄ is expressed in radians, and | Ψ ₄ | represents the absolute value of Ψ ₄ . Continuing the example, for a particular periodic error of | Ψ ₄ | = 0.1 radians, the periodic error in phase corresponds to the periodic error in the 5 nm distance measurement in the example, and the particular periodic error is , The variance (n ₅ −n ₄ ) is limited to a relative accuracy that can be measured to ≈0.2%. If the source for the λ ₄ beam is an NbYAG laser with λ ₄ = 1.06 μm, the corresponding limit in the relative accuracy with which the dispersion (n ₅ −n ₄ ) can be measured is ≈0. 6%.

The limitation of the effect of the cyclic error on the relative accuracy with which the dispersion (n ₅ −n ₄ ) can be determined is the refraction of the gas in the measurement path of the distance measuring interferometer if the cyclic error effect is not compensated. The sex effect propagates directly to the limit of the effect of the cyclic error on the relative accuracy that can be determined using a dispersive interferometer. From the equation (61), the magnitude of the periodic error contribution of ψ _m entered through Q _ψ is ψ ₄ = (˜ψ ₄ −ψ ₄ −
It is clear that ≈ Γ | Ψ _m | relative to the magnitude of the periodic error contribution | Ψ ₄ | entered via the ζ ₄ ) term. For λ ₄ = 2λ ₅ , λ ₄ = 0.633 μm, and also λ ₄ = 2λ ₅ , λ ₄ = 1.06 μm, the values of Γ are 22 and 75, respectively.
Is. Therefore, the effect of the periodic error contribution to the correction term in Eq. (61) for the refractive index of the gas in the measurement path is that the effect of the periodic error contribution resulting from the correction term is directly ψ ₄ = (˜ψ ₄ If the effect is equal to or less than the effect of the periodic error generated from the term −Ψ ₄ −ζ ₄ ), it must be reduced by about 1.5 times or more.

The remaining description of the third embodiment is the same as the corresponding parts of the description given for the first embodiment. L ₅ can also be determined using ψ ₅ instead of ψ ₄ in the first variant of the third embodiment. The corresponding formula for the determination of L ₅ is:

[0225]

[Equation 51] The rest of the description of the first variant of the third embodiment is the same as the corresponding parts of the description given for the third embodiment.

The quantity L ₄ , which is respectively according to the third embodiment and the quantity L ₅ , which is according to the first variant of the third embodiment, deviate from the scope and spirit of the present invention. To obtain a reduced statistical error in the determination of changes in physical path length,
It will be apparent to those skilled in the art that it can be determined and used.

It will also be apparent to those skilled in the art that L ₅ can be a distance determined by the third embodiment rather than L ₄ without departing from the scope or spirit of the invention. Will be.

Furthermore, in end-use applications where K / χ must be known to one precision and / or χ must be known to another precision, a periodic error in the measured wavelength And the value of the wavelength ratio obtained by the wavelength measurement and monitoring device deviates from the device and method of the first and second embodiments and their variants, and the scope and spirit of the invention. However, it will be apparent to a person skilled in the art that it can be measured and compensated by the application of a wavelength monitor as described later herein in the sixth embodiment of the invention and its variants. .

In end-use applications, where Γ is measured for the gas in measurement path 398, it may be further necessary to measure and compensate for the effects of cyclic error.
What will be described later in the present specification in the sixth embodiment and its modifications,
It can be used in obtaining the measured value of Γ compensated for the effects of periodic errors.

A second variant of the third embodiment will be described. In the third embodiment, the effects of cyclic errors are compensated by using the corresponding method and apparatus of the first embodiment. In the second modification of the third embodiment, the effect of the cyclic error is
Compensation by using corresponding methods and apparatus of variations of the embodiment of. The remaining description of the second variant of the third embodiment is the same as the corresponding parts of the description given for the first and third embodiments and variants thereof.

A fourth embodiment of the invention is described by means of the preferred device and method of the fourth embodiment, which describes the dispersion of the gas in the measurement path and the change in the optical path length of the measurement path by the gas. Includes devices and methods for measuring and monitoring. The fourth embodiment further includes an apparatus and method for compensating for the effects of periodic errors in the dispersion of the measured gas and the measured changes in the optical path length of the measurement path due to the gas. The fourth embodiment is from the fourth of several different categories. The refractive index and / or the physical length of the gas in the measurement path may have changed. In addition, the ratio of the wavelengths of the light beam produced by the adapted source matches some relative accuracy to known ratio values, consisting of non-zero quantities. The non-zero quantity may include one or more low order non-zero integers.

In the third embodiment and its variants, the effect of the cyclic error is that by using the corresponding method and device of the first embodiment and its variants, ie in the space of electronic interference signals. It is compensated for by compensating for the effects of periodic errors. In the fourth embodiment, the effect of the periodic error is by using the corresponding method and apparatus of the second embodiment and its variants, ie the effect of the periodic error in the space of the phase of the electronic interference signal. By compensating for

The effect of the periodic error in the correction for the effect of the gas in the measurement path, the correction generated from the optical dispersion related signal is the effect of the cyclic error in the signal used for the determination of the optical path length change It is about 1.5 times larger than the effect.

According to a preferred apparatus and method of the fourth embodiment, the fourth embodiment comprises a light beam 309, a source of light beam 309, an interferometer 369, a translator 367 and the third shown in FIG. 4a. Embodiments of detector systems 389 and 390. The fourth embodiment further includes the electronic processor 427 shown in Figures 5a and 5b.
including.

[0235]   Corresponding to the electronic signals 321, 322, 323, and 324 shown in FIG. 4a,
The electronic signals of the fourth embodiment are referred to below as electronic signals 421, 422, 423, respectively.
, And 424. Of the electronic drivers 305 and 306 of the fourth embodiment
Frequency is f₆And f₇And the angular frequency ω₆And ω₇Have
. In the fourth embodiment, the angular frequency ω_{6, Ny}And ω_{7, Ny}Is the detector system
The angular Nyquist frequencies of 389 and 390. In the fourth embodiment, the radiation source 3
The wavelengths of 01 and 302 are λ₆And λ₇And the known approximation ratio l ₆ / L₇Have. Reference signal s_{6, Ref}And s_{7, Ref}Are electronic signals 421 and
And 422. Heterodyne signal s of the fourth embodiment₆And s₇Is
Each is the heterodyne signal s of the third embodiment._FourAnd s_FiveCorresponding to. Hetero
Dyne signal s₆And s₇Are transmitted as electronic signals 423 and 424, respectively.
It

Referring to FIG. 5a, the phase ˜ψ ₆ is determined by certain elements of electronic processor 427, which include electronic processors 450A, 451A, and 452A, each of which is the electronic processor of the second embodiment. It performs similar functions to 250, 251A, and 252. The phase ~ φ ₇ is determined by some other element of the electronic processor 427, some other element of which is the electronic processor 450B, 451.
C, and 452B, which perform similar functions to the electronic processors 250, 251A, and 252 of the second embodiment, respectively. Elements 4275A, 4275B, 4276, and 4277 of the fourth embodiment perform similar functions to elements 3275A, 3275B, 3276, and 3277 of the third embodiment to determine ~ θ and ~ Φ. The definitions of ~ θ and ~ Φ in the fourth embodiment are as follows.

[0237]

[Equation 52]

[Equation 53] Wherein a ~ψ ₆ = α ₆ -ω ₆ t and _{~ψ 7 = α 7 -ω 7 t} . The description of α ₆ and α ₇ is the same as the corresponding parts of the description given for α ₃ of the second embodiment.

Electronic processor 427 further includes electronic processors 452C, 453, 454, and 455 for determining Z _{Ψ, M} of Q _{Ψ, M.}

[0239]

[Equation 54] The electronic processors 452C, 453, 454 and 455 of the fourth embodiment perform similar functions to the electronic processors 252, 253, 254 and 255 of the second embodiment. The phases ~ Φ and _{ZΨ, M} are transmitted to the electronic processor 456 where ~ Φ- _{ZΨ, M} is generated. The electronic processor 456 of the fourth embodiment performs similar functions to the electronic processor 256 of the second embodiment.

The cyclic error compensated phase ~ Φ-Z _{Ψ, M} is transmitted to the digital computer 429 as signal 428. Digital computer 429 calculates the variance (n ₇ -n ₆ ) according to the following formula:

[0241]

[Equation 55] The effect of the cyclic error on ˜θ, ζ _ψ is included in Eq. (74) for completeness. However, ζ _Ψ is not compensated for in the fourth embodiment. The effect of ζ _Ψ in the calculation of the variance (n ₇ −n ₆ ) is reduced by the coefficient (K / χ) relative to the effect of Z _Ψ , and therefore the effect of ζ _Ψ is | K / χ | << 1. Note that this is negligible for some end use applications.

In applications related to range finding interferometers, heterodyne phase ~ ψ ₆ , and phases ~ θ and ~ Φ are used to describe range L ₆ as the refractive index of the gas in the measurement path of the range finding interferometer. The following formula can be used as a quantity that is independent of the effect of and corrected for the effect of the periodic error in the dispersion-related signal.

[0243]

[Equation 56] The remaining description of the variants of the fourth embodiment is the same as the corresponding parts of the description given for the second and third embodiments of the invention.

5c and 5d show in schematic form an electronic processor 527A according to a preferred apparatus and method of the fifth embodiment of the present invention. The fifth embodiment is
From the fourth category of embodiments, beam 309, source of beam 309, interferometer 369, detector system 389, and digital computer 329 of the third embodiment shown in FIG. 4a, and FIG. 5c. And an electronic processor 427A shown in FIG. 5d.

In the fifth embodiment, the dispersion of gas in the measurement path, the change in the optical path length of the measurement path due to the gas, and the change in the optical path length of the measurement path due to the change in the physical path length of the measurement path are described. , Apparatus and methods for measuring and monitoring. The fifth embodiment further comprises the optical path length of the measurement path in the dispersion of the gas measured in the measurement path, in the change of the optical path length of the measurement path by the gas and by the change of the physical path length of the measurement path. Apparatus and method for measuring and compensating for the effects of cyclical errors on changes in

In the fourth embodiment, the effects of cyclic errors are compensated by using the corresponding method and apparatus of the first embodiment and its variants. In the fifth embodiment, the effect of the cyclic error is also compensated by using the corresponding method and device of the first embodiment and its variants.

[0247]   The electronic processor 427A includes electronic processors 450A, 451A, 451B,
452A, 453A, 454A, 455A, and 456A, which are
2 embodiment electronic processors 250, 251A, 251B, 252, 253,
Perform a function similar to 254, 255, and 256 to obtain Ψ_{6, M}And ~ ψ₆−Ψ _{6, M} To generate. Electronic processor 427A further includes electronic processor 450B,
451C, 451D, and 452B, which are 250, 251A, 25
1B, and perform a function similar to 252,₇To generate. Fifth embodiment
State electronic processors 4275A, 4275B, 4276, and 4277 are electrically powered.
Performs similar functions to child processors 453B, 454B, 455B, and 456B.
And these are the electronic processors 4275A, 4275B, 42 of the fourth embodiment.
Perform a function similar to 76, and 4277 to generate ~? And ~ ?. Electric
The child processors 452C, 453B, 454B, 455B, and 456B are
4 embodiments electronic processors 452C, 453, 454, 455, and 45
Perform a function similar to 6 to_{6, M}And ~ Φ-Z_{6, M}To generate.

The cyclic error-corrected phase ˜φ ₆ −Ψ _{6, M} , the phases ˜θ and ˜Φ−Z _{Ψ, M} , and the cyclic error correction terms Ψ _{6, M} and Z _{Ψ, M} are digital computers 329. Signal 428A and used by the digital computer 329 to make the distance L ₆ independent of the effect of the refractive index of the gas in the measurement path of the distance measuring interferometer, and periodic in the dispersion and distance measurement related signals. As a quantity corrected for the effect of error, determined using equation (75) below, ζ _{Ψ, M} is calculated by the following formula:

[0249]

[Equation 57] The remaining description of the fifth embodiment is the same as the corresponding parts of the description given for the second, third and fourth embodiments and variants thereof.

A sixth embodiment of the preferred apparatus and method of the sixth embodiment will be described.
This sixth embodiment is an apparatus for measuring and correcting periodic errors in both dispersion measurements on signals and refraction measurements on signals or refraction measurements on signals used to determine the intrinsic optical properties of a gas. And both methods. This sixth embodiment further includes both an apparatus and method for measuring and correcting for periodic errors in the wavelength measurement and / or associated signals used to determine and / or monitor the wavelength of the light beam. There is. This sixth embodiment derives from the fifth category of several different categories.

The apparatus and method of the sixth embodiment includes the apparatus and method of the fourth embodiment and measures the dispersion of the gas and the refraction index of the gas to be corrected for the effects of periodic error. Determine the corresponding mutual dispersed powers of the gases. For determining the refractive index of the gas, the measuring path at each wavelength is evacuated. This vacuum measurement path can also be used to measure and monitor wavelengths corrected for the effects of periodic errors. The second wavelength used to measure the dispersion corrected for the periodic error can be measured and monitored by providing a measurement path for the second wavelength.

To further describe the apparatus and method for measuring and monitoring the intrinsic optical properties of gas and light beam wavelengths, see “Apparatus And Met.
hods For Measuring Intrinsic Optical
Reference is made to U.S. patent application Ser. No. 09 / 323,515 entitled "Properties Of A Gas" (supra). The application is incorporated herein by reference.

The rest of the description of the sixth embodiment is similar to the corresponding parts of the description given for the fourth embodiment and its variants. A modification of the sixth embodiment according to a preferred apparatus and method of the modification of the sixth embodiment will be described. This variation provides an apparatus and method for measuring and correcting periodic errors in both dispersion measurements on signals and refraction measurements on signals or refraction measurements on signals used to determine the intrinsic optical properties of a gas. Both are included. This variation of the sixth embodiment provides both an apparatus and method for measuring and correcting periodic errors in the wavelength measurement and / or associated signals used to determine and / or monitor the wavelength of a light beam. Including further.
This variant of the sixth embodiment derives from the fifth category of several different categories.

The apparatus and method of the modification of the sixth embodiment includes the apparatus and method of the fifth embodiment, and measures the dispersion of gas and the refractive index of gas to measure the effect of periodic error. Determine the corresponding mutual dispersed powers of the gases to be corrected. For determining the refractive index of the gas, a vacuum is applied to the measurement path at each wavelength. This vacuum measurement path can also be used to measure and monitor wavelengths corrected for the effects of periodic errors. The second wavelength used to measure the dispersion corrected for the periodic error can be measured and monitored by providing a measurement path for the second wavelength.

The rest of the description of the variants of the sixth embodiment is similar to the corresponding parts of the description given for the fifth and sixth embodiments. Modifications of the signal processing technique in all the above-described embodiments are also within the scope of the present invention. For example, a window function can be added to the interferometric data before analyzing its spectrum to better resolve peaks corresponding to periodic errors. In particular, a window function can be chosen to suppress the contribution of the heterodyne interference peak at the dominant frequency at ω + φ down to the data analyzed.

The relevance of such window functions can be demonstrated by considering a Fourier transform analysis of a sliding window of interfering data that includes periodic errors. The Fourier transform of the sliding window is the interference signal, eg s (t
) Is sampled over a time window of duration τ and then the sampled data is Fourier transformed. The transformed data thereby corresponds to the Fourier transform of the unwindowed interfering signal that has been convolved with the Fourier transform of the time window. This is a sink function. The convolution of the sink function with the dominant peak in the interfering data produces a background in the transformed data that corresponds to the wing of the sink function. This background can mask the peaks of the cyclic error. The reason is that the amplitude of such peaks is generally much smaller than the amplitude of the peak at the dominant frequency at ω + φ, making it more difficult to characterize the coefficient of periodic error accurately.

To address such difficulties, embodiments include one or more electronic processors. These electronic processors employ a window function to suppress the wideband wings of the sinc function associated with the Fourier transform of the sliding window. For example, the aforementioned processors 151B, 252, 257, 351B, 351
Any of D, 452A, and 452C can be modified and a window function applied to input data to the processor before computing the Fourier transform of the input data. For example, suitable window functions are approximate Gaussian window, approximate Lorentz window, cosine bell window.
window, a triangular window, and any other window that smooths the data near its endpoints. The processor multiplies the input data by such a window function. This window function is chosen, for example, to have a time constant that can be compared to τ and then Fourier transform the data so windowed. Since the window function reduces the amplitude of the data near its endpoint more slowly than the amplitude of the sliding window Fourier transform only, the background caused by the dominant peaks in the spectral data is reduced and the peaks of the periodic error are reduced. It can be identified more accurately.

One inexpensive computer-based technique for implementing the triangular window function is to compute a series of data samples from the data collection part of the sliding window. In particular, consider a detector that continuously samples an N-point data array. In this case, each successive data array is incremented by less than N, eg, 1
Is shifted by the increment of. A triangular window function can be generated by adding a series of data arrays at corresponding points. Thus, for example, if a contiguous data array is shifted by one increment, M contiguous data arrays can be added to produce an N + M-1 point data array. This is then Fourier transformed, and the background of the Fourier transform is reduced because it is continuously added (which produces a triangular window).

Other window functions are possible. For example, the processor may choose the frequency of the periodic error and employ a window function that suppresses the frequency of the dominant peak ω + φ. Alternatively, or in addition, the dominant frequency contribution to the data can be removed from the data in either the time or frequency domain to "pre-bleach" the data. By removing the contribution of the dominant peak, the peaks of the cyclic error can be more accurately resolved and quantified.

For example, the aforementioned processors 151B, 252, 257, 351B, 351D
, 452A, and 452C can be changed as follows. First, a sliding window Fourier transform is applied to the input data. The amplitude and phase of the dominant peak are determined based on the Fourier transform. next,
A signal equal to the convolution of the delta function at the dominant frequency and the sinc function corresponding to the sliding window is subtracted from the Fourier transformed data, thereby removing the contribution made by the dominant peak and eliminating the peak of the periodic error. Make it clear. Alternatively, the contribution in the time domain can be removed by subtracting the sinusoidal term contribution at the dominant frequency from the input data sampled by the sliding window. This dominant frequency has the amplitude and phase determined by the Fourier transform of the sliding window. The resulting input data is then Fourier transformed to represent peaks of periodic error. In either domain, the procedure can be iteratively refined based on subsequent calculations of the contribution of the periodic error to the amplitude and phase of the dominant peak.

Another technique that can be implemented by the electronic processor of the embodiments described above is:
The use of a tuned filter (also called phase lock-in) to more accurately determine the cyclic error coefficient. This tuned filter can be used if a special set of periodic error terms is identified as making a statistically significant contribution to the interfering signal. The tuned filter can then be used repeatedly to update the coefficient of periodic error while using the interferometry system. This tuned filter will now be described with reference to FIG. FIG. 8 is a schematic diagram of the electronic processor 800. For the purposes of this description, the electronic processor 800 is a component of the electronic processor 127 shown in Figure 2b as part of the first embodiment. For example,
As a component of any of the electronic processors 127A, 227, 227A, 327, 427, and 427A, the electronic processor 800 can also be implemented in a direct manner, as in any other embodiment.

[0262]   Please refer to FIG. The electronic processor 800 outputs the interference signal s from the detector 185.₂(
part of the signal 123 indicating t), the Nyquist frequency ω from the detector_{2, Ny}Signal 1 indicating
23, and the reference signal s from the driver 105._{2, Ref}Signal indicating (t)
A part of 121 is received as an input signal. Signal s_{2, Ref}(T) and s₂(T)
Pass through spectrum analyzers 851A and 851B, respectively. Spect
Rule analyzer 851A uses the reference signal s_{2, Ref}Heterodyne reference frequency based on (t)
Number ω₂And the spectrum analyzer 851B determines the interference signal s₂Analyzing (t), s ₂ The frequency of the dominant peak at (t) is determined. This dominant peak is ω₂+ / Φ ₂ (Or its alias). ω₂And ω₂+ / Φ₂The value of
It is sent to the processor 853. This processor 853 has the Nyquist frequency ω_{2, Ny} And a signal 802 indicating the relevant cyclic error term are received as inputs.
. As mentioned above, such terms are sent from electronic processor 154. This phone
The child processor 154 performs the chi-square test executed by the electronic processor 153.
On the basis of this, information about the statistically significant periodic error terms is stored. input signal
Processor 853 determines that each relevant cyclic error term is currently sampled.
Shift of the converted data (Doppler shift) φ₂Against
S₂The frequency appearing in the signal of (t) is determined. In particular, the processor 853
, Which frequency of the periodic error ~ ω_{2, v}Is the magnitude of the Doppler shift (if any)
Therefore, the alias ~ ω based on equations (6) and (7)_{2, vA}As present
Decide whether or not The processor 853 then determines the frequency of the cyclic error ~ ω '._{2, v}
To the electronic processor 854. Here ~ ω '_{2, v}A basic if needed
Frequency of periodic error ~ ω_{2, v}Or its alias ~ ω_{2, vA}Indicates either

[0263]   Note that FIG. 8 is referred to. The electronic processor 854 receives the interference signal s from the detector 185. ₂ Another part of the signal 123 indicating (t) is received as an additional input. Cyclic error
Difference frequency ~ ω '_{2, v}For each of the₂Co to (t)
s ~ ω '_{2, v}And sin ~ ω '_{2, v}And output two output signals 831
And 832. These signals are sent to the processor 855. Kosai
S and sine terms multiply₂Each frequency in (t) is the signal
+ ~ Ω 'in each of 831 and 832_{2, v}And- ~ ω '_{2, v}Only shifted
Be done. The latter shift has a lower frequency term (eg,
Zero frequency term). Processor 855 is a low pass filter. This
Low-pass filter, for example, digitally integrates the signal over a time constant T.
To remove the high frequency terms and retain only the low frequency terms. In particular
, This integration yields:

[0264]

[Equation 58] and

[0265]

[Equation 59]   Processor 855 then provides the integration result for equations (77) and (78).
Then, by using the arctangent calculation, the amplitude A of the coefficient of the periodic error is _{2, v} And phase ζ_{2, v}To decide. Alternatively, the processor 855 may
When using the complex representation for interfering signals that include differences, the complex representation for the periodic error terms
The amplitude can be calculated. Processors 854 and 855 are
Repeat the calculation for each of the error terms. The processor 855 then
The difference coefficient may be one or more successors in processor 127, such as processor 155.
Send to the processor. Where these coefficients are the contributions of the periodic error term from the interfering signal.
Finally used to get rid of.

In particular, the processors 851A, 851B, and 853 are
Since the frequency ~ ω ' _{2, v} is tuned by monitoring φ ₂ , the time constant (eg, integration time) of the low-pass filter in the processor 855 can be lengthened compared to the conversion rate of the Doppler shift. . For this reason, the time constant T is made sufficiently long to generate an accurate value for the coefficient of the periodic error even though the signal-to-noise ratio at s ₂ (t) is small. This is especially important in applications such as microlithography. In this microlithography there is a desire to rapidly change the slew rate of the stage (and consequently the Doppler shift), thereby increasing the productivity of the microlithography tool.

In a further embodiment of the electronic processor 800, the second portion of the signal 123 indicative of the interference signal s ₂ (t) from the detector 185 may be pre-bleached in the time domain, as described above. it can. In particular, this signal is pre-bleached before passing through the electronic processor 854, which removes the dominant heterodyne term contribution at the frequency ω ₂ + · φ ₂ (or its alias), Generate a signal that represents an approximation for (defined) s _{2, Ψ} (t). This signal is then sent to electronic processor 854.

Another modification of the signal processing technique of the above-described embodiment will be described. Aspects of the invention generally propose to characterize the contribution of the periodic error to the interfering signal as a spectral representation. As detailed above, whether a particular periodic error term contributes to the dominant peak in the interfering signal depends on the Doppler shift and the Nyquist frequency. Since the Doppler shift changes during the operation of the interferometric system, a particular periodic error term can be characterized if the Doppler shift spectrally separates such periodic error terms from the dominant terms. . Finally, a spectral representation of all statistically relevant periodic error terms is constructed, and the contribution of the periodic error to the interfering signal in the time domain is subtracted based on the spectral representation and prior evaluation of φ. By doing so, it is possible to iteratively determine the phase φ of the interference signal (without the contribution of the periodic error). For example, the processors 152, 155 and 156 in the processor 127 of the first embodiment perform such iterative calculations.

In another scheme, the contribution of the periodic error is subtracted from the interfering signal in the frequency domain to iteratively determine the phase φ. In such cases, only those periodic errors that contribute to the interfering signal at the dominant frequency need be considered. For example, FIG. 9 is a schematic diagram of an electronic processor 900 that implements such a scheme. For the purposes of this description, the electronic processor 900 is shown in Figure 2b as part of the first embodiment.
It is a component of the electronic processor 127 shown in FIG. For example, as a component of any of the electronic processors 127A, 227, 227A, 327, 427, and 427A, as in any other embodiment, the electronic processor 90
It is also possible to implement 0 in a straightforward way.

[0270]   Please refer to FIG. The electronic processor 900 outputs the interference signal s from the detector 185.₂(
part of the signal 123 indicating t), the Nyquist frequency ω from the detector_{2, Ny}Signal 1 indicating
23, and the reference signal s from the driver 105._{2, Ref}Signal indicating (t)
A part of 121 is received as an input signal. Signal s_{2, Ref}(T) and s₂(T)
Pass through spectrum analyzers 951A and 951B, respectively. Spect
Of the reference signal s_{2, Ref}Heterodyne reference frequency based on (t)
Number ω₂And the spectrum analyzer 951B determines that the interference signal s₂Analyzing (t), s ₂ The frequency of the dominant peak at (t) is determined. This dominant peak is ω₂+ / Φ ₂ (Or its alias). ω₂And ω₂+ / Φ₂The value of
It is sent to the processor 953. This processor 953 uses the Nyquist frequency ω_{2, Ny} And a coefficient of the cyclic error, eg, determined by the processor 800.
Amplitude A_{2, v}And phase ζ_{2, v}The signal 902 indicating the value of is received as an input. Professional
Sessa 953 (eg, based on equation (2), equation (6), and equation (7))
Which periodic error term is at the dominant frequency for the currently sampled data
Signal s₂Determine whether it contributes to (t). Then the corresponding cyclic error coefficient is
Send to processor 954.

Still referring to FIG. Spectrum analyzer 951B are, for example, by the Fourier transform of the sliding window, further determining the amplitude to A ₂ and phase to [phi] ₂ of the dominant peaks in the s ₂ (t), and sends the amplitude and phase to the processor 954. Processor 954 then determines the values for phase φ ₂ that are consistent with amplitude ˜A ₂ and phase ˜φ ₂ , and the periodic error from processor 953 determined to contribute to the interfering signal at the dominant frequency. By determining the term, the phase φ ₂ for the interference signal without periodic error is repeatedly determined. In some circumstances, the value for phase φ ₂ determined by the frequency domain technique of processor 900 was determined by the time domain technique because only those periodic errors that contribute in the dominant frequency are used. More accurate than the value.

Processors 127, 127A, 227, 227A, 327, 427, 427A
It should also be noted that embodiments that combine features of 800, 800, and 900 may be modified to eliminate redundant components. For example, processor 151A
And 851A perform the same function, processor 800 will cause processor 12
7 components, the electronic processor 851A in the processor 800 can be replaced by the processor 151A in the processor 127.

The interferometry system described above quantifies non-linearities (eg, periodic errors) and uses this quantified non-linearity to measure distances where such non-linearity exists, the variance of Correct the measured value and the measured value of the intrinsic optical property. As a result, such interferometry systems provide accurate measurements. Such a system
It is particularly useful for lithographic applications used when manufacturing large scale integrated circuits such as computer chips and the like. Lithography is an important technology driver for the semiconductor manufacturing industry. The overlay improvement is a 100 nm line width (
It is one of the five most difficult challenges to reach the design rule. For example, S
emiconductor industry Roadmap (1997)
Page 82 of the.

The overlay is directly dependent on the performance, or accuracy, of the distance measuring interferometer used in positioning the stage for the wafer and reticle (or mask). Lithography tools produce $ 50 million to $ 100 million annually in products, so the economic value from distance-measuring interferometers with improved performance is significant. Each 1% increase in lithographic tool output results in approximately $ 1 million annually in economic benefits for integrated circuit manufacturers and a significant competitive advantage over lithographic tool vendors .

The function of the lithographic tool is to direct the spatially patterned radiation onto the photoresist coated wafer. This process involves determining which location on the wafer receives the radiation (alignment) and applying the radiation to the photoresist at that location (exposure).

To properly position the wafer, the wafer contains alignment marks on the wafer that can be measured by dedicated sensors. The measured position of the alignment mark defines the position of the wafer within the tool. This information, along with the desired patterning specifications for the wafer surface, guides the alignment of the wafer to the spatially patterned radiation. Based on such information, a moveable stage supporting the photoresist coated wafer moves the wafer so that the radiation exposes the correct location on the wafer.

During exposure, the radiation source illuminates the patterned reticle. The reticle scatters the radiation to produce spatially patterned radiation. This reticle is also called a mask, and these terms are used interchangeably in the following description.
In the case of reduction lithography, a reduction lens collects the scattered radiation to form a reduced image of the pattern on the reticle. Alternatively, in the case of proximity printing, the scattered radiation propagates a short distance (typically on the order of microns) before contacting the wafer, producing a 1: 1 image of the reticle's pattern. This radiation initiates a photochemical process in the resist. This process converts the pattern of radiation into a latent image in the resist.

Interferometry systems are an important component of a positioning mechanism that controls the position of the wafer and reticle and registers the image of the reticle on the wafer. If such interferometry systems include the phase measuring section described above, the accuracy of the distances measured by these systems is increased because the contribution of periodic errors to the distance measurement is minimized.

Lithographic systems are also commonly referred to as exposure systems and typically include an illumination system and a wafer positioning system. This irradiation system is
A radiation source is provided that provides radiation such as visible, x-ray, electron, or ion radiation, and a reticle or mask that imparts a pattern to the radiation, which produces spatially patterned radiation. Further, for reduction lithography, the illumination system can include a lens assembly that images the spatially patterned radiation onto the wafer. This imaged radiation exposes the resist coated on the wafer. The illumination system also includes a masking stage that supports the mask and a positioning system that adjusts the position of the masking stage with respect to radiation directed through the mask. The wafer positioning system comprises a wafer stage that supports the wafer and a positioning system that adjusts the position of the wafer stage with respect to the imaged radiation. Fabrication of integrated circuits involves multiple exposure steps. For general inquiries regarding lithography, see, eg, J. R. Sheets and B.I. W. Smi
th's "Microlithography: Science and Tec"
"hology" (Marcel Dekker, Inc., New York, 1)
998). The contents of this document are incorporated herein by reference.

The interferometry system described above is used to accurately position each wafer stage and mask stage relative to other components of the exposure system, such as a lens assembly, radiation source, or support structure. Can be measured. In such a case, the interferometry system can be attached to a stationary structure and the measurement object can be attached to movable components such as a mask stage and a wafer stage. Alternatively, the states can be reversed, such that the interferometry system is mounted on a movable object and the measurement object is mounted on a stationary object.

More generally, such interferometry systems can be used to measure the position of any one component of the exposure system relative to any other component of the exposure system. Here, the interferometry system is attached to or supported by one of the components and the measurement object is attached to or supported by another component.

An example of a lithographic scanner 1100 using interferometry system 1126 is shown in FIG. 6a. This interferometry system uses wafers (
It is used to accurately measure the position of (not shown). Here, stage 11
22 is used to position and support the wafer with respect to the exposure station. The scanner 1100 includes a frame 1102. The frame supports other support structures and various components retained on these structures. A lens housing 1106 is attached to an upper portion of the exposure base 1104. A reticle or mask stage 1116 used to support the reticle or mask is mounted on top of the lens housing 1106. The positioning system for positioning the mask with respect to the exposure station is indicated schematically by element 1117. Positioning system 1117 can include, for example, piezoelectric transducer elements and corresponding control electronics. Although not included in this described embodiment, one or more interferometry systems described above are used to accurately monitor the position of the masking stage and the position in the process of manufacturing the lithographic structure. It can also accurately measure the position of other moveable elements that need to (see the above-mentioned Sheets and Smit).
h's "Microlithography: Science and Tech"
Noology ").

A support base 1113 that holds the wafer stage 1122 is suspended below the exposure base 1104. Stage 1122 includes a plane mirror 1128 that reflects a measurement beam 1154 directed to the stage by interferometry system 1126. A positioning system for positioning the stage 1122 with respect to the interferometry system 1126 is shown schematically by element 1119. The positioning system 1119 can include, for example, piezoelectric transducer elements and corresponding control electronics. The measurement beam is reflected back toward the interferometer system mounted on the exposure base 1104. This interferometry system
It can be any of the previously described embodiments.

During operation, a beam of radiation 1110, eg, an ultraviolet (UV) beam from an ultraviolet laser (not shown), passes through the beam forming optics assembly 1112 and the mirror 11
After being reflected at 14, proceed downward. The radiation beam then passes through a mask (not shown) held by the mask stage 1116. This mask (
(Not shown) is a lens assembly 1 held in a lens housing 1106.
An image is formed on the wafer (not shown) on the wafer stage 1122 via 108. The base 1104 and the various components supported thereby are
It is isolated from environmental vibrations by a braking system represented by spring 1120.

In other embodiments of lithographic scanners, one or more interferometric systems described above can be used to measure distances along multiple axes and angles. These axes and angles relate to, for example, but not limited to, the wafer and reticle (or mask). Also, other wafers can be used to expose the wafer other than a UV laser beam, including, for example, an X-ray beam, an electron beam, an ion beam, and a visible light beam.

In some embodiments, the lithographic scanner comprises a column reference (column).
n reference) can include those known to those skilled in the art. In such an embodiment, interferometry system 1126 directs a reference beam (not shown) along an external reference path that contacts a reference mirror (not shown) located on a structure. The reference mirror directs the reference beam, for example, to the lens housing 1106. The reference mirror reflects the reference beam back to the interferometry system. The interfering signal produced by the interferometry system 1126 when the measurement beam 1154 reflected from the stage 1122 and the reference beam reflected from the reference mirror mounted on the lens housing 1106 combine to determine the position of the stage relative to the radiation beam. Shows the change of. Further, in other embodiments, interferometry system 1126 can be positioned to measure changes in the position of reticle (or mask) stage 1116 or other moveable components of the scanner system. Finally, interferometry systems can be used in a similar manner in addition to scanners or with lithography systems that include steppers without scanners.

As is well known to those skilled in the art, lithography is an important part of the manufacturing method for manufacturing semiconductor devices. For example, US Pat. No. 5,483,343 outlines the steps of such a manufacturing method. These steps are described below with reference to Figures 6b and 6c. FIG. 6b illustrates a semiconductor chip (eg, IC or L
6) is a flow chart of the procedure for manufacturing a semiconductor device such as SI), a liquid crystal panel or a CCD. Step 1151 is a design process for designing a circuit of a semiconductor device. Step 1152 is a process of manufacturing a mask based on the pattern design of the circuit. Step 1153 is a process of manufacturing a wafer by using a material such as silicon.

[0288] Step 1154 is a wafer process called pretreatment, in which circuits are lithographically formed on the wafer by using the prepared mask and wafer. In order to form circuits corresponding to these patterns on the mask on the wafer with sufficient spatial resolution, it is necessary to position the lithography tool on the wafer by interferometry. The interferometric methods and systems described herein are particularly useful for improving the effectiveness of lithography used in wafer processing.

[0289] Step 1155 is an assembling step called post-processing, in which the wafer processed in step 1154 is formed into a semiconductor chip. This step includes assembly (dicing and bonding) and packaging (chip sealing). Step 1156 is an inspection step, in which the operability of the semiconductor device manufactured in step 1155 is checked.
Durability check etc. are executed. Through these processes, the semiconductor device is completed and shipped (step 1157).

FIG. 6c is a flow chart showing details of the wafer process. Step 116
1 is an oxidation step of oxidizing the surface of the wafer. Step 1162 is a CVD process for forming an insulating film on the surface of the wafer. Step 1163 is an electrode forming step of forming electrodes on the wafer by vacuum evaporation. Step 116
Step 4 is an ion implantation step of implanting ions into the wafer. Step 1165
Is a resist process of adding a resist (photosensitive material) to the wafer. Step 1166 is an exposure process in which the circuit pattern of the mask is printed on the wafer by exposure (that is, lithography) through the exposure apparatus described above. Again, as mentioned above, the use of the interferometry systems and methods described herein improves the accuracy and resolution of such lithographic steps.

Step 1167 is a developing process for developing the exposed wafer. Step 1168 is an etching process for removing a portion other than the developed resist image. Step 1169 is a resist separation process for separating the resist material remaining on the wafer after undergoing the etching process. By repeating these steps, circuit patterns are formed and overlaid on the wafer.

The interferometry system described above can also be used in other applications where it is necessary to accurately measure the relative position of an object. This interferometry system is used in applications where a writing beam, such as a laser, x-ray, ion, or electron beam, marks a pattern on a substrate when either the substrate or the beam is in motion. The relative movement between the substrate and the writing beam can be measured.

As an example, a schematic diagram of a beam writing system 1200 is shown in FIG. A source 1210 produces a writing beam 1212 and a beam focusing assembly 121.
4 is a substrate 1216 supported by a movable stage 1218 for a radiation beam.
Turn to. To determine the relative position of the stage, the interferometry system 1220
A reference beam 1222 is directed to a mirror 1224 mounted on a beam focusing assembly 1214 and a measurement beam 1226 is directed to a mirror 1228 mounted on a stage 1218. This beam writing system is an example of a system that uses a column reference because the reference beam contacts a mirror mounted on the beam focusing assembly. The interferometry system 1220 can be any of the interferometry systems previously described. The change in position measured by the interferometry system is
This corresponds to a change in the relative position of the writing beam 1212 on the substrate 1216. Interferometry system 1220 sends a measurement signal 1232 to controller 1232 that is indicative of the relative position of writing beam 1212 on substrate 1216. This controller 1230
Output signal 1236 to base 1236 supporting and positioning stage 1218.
To send. Further, the controller 1230 sends a signal 1238 to the source 1210,
Write beam 1212 such that the write beam contacts the substrate with sufficient brightness to cause photophysical or photochemical changes only at selected locations on the substrate.
Change or block the brightness of the.

Further, in some embodiments, the controller 1230 may use, for example, signal 1
244 can be used to cause the beam focusing assembly 1214 to scan the writing beam across the substrate area. As a result, controller 1230 directs other components of the system to pattern the substrate. This patterning is generally based on electronic design patterns stored in the controller.
In some applications, the writing beam patterns the resist coated on the substrate, and in other applications the writing beam directly patterns, eg etches, the substrate.

An important application of such a system is the manufacture of masks and reticles used in the interferometric method described above. For example, an electron beam can be used to pattern a chromium-coated glass substrate to produce an interferometric mask. If the writing beam is an electron beam, the beam writing system encloses the path of the electron beam with a vacuum. Also, when the writing beam is, for example, an electron beam or an ion beam, the beam focusing assembly may generate an electric field such as a quadrapole lens that focuses and directs charged particles onto a substrate under vacuum. Includes vessels. If the writing beam is a radiation beam, eg X-ray, UV, or visible radiation,
The beam focusing assembly includes corresponding optics that focus and direct the radiation onto the substrate.

Other aspects, advantages, and modifications are intended to be covered by the following claims. In addition, in the present specification, "~" at the beginning of a character such as "~ ω", "~ ψ", "~ θ", "~ A" is used in the English language at the time of international application.

[0297]

[Equation 60] As described above, it is attached above the character, but in the text, it is written before the character for convenience. Similarly, “• ψ”, “^ s”, and “￣L” similarly have “·”, “^”, and “￣”.
"Is attached to the letter immediately after it in the English text at the time of international application, but is written before the letter for convenience in the text.

[0298]   Further, in the present specification, θ is the English language at the time of international application.

[0299]

[Equation 61] However, it was written as θ for convenience.

[Brief description of drawings]

FIG. 1 is a general schematic diagram of an interferometry system for quantifying and / or monitoring non-linearities caused by system characteristics.

FIG. 2a is a schematic diagram of a first embodiment of an interferometry system for quantifying non-linearity.

2b is a schematic diagram of various embodiments for an electronic processor in the interferometry system of FIG. 2a.

2c is a schematic diagram of various embodiments for an electronic processor in the interferometry system of FIG. 2a.

FIG. 2d is a graph illustrating frequencies of various types of non-linearities.

2e shows two input beams generated for the interferometric system of FIG. 2a,
FIG. 5 is a schematic diagram of different embodiments for a source for quantifying zero frequency shift periodic error.

FIG. 2f produces two input beams for the interferometry system of FIG. 2a,
FIG. 5 is a schematic diagram of different embodiments for a source for quantifying zero frequency shift periodic error.

FIG. 3a is a schematic diagram of a second embodiment of an interferometry system for quantifying non-linearity.

3b is a schematic diagram of various embodiments for an electronic processor in the interferometry system of FIG. 3a.

3c is a schematic diagram of various embodiments for an electronic processor in the interferometry system of FIG. 3a.

FIG. 4a is a schematic diagram of a third embodiment of an interferometry system for quantifying non-linearity.

4b is a schematic diagram of an electronic processor in the interferometry system of FIG. 4a.

4c is a schematic diagram of an electronic processor in the interferometry system of FIG. 4a.

FIG. 5a is a schematic diagram of an electronic processor for use with the interferometry system of FIG. 4a in a fourth embodiment of the invention.

FIG. 5b is a schematic diagram of an electronic processor for use with the interferometry system of FIG. 4a in a fourth embodiment of the invention.

FIG. 5c is a schematic diagram of an electronic processor for use with the interferometry system of FIG. 4a in a fifth embodiment of the invention.

FIG. 5d is a schematic diagram of an electronic processor for use with the interferometry system of FIG. 4a in a fifth embodiment of the invention.

FIG. 6a is a schematic illustration of a lithographic system, including an interferometry system, as described herein and used to make integrated circuits.

FIG. 6b is a flowchart that describes steps for making an integrated circuit.

FIG. 6c is a flowchart describing steps for making an integrated circuit.

FIG. 7 is a schematic diagram of a beam writing system including the interferometry system described herein.

FIG. 8 is a schematic diagram of an electronic processor for use in embodiments of the interferometry system described herein.

FIG. 9 is a schematic diagram of another electronic processor for use in the interferometry system embodiments described herein.

─────────────────────────────────────────────────── ─── Continuation of front page (51) Int.Cl. ⁷ Identification code FI theme code (reference) H01L 21/027 H01L 21/30 503B (31) Priority claim number 09 / 583,368 (32) Priority date Heisei May 31, 2012 (May 31, 2000) (33) Priority claiming countries United States (US) (81) Designated countries EP (AT, BE, CH, CY, DE, DK, ES, FI, FR, GB , GR, IE, IT, LU, MC, NL, PT, SE, TR), CN, JP, KR, US F terms (reference) 2F064 AA01 BB01 CC10 EE01 GG22 JJ15 2G059 AA02 AA03 BB01 EE05 EE09 EE11 EE12 GG01 GG04 GG09 JJ07 JJ12 JJ13 JJ18 JJ19 JJ22 KK01 MM01 5F046 BA04 BA05 CC01 CC02 CC16

Claims (66)

[Claims] 1. An interferometer for directing two beams along separate paths defining an optical path length difference during operation and then combining each beam to produce a pair of overlapping exit beams. And a detector for generating an interference signal s (t) representing the optical path length difference in response to optical interference between the pair of superposed outgoing beams, wherein the signal s (t) is 2 A signal having a frequency equal to the sum of the frequency division ω that can exist between two beams and the Doppler shift ψ determined by the rate of change of the optical path length difference, and the signal due to the characteristics of the interferometry system. s (t) is a detector and an analyzer coupled to the detector, each further comprising an additional term, each having an additional term having a frequency not equal to the sum of the frequency division ω and the Doppler shift ψ Between i) the principal term and the value of the Doppler shift and Quantifying at least one additional term based on the value of s (t) that at least one additional term is spectrally separated, and ii) using the quantified at least one additional term, Doppler An interferometric system comprising: an analyzer that evaluates a change in optical path length difference corresponding to another value of s (t) that the main term and at least one additional term do not spectrally overlap depending on the value of the shift. . 2. The system of claim 1, wherein the detector comprises a photodetector, an amplifier and an analog to digital converter. 3. The system of claim 1, wherein the frequency division between the two beams is non-zero. 4. The system of claim 1, wherein at least one additional term is a plurality of additional terms. 5. The analyzer uses the expression s (t) to quantify at least one additional term.
) ∝cos (ωt + ψ + ζ _1,0,1,0 ) + NL is used to calculate the Doppler shift / ψ for the value of s (t), where NL is the initial quantification of the additional term and ψ = Lkn
Where L is the physical path length difference, k is the wave number, n is the index of refraction, ω is the angular frequency division between the two beams, t is time, and ζ _1, The interferometry system of claim 1, wherein _0,1,0 is a phase offset. 6. The interferometric system of claim 5, wherein the initial quantification is NL = 0. 7. The interferometric system of claim 1, wherein the analyzer quantifies at least one additional term by evaluating a corresponding coefficient of the representation of s (t) taking into account each additional term. 8. The representation of s (t) can be represented as: ## EQU1 ## ω is the angular frequency division between the two beams, and _{ω'u '} is the detector, analyzer and 2
Is a frequency caused by at least one of the sources of the two beams and is not equal to ω, L is the physical path length difference, λ is the wavelength of the beam in the first set, and n is the index of refraction. , C is the speed of light in a vacuum, and t is time, the main term corresponds to a _1,0,1,0 cos (ωt + ψ + ζ _1,0,1,0 ) and the additional term is the remaining term. The interferometric measurement according to claim 7, wherein the amplitudes a _v and B _v and the phase ζ _v define each coefficient for the expression of s (t), and v is a subscript that means a general index. system. 9. The analyzer calculates a frequency spectrum corresponding to each value of s (t) of a given set to quantify at least one additional term, and each sinusoid in the representation of s (t). At an angular frequency ~ ω equal to the derivative with respect to time of a sinusoidal argument that does not correspond to the principal term, or at an alias ~ ω _{A of} ~ at least 1 based on the amplitude and phase of the frequency spectrum. 9. The system of claim 8, wherein the coefficient for the additional terms is evaluated. 10. The system of claim 9, wherein the frequency spectrum is a Fourier transform of each value of s (t) in a predetermined set. 11. s (t) is s (t) = A (where α (t) is the phase of s (t).
t) cos (α (t)) and the frequency spectrum is α
10. The system of claim 9, which is the Fourier transform of (t). 12. The detector has a sampling rate that defines a Nyquist frequency ω _Ny , and the analyzer has: For a positive integer r that satisfies At ～Omega alias ～Omega _A is, to evaluate the respective coefficients for additional term of at least one based on the amplitude and phase of the frequency spectrum, the system of claim 9, wherein. 13. ~ω is one of u 'omega + omega against ≠ _{0' u} ', The system of claim 9. 14. The system of claim 9, wherein ω is one of q (ω + · ψ). 15. ~ ω is u for p ≠ 0 when p ≠ 1 and u = 0.
The system according to claim 9, which is one of ω + p · ψ + p ⁺ · ψ. 16. The analyzer normalizes the amplitude and phase of the frequency spectrum at the angular frequency ˜ω to evaluate each coefficient for at least one additional term by at least one non-zero of ψ. 10. The system of claim 9, considering the derivative of. 17. The analyzer includes at least one addition based on each value of s (t) of the first set having a Doppler shift large enough to spectrally separate the additional frequency from the dominant frequency. For each value of s (t) in the second set that the term is quantified and the Doppler shift is different from each value in the first set and large enough to spectrally separate the additional frequency from the dominant frequency. The system of claim 1, further quantifying the at least one additional term based on. 18. The analyzer of claim 17, wherein the analyzer quantifies at least one additional term as a function of Doppler shift by interpolating a quantified value for each value of s (t) of each set. system. 19. The analyzer, based on each value of s (t) of a plurality of sets, each set corresponding to a different Doppler shift, determines the dependence of each of the evaluated coefficients on the Doppler shift. The system of claim 9, determining. 20. At least one additional term is a plurality of additional terms, and in order to quantify the plurality of additional terms, the analyzer includes a frequency at a corresponding plurality of angular frequencies ~ ω _v or their aliases. Evaluating the coefficient for each of the above-mentioned additional terms based on the amplitude and phase of the spectrum, each ~ ω _v relates to the time of one sinusoid argument that does not correspond to the main term in each sinusoid in the expression of s (t). 10. The system of claim 9, which is equal to the derivative. 21. The analyzer comprises B _{1,0,1,0, q, q-2j} and ζ _1,0, where q is an odd number and j is a non-negative integer less than q / 2−1 _{. Determine} B _{1,0,1,0, q, 1} and ζ _{1,0,1,0, q, 1} by evaluating the coefficients corresponding to at least some of _{1,0, q, q-2j} 21. The system of claim 20. 22. The analyzer is s (t) ∝cos (ωt + ψ + ζ _1,0,1,0 )
By determining the value for ψ = Lkn, which is self-consistent with + NL (ψ, · ψ), s
Evaluating the change in optical path length difference corresponding to other values of (t), where NL represents at least one quantified additional term, L is the physical path length difference, and k is the wavenumber. And
n is the index of refraction, ω is the angular frequency difference between the two beams, t is time,
The system of claim 1, wherein ζ _1,0,1,0 is a phase offset. 23. The system of claim 22, wherein the analyzer determines the value for ψ by iteratively improving the evaluation of the value for ψ. 24. The system of claim 1, wherein during operation the analyzer uses the estimated change in optical path length to determine a change in physical path length. 25. The system of claim 1, wherein during operation the analyzer uses the estimated change in optical path length to determine a change in dispersion. 26. The system of claim 1, wherein during operation the analyzer uses the estimated change in optical path length to determine an intrinsic value of the gas. 27. The system of claim 1, wherein during operation the analyzer monitors the wavelength of each beam using the estimated change in optical path length. 28. During operation, an interferometer that directs two beams along separate paths defining an optical path difference and then combines the beams to produce a pair of overlapping exit beams. And a signal s (t that represents interference in response to optical interference between the pair of output beams that overlap.
), The signal s (t) is a function of the optical path length difference,
Due to the characteristics of the interferometry system, the signal s (t) is represented as s (t) = acos.
Deviating from (ωt + ψ + ζ), where ψ = Lkn, L is the physical path length difference, k is the wave number, n is the index of refraction, and ω is the angle that may exist between the two beams. A frequency difference, t is time, a is an amplitude that is constant with respect to ψ, and ζ is a phase offset that is constant with respect to ψ and · ψ, and a detector coupled to the detector. An analyzer which, during operation, i) Fourier transforms each value of s (t) in at least one set in which the rate of change of optical path length difference is not zero (.ψ ≠ 0), and Defines a power spectrum equal to the squared absolute value of the Fourier transform, ii) at least some based on the amplitude and phase of the Fourier transform at a frequency different from ω + · ψ and corresponding to the peak of the power spectrum. Quantifies the deviation of And iii) an analyzer that evaluates a change in the optical path length difference corresponding to a specific value of s (t) by using the quantified deviation described above. 29. During operation, an interferometer that directs two beams along separate paths defining an optical path length difference and then combines each beam to produce a pair of overlapping exit beams. And a signal s (t that represents interference in response to optical interference between the pair of output beams that overlap.
), The signal s (t) is a function of the optical path length difference,
Due to the characteristics of the interferometry system, the signal s (t) is represented as s (t) = acos.
Deviating from (ωt + ψ + ζ), where ψ = Lkn, L is the physical path length difference, k is the wave number, n is the index of refraction, and ω is the angle that may exist between the two beams. Is the frequency difference, t is the time, a is the amplitude that is constant with respect to ψ, ζ is the phase offset that is constant with respect to ψ and · ψ, and s (t) is α (
a detector and an analyzer coupled to said detector, which can be expressed as s (t) = A (t) cos (α (t)), where t) is the phase of s (t), In the meantime, i) the phase α (t) with respect to s (t) is extracted, and ii) the change speed of the optical path length difference is not zero (· ψ ≠ 0)
Fourier transform is performed on each value of α (t) of at least one set, and this Fourier transform defines a power spectrum equal to the squared absolute value of the Fourier transform, and is different from iii) ω + · ψ and the power Quantifying at least some deviations based on the amplitude and phase of the Fourier transform at a frequency corresponding to the peak of the spectrum, and iv) using the quantified deviations, the optical path corresponding to a particular value of s (t) An interferometry system equipped with an analyzer that evaluates changes in length difference. 30. During operation, an interferometer that directs two beams along separate paths defining an optical path difference and then combines each beam to produce a pair of overlapping exit beams. And a detector for generating an interference signal s (t) representing the optical path length difference in response to optical interference between the pair of superposed outgoing beams, wherein the signal s (t) is 2 A signal having a frequency equal to the sum of the frequency division ω that can exist between two beams and the Doppler shift ψ determined by the rate of change of the optical path length difference, and the signal due to the characteristics of the interferometry system. s (t) is a detector and an analyzer coupled to the detector, each further comprising an additional term, each having an additional term having a frequency not equal to the sum of the frequency division ω and the Doppler shift ψ The frequency of the signal s (t) is monitored during And an analyzer that generates a signal indicating system deterioration when the amplitude of the frequency corresponding to one of the additional terms exceeds a threshold value, and is connected to the analyzer to respond to the system deterioration signal. An interferometry system with an alarm mechanism that 31. The system of claim 30, wherein the alarm mechanism comprises at least one of a visual display, an acoustic system, an alarm light and a printer. 32. During operation, the analyzer includes at least one set of s (t
31. The system of claim 30, wherein the frequency at s (t) is monitored by Fourier transforming each value of). 33. s (t) is α (t) where s (t) is the phase of s (t) = A (
t) cos (α (t)) and during operation the analyzer extracts the phase α (t) from each value of s (t) of at least one set, and the extracted phase Fourier transform of α (t) yields s (t)
31. The system of claim 30, which monitors the frequency at. 34. During operation, the analyzer is based on the value of s (t) at which the main term and at least one additional term are spectrally separated by the value of the Doppler shift in s (t). 31. The system of claim 30, which monitors frequency. 35. s (t) can be expressed as: ω is the angular frequency division between the two beams, and _{ω'u '} is the detector, analyzer and 2
Is a frequency caused by at least one of the sources of the two beams and is not equal to ω, L is the physical path length difference, λ is the wavelength of the beam in the first set, and n is the index of refraction. , C is the speed of light in a vacuum, and t is time, and each additional term corresponds to a term other than a _1,0,1,0 cos (ωt + ψ + ζ _1,0,1,0 ),
31. The system according to claim 30. 36. During operation, the analyzer compares the amplitude of one of the frequencies ω + ω ′ _{u ′} for u ′ ≠ 0 with the threshold to generate a signal indicative of system degradation. 36. The system of claim 35, wherein 37. During operation, the analyzer determines whether to generate a signal indicative of system degradation by comparing the amplitude of one of the frequencies q (ω + · ψ) with the threshold. 36. The system of claim 35, wherein 38. During operation, the analyzer is p ≠ 1 and u = 0 when u = 0.
By comparing the amplitude of the frequency in one of uω + p · ψ + p ⁺ · ψ for ≠ 0 with the threshold value, it is determined whether or not to generate a signal indicating system deterioration.
The system of claim 35. 39. A source that, during operation, provides a first set of two beams with a frequency division ω and a second set of two beams with a frequency division ω _T not equal to ω; Between the first beam of the first set and the first beam of the second set along a measurement path, and the second beam of the first set and the second beam of the second set. An interferometer that directs along a reference path and then combines the beams of both sets to form an output beam, the measurement path and the reference path defining an optical path length difference; A detector responsive to optical interference between the beams to generate a signal S (t) representative of the interference as a function of the optical path length difference; and the signal S (t) in the absence of the second set of beams. ) Is determined by the frequency division ω and the speed of change of the optical path length difference. Each zero frequency that is equal to s (t) including the main term at a frequency equal to the sum of the Doppler shift and ψ, and contributes to s (t) at the same frequency as the main frequency due to the characteristics of the interferometry system. If a shift cyclic error is introduced and the second set of beams is present, the property producing a zero frequency shift cyclic error contribution to s (t) produces a multiline in the frequency spectrum of S (t), The multiplex has analyzers coupled to the detector, with each neighboring peak separated by ω-ω _T , and during operation, distinguishing each frequency in S (t) to An interferometric measurement comprising: an analyzer for identifying and quantifying at least one zero frequency shift cyclic error based on the amplitude and phase of at least one peak in the multiline. Stem. 40. During operation, the analyzer quantifies a plurality of zero frequency shift cyclic errors based on the amplitude and phase of each of a plurality of peaks in the multiplex line.
The system of claim 39. 41. The analyzer is also coupled to the source, and during operation the analyzer selects the first set of beams for the interferometer with the source rather than the second set of beams. 40. The system of claim 39, wherein the system comprises: 42. During operation, when the analyzer selectively provides the interferometer with the first set of beams with the source rather than the second set of beams, the analyzer includes s ( 42. The system of claim 41, wherein the optical path length difference is determined based on t) and at least one of each quantified zero frequency shift cyclic error. 43. During operation, the analyzer is configured to include at least one set of S (t)
40. The system of claim 39, wherein each frequency in S (t) is distinguished by Fourier transforming each value of. 44. S (t) = S (t) = α _S (t) as the phase of S (t)
Together can be expressed as _{A S (t) cos (α} S (t)), the analyzer during operation, alpha of at least one of the set by extracting S (t) from the phase α _S (t) _S 40. The system of claim 39, wherein each frequency of S (t) is distinguished by Fourier transforming each value of (t). 45. The multiplex includes a peak at the dominant frequency.
9. The system according to 9. 46. The system of claim 39, wherein the detector samples the value of S (t) at a rate that defines the Nyquist frequency and the frequency divisions are each less than the Nyquist frequency. 47. The detector samples the value of S (t) at a rate that defines the Nyquist frequency and is between the mean frequency of the beams of the first set and the mean frequency of the beams of the second set. 4. The difference between is greater than the Nyquist frequency.
9. The system according to 9. 48. The detector is S (t) at a rate that defines a Nyquist frequency ω _Ny.
) Is sampled and ω <ω _Ny , ω _T <ω _Ny and │ω−ω _T │ << ω
40. The system of claim 39, wherein 49. The system according to claim 48, wherein | ω−ω _T | <(ω / 100). 50. The source comprises first and second lasers, the first set of beams being derived from the first laser and the second set of beams being derived from the second laser. Item 39. The system according to item 39. 51. The source comprises first and second lasers and first and second acousto-optic modulators, wherein the first set of beams is derived from the first lasers and the first acousto-optic modulators. 40. The system of claim 39, wherein the second set of beams is derived from the second laser and the second acousto-optic modulator. 52. The source comprises a laser and first and second acousto-optic modulators, a first beam derived from the laser passing through the first acousto-optic modulator of the first set. 40. A beam is generated and a second beam derived from the laser passes through the second acousto-optic modulator to generate the second set of beams.
The system described. 53. The system of claim 52, wherein the first and second beams derived from the laser correspond to adjacent longitudinal modes of the laser. 54. During operation, the analyzer discriminates the frequency multilines in S (t) for each of a plurality of Doppler shifts and the dependence of the quantified zero frequency shift circulation on the Doppler shifts. 40. The system of claim 39, which quantifies 55. During operation, the analyzer produces a signal representative of system degradation when the amplitude of the multiplex exceeds a threshold, and the system is coupled to the analyzer. 40. The system of claim 39, further comprising an alarm mechanism responsive to the deterioration signal. 56. The system of claim 55, wherein the alert mechanism comprises at least one of a visual display, an acoustic speaker, a printer and an alert light. 57. The above representation of s (t) can be expressed as: omega _'u' is the detector is a frequency not equal to omega with caused by at least one of the analyzer and the radiation source, L is the physical path length difference, lambda is the wavelength of the beam in the first set by, n is the refractive index, c is the velocity of light in a vacuum, and, t is time, nonlinearity _{a 1,0,1,0 cos (ωt + ψ +} ζ 1,0, 1,0) other than And the quantified zero frequency shift cyclic error _causes B _{1,0,1,0, q, 1} and ζ _1,0,1, for one of q = 3, 5, 7 ... 40. The system of claim 39, corresponding to _{0, q, 1} . 58. A stage for supporting a wafer, an illumination system for imaging spatially patterned radiation on the wafer, and a positioning system for adjusting the position of the stage relative to the imaged radiation. A lithographic system for use in making integrated circuits on a wafer, comprising: the interferometric measurement system of claim 1, 28, 29, 30 or 39 for measuring the position of the stage. 59. A stage for supporting a wafer, a radiation source, a mask, a positioning system, a lens assembly, and 1.
, 28, 29, 30 or 39, the illumination system comprising the interferometric system according to claim 28, 28, 29, 30 or 39, wherein the source directs radiation through the mask during operation to produce spatially patterned radiation. Generating, the positioning system adjusts the position of the mask with respect to radiation from the source, the lens assembly images the spatially patterned radiation onto the wafer and the interference. A lithographic system used to fabricate integrated circuits on a wafer, the measurement system measuring the position of the mask with respect to radiation from the source. 60. A source for providing a writing beam for patterning a substrate, a stage for supporting the substrate, a beam steering assembly for providing the writing beam to the substrate, the stage and the beam steering assembly. A positioning system for positioning the stages relative to each other and measuring the position of the stage relative to the beam steering assembly.
28. A beam writing system for use in making a lithographic mask, comprising: the interferometric measurement system according to 28, 29, 30 or 39. 61. An interferometry method for use with an interferometry system, comprising: directing two beams along separate paths; and combining the beams to produce a pair of exit beams. And a step of defining the optical path length difference in the separate path, and measuring the optical interference between the pair of superposed outgoing beams to obtain an interference signal s (t) representing the optical path difference. ), The signal s (t) is the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. Due to the characteristics of the interferometric system, the signal s (t) includes a main term having a frequency equal to
further including additional terms each having a frequency that is not equal to the sum of ψ and a value of s (t) such that the value of the Doppler shift spectrally separates the main term and at least one additional term. Quantifying at least one additional term based on, and using at least one additional quantified term, the value of the Doppler shift indicates that the main term and the at least one additional term do not spectrally overlap. evaluating the change in optical path length difference corresponding to another value of t); 62. An interferometry method for use with an interferometry system, comprising directing two beams along separate paths and producing a pair of exit beams that combine and superimpose the beams. And a step of defining the optical path length difference in the separate path, and measuring the optical interference between the pair of superposed outgoing beams to obtain an interference signal s (t) representing the optical path difference. ), The signal s (t) is the sum of the frequency division ω that may exist between the two beams and the Doppler shift ψ defined by the rate of change of the optical path length difference. Due to the characteristics of the interferometric system, the signal s (t) includes a main term having a frequency equal to
further including additional terms each having a frequency not equal to the sum of ψ, monitoring the frequency of the signal s (t), and adding a frequency corresponding to one of the additional terms An interferometric method comprising the step of alerting the operator when the amplitude exceeds a threshold value. 63. An interferometry method for use with an interferometry system, the first set of two beams having a frequency division ω and the second set of two beams having a frequency division ω _T not equal to ω. Directing a first beam of the first set and a first beam of the second set along a measurement path and a second beam of the first set and a second beam of the second set. Directing the beam along a reference path, and combining the beams of both sets to form an output beam, wherein the measurement path and the reference path define an optical path length difference; Measuring the optical interference between the beams in a beam and generating a signal S (t) representative of the interference as a function of the optical path length difference, and the signal S (t if the second set of beams is absent. t) is the above frequency division ω It is equal to s (t) including the main term at a frequency equal to the sum of the Doppler shift and ψ determined by the rate of change of the optical path length difference, and s ( If each zero frequency shift cyclic error contributing to t) is caused and the second set of beams is present, the property producing a zero frequency shift cyclic error contribution to s (t) is the frequency spectrum of S (t). And having multiple neighboring peaks separated by ω-ω _T, and distinguishing the multiplet by distinguishing each frequency in S (t), at least in the multiplet Quantifying at least one zero frequency shift cyclic error based on the amplitude and phase of one peak; 64. Supporting the wafer on a stage, imaging spatially patterned radiation on the wafer, and adjusting the position of the stage with respect to the imaged radiation. A lithographic method comprising: measuring the relative position of the stage using the interference measuring method according to claim 61, 62 or 63. 65. Supporting the wafer, directing radiation from a source to the mask to produce spatially patterned radiation, and positioning the mask with respect to the radiation. 64. Measuring the position of the mask with respect to the radiation using the interferometry method of claim 61, 62 or 63; imaging the spatially patterned radiation on the wafer. A lithographic method comprising. 66. Providing a writing beam for patterning a substrate, supporting the substrate on a stage, supplying the writing beam to the substrate, and providing the writing beam with the writing beam. 64. A beam writing method comprising: positioning a stage; and measuring a relative position of the stage using the interferometric measuring method according to claim 61, 62 or 63.