JP2006170796A - Method and device of reducing periodic error of optical interferometer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve problems wherein an orthogonal two-phase signal of a homodyne optical interferometer used for a high-precision length measuring system or the like includes an error by an optical system and electric circuit system, the Lissajous's waveform is out of round, and the error becomes a position error as it is when the measuring result is used and positional servo is applied in real time. <P>SOLUTION: The signal including the error is converted into the polar coordinate, and then a correction value (amplitude, zero point, and phase difference) of the orthogonal two-phase signal of the interferometer is determined by a least squares method based on the relation between the phase angle and radius variation. Based on these values, the orthogonal two-phase signal of the interferometer is corrected so that the radius of the polar coordinate is constant, and the periodic error is reduced. The orthogonal two-phase signal of the interferometer is converted into the polar coordinate, then calculation for emphasizing only a changed part of the radius element is performed, it is converted into the orthogonal coordinate again, and it is displayed similarly to the Lissajous's waveform, thereby obtaining a display resolution required for adjustment. <P>COPYRIGHT: (C)2006,JPO&amp;NCIPI

Description

  The present invention relates to an optical interferometer used in a high-precision length measuring system or the like.

First, the measurement principle of the optical interferometer will be described with reference to the drawings.
In FIG. 11, a laser beam I ₀ emitted from the laser oscillator 1 is guided to a polarization beam splitter (hereinafter referred to as “PBS”) 2 through a λ / 2 wavelength plate 5. In PBS 2, separates the laser beam I ₀ to the reference light I _s and the measurement light I _m. The intensity ratio of the measured light I _m and the reference beam I _s rotates the lambda / 2 wave plate 5 to the optical axis within a plane perpendicular, adjusted by rotating the polarization plane of the laser beam I _0. Usually it is almost the same amount. Measurement light I _m is reflected by the moving prism 4, again, is led to the PBS 2. Reference light I _s is reflected by the reference prism 3, is guided to the PBS 2 is reflected, overlaps with the measurement light I _m. Measurement light I _m and the reference beam I _s superimposed is through the mirror 6 and is guided to the polarizer 20. Direction of the polarizer, a 45 °, the reference light I _s and the measurement light I _m is approximately the same amount transmitted. Reference light I _s and the measurement light I _m of the polarization direction matched is guided to a photodetector 11, measures the interference intensity.

Interference intensity is determined from the optical path difference between the measurement light I _m and the reference beam I _s, the wavelength of the laser light I ₀ lambda, the optical path difference and x, also, the measurement light I _m on optical detector 11 when the light quantity of the reference light I _s are equal, interference strength
P (x) = I _m · (1 + cos (kx)) k = 2π / λ
It becomes. Therefore, a change in optical path difference x between the measurement light I _m and the reference beam I _s, i.e., repeat the dark to vibrate when displacing the moving prism 4 sinusoidally. This repetition of light and dark becomes the output of the photodetector 11. By counting this, the displacement d of the moving prism 4 can be measured. However, since the period of light and dark is λ / 2, the resolution of displacement measurement is λ / 2 as it is, and high-precision displacement measurement cannot be performed.

FIG. 12 shows an example of a method for improving the resolution. The laser beam emitted from the laser oscillator 1 is guided to the mirror 6 in the same manner as in FIG. After reflected by the mirror 6, rotated 45 degrees the polarization direction of the measuring beam I _m and the reference beam I _s by lambda / 2 wavelength plate 7. These lights then divided into two directions while maintaining the polarization state by the non-polarizing beam splitter 8, the light transmitted is divided by the polarization component of the measuring light I _m and the reference beam I _s at PBS9a, and paper The parallel component is transmitted, the component perpendicular to the paper surface is reflected to the photodetector 11a, and is guided to the photodetector 11b. Further, non-polarized light after the polarization of the measuring beam I _m and the reference beam I _s circularly polarized light by light is lambda / 4 wave plate 10 reflected by the beam splitter 8, the measurement light I _m and the reference beam I _s at PBS9b The component parallel to the paper surface is transmitted and the component perpendicular to the paper surface is reflected and guided to the light detector 11d.

The optical system is intended to produce a specific phase difference in the optical path difference between the measurement light I _m and the reference beam I _s, in the above description, the phase difference 0 ° to the optical detector 11a, the photodetector 11b Produces an interference intensity after applying a phase difference of 180 °, a phase difference of 90 ° to the photodetector 11c, and a phase difference of 270 ° to the photodetector 11d. That is, the outputs Pa to Pd of the photodetectors 11a to 11d are
Pa (x) = I _m / 2 · (1 + cos (kx))
Pb (x) = I _m / 2 · (1 + cos (kx + π))
Pc (x) = I _m / 2 · (1 + cos (kx + π / 2))
Pd (x) = I _m / 2 · (1 + cos (kx + 3π / 2)) k = 2π / λ
It becomes.

Therefore, if Pa and Pb are derived from the difference circuit 12a, the difference Va is taken, Pc and Pd are derived from the difference circuit 12b, and the difference Vb is taken.
Va ＝ I _m・ cos （kx）
Vb ＝ I _m・ sin （kx）
It becomes.

FIG. 13 shows the relationship between Va and Vb. Va on the horizontal axis and the vertical axis Taking Vb, so that always passes through the center of the intersection of the two axes was a circle of radius I _m. Considering this as polar coordinates, the radius is constant and only the phase angle changes. Therefore, by calculating the phase angle from Va and Vb, the resolution that was λ / 2 can be dramatically improved.

  Further, as shown in FIG. 14, even if the optical path difference changes continuously, the detectable phase difference is only between 0 and 2π, so it is determined whether the jump from 0 to 2π or the jump from 2π to 0 However, it is necessary to connect the phase angles. In FIG. 12, the phase calculation circuit 14 calculates the phase angle, and the phase connection circuit 15 connects and outputs the phase angle.

  However, the operation described so far is an ideal case. Actually, there are manufacturing errors of each optical element, optical adjustment errors, errors in the electric circuit system, and the like. As shown in FIG. Is not a perfect circle but an ellipse. Then, as shown in FIG. 16, when the radius is constant, the detection phase includes non-linearity, and when it is phase-coupled, a periodic error such as a measured optical path difference in the figure results. It leads to deterioration of measurement accuracy.

As these improvement methods, there is a method of performing error analysis from data after measurement and correcting a periodic error (for example, see Non-Patent Documents 1 to 3 below).
PLMHeydemann, Determination and correction of quadrature fringe measurement errorsin interferometers, Appl.Opt., 20, 1981, 3382-3384 KP Brich, Opticalfringe subdivision with nanometric accuracy, Precision Eng, Oct 1990 Vol12 No4 Ozeki et al., "Study on interior position uncertainty reduction method using two-phase sine wave signal of laser interferometer", Journal of Precision Engineering, Vol.69, No9, 2003

  As described above, quadrature two-phase signals of homodyne optical interferometers used in high-accuracy measurement systems, etc. include errors (amplitude difference of each signal, zero point, and their phase difference) due to the optical system and electrical circuit system. The Lissajous waveform is not a perfect circle. In this state, a periodic error is included in the measurement result. In the case where the position servo is applied in real time using this measurement result, there is a problem that the position error is generated as it is.

  In addition, when the interferometer was optically adjusted, a Lissajous waveform was displayed as a quadrature two-phase signal, and the waveform was brought close to a perfect circle. However, the normal Lissajous waveform cannot increase the display resolution and has become a bottleneck for adjustment.

  After the signal including an error is converted into polar coordinates, a correction value (amplitude, zero point, and phase difference) of the interferometer quadrature two-phase signal is obtained by the method of least squares from the relationship between the phase angle and the radius change. With these values, the interferometer quadrature two-phase signal is corrected so that the radius of the polar coordinates is constant, and periodic errors are reduced. After converting the interferometer quadrature two-phase signal to polar coordinates, the calculation that emphasizes only the variation of the radius component is performed, and then converted to the quadrature coordinates again, and displayed in the same way as the Lissajous waveform, so that the display resolution required for adjustment is increased. Obtainable.

  Reduction of the periodic error of the interferometer can be achieved in real time, and the adjustment accuracy of the interferometer can be improved.

  Hereinafter, the present invention will be described with reference to the drawings so that the present invention can be better understood.

  An embodiment of the present invention will be described with reference to FIGS.

Laser light I ₀ emitted from the laser oscillator 1 is guided to the PBS 2 through the λ / 2 wavelength plate 5. In PBS 2, separates the laser beam I ₀ to the reference light I _s and the measurement light I _m. The intensity ratio of the measured light I _m and the reference beam I _s rotates the lambda / 2 wave plate 5 to the optical axis within a plane perpendicular, adjusted by rotating the polarization plane of the laser beam I _0. Usually it is almost the same amount. Measurement light I _m is reflected by the moving prism 4, again, is led to the PBS 2.

Reference light I _s is reflected by the reference prism 3 is rotated by 45 degrees the polarization direction of the measuring beam I _m and the reference beam I _s by lambda / 2 wavelength plate 7. These lights then divided into two directions while maintaining the polarization state by the non-polarizing beam splitter 8, the transmitted light is split by the polarization component of the measuring light I _m and the reference beam I _s at PBS9a, paper And the component perpendicular to the paper surface are reflected and guided to the photodetector 11b.

The light reflected by the non-polarizing beam splitter 8, lambda / 4 after the circularly polarized light the polarization of the measuring beam I _m and the reference beam I _s by the wavelength plate 10, the measurement light I _m and the reference beam I at PBS9b _The component divided by the polarization component of _s and parallel to the paper surface is transmitted, and the component perpendicular to the paper surface is reflected by the light detector 11c and guided to the light detector 11d.

The optical system is intended to produce a specific phase difference in the optical path difference between the measurement light I _m and the reference beam I _s, in the above description, the phase difference 0 ° to the optical detector 11a, the photodetector 11b Produces an interference intensity after applying a phase difference of 180 °, a phase difference of 90 ° to the photodetector 11c, and a phase difference of 270 ° to the photodetector 11d. The outputs Pa to Pd of the respective photodetectors 11a to 11d are set, Pa and Pb are derived from the difference circuit 12a, the difference Va is taken, Pc and Pd are led from the difference circuit 12b, and the difference Vb is taken. Since the measurement error described above is included as it is, the phase calculation circuit 14 calculates the phase angle from the corrected Va ′ and Vb ′ by the correction circuit 13, and the phase connection circuit 15 concatenates the phase angles and outputs them. is doing.

Next, a method for correcting Va and Vb will be described. As shown in FIG. 15, the outputs Va and Vb of a general optical interferometer are different from the above-described ideal interference signals, and include errors of respective amplification degrees (Ga, Gb) and zero points (Va0, Vb0). Deviation (φ) from the ideal 90 degree phase occurs due to the error of the optical element. The interference signal including the above error is
Va ＝ Ga × cos (θ) + Va0
Vb = Gb × sin (θ + φ) + Vb0
It is represented by

Therefore, the radius r 'and the phase θ' from the origin are
Thus, if the phase is obtained as it is, θ ′ ≠ θ, which includes an error.

Therefore, as shown in FIG.
Va '= (Va- Va0') / Ga '
Vb '' = (Vb- Vb0 ') / Gb'
Vb '= (Vb''-Va' × sinθ ') / cosθ'
After performing the above calculation and converting into Va ′ and Vb ′ with little error, θ ′ is detected and set as a measurement displacement.
The correction calculation data Ga ′, Gb ′, Va0 ′, Vb0 ′, φ ′ are corrected using ΔGa, ΔGb, ΔVa0, ΔVb0, Δφ obtained by the error detection circuit 120 using the values of the correction value register 110, Reduce errors.

First, consider a case where only Ga has an error (Ga ≠ 1).
Va = (1 + ΔGa) × cos (θ)
Vb ＝ sinθ
Therefore, an ellipse having the Va axis as a major axis as shown in FIG. From now on, r 'and θ'
It becomes. This relationship is shown in FIG.

This variation has a component of cos (2θ ′) or cos (θ ′) ^ 2.
Here, the fluctuation is confirmed. The difference between the ideal circle (r = 1) and r 'is
Here, since ΔGa ² is 1 >>, if this term is omitted and the square root is expressed by up to two terms in the series expansion,
r'-1 ≒ 1 + ΔGa × cos ² θ-1 = ΔGa × cos ² θ
It becomes.

  From this, ΔGa is obtained using the idea of the method of least squares (a statistical method is used to minimize the influence of noise and the like). Originally, it should be evaluated based on the relationship between r ′ and θ ′. However, as ΔGa becomes smaller, θ ′ → θ, and therefore, evaluation is performed with θ ′ = θ.

Of N interference signals containing only Ga errors, r ′ _k and θ _k are obtained from k-th Va _k ′ and Vb _k ′, and ΔGa is obtained from this.
It becomes. In order to obtain ΔGa with high accuracy, it is necessary that θ ₁ to θ _n be dispersed at an angle that is half or more of the Lissajous waveform round. For higher accuracy, data of one round or more is required. The operation used is desirable.

Similarly, ΔGb, ΔVa0, ΔVb0, Δφ are
It becomes.

  These calculations are performed by the error detection circuit 120. Both increase the correction accuracy by iterative calculation. The end of the iterative calculation may be terminated at a predetermined number of times, may be terminated when a predetermined correction accuracy is reached, or may be terminated by a combination thereof.

  In addition, the above five formulas all include trigonometric functions, and when ΔGa, ΔGb, ΔVa0, ΔVb0, and Δφ are large, there is crosstalk with each other, and the convergence efficiency deteriorates as it is. It is necessary to correct ΔGa, ΔGb, ΔVa0, ΔVb0, Δφ in consideration of the crosstalk.

  The effect of the correction is shown in FIGS. FIG. 5 shows a part of the output of the interferometer before correction when the moving mirror 4 in FIG. 1 is moved in a triangular wave shape. The horizontal axis is time, and the left side is the interferometer output. The interferometer output increases with time after a minimum value, reaches a maximum value, and then starts decreasing again. When attention is paid to the portion increasing with time, there is a slight swell. In order to confirm this, an approximated curve of a cubic equation is obtained from these parts by the method of least squares, and the difference from the approximated curve is shown as the residual on the right side of the vertical axis. It can be seen that the residual repeats periodically with a swing width of about 5 nm. FIG. 6 shows the corrected interferometer output. The residual is 0.2 nm or less in terms of the fluctuation width, and it can be seen that the residual is greatly improved.

  Next, an embodiment of a method for increasing the display resolution of the Lissajous waveform will be described. This will be described with reference to FIGS.

FIG. 7 shows a block diagram of the present invention. Interferometer quadrature two-phase signals Va ′ and Vb ′ are converted into a radial component r and an angle component θ by a polar coordinate conversion circuit 130. Of these, the radial component r is calculated by r ′ = (r−r ₀ ) * r _G + r _{r in} the display calculation circuit 140, and then the orthogonal coordinate conversion circuit 150 emphasizes the radial component r. _a and r _b are obtained. By observing this, the display resolution can be improved. Each correction value _{r 0, r G, r r} of the display operation circuit 140, _r 0 in the correction value register B _160, r G, is varied by changing the _{r r.}

FIG. 8 to Q show an example of the calculation result. FIG. 8 shows interferometric quadrature signals Va ′ and Vb ′ and r _a and r _b when r ₀ = 0, r _G = 1 and r _r = 0, and no emphasis is given. .

FIG. 9 shows r _a and r _b in the case of r ₀ = 1, r _G = 20, and r _r = 0, and only the change in the radial component is highlighted 20 times. Compared to FIG. 8, it can be seen that the variation is clearly displayed. It is suitable for monitoring the interference state of the interferometer, but it is not suitable for adjusting the interferometer because the direction of fluctuation cannot be determined.

In this way, a Lissajous waveform suitable for the purpose of use can be displayed by changing the combination of the correction values r ₀ , r _G , and r _r .

1 is a block diagram showing a first embodiment of the present invention. FIG. 3 is a diagram for explaining a first embodiment of the present invention. FIG. 3 is a diagram for explaining a first embodiment of the present invention. 1 is a block diagram showing the main part of a first embodiment of the present invention. It is a figure which shows the residual before performing the correction | amendment by this invention. It is a figure which shows the residual after performing the correction | amendment by this invention. It is a block diagram which shows 2nd Example of this invention. It is a figure for demonstrating 2nd Example of this invention. It is a figure for demonstrating the effect of 2nd Example of this invention. It is a figure for demonstrating the effect of 2nd Example of this invention. It is a block diagram which shows the principle of operation of an optical interferometer. It is a block diagram which shows the precision improvement of an optical interferometer. It is a figure for demonstrating the principle of operation of an optical interferometer. It is a figure for demonstrating the principle of operation of an optical interferometer. It is a figure for demonstrating the principle of operation of an optical interferometer. It is a figure for demonstrating the principle of operation of an optical interferometer.

Explanation of symbols

1 Laser oscillator 2 Polarizing beam splitter (PBS)
3 Reference prism 4 Moving prism 5 λ / 2 wave plate 6 Mirror 7 λ / 2 wave plate b
8 Non-polarizing beam splitter 9 PBS
10 λ / 4 wavelength plate 11 photodetector 12 difference circuit 13 correction circuit 14 phase calculation circuit 15 phase coupling circuit 20 polarizer 100 correction calculation circuit 110 correction value register 120 error detection circuit 130 polar coordinate conversion circuit 140 display calculation circuit 150 orthogonal coordinate Conversion circuit 160 Correction value register B

Claims (6)

  In a method for reducing a periodic error of an optical interferometer used for length measurement, an error factor that generates a periodic error is identified, and the periodic error is reduced using the identified error factor, Reduction method.   2. The method for reducing a periodic error of an optical interferometer according to claim 1, wherein the orthogonal two-phase signal of the optical interferometer is subjected to polar coordinate conversion, and an error factor that causes a periodic error due to a variation in radius with respect to the phase angle is specified. A periodic error reduction method for an optical interferometer.   2. The method of reducing a periodic error of an optical interferometer according to claim 1, wherein only the variation of the radius with respect to the phase angle is amplified and output to the monitor, and the interferometer is optically adjusted so that the variation is minimized. A periodic error reduction method for an optical interferometer.   An optical interferometer periodic error reduction apparatus for use in length measurement, comprising: a detector that identifies an error factor that generates a periodic error; and a correction circuit that reduces the periodic error using the identified error factor. Interferometer periodic error reduction device.   5. An optical interferometer periodic error reduction apparatus according to claim 4, wherein only the variation of the radius with respect to the phase angle is amplified and output to the monitor, and the interferometer is optically adjusted so that the variation is minimized. A periodic error reduction device for an optical interferometer. 5. The apparatus for reducing periodic errors of an optical interferometer according to claim 4, wherein only the variation of the radius with respect to the phase angle is amplified and output to the monitor, and the interferometer is optically adjusted so that the variation is minimized. A periodic error reduction device for an optical interferometer.