JP2016169959A - Method and device for measuring shape of transparent plate - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method and a device for measuring a shape that can accurately and easily determine the front surface height, the back surface height of a specific part of a transparent plate to be measured, and the absolute value of the thickness of the plate.SOLUTION: The wavelength of an illumination light from an illumination light source is temporally scanned, an interference figure is continuously imaged by imaging means while the interference figure is being changed, and a predetermined model function is applied to an interference brightness signal obtained by the imaging, whereby at least one of the front surface height and the back surface height of each part of a measurement sample and the plate thickness distribution is measured.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a shape measuring method and a shape measuring apparatus for measuring an uneven shape and thickness of an outer surface of a sample to be measured, which is a transparent plate, and in particular, using a wavelength scanning light source and a Fizeau interferometer in a non-contact manner. The present invention relates to a method for measuring at least one of a surface height and a plate thickness, and an apparatus using the same.

  Conventionally, a wavelength scanning interferometry is known as a method for measuring the outer surface unevenness shape and thickness of a transparent plate such as a glass plate (Patent Document 1, Non-Patent Document 1). In the method of Non-Patent Document 1, using a wavelength tunable laser as a light source and using a Twiman Green interferometer, interference fringes due to reflected light from three interfaces of the reference surface and the front and back surfaces of the target sample are detected by a CCD camera or the like. An image is picked up by an image pickup device, and the obtained interference fringe image is analyzed to measure the outer surface unevenness shape and thickness of the sample.

  Patent Document 1 discloses an interference fringe analysis method using a Fizeau interferometer that is resistant to vibration and can be compactly configured because the reference optical path and the measurement optical path are the same optical path, and can be applied to a large sample. .

  In the transparent plate measurement by the wavelength scanning interferometry, interference fringes due to reflected light from the three interfaces of the reference surface and the front and back surfaces of the target sample are observed, so that the surface height and thickness are measured. Therefore, it is necessary to separate these superimposed signals.

  In Non-Patent Document 1, seven unknown variables including a surface height, a back surface height, and a phase value of thickness are estimated by fitting a luminance waveform obtained from an interference fringe image with a model function and a least-squares fit. .

  In Patent Document 1, the distance L so that the ratio of the distance L on the optical axis between the reference surface and the surface of the plate to be measured and the optical thickness nT of the plate to be measured satisfies approximately L = nT / 3. And imaging interference fringe information obtained by optical interference of the light flux from the front and back surfaces of the measured flat plate, and changing the wavelength λ of the output light at that time, from the measured flat plate surface and the reference surface In the interferometer apparatus provided with an imaging means for continuously capturing 19 images each time the phase difference of the reflected light flux changes by approximately π / 6, from 19 pieces of interference fringe image information obtained by the imaging The phase information on the optical thickness non-uniformity of the measured flat plate, the front surface height, and the back surface height is obtained.

JP 2003-139511 A

K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi: “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29, 3280-3285 ( 1990)

  However, the conventional method has the following problems. That is, in the method of Non-Patent Document 1, the luminance waveform obtained from 60 interference fringe images picked up while scanning the wavelength is fitted to the model function and the least-squares to thereby change the surface height fluctuation component and the back surface height. 7 unknown variables including the fluctuation components are estimated. However, this method can only obtain a relative surface irregularity shape and thickness distribution, but cannot obtain an absolute value. In addition, because there are many unknown variables, they are susceptible to noise. For this reason, the measurement accuracy obtained is also the mean square deviation (RMS) of 1/50 or less of the wavelength, which does not satisfy the current industry requirements.

  On the other hand, in the method of Patent Document 1, there is a restriction on the sample position. That is, it is necessary to strictly adjust the distance between the reference surface and the sample surface so that the frequency of the superimposed sine wave becomes an integer ratio. Also, in this method, since the phase is obtained, only the relative outer surface uneven shape and thickness distribution are obtained, and the absolute value cannot be obtained.

  Therefore, in the conventional method, there is a problem that the absolute values of the surface height, the back surface height, and the plate thickness of the sample to be measured cannot be obtained with high accuracy and simple operation.

  The present invention has been made in view of such circumstances, and the surface height of a specific portion of the sample to be measured, which is a transparent plate, the height of the back surface, the absolute value of at least one of the plate thicknesses, And it aims at providing the shape measuring method and shape measuring apparatus of a transparent plate which can be calculated | required by simple operation.

In order to achieve such an object, the present invention has the following configuration.
That is, the shape measuring method of the present invention is
An illumination light source capable of temporally changing the wavelength of the output light;
An optical system unit that guides the parallel light flux to the sample to be measured on the reference surface and a transparent plate after making the light flux from the illumination light source a parallel light flux;
Imaging means for continuously capturing an interference image obtained by interference of reflected light from the reference surface, the surface of the sample to be measured, and the back surface of the sample to be measured;
A method for measuring the shape of a transparent plate using a shape measuring device comprising:
The wavelength of the illumination light from the illumination light source is temporally scanned and the interference image is continuously captured by the imaging unit while changing the interference image.
By fitting a model function based on the following equation (1) to the interference luminance signal obtained by imaging, the surface height, the back surface height, and the plate thickness distribution at each position of the sample to be measured It is characterized by measuring at least one of them.

In the formula (1),
I (t): Observation luminance model function value t: Time (s)
I ₀ : Light incident on the reference surface L _S : Physical distance (surface height) between the reference surface and the surface of the sample to be measured
L _B : Optical distance between the reference surface and the back of the sample to be measured L _B -L _S : Optical plate thickness c: Speed of wavelength scanning (nm / s)
λ ₀ : initial wavelength (nm)
a: DC component b _S of interference luminance signal when I ₀ = 1: Amplitude b _B of interference luminance signal by reference surface and back surface of sample to be measured b _B : Amplitude b _T of interference luminance signal by reference surface and back surface of sample to be measured: This is the amplitude of the interference luminance signal from the measured sample surface and the measured sample back surface.

The shape measuring device of the present invention is
An illumination light source capable of temporally changing the wavelength of the output light;
An optical system unit that guides the parallel light flux to the sample to be measured on the reference surface and a transparent plate after making the light flux from the illumination light source a parallel light flux;
Imaging means for continuously capturing an interference image obtained by interference of reflected light from the reference surface, the surface of the sample to be measured, and the back surface of the sample to be measured;
Analyzing means for analyzing an interference image captured by the imaging means;
A transparent plate shape measuring apparatus comprising:
The wavelength of the illumination light from the illumination light source is temporally scanned and the interference image is continuously captured by the imaging unit while changing the interference image.
In the analysis means, by applying a model function based on the following formula (1) to the interference luminance signal of the interference image obtained by imaging, the surface height at each position of the measured sample, A shape measuring method comprising measuring at least one of a back surface height and a plate thickness distribution.

In the formula (1),
I (t): Observation luminance model function value t: Time (s)
I ₀ : Light incident on the reference surface L _S : Physical distance (surface height) between the reference surface and the surface of the sample to be measured
L _B : Optical distance between the reference surface and the back of the sample to be measured L _B -L _S : Optical plate thickness c: Speed of wavelength scanning (nm / s)
λ ₀ : initial wavelength (nm)
a: DC component b _S of interference luminance signal when I ₀ = 1: Amplitude b _B of interference luminance signal by reference surface and back surface of sample to be measured b _B : Amplitude b _T of interference luminance signal by reference surface and back surface of sample to be measured: This is the amplitude of the interference luminance signal from the measured sample surface and the measured sample back surface.

  By using such a shape measuring method and shape measuring apparatus, based on the physical model of the interference fringes of the sample to be measured, the surface height, the back surface height, the plate thickness of the transparent plate as the sample to be measured are simultaneously Can be obtained independently.

In the present invention, the plate thickness T ′ and the back surface height L _B ′ of the sample to be measured are obtained based on the following formulas (20) and (21).

In the formulas (20) and (21),
n: Refractive index of the sample to be measured.

  In the present invention, the least square method that minimizes the sum of square errors of the actual measurement value (Ii) and the observed luminance model function value (I (ti)) represented by the following formula (2) is used as the adaptation method. Thus, the unknown variable of the equation (1) is obtained.

In the formula (2),
i: Observation data number n: Number of observation data I _i : Actual measurement value i (t _i ): Observation luminance model function value.

  By doing so, the influence of various noise components included in the observed luminance value can be minimized, and the shape can be measured stably.

Further, in the present invention, the unknown variables in the equation (1) include the reference surface incident light quantity (I ₀ ), the surface height of the sample to be measured (L _S ), the optical back surface distance (L _B ) of the sample to be measured, And a limited selection from the group consisting of the optical plate thickness (L _B -L _S ) of the sample to be measured.

  By doing in this way, the unknown variable calculated | required by a conformity is normally limited to three of reference surface incident light quantity, the surface height of a to-be-measured sample, and the back surface height of a to-be-measured sample, and is stable and becomes noise. Strong shape measurement can be performed.

In the present invention, the parameters a, b _S , b _B , and b _{T in the} formula (1) are set to the following formulas (3) assuming that the reference plate refractive index n _R and the measured sample refractive index n are known. ) To (6).

In the above formulas (3) to (6), R _R is the interface reflectance of the reference surface, R _S is the interface reflectance of the surface of the sample to be measured, and is obtained by the following formulas (7) and (8).

By doing so, an optically simple Fizeau interferometer is adopted as the optical unit, and the unknown variable is utilized by utilizing the known reference plate refractive index n _R and measured sample refractive index n. The number of can be reduced.

In the present invention, among the surface height (L _S ) of the sample to be measured, the optical back surface distance (L _B ) of the sample to be measured, and the optical plate thickness (L _B −L _S ) of the sample to be measured It is characterized in that at least one of the initial values is changed, and the model function of the equation (1) is adapted a plurality of times and the optimum value of the adaptation is searched.

  By doing in this way, even when it is desired to obtain the absolute value, not the relative value, of the surface height, the back surface height, and the plate thickness of the sample to be measured, it is possible to select from the local solutions that exist at half the wavelength. You can search for the correct result.

In the present invention, the surface height and the back surface of the sample to be measured are preferably fitted to the luminance data (interferogram) obtained by using the Fizeau interferometer and the wavelength scanning light source, preferably by the least square fitting. Height and plate thickness can be obtained simultaneously.
In particular, by giving a rough initial value to the model function, the absolute value of the surface height, the back surface height, and the plate thickness of the sample to be measured can be measured with high accuracy on the order of nm.

  Furthermore, the shape measuring apparatus of the present invention only needs to be provided with an imaging means such as a Fizeau interferometer, a wavelength scanning light source, a CCD camera, and an analyzing means such as a personal computer, and can be easily configured as an industrial measuring apparatus. it can.

  Further, it is not necessary to adjust the distance between the sample to be measured and the reference surface, which is necessary in the conventional method, and the operability can be remarkably improved.

FIG. 1 is a schematic configuration diagram for explaining a first embodiment of the shape measuring apparatus of the present invention. FIG. 2 is an example of a three-beam interference image. FIG. 3 is a schematic diagram showing incident light and reflected light of the Fizeau interferometer in the first embodiment. FIG. 4 is a diagram illustrating a square error when the surface height is changed. FIG. 5 is an enlarged view in which the vertical axis of FIG. 4 is enlarged. FIG. 6 is a diagram showing the wavelength scanning conditions of the first embodiment. FIG. 7 is a diagram showing the luminance signal of the first embodiment. FIG. 8 is a diagram showing the measurement results according to the second example. FIG. 9 is a diagram illustrating an example of a three-beam interference image according to the third embodiment. FIG. 10 is a diagram showing the luminance signal of the third embodiment. FIG. 11 is a diagram showing a measurement result according to the third example. FIG. 12 is a diagram showing a measurement result according to the third example. FIG. 13 is a diagram showing a measurement result according to the third example.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 is a schematic configuration diagram for explaining a first embodiment of the shape measuring apparatus of the present invention.

The shape measuring apparatus 1 includes an optical system unit 20 and an analysis unit 22 that analyzes an interference signal from the optical system unit 20.
The optical system unit 20 is a Fizeau interferometer, and the light beam of the laser light emitted from the illumination light source 10 is converted into a parallel light beam through the collimating lens 11 and is applied to the reference plate 13 and the sample 14 to be measured. Then, the reflected light from the reference surface R of the reference plate 13 and the front surface S and back surface B of the sample 14 to be measured interferes with each other and travels backward in the optical path of the irradiation light, passes through the beam splitter 12, and passes through the imaging lens 15. An interference image is formed, and the formed interference image is picked up by an image pickup means 16 such as a CCD camera. As will be described later, the captured interference image (interference image) is analyzed by the analysis means 22 to measure the surface height, the back surface height, and the plate thickness of the sample 14 to be measured.

In the present specification, the “surface height” means a physical distance from the reference surface R of the reference plate 13 to the surface S of the sample 14 to be measured (RS surface distance L _S described later). , “Back surface height” means the physical distance from the reference surface R of the reference plate 13 to the back surface B of the sample 14 to be measured (physical back surface distance L _B ′ defined by equation (21) described later). doing.

  The illumination light source 10 is a wavelength tunable laser. In this embodiment, a commercially available Velocity6700 wide range tunable laser (wavelength range of 630 to 640 nm) manufactured by New Focus is used, and the wavelength is scanned linearly with time.

  The image pickup means 16 picks up an image of interference fringes that changes in accordance with the change in the wavelength of the illumination light. In this embodiment, a commercially available monochrome CCD camera is used. The image data is collected by the analysis means 22. The imaging means 16 is not particularly limited, and for example, a color CCD camera or a CMOS camera can be used.

  The analysis unit 22 can be configured by a computer system including a CPU that performs predetermined arithmetic processing, a memory that stores data, an input unit such as a mouse and a keyboard that inputs setting information, a monitor that displays an image, and the like.

  In the shape measuring apparatus 1 configured as described above, a tunable laser is used as the illumination light source 10, and scanning is possible at an arbitrary speed. When the sample to be measured is transparent, as shown in FIG. 2, the interference image captured by the imaging unit 16 includes (1) a reference surface and a surface of the sample to be measured, (2) a reference surface and a back surface of the sample to be measured, (3 ) A three-beam interference image is formed by superimposing three interference images of the measured sample surface and the measured sample back surface. In the present invention, by separating these three interference images, the surface height of the measured sample is The back surface height and plate thickness are measured.

  By applying the model function based on Equation (1) to the interference fringe luminance signal obtained using the surface shape measuring apparatus, the surface height and back surface height at each position of the surface of the sample to be measured Find at least one of the plate thicknesses.

Hereinafter, Formula (1) is demonstrated.
In the Fizeau interferometer, when the reference surface R, the sample surface S to be measured, and the sample back surface B to be measured are arranged as shown in FIG. 3, the amount of light reflected from each interface is I _S , I _B , I _R , R -S interplanar distance L _S, the R-B plane between the optical distance (OPD) and L _B, the observed intensity I is the reflected light from the reflection light and the measured sample surface from RS interference (reference plane (Interference) and SB interference (reflected light from the surface of the sample to be measured and reflected light from the back surface of the sample to be measured) are expressed as shown in Expression (9) by focusing on the phase inversion.

Here, the amount of reflected light at each interface of the Fizeau interferometer is examined.
When the refractive index of the reference plate is n _R and the refractive index of the sample to be measured is n, the interface reflectance R _R of the reference surface and the interface reflectance R _S of the sample to be measured are respectively calculated from the Fresnel formula.

It is represented by

Also, if the reference surface incident light quantity is I ₀ ,
Reference surface reflection light quantity I _R = I ₀ R _R (25)
Sample surface reflected light quantity I _S = I ₀ (1−R _R ) ² R _S (26)
Measured sample back surface reflected light quantity I _B = I ₀ (1-R _R ) ² (1-R _S ) ² (27)
It is.

Next, wavelength scanning is considered. Assuming that the initial wavelength is λ ₀ , the wavelength scanning speed is c, and the time is t, the wavelength can be expressed by Expression (10).

At this time, the phase value φ of the distance L is usually λ ₀ >> ct, so that the frequency of each waveform is f.

However,

Can be approximated.

Rewriting equation (9) and placing the optical plate thickness as T = L _B −L _S ,

Here, f _S , f _B , and f _T are signal components included in the interference luminance signal I (t) when L = L _S , L = L _B , and L = T in Equation (13), respectively. Means the frequency.

  Substituting equations (25), (26), and (27) into equation (14)

However,

Is obtained.

a is the DC component of the interference luminance signal when I ₀ = 1, b _S is the amplitude of the interference signal from the reference surface R and the sample surface S to be measured, and b _B is the reference surface R and the sample back surface to be measured. B is the amplitude of the interference signal. These values are obtained by equations (16) to (19) from the values of the reference plate refractive index n _R and the measured sample refractive index n, which are known values.

  Then, substituting Equations (12) and (13) into Equation (15),

Is obtained.

This model formula is the sum of three cos waves with different frequencies, and there are three unknown variables, I ₀ , L _S , and L _B. These are obtained by least squares fitting with the observed values I _i (i = 1, 2,..., N) (minimizing F which is the square error sum SSE shown by the following equation).

In order to obtain each measurement value with the shape measurement method of the present invention, the frequencies of the cosine waves must be different from each other. For this purpose, L _S , L _B , and L _B -L _S need only be different from each other, and usually no special operation is required. This is a great advantage compared to the conventional method according to Patent Document 1 that requires position adjustment.

From the obtained L _S and L _B and the measured sample refractive index n, the plate thickness T ′ and the physical back surface distance L _B ′ are obtained by the equations (20) and (21).

  Although the absolute value of each measurement value can be obtained by the method described above, it is necessary to give a correct initial value for this purpose. In other words, the least square fit described above has local solutions at intervals of about ½ of the wavelength, and therefore it is necessary to give an initial value with an accuracy of ½ or less of the wavelength for correct absolute value measurement. However, preliminary estimation with this accuracy is not easy in practice.

  A Fourier transform method is known as a method for estimating an absolute value from luminance data obtained by wavelength scanning. This obtains the peak of the frequency spectrum and converts it to the optical distance (OPD) by the equation (13).

However, the distance resolution ΔL obtained by converting the frequency resolution obtained by discrete Fourier transform (FFT) into OPD depends on the initial wavelength λ _{0 of} wavelength scanning and the scanning width Δλ, and is expressed by equation (22). The

In the case of the initial wavelength λ ₀ = 600 nm, ΔL = 18 μm when Δλ = 10 nm, ΔL = 1.8 μm when Δλ = 100 nm, and it is difficult to obtain an accuracy of 300 nm which is ½ of the wavelength. Therefore, high-precision measurement is possible by using the following method.

First, the order skip phenomenon is analyzed. The model formula is a sum of cos functions and is a periodic function.
Since ct is the wavelength scanning amount and ct << λ ₀ ,

Therefore, the cos function related to L _S on the right side of Expression (1) is expressed as the following expression.

This respect L _S, the period is a periodic function of λ _0/2. That is, in the least squares fit problems of formula (2) is lambda _0/2 intervals, with local solutions. This is apparent from FIG. 8 in which the relationship between the square error sum SSE and the error of S is plotted.

  Pay attention to the first term in the cos function ignored in the above equation (24). In a state where this cannot be ignored, the SSE is not a complete periodic function, so there is a possibility that a difference occurs in the SSE of the local solution and a global optimum solution is obtained.

  FIG. 4 is a diagram illustrating a square error when the surface height is changed. FIG. 5 is an enlarged view of the vertical axis of FIG. 4, and the SSE increases as the distance from the true value increases. That is, comparing the SSEs of local solutions, the solution with the smallest SSE is the global optimal solution and is a true value.

  On the other hand, since real data has noise, a noise component is added to SSE. In order to significantly increase the SSE difference of the local solution than the SSE variation due to noise, the wavelength scanning width Δλ = cτ (τ is the scanning time) may be made as large as possible. If such conditions are selected, a global optimum solution can be obtained by the “multi-start method” in which a plurality of adaptations with different initial values are performed.

  In the method of the present invention, the model function of equation (1) is changed by changing the surface height of the sample 14 to be measured, the back surface height of the sample 14 to be measured, or the initial value of the plate thickness T of the sample 14 to be measured. It is preferable to search for an optimal value of the matching by performing a plurality of times of matching.

  EXAMPLES Hereinafter, although this invention is demonstrated further more concretely based on an Example, this invention is not limited to these Examples.

[Example 1]
An experimental example obtained using the above calculation method is shown as Example 1.
(1) Experimental method A theoretical interferogram was created under the following conditions.
Wavelength scanning speed c: 0.01 nm / s (FIG. 6)
Initial wavelength λ ₀ : 600 nm
Number of observation data: 256
Camera imaging speed: 30 fps
Surface distance (reference surface standard) L _S : 10 mm
Physical thickness T ': 10mm
Reference plate, measured sample refractive index: 1.46

Therefore, the back surface distance (reference surface standard; OPD) L _B : 24.6 mm. The obtained waveform is shown in FIG.
For the least squares fit, Solver, an optimization tool of MS Excel (registered trademark), was used. The initial values were set to I ₀ = 95, L _S = 10000050 nm, and L _B = 24600025 nm.

(2) Experimental results Table 1 shows the results. The estimation error of the distance between the front surface and the back surface was 1 nm or less. In addition, signal waveforms of the front surface, back surface, and plate thickness extracted by conformity are shown in FIGS. 7B, 7C, and 7D. As shown in Equation (13), the frequency of each waveform (the front surface is 0.56 Hz, the back surface is 1.37 Hz, the plate thickness is 0.81 Hz) is the inter-interface distance (10 mm, 24.6 mm, and 14.6 mm, respectively). It is proportional to

[Example 2]
An experimental example in which the absolute value of the line shape of the sample to be measured was measured using the calculation method based on the multi-start method is shown as Example 2.
(1) Experimental Method A theoretical interferogram was created by adding the condition that the surface was inclined by 1000 nm and the plate thickness was 100 nm spherically projected at the center to the conditions of Example 1. The number of pixels in the horizontal direction (x coordinate) was 164, and the measurement conditions were a wavelength scanning speed of 0.1 nm / s and an observation data number of 256. Multistart conditions, L _S, the initial value of L _B, x = an estimated value of 82 points L _S = 10000500nm, mainly L _B = 24600500nm, ± 500nm changed range, and the increments of the 250 nm. That is, 5 × 5 = 25 combinations of initial values are used for adaptation, and a solution having the smallest square error sum SSE is defined as a global optimum solution. Note that the step needs to be 300 nm or less, which is a half of the wavelength, and is 250 nm here.
(2) Experimental results The results obtained are shown in FIG. Both the front surface shape L _S and the back surface shape L _B are correctly measured.

[Example 3]
An example in which an actual sample was measured using the method according to the present invention is shown as Example 3.
(1) Experimental method Interferogram was acquired on condition of the following.
Sample to be measured: transparent glass (refractive index: 1.51)
Wavelength scanning speed c: 0.1 nm / s
Initial wavelength λ ₀ : 630 nm
Number of observation data: 256
Camera imaging speed: 25 fps
Surface distance (reference surface standard) L _S : about 11.35 mm
Physical thickness T ′: about 2.85 mm
Reference plate refractive index: 1.46

A part of the interference fringe image captured by the camera (75 × 75 pixels) was used as a sample to be measured. An example of the image is shown in FIG.
The least square method fit used Solver, an optimization tool of MS Excel (registered trademark). The initial values were L _S = 11.35 mm, T ′ = 2.85 mm, and a multi-start method with a search range of ± 1000 nm and a step of 250 nm was adopted.
(2) Experimental result FIG. 10 shows a luminance waveform at the center pixel of the screen and a model waveform adapted thereto. Moreover, the measurement result of surface shape, back surface shape, and plate | board thickness distribution is shown in FIGS. It has been measured that the surface is inclined in the horizontal direction and the thickness distribution is present in the vertical direction.

DESCRIPTION OF SYMBOLS 1 Shape measuring apparatus 10 Illumination light source 11 Collimating lens 12 Beam splitter 13 Reference plate 14 Sample 15 to be measured Imaging lens 16 Imaging means 20 Optical system unit 22 Analysis means

Claims (12)

An illumination light source capable of temporally changing the wavelength of the output light;
An optical system unit that guides the parallel light flux to the sample to be measured on the reference surface and a transparent plate after making the light flux from the illumination light source a parallel light flux;
Imaging means for continuously capturing an interference image obtained by interference of reflected light from the reference surface, the surface of the sample to be measured, and the back surface of the sample to be measured;
A method for measuring the shape of a transparent plate using a shape measuring device comprising:
The wavelength of the illumination light from the illumination light source is temporally scanned and the interference image is continuously captured by the imaging unit while changing the interference image.
By fitting a model function based on the following equation (1) to the interference luminance signal obtained by imaging, the surface height, the back surface height, and the plate thickness distribution at each position of the sample to be measured A shape measuring method characterized by measuring at least one of them.
In the formula (1),
I (t): Observation luminance model function value t: Time (s)
I ₀ : Light incident on the reference surface L _S : Physical distance (surface height) between the reference surface and the surface of the sample to be measured
L _B : Optical distance between the reference surface and the back of the sample to be measured L _B -L _S : Optical plate thickness c: Speed of wavelength scanning (nm / s)
λ ₀ : initial wavelength (nm)
a: DC component b _S of interference luminance signal when I ₀ = 1: Amplitude b _B of interference luminance signal by reference surface and back surface of sample to be measured b _B : Amplitude b _T of interference luminance signal by reference surface and back surface of sample to be measured: This is the amplitude of the interference luminance signal from the measured sample surface and the measured sample back surface. The shape measuring method according to claim 1, wherein the thickness T ′ and the back surface height L _B ′ of the sample to be measured are obtained based on the following formulas (20) and (21).
In the formulas (20) and (21),
n: Refractive index of the sample to be measured. As the fitting method, a least square method that minimizes the sum of square errors of the actual measurement value (Ii) and the observed luminance model function value (I (ti)) represented by the following equation (2) is used. 3. The shape measuring method according to claim 1, wherein the unknown variable of 1) is obtained.
In the formula (2),
i: Observation data number n: Number of observation data I _i : Actual measurement value i (t _i ): Observation luminance model function value. The unknown variables in the equation (1) are the reference plane incident light quantity (I ₀ ), the surface height (L _S ) of the sample to be measured, the optical back surface distance (L _B ′) of the sample to be measured, and the sample to be measured. 4. The shape measuring method according to claim 1, wherein the shape measuring method is selected from the group consisting of the optical plate thicknesses (L _B -L _S ). The parameters a, b _S , b _B , and b _{T in the} formula (1) are the following formulas (3) to (6) with the reference plate refractive index n _R and the measured sample refractive index n known, respectively. It is calculated | required by these, The shape measuring method in any one of Claim 1 to 4 characterized by the above-mentioned.
In the above formulas (3) to (6), RR is the interface reflectance of the reference surface, and RS is the interface reflectance of the surface of the sample to be measured, which is determined by the following formulas (7) and (8).
Initial stage of at least one of the surface height (L _S ) of the sample to be measured, the optical back surface distance (L _B ) of the sample to be measured, and the optical plate thickness (L _B −L _S ) of the sample to be measured The shape measurement method according to claim 1, wherein the value is changed, and the fit to the model function of the expression (1) is performed a plurality of times to search for the optimum value of the fit. An illumination light source capable of temporally changing the wavelength of the output light;
An optical system unit that guides the parallel light flux to the sample to be measured on the reference surface and a transparent plate after making the light flux from the illumination light source a parallel light flux;
Imaging means for continuously capturing an interference image obtained by interference of reflected light from the reference surface, the surface of the sample to be measured, and the back surface of the sample to be measured;
Analyzing means for analyzing an interference image captured by the imaging means;
A transparent plate shape measuring apparatus comprising:
The wavelength of the illumination light from the illumination light source is temporally scanned and the interference image is continuously captured by the imaging unit while changing the interference image.
In the analysis means, by applying a model function based on the following formula (1) to the interference luminance signal of the interference image obtained by imaging, the surface height at each position of the measured sample, A shape measuring apparatus for measuring at least one of a back surface height and a plate thickness distribution.
In the formula (1),
I (t): Observation luminance model function value t: Time (s)
I ₀ : Light incident on the reference surface L _S : Physical distance (surface height) between the reference surface and the surface of the sample to be measured
L _B : Optical distance between the reference surface and the back of the sample to be measured L _B -L _S : Optical plate thickness c: Speed of wavelength scanning (nm / s)
λ ₀ : initial wavelength (nm)
a: DC component b _S of interference luminance signal when I ₀ = 1: Amplitude b _B of interference luminance signal by reference surface and back surface of sample to be measured b _B : Amplitude b _T of interference luminance signal by reference surface and back surface of sample to be measured: This is the amplitude of the interference luminance signal from the measured sample surface and the measured sample back surface. The shape measuring apparatus according to claim 7, wherein the thickness T ′ and the back surface height L _B ′ of the sample to be measured are obtained based on the following formulas (20) and (21).
In the formulas (20) and (21),
n: Refractive index of the sample to be measured. As the fitting method, a least square method that minimizes the sum of square errors of the actual measurement value (Ii) and the observed luminance model function value (I (ti)) represented by the following equation (2) is used. 9. The shape measuring apparatus according to claim 7, wherein the unknown variable of 1) is obtained.
In the formula (2),
i: Observation data number n: Number of observation data I _i : Actual measurement value i (t _i ): Observation luminance model function value. The unknown variables in the equation (1) are the reference surface incident light quantity (I ₀ ), the surface height (L _S ) of the sample to be measured, the optical back surface distance (L _B ) of the sample to be measured, and the 10. The shape measuring device according to claim 7, wherein the shape measuring device is selected from a group consisting of optical plate thicknesses (L _B -L _S ). The parameters a, b _S , b _B , and b _{T in the} formula (1) are the following formulas (3) to (6) with the reference plate refractive index n _R and the measured sample refractive index n known, respectively. It is calculated | required by these, The shape measuring method in any one of Claim 7 to 10 characterized by the above-mentioned.
In the above formulas (3) to (6), RR is the interface reflectance of the reference surface, and RS is the interface reflectance of the surface of the sample to be measured, which is determined by the following formulas (7) and (8).
Initial stage of at least one of the surface height (L _S ) of the sample to be measured, the optical back surface distance (L _B ) of the sample to be measured, and the optical plate thickness (L _B −L _S ) of the sample to be measured The shape measuring apparatus according to claim 7, wherein the value is changed, the model function of the expression (1) is adapted a plurality of times, and the optimum value of the adaptation is searched.