JP2016176784A - Surface shape measuring apparatus and surface shape measuring method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable accurate measurement of a surface shape of a measurement surface, even when an error occurs in the number of pixels allocated for detecting one wavelength component of interference fringes generated in a state where at least one of the measurement surface and a reference surface is inclined.SOLUTION: A first calculation section 73, assuming that 4 pixels of an imaging element 20 are allocated for detecting one wavelength component of interference fringes, specifies a prediction function indicating a prediction value Pof a received signal outputted from an nth pixel of the imaging element 20 obtained by imaging a two-dimensional image of interference fringes, as a predetermined formula where A1, B, β, φ are undetermined coefficients, considers that the undetermined coefficients are equal in the plurality of continuous pixels of the imaging element 20, and uses the predetermined formula and an actual measurement value of the received signal outputted from each of the plurality of continuous pixels including the nth pixel obtained by imaging the two-dimensional image of the interference fringes, thereby calculating solutions to the undetermined coefficients. The second calculation section 74 uses the solution of φ indicating a phase, from among the solutions of the undetermined coefficients calculated by the first calculation section 73, thereby calculating a height at a position of a measurement surface 90 corresponding to the nth pixel.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a technique for measuring a surface shape in a non-contact manner using interference fringes.

  The surface shape of the measurement surface is measured in a non-contact manner using the phase of interference fringes generated by causing the reflected light of the light irradiated on the measurement surface to interfere with the reflected light of the light irradiated on the reference surface. Technology is known. According to this measurement technique, measurement accuracy of nanometer order or less can be realized, and for example, it is used for measurement of the surface shape of a semiconductor wafer.

  In the measurement technique, as a method of calculating the phase of the interference fringes, a method using phase shift (for example, see Patent Document 1), a method using Fourier transform (for example, see Patent Document 1 and Patent Document 2), correlation, and the like. There is a method using integration (for example, see Non-Patent Document 1).

  In the method using the phase shift, it is necessary to capture a plurality of interference fringe images by changing the distance between the measurement surface and the reference surface. If the measurement surface and the reference surface vibrate due to disturbance vibration or the like while adjusting the distance between the measurement surface and the reference surface, the distance between the measurement surface and the reference surface cannot be set accurately. Due to this, the measurement accuracy of the surface shape may be lowered.

  In the method using the Fourier transform, the phase can be calculated from one interference fringe image. Therefore, even if the measurement surface and the reference surface vibrate due to disturbance vibration or the like, the measurement accuracy of the surface shape does not decrease.

However, the method using the Fourier transform has the following drawbacks.
(1) Since the spatial frequency of the interference fringe is singular at the location where the interference fringe is interrupted (for example, the location corresponding to the end of the measurement surface), the method using the Fourier transform causes the phase of the interference fringe at that location. Is difficult to analyze. Therefore, the shape of the portion where the interference fringes are interrupted cannot be measured, or the measurement accuracy is lowered.
(2) In the method using Fourier transform, processing for Fourier transforming the entire image of interference fringes is performed. Therefore, if there is a foreign substance such as dust in the local area of the measurement surface, it will be analyzed including the foreign substance, resulting in a decrease in measurement accuracy.

  In the method using the correlation integration, since the phase of the interference fringe is calculated from the local area of the interference fringe, the drawbacks (1) and (2) can be solved.

JP 2007-333428 A (paragraphs 0011 and 0017) JP 2002-296003 A

S. TOYOOKA and M.K. TOMINAGA (S. Toyooka and M. Tominaga), “SPATIAL FRING SCANNNING FOR OPTICAL PHASE MEASUREMENT (spatial fringe scanning for optical phase measurement)”, OPTIC COMMUNICATIONS (optical communication), Volume 51, volume 51 g, 1984, pp. 68-70

  Although the phase of the interference fringes is calculated using the correlation integration described in Non-Patent Document 1, it is effective only under the condition that the spatial frequency of the interference fringes substantially matches a predetermined spatial frequency. When the sample surface is a curved surface, the spatial frequency of the interference fringes changes in the sample surface, so that it is necessary to adjust the inclination of the measurement surface with respect to the reference surface for each measurement.

  It is an object of the present invention to provide a surface shape of a measurement surface even if an error occurs in the number of pixels assigned to detect one wavelength component of an interference fringe generated with at least one of the measurement surface and the reference surface tilted. It is to provide a surface shape measuring apparatus and a surface shape measuring method capable of accurately measuring the above.

A surface shape measuring apparatus according to an aspect of the present invention has an optical axis passing through a measurement surface and a reference surface, and at least one of the measurement surface and the inclined surface is inclined with respect to a surface orthogonal to the optical axis. An optical system that generates interference fringes by causing interference between reflected light of the light applied to the measurement surface and reflected light of the light applied to the reference surface, and the optical system generated by the optical system. By imaging the two-dimensional image of the interference fringes when the number of pixels of the imaging element that captures the two-dimensional image of the interference fringes and the number of pixels of the imaging element allocated to detect one wavelength component of the interference fringes is four. The prediction function indicating the predicted value P _n of the received light signal output from the nth pixel of the image sensor is represented by the following equation with A1, B, β, and φ as undetermined coefficients, and a plurality of continuous pixels of the image sensor The undetermined coefficients are considered equal The solution of the undetermined coefficient is calculated using the measured value of the received light signal output from each of a plurality of consecutive pixels including the n-th pixel by photographing the two-dimensional image of the interference fringes And the measurement surface corresponding to the nth pixel using the solution of φ indicating the phase among the solutions of the undetermined coefficient calculated by the first calculation unit. A second calculation unit that calculates the height of the undetermined coefficient for each of a predetermined number of pixels constituting the imaging device, and the second calculation unit The calculation unit calculates a height of a portion of the measurement surface corresponding to each of the predetermined number of pixels using the solution of φ of each of the predetermined number of pixels.

(Here, n represents an integer, and ω represents a spatial frequency.)

  Since each pixel constituting the imaging element has a finite aperture, the intensity of the light reception signal output from each pixel depends on the size of each pixel. If the pixel is large, the intensity of the light reception signal output from the pixel increases. If the pixel is small, the intensity of the light reception signal output from the pixel decreases. The interference fringes have a spatial intensity distribution, and when the density of the interference fringes is high, in particular, the intensity of the received light signal output from each pixel depends on the size of each pixel.

In the first aspect of the present invention, it is assumed that one wavelength component of the interference fringe is detected by four pixels, and the above equation of the prediction function indicating the prediction value _Pn is derived. In the first aspect of the present invention, the phase φ is calculated by calculating the undetermined coefficient of the above formula from the above formula and the actually measured value of the received light signal of the interference fringes. Therefore, according to the first aspect of the present invention, the number of pixels assigned to detect one wavelength component of an interference fringe generated in a state where at least one of the measurement surface and the reference surface is inclined. Even if an error occurs, the surface shape of the measurement surface can be measured accurately.

  According to the first aspect of the present invention, the phase of the interference fringe is calculated for each local area of the interference fringe, so that the interference fringe is interrupted (for example, the part corresponding to the end of the measurement surface) Even if foreign matter such as dust exists locally on the measurement surface, the surface shape of the measurement surface can be accurately measured. The “plurality” of the plurality of pixels is a number necessary to calculate the undetermined coefficient, and the “predetermined number” is an arbitrary value equal to or less than the total number of pixels of the image sensor.

  In the above configuration, the stage on which the sample having the measurement surface is placed, and the interference fringes wider than the imaging field of view by the imaging device, a plurality of the narrower than the imaging field of view so that adjacent regions partially overlap. A dividing unit that divides into regions, a stage control unit that sequentially moves a plurality of the regions to the imaging field by moving the stage, and a two-dimensional image of the region that has moved to the imaging field of view It further includes an imaging control unit that causes the element to capture an image, and an image generation unit that generates a two-dimensional image of the interference fringes by connecting two-dimensional images of the plurality of regions using the partial overlap as a mark.

  According to this configuration, even when the area of the measurement surface is large, the accuracy of measuring the surface shape of the measurement surface can be increased.

  In the above configuration, a Fizeau interferometer including the optical system and the imaging element is provided.

  According to this configuration, since a two-dimensional image of interference fringes is taken with the Fizeau interferometer, the surface shape of the measurement surface can be measured using the advantages of the Fizeau interferometer. The advantage of the Fizeau interferometer is that, for example, the optical path of the measurement light and the optical path of the reference light are almost the same, so that the Fizeau interferometer is hardly affected by disturbances such as air fluctuations in the optical system.

The surface shape measurement method according to the second aspect of the present invention has an optical axis that passes through the measurement surface and the reference surface, and at least one of the measurement surface and the inclined surface with respect to a surface orthogonal to the optical axis. In a tilted state, a generation step of generating interference fringes by causing interference between reflected light of light irradiated on the measurement surface and reflected light of light irradiated on the reference surface, and generated by the generation step An imaging step for imaging a two-dimensional image of the interference fringe using an imaging element, and the number of pixels of the imaging element assigned to detect one wavelength component of the interference fringe imaged by the imaging step is four. The prediction function indicating the predicted value P _n of the received light signal output from the n-th pixel of the image pickup device by taking a two-dimensional image of the interference fringes, and A1, B, β, and φ are undetermined coefficients. And the following formula It is assumed that the undetermined coefficient is equal in a plurality of continuous pixels of the element, and is output from each of the plurality of continuous pixels including the nth pixel by photographing the two-dimensional image of the equation and the interference fringes. A first calculation step of calculating a solution of the undetermined coefficient using an actual measurement value of the received light signal, and a solution of φ indicating the phase among the solutions of the undetermined coefficient calculated by the first calculation step. And a second calculation step for calculating the height of the portion of the measurement surface corresponding to the nth pixel, wherein the first calculation step includes a predetermined number of pixels constituting the image sensor. And the second calculation step uses the solution of φ for each of the predetermined number of pixels to calculate the measurement surface corresponding to each of the predetermined number of pixels. Location To calculate the height.

(Here, n represents an integer, and ω represents a spatial frequency.)

  The second aspect of the present invention has the same effects as the first aspect of the present invention.

  According to the present invention, even if an error occurs in the number of pixels allocated to detect one wavelength component of an interference fringe generated with at least one of the measurement surface and the reference surface tilted, the surface shape of the measurement surface Can be measured accurately.

It is a block diagram which shows the structure of the surface shape measuring apparatus which concerns on 1st Embodiment. It is an imaging figure which shows an example of the two-dimensional image of the interference fringe image | photographed with the image pick-up element. FIG. 3 is an enlarged view of a part of the two-dimensional image of interference fringes shown in FIG. 2. It is a wave form diagram which shows the waveform of the interference fringe produced | generated on the conditions that (beta) is 20% of (omega). FIG. 5 is a graph showing a result of calculating a phase using the method disclosed in Non-Patent Document 1 for the interference fringe waveform shown in FIG. 4. It is a graph which shows the result of having subtracted the linear phase change from the graph shown in FIG. It is a mimetic diagram showing one pixel of an image sensor. It is a mimetic diagram showing pixel n, pixel n + 1, pixel n + 2, and pixel n + 3 which are four continuous pixels of an image sensor. It is a wave form diagram which shows the 1st example of the waveform of an interference fringe. It is a graph which shows the data of the phase of a part with a measurement surface. It is a wave form diagram which shows the waveform of the interference fringe corresponding to the data shown in FIG. It is a graph which shows the result of having calculated the phase using the value (actual value) of the received light signal shown in FIG. 11, and simultaneous equations _Fn , _{Fn + 1} , _{Fn + 2} . It is a graph which shows the result of having calculated the phase using the value (actual measurement value) of the received light signal shown in FIG. 11, and the method disclosed in the nonpatent literature 1. FIG. It is a block diagram which shows the structure of the surface shape measuring apparatus which concerns on the modification of 1st Embodiment. It is a block diagram which shows the structure of the surface shape measuring apparatus which concerns on 2nd Embodiment. It is explanatory drawing explaining an example of the interference fringe divided | segmented into the several area | region by the division part. It is explanatory drawing explaining the method to connect the two-dimensional image of two area | regions.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1 is a block diagram showing a configuration of a surface shape measuring apparatus 1a according to the first embodiment. The surface shape measuring apparatus 1 a includes a camera 2, a laser light source 3, a stage device 4, a stage control unit 5, an optical system 6, and a computer 7. The camera 2, the laser light source 3, the stage device 4, the stage controller 5, and the optical system 6 constitute a Fizeau interferometer.

  The camera 2 is a digital camera including an image sensor 20 that is a two-dimensional image sensor (for example, a CCD image sensor or a CMOS image sensor). A lens 60, a beam splitter 61, a lens 62, a flat glass 63, and a stage device 4 are arranged on the optical axis of the camera 2 in the order close to the camera 2. The optical axis of the camera 2 coincides with the optical axis 66 of the optical system.

  The laser light source 3 is, for example, a HeNe laser that emits light having a wavelength of 633 nm. The optical axis of the laser light source 3 intersects with the optical axis of the camera 2. A lens 64 and a beam splitter 61 are arranged on the optical axis of the laser light source 3 in the order close to the laser light source 3.

  The stage device 4 includes a stage 40, a drive unit 41, and a base unit 42. A sample 9 having a measurement surface 90 is placed on the stage 40. The stage 40 is supported by the base part 42 via the drive part 41. The drive unit 41 (for example, a piezo element) is used for controlling the tilt angle of the stage 40.

  The stage control unit 5 controls the tilt of the stage 40 by controlling the drive unit 41 based on the setting value of the tilt angle of the stage 40 transmitted from the computer 7.

  The optical system 6 includes the lens 60, the beam splitter 61, the lens 62, the flat glass 63, and the lens 64 described above. As will be described later, the optical system 6 has an optical axis 66 that passes through the measurement surface 90 and the reference surface (the upper surface 65 of the flat glass 63) and is perpendicular to the optical axis 66 (horizontal plane in FIG. 1). Then, in a state where at least one of the measurement surface 90 and the inclined surface is inclined, reflected light (measurement light) of light irradiated on the measurement surface 90 and reflected light (reference light) of light irradiated on the reference surface Interference fringes are generated by causing interference. This interference fringe is photographed by the image sensor 20.

  The computer 7 analyzes the two-dimensional image of the interference fringes photographed by the image sensor 20 and calculates the surface shape of the measurement surface 90.

  The computer 7 includes a control unit 70, an input unit 71, and an output unit 72.

  The control unit 70 includes a CPU, a RAM, a ROM, and the like, and includes a first calculation unit 73 and a second calculation unit 74 as functional blocks. The first calculation unit 73 and the second calculation unit 74 will be described in detail later.

  The input unit 71 is a device for inputting commands (commands), data, and the like from the outside to the control unit 70, and is, for example, a touch panel or a keyboard.

  The output unit 72 is a device for outputting the command and data input from the input unit 71 to the control unit 70 and the surface shape of the measurement surface 90 calculated by the control unit 70. For example, the output unit 72 is an LCD (liquid crystal display). Display devices, and printing devices such as printers.

  The generation of interference fringes will be described. The light emitted from the laser light source 3 toward the lens 64 becomes divergent light at the lens 64. A part of the diverging light is reflected by the beam splitter 61 toward the lens 62 and is converted into a parallel light beam by the lens 62. The parallel light beam is applied to the flat glass 63. A non-reflective coating is applied to the lower surface of the flat glass 63. A part of the parallel light beam irradiated to the flat glass 63 is reflected by the upper surface 65 of the flat glass 63, and the rest passes through the flat glass 63.

  The light transmitted through the flat glass 63 is irradiated on the measurement surface 90. As a result, the reflected light (hereinafter, “measurement light”) reflected by the measurement surface 90 passes through the flat glass 63, the lens 62, the beam splitter 61, and the lens 60 and is sent to the imaging device 20.

  On the other hand, reflected light (hereinafter referred to as reference light) reflected by the upper surface 65 of the flat glass 63 passes through the lens 62, the beam splitter 61, and the lens 60 and is sent to the imaging device 20. The upper surface 65 of the flat glass 63 functions as a reference surface.

  The upper surface 65 (reference surface) of the flat glass 63 is horizontal. Since the sample 9 having the measurement surface 90 is placed on the stage 40 which is inclined with respect to the surface orthogonal to the optical axis 66, the measurement surface 90 is inclined. For this reason, interference fringes are generated when the measurement light and the reference light interfere with each other (by strengthening or canceling each other) due to the optical path difference between the measurement light and the reference light. Note that interference fringes may be generated by inclining the reference surface with respect to the surface orthogonal to the optical axis 66, and both the measurement surface 90 and the reference surface are orthogonal to the optical axis 66. The interference fringes may be generated by tilting.

  FIG. 2 is a photographing diagram showing an example of a two-dimensional image of interference fringes photographed by the image sensor 20. FIG. 3 is an enlarged view of a part 10 of the two-dimensional image of the interference fringes shown in FIG. The interference fringes are configured by alternately repeating the bright pattern 10a and the dark pattern 10b in the space. For example, the interference fringes are configured such that 100 to 200 bright patterns 10a and dark patterns 10b are alternately repeated in the entire measurement surface 90.

  The light intensity I of the interference fringe imaged by the image sensor 20 is generally represented by the equation (1), where D is the optical path difference.

  A and B are coefficients depending on the reflectance of the optical system 6 and the measurement surface 90, and the like. φ is a phase and has shape information (height information) of the measurement surface 90.

  When the spatial frequency (angular frequency) of the interference fringes due to the inclination of the measurement surface 90 is ω + β, the light intensity I of the interference fringes at the position x is expressed by Equation (2).

  ω is a value indicating the inclination of the measurement surface 90 (ideal inclination of the measurement surface 90) when the number of pixels of the image sensor 20 assigned to detect one wavelength component of the interference fringes is four. β represents an error with respect to an ideal inclination. When the inclination of the measurement surface 90 can be adjusted so that the number of pixels of the image sensor 20 assigned to detect one wavelength component of the interference fringe is 4, β becomes 0.

  Non-Patent Document 1 described in the background art discloses a phase extraction method using quadrature detection as a method of extracting phase φ from Expression (2). More specifically, a value V1 obtained by multiplying equation (2) by sin (ωx) and cos (ωx) is obtained, an arctangent V2 of V1 is obtained, and a phase φ is obtained from V2.

  According to the method disclosed in Non-Patent Document 1, when ω is sufficiently large with respect to β, that is, when the “error” described in the problem to be solved by the invention is extremely small, the measurement accuracy of the planar shape is improved. Has no effect. However, otherwise the measurement accuracy is reduced.

  This will be specifically described. FIG. 4 is a waveform diagram showing a waveform of interference fringes generated under the condition that β is 20% of ω. This condition is an example when ω is not sufficiently large with respect to β. In FIG. 4, the horizontal axis indicates the position of each pixel in a pixel group composed of 50 continuous pixels among all the pixels constituting the image sensor 20. For example, 0 indicates the position of the first pixel, 1 indicates the position of the next pixel, and 2 indicates the position of the next pixel. The vertical axis indicates the level of the light reception signal output from each pixel of the image sensor 20 when the image sensor 20 captures the interference fringes.

  FIG. 5 is a graph showing the result of calculating the phase φ using the method disclosed in Non-Patent Document 1 for the interference fringe waveform shown in FIG. The horizontal axis in FIG. 5 is the same as the horizontal axis in FIG. 4, and the vertical axis in FIG. 5 indicates the phase φ. Since the graph shown in FIG. 5 includes the linear phase change βx caused by the inclination of the measurement surface 90, the result of subtracting the linear phase change βx from the graph shown in FIG. 5 is shown in FIG. The horizontal axis of FIG. 6 is the same as the horizontal axis of the graph of FIG. 4, and the vertical axis shows the phase difference between the phase shown in the graph of FIG. 5 and the linear phase change βx.

  The reason why the relatively large jaggedness is generated in the graph of FIG. 6 is that ω is not sufficiently large with respect to β, that is, the error of the tilt of the stage 40 is large. When the phase difference is regarded as the phase of the interference fringes, it can be seen that an error of about 0.02 rad occurs in the phase. When this error is converted into the height of the measurement surface 90 (= phase · λ / 4π), the error is about 1 nm. By averaging the phases spatially, errors can be reduced, but when averaged, the spatial resolution is reduced in the measurement space.

  Calculation of the phase φ using the first embodiment will be described. FIG. 7 is a schematic diagram showing one pixel of the image sensor 20. Each pixel constituting the image sensor 20 has a finite aperture. Therefore, when an interference fringe is imaged by the image sensor 20, the light reception signal P output from one pixel is expressed by Expression (3). Can show.

  A, B, ω, β, and φ have already been described. The areas received by one pixel are indicated by N1 and N2. The area is actually two-dimensional, but is shown in one dimension for simplicity.

A pixel n is a pixel n among all the pixels constituting the image sensor 20. When taken interference fringe by the image sensor 20, the predicted value of the light receiving signal output from the pixel n and P _n. In the prediction function representing the predicted value P _n, the prediction value P _n will depend on the number of pixels allocated to detect one wavelength component of the interference fringes. In the first embodiment, assuming that one wavelength component of an interference fringe is detected by four pixels, a prediction function indicating a prediction value _Pn is derived. Actually, the measurement surface 90 cannot be tilted accurately so that the number of pixels allocated to detect one wavelength component of the interference fringe is 4, and an error occurs.

Based on Expression (3), a prediction function indicating the predicted value P _n can be expressed by Expression (4). n is an integer of 1 or more, and indicates each pixel (in other words, each position on the measurement surface 90) that constitutes the imaging element 20. For example, “1” is the first pixel, “2” is the adjacent second pixel, and “3” indicates the adjacent third pixel.

  If ω + β is K, Equation (4) can be expressed by Equation (5).

  A1 is a coefficient depending on the reflectance of the optical system 6 and the measurement surface 90, and is a coefficient corresponding to the above A.

FIG. 8 is a schematic diagram illustrating a pixel n, a pixel n + 1, a pixel n + 2, and a pixel n + 3, which are four consecutive pixels of the image sensor 20. Assuming that A1, B, β, and φ are equal in the predicted values of the received light signals output from these successive pixels, an equation (5) substituting the measured value of P _n (the value of the received light signal output from pixel n). ) Is replaced with the formula (5-1), the measured value of P _{n + 1} (the value of the light reception signal output from the pixel n + 1) is substituted into the formula (5), the formula (5-2), and the measured value of P _{n + 2} (from the pixel n + 2). Expression (5) substituting the value of the received light reception signal) is replaced with Expression (5-3), and Expression (5) is substituted with the actual measurement value of P _{n + 3} (value of the light reception signal output from pixel n + 3) ( 5-4).

Although the undetermined coefficients A1, B, K, and φ can be calculated from the equations (5-1) to (5-4), in the first embodiment, the following simultaneous equations F _n , F _{n + 1} , F with A1 eliminated _The undetermined coefficients B, K, and φ are calculated using _{n + 2} .

F _n = P _{n + 1} −P _n
F _{n + 1} = P _{n + 2} −P _{n + 1}
F _{n + 2} = P _{n + 3} −P _{n + 2}
The calculation of the undetermined coefficient described above is realized by the first calculation unit 73. That is, when the number of pixels of the image sensor 20 allocated to detect one wavelength component of the interference fringe is 4, the first calculation unit 73 captures the n of the image sensor 20 by capturing a two-dimensional image of the interference fringe. The prediction function indicating the predicted value P _n of the received light signal output from the th pixel is represented by Expression (4) using A1, B, β, and φ as undetermined coefficients. It is assumed that the coefficients are equal, and using formula (4) and the measured value of the received light signal output from each of a plurality of consecutive pixels including the nth pixel by photographing a two-dimensional image of interference fringes, an undetermined coefficient Calculate the solution of Then, the first calculation unit 73 calculates an undetermined coefficient solution for each of a predetermined number of pixels constituting the image sensor 20. The “plurality” of the plurality of pixels is a number necessary to calculate the undetermined coefficient, and the “predetermined number” is an arbitrary value equal to or less than the total number of pixels of the image sensor 20.

A first example of analysis using simultaneous equations F _n , F _{n + 1} , and F _{n + 2} will be described. FIG. 9 is a waveform diagram showing a first example of the interference fringe waveform. The horizontal axis in FIG. 9 is the same as the horizontal axis in FIG. 4, and the vertical axis is the same as the vertical axis in FIG. Since A1 is eliminated in the simultaneous equations, the waveform of the interference fringes shown in FIG. 9 can be expressed by equation (6) with B = 1.1, β = 0.3, and φ = 0.2. .

B, β, and φ calculated using simultaneous equations F _n , F _{n + 1} , and F _{n + 2} with the level of the received light signal shown in the waveform diagram of FIG. 9 as an actual measurement value are B = 1.1 and β = For 0.3 and φ = 0, an error of 0.1% or less was achieved.

A second example of analysis using simultaneous equations F _n , F _{n + 1} , and F _{n + 2} will be described in comparison with an analysis example using the method disclosed in Non-Patent Document 1. FIG. 10 is a graph showing phase data at a certain location on the measurement surface 90. This graph is model data for evaluation. The horizontal axis in FIG. 10 indicates the position of each pixel in a pixel group composed of 40 consecutive pixels among all the pixels constituting the image sensor 20. The vertical axis in FIG. 10 indicates the phase φ.

  FIG. 11 is a waveform diagram showing a waveform of interference fringes corresponding to the data shown in FIG. Here, ω is π / 2 and β is 0.2. The horizontal axis in FIG. 11 is the same as the horizontal axis in FIG. 10, and the vertical axis is the same as the vertical axis in FIG.

FIG. 12 is a graph showing the result of calculating the phase φ using the value (actual value) of the received light signal and the simultaneous equations F _n , F _{n + 1} , and F _{n + 2} shown in FIG. The horizontal axis in FIG. 12 is the same as the horizontal axis in FIG. 10, and the vertical axis in FIG. 12 is the same as the vertical axis in FIG.

  The calculation of the phase φ is realized by the second calculation unit 74. That is, the second calculation unit 74 uses the solution of φ indicating the phase among the solutions of the undetermined coefficients calculated by the first calculation unit 73, and calculates the location of the measurement surface 90 corresponding to the nth pixel. Calculate the height. Since the height of the measurement surface 90 = phase · λ / 4π, the second calculation unit 74 can calculate the height of the measurement surface 90 corresponding to the nth pixel from the equation. The second calculation unit 74 calculates the height of the location on the measurement surface 90 corresponding to each of the predetermined number of pixels using the solution of φ of each of the predetermined number of pixels. The “predetermined number” is an arbitrary value equal to or less than the total number of pixels of the image sensor 20 as described above.

  The first calculation unit 73 calculates the solution of the undetermined coefficient for each pixel constituting the image sensor 20, and the second calculation unit 74 uses φ corresponding to each pixel constituting the image sensor 20. The height of the measurement surface 90 corresponding to each pixel is calculated. Thereby, the surface shape of the measurement surface 90 is calculated.

  FIG. 13 is a graph showing the result of calculating the phase φ using the value (actual value) of the received light signal shown in FIG. 11 and the method disclosed in Non-Patent Document 1. The horizontal axis in FIG. 13 is the same as the horizontal axis in FIG. 10, and the vertical axis in FIG. 13 is the same as the vertical axis in FIG.

  It can be seen that the graph shown in FIG. 12 is closer to the graph shown in FIG. 10 than the graph shown in FIG. Therefore, according to the first embodiment, as compared with the case where the method disclosed in Non-Patent Document 1 is used, even if an error occurs in the number of pixels assigned to detect one wavelength component of interference fringes, measurement is performed. The surface shape of the surface 90 can be accurately measured.

  The main effects of the first embodiment will be described. Since each pixel constituting the image sensor 20 has a finite aperture, the intensity of the light reception signal output from each pixel depends on the size of each pixel. When this is expressed by an equation, the above equation (3) is obtained. If the pixel is large, the intensity of the light reception signal output from the pixel increases. If the pixel is small, the intensity of the light reception signal output from the pixel decreases. The interference fringes have a spatial intensity distribution, and when the density of the interference fringes is high, in particular, the intensity of the received light signal output from each pixel depends on the size of each pixel.

In the first embodiment, it is assumed that one wavelength component of the interference fringe is detected by four pixels, and the prediction function equation (4) indicating the prediction value P _n is derived based on the equation (3). In the first embodiment, the phase φ is calculated by calculating the undetermined coefficient of Expression (4) from Expression (4) and the actually measured value of the interference fringe light reception signal (in practice, the calculation of For convenience, the equation (5) is derived from the equation (4), and the undetermined coefficient of the equation (5) is calculated from the equation (5) and the actually measured value of the interference fringe light reception signal. 4) and from the actual measurement value of the interference fringe light reception signal, it is substantially the same as calculating the undetermined coefficient of equation (4)). Therefore, according to the first embodiment, an interference fringe generated with the measurement surface 90 tilted by tilting the stage 40 shown in FIG. 1 is assigned to detect one wavelength component of the interference fringe. Even if an error occurs in the number of pixels, the surface shape of the measurement surface 90 can be accurately measured.

  And according to 1st Embodiment, since the phase of an interference fringe there is calculated for every local of an interference fringe, the location (for example, location corresponding to the edge part of the measurement surface 90) and a measurement surface where an interference fringe is interrupted Even if foreign matter such as dust exists locally at 90, the surface shape of the measurement surface 90 can be measured accurately.

  Equation (4) assumes that there is no multiple interference in the interference between the measurement light and the reference light. Therefore, the first embodiment is particularly effective when there is no multiple interference in the interference between the measurement light and the reference light.

  Further, according to the first embodiment, since a two-dimensional image of interference fringes is taken with the Fizeau interferometer, the surface shape of the measurement surface 90 can be measured using the advantage of the Fizeau interferometer. The advantage of the Fizeau interferometer is that, for example, the optical path of the measurement light and the optical path of the reference light are generally the same, so that the Fizeau interferometer is hardly affected by disturbances such as air fluctuations in the optical system 6.

  In the first embodiment, the surface shape measuring apparatus 1a shown in FIG. 1 measures the surface shape with the measurement surface 90 horizontal, and the measurement surface 90 is placed in a state where the sample 9 having the measurement surface 90 is leaned. The surface shape may be measured. This will be briefly described as a modified example. FIG. 14 is a block diagram showing a configuration of a surface shape measuring apparatus 1b according to a modification of the first embodiment. In FIG. 14, the same components as those of the surface shape measuring apparatus 1a shown in FIG. In FIG. 14, the stage controller 5 and the computer 7 shown in FIG. 1 are not shown.

  The surface shape measuring apparatus 1b is a type that adjusts the inclination of the reference surface rather than adjusting the inclination of the measurement surface 90, and includes the vibration isolation table 11, the holding unit 12, the unit 13, the unit 14, and the stage device 4. . The holding unit 12 is attached to the vibration isolation table 11.

  The unit 13, unit 14, and stage device 4 are arranged in this order along the optical axis of the camera 2.

  The unit 13 includes a camera 2, a laser light source 3, a lens 60, a beam splitter 61, and a lens 64, and is held by the holding unit 12.

  The unit 14 includes a lens 62 and is held by the holding unit 12.

  The holding unit 12 holds the stage device 4 in a state where the stage device 4 is raised.

  The stage device 4 includes a stage 40, a drive unit 41, a flat glass 63, and a holding unit 15. The sample 9 having the measurement surface 90 is leaned against the stage 40. The stage 40 supports the holding unit 15 via the driving unit 41. The holding unit 15 holds the flat glass 63. The tilt of the flat glass 63 is controlled by controlling the tilt of the holding unit 15 by the driving unit 41.

  When the thin sample 9 is leveled, the sample 9 may be bent due to its own weight. According to the modified example, since the sample 9 is in a leaning state, such bending can be prevented.

  The second embodiment will be described mainly with respect to differences from the first embodiment. The second embodiment is a technique for measuring the surface shape of a measurement surface having a large area. The second embodiment will be briefly described. In the second embodiment, the interference fringes are divided into a plurality of regions, two-dimensional images of the plurality of regions are photographed, and the photographed two-dimensional images are connected.

  If the area of the measurement surface 90 is large, the area of interference fringes also increases. In order to photograph an interference fringe having a large area using the image sensor 20 provided in the surface shape measuring apparatus 1a shown in FIG. 1, the optical system 6 needs to correspond to this photographing. For example, it is necessary to use for the large-diameter lens 62. This increases the cost of the optical system 6. The spatial resolution is determined by the number of pixels of the image sensor 20. At present, the upper limit of the number of pixels is generally 4000 × 4000. For this reason, if an interference fringe with a large area is imaged using the imaging device 20 provided in the surface shape measuring apparatus 1a shown in FIG. 1, the spatial resolution is lowered.

  Further, as in the first embodiment and the second embodiment, when the phase φ is calculated using the convergence calculation for the waveform of the local interference fringe, it is assigned to detect one wavelength component of the interference fringe. It is desirable to set the inclination of the measurement surface 90 on the stage 40 so that the number of pixels becomes a value in the vicinity of 4. However, if the undulation (unevenness) of the measurement surface 90 is large, the measurement surface 90 is measured by the stage 40 so that the number of pixels allocated to detect one wavelength component of the interference fringe becomes a value close to 4 over the entire measurement surface 90. It is difficult to set 90 slopes.

  Therefore, in the second embodiment, the interference fringes are divided into a plurality of areas and photographed. FIG. 15 is a block diagram showing a configuration of a surface shape measuring apparatus 1c according to the second embodiment. About the same component as the surface shape measuring apparatus 1a shown in FIG. 1, description is abbreviate | omitted by attaching | subjecting the same code | symbol.

  The stage 40 includes a horizontal slide part 43. The horizontal slide unit 43 supports the stage 40 via the drive unit 41 and moves horizontally on the base unit 42 together with the stage 40 and the drive unit 41 according to the control of the stage control unit 5.

  The control unit 70 includes functions of a dividing unit 75, a shooting control unit 76, and an image generating unit 77.

  The dividing unit 75 divides the interference fringes wider than the photographing field of view by the image sensor 20 into a plurality of regions narrower than the photographing field so that adjacent regions partially overlap.

  FIG. 16 is an explanatory diagram for explaining an example of the interference fringes 30 divided into a plurality of regions 31 by the dividing unit 75. The interference fringe 30 is divided into nine regions 31. Each area 31 is narrower than the field of view 32 and adjacent areas 31 partially overlap. Each area 31 is a virtual area, and a dotted line that defines each area 31 does not actually exist.

  The stage control unit 5 moves the horizontal slide unit 43 horizontally, thereby moving the stage 40 horizontally, and sequentially moves a plurality of regions 31 (here, nine regions 31) to the imaging field of view 32.

  The imaging control unit 76 causes the imaging device 20 to capture a two-dimensional image of the region 31 that has moved to the imaging visual field 32.

  As described above, if the undulation (unevenness) of the measurement surface 90 is large, the stage control is performed so that the number of pixels allocated to detect one wavelength component of the interference fringe is a value close to 4 over the entire measurement surface 90. It is difficult for the unit 5 to set the inclination of the measurement surface 90. Therefore, the stage control unit 5 adjusts the inclination of the measurement surface 90 (region 31) for each region 31. As a result, the absolute position of the measurement surface 90 changes every time the region 31 is imaged.

  Therefore, the image generation unit 77 connects the two-dimensional images of the plurality of regions 31 photographed by the imaging element 20 using the partial overlap as a mark, and generates a two-dimensional image of the interference fringes 30.

  FIG. 17 is an explanatory diagram for explaining a method of connecting two-dimensional images of two adjacent regions 31a and 31b. A partial overlap between the two-dimensional image of the region 31 a and the two-dimensional image of the region 31 b is shown as an overlapping portion 33. The image generation unit 77 determines three points that are not on a straight line in the overlapping portion 33, and the two points of the region 31a overlap so that the three points of the two-dimensional image of the region 31a and the three points of the two-dimensional image of the region 31b overlap. The two-dimensional image and the two-dimensional image of the region 31b are connected.

  According to the second embodiment, the accuracy of measuring the surface shape of the measurement surface 90 can be increased even when the area of the measurement surface 90 is large.

1a, 1b, 1c Surface shape measuring device 6 Optical system 20 Imaging device 40 Stage 65 Upper surface of flat glass (an example of reference surface)
66 Optical axis 90 Measuring surface

Claims (4)

An optical axis passing through the measurement surface and the reference surface, and at least one of the measurement surface and the inclined surface is inclined with respect to a surface orthogonal to the optical axis; An optical system that generates interference fringes by causing interference between reflected light and reflected light of light irradiated on the reference surface;
An image sensor that captures a two-dimensional image of the interference fringes generated by the optical system;
When the number of pixels of the image sensor assigned to detect one wavelength component of the interference fringe is 4, light reception output from the nth pixel of the image sensor by capturing a two-dimensional image of the interference fringe The prediction function indicating the predicted value P _{n of the} signal is represented by the following equation where A1, B, β, and φ are undetermined coefficients, and the undetermined coefficients are considered to be equal in a plurality of consecutive pixels of the image sensor, And a first solution that calculates a solution of the undetermined coefficient using an actual measurement value of a light reception signal output from each of a plurality of consecutive pixels including the nth pixel by capturing a two-dimensional image of the interference fringes. A calculation unit;
Second of calculating the height of the position of the measurement surface corresponding to the nth pixel using the solution of φ indicating the phase among the solutions of the undetermined coefficient calculated by the first calculation unit. And a calculation unit of
The first calculation unit calculates a solution of the undetermined coefficient for each of a predetermined number of pixels constituting the image sensor,
The second calculation unit is a surface shape measurement device that calculates a height of a portion of the measurement surface corresponding to each of the predetermined number of pixels using a solution of φ of each of the predetermined number of pixels.

(Here, n represents an integer, and ω represents a spatial frequency.) A stage on which a sample having the measurement surface is placed;
A division unit that divides the interference fringes wider than the imaging field of view by the image sensor into a plurality of regions narrower than the imaging field so that adjacent regions partially overlap;
A stage control unit that moves the plurality of regions in order in the imaging field of view by moving the stage;
An imaging control unit that causes the imaging device to capture a two-dimensional image of the region that has moved to the imaging field;
The surface shape measurement apparatus according to claim 1, further comprising: an image generation unit that generates a two-dimensional image of the interference fringes by connecting two-dimensional images of the plurality of regions using the partial overlap as a mark. .   The surface shape measuring apparatus of Claim 1 or 2 provided with the Fizeau interferometer containing the said optical system and the said image pick-up element. An optical axis passing through the measurement surface and the reference surface, and at least one of the measurement surface and the inclined surface is inclined with respect to a surface orthogonal to the optical axis; Generating the interference fringes by causing the reflected light and the reflected light of the light irradiated on the reference surface to interfere with each other;
A photographing step of photographing a two-dimensional image of the interference fringes generated by the generating step using an imaging element;
When the number of pixels of the image sensor allocated to detect one wavelength component of the interference fringe imaged in the imaging step is 4, the n-th image sensor image is captured by capturing a two-dimensional image of the interference fringe. The prediction function indicating the predicted value P _n of the received light signal output from each pixel is represented by the following equation where A1, B, β, and φ are undetermined coefficients, and the undetermined coefficient is determined for a plurality of consecutive pixels of the image sensor. The undetermined coefficient of the undetermined coefficient by using the measured value of the received light signal output from each of a plurality of consecutive pixels including the n-th pixel by photographing the two-dimensional image of the interference fringes. A first calculating step for calculating a solution;
Secondly, the height of the portion of the measurement surface corresponding to the nth pixel is calculated using the solution of φ indicating the phase among the solutions of the undetermined coefficient calculated in the first calculation step. And a calculation step of
The first calculating step calculates a solution of the undetermined coefficient for each of a predetermined number of pixels constituting the image sensor,
The second calculation step is a surface shape measurement method for calculating a height of a portion of the measurement surface corresponding to each of the predetermined number of pixels using a solution of φ of each of the predetermined number of pixels.

(Here, n represents an integer, and ω represents a spatial frequency.)