JP2010151781A - Frequency estimation method, frequency estimating device, surface shape measurement method, and surface shape measurement device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a frequency estimation method for shortening a processing time while being low in calculation load, and to provide a frequency estimation device, a surface shape measurement method, and a surface shape measurement device. <P>SOLUTION: The frequency estimation method for estimating frequencies in cyclic observed data such as an interference stripe and electric signals includes: a step for obtaining data; a step for adapting a sine wave function of assumed optional frequencies as model signals to the observed data; a step for obtaining a shift amount of a partial phase of the observed data and the model signals; and a step for calculating the frequencies of the observed data on the basis of the frequencies of the model signals and phase inclination concerning the shift amount of the phase. <P>COPYRIGHT: (C)2010,JPO&amp;INPIT

Description

  The present invention relates to a frequency estimation method, a frequency estimation device, a surface shape measurement method, and a surface shape measurement device. More specifically, a frequency estimation method and apparatus for estimating a frequency in periodic observation data such as interference fringes and electrical signals, and the frequency estimation method or apparatus are incorporated so that unevenness of a measurement object having flatness is obtained, for example. The present invention relates to a surface shape measuring method and apparatus for measuring.

  Semiconductor wafers, liquid crystal panels, plasma display panels, magnetic films, and the like are evaluated for surface flatness by measuring surface irregularities using a predetermined surface shape measuring method and apparatus surface shape measuring apparatus.

  As a conventional surface shape measuring method, there is one disclosed in Patent Document 1. In the surface shape measuring method of Patent Document 1, the surface shape is measured using interference fringes. Specifically, the surface shape is measured by estimating the frequency of the interference fringes appearing on the surface to be measured, and applying the approximate sine waveform of the estimated frequency to the interference fringe signal to obtain the phase. Prony method is used for frequency estimation of interference fringes.

  Further, as a conventional surface shape measuring method, there is one disclosed in Patent Document 2. The surface shape measuring method of Patent Document 2 also measures the surface shape using interference fringes. Specifically, the surface shape is measured by applying an approximate sine waveform of the estimated frequency to the interference fringe signal to obtain the phase. There is no specific description about the frequency estimation method of interference fringes.

  Moreover, there exists a thing of patent document 3 as a conventional surface contour measuring method. The surface contour measuring method of Patent Document 3 measures the surface contour by fringe pattern projection. Specifically, the surface contour is measured by projecting a stripe pattern onto the measurement target surface. There is no specific description about the method of estimating the number of fringes of the projected fringe pattern.

  As a conventional fringe projection method for projecting interference fringes onto a measurement object, there is one disclosed in Patent Document 4. Specifically, the surface contour is measured by projecting a stripe pattern onto the measurement target surface. There is no specific description about the frequency estimation method of interference fringes.

  For the frequency estimation method of interference fringes, for example, Fourier transform can be used in addition to the Prony method.

Japanese Patent Application No. 2007-021870 Japanese Patent Application No. 2006-024825 JP 2001-552052 A Japanese Patent Application No. 2000-395589

  When the Prony method and the Fourier transform as described above are used for the frequency estimation method of interference fringes, these require complicated calculation processes, which causes a problem of high calculation load and long processing time.

  The present invention has been made in view of such circumstances, and mainly provides a frequency estimation method, a frequency estimation device, a surface shape measurement method, and a surface shape measurement device that require a low calculation load and a short processing time. Objective.

  A first invention is a frequency estimation method for estimating a frequency in periodic observation data such as interference fringes and electrical signals, the step of acquiring the observation data, and a sine wave function of an arbitrary arbitrary frequency as a model signal. On the basis of the observation data, a step of obtaining a partial phase shift amount between the observation data and the model signal, a frequency of the model signal, and a phase gradient with respect to the phase shift amount And calculating the frequency of the observation data.

  (Action / Effect) According to this method, the partial phase shift amount between the observed data and the assumed sine wave function of any frequency is obtained, and the frequency is obtained by using the phase gradient for this phase shift amount. Can be obtained accurately. In this method, since it is not necessary to use complicated arithmetic processing such as Fourier transform that is generally used, the calculation load is reduced and the processing time can be shortened. That is, work efficiency can be improved.

  According to a second invention, in the frequency estimation method according to the first invention, the calculation of the phase shift amount is obtained by applying partial observation data to a sinusoidal function of an assumed arbitrary frequency by a least square method. It is characterized by.

  (Operation / Effect) According to this method, the phase shift amount can be easily obtained by the calculation of the least square method.

  A third invention is characterized in that, in the frequency estimation method according to the second invention, phase connection is made in advance at the order jump boundary of the phase shift amount before calculating the phase gradient for the phase shift amount. And

  (Operation / Effect) According to this method, calculation error due to the order jump can be prevented no matter which point is used when calculating the phase gradient.

  According to a fourth invention, in the frequency estimation method according to the second invention, when calculating the phase gradient for the phase shift amount, the phase gradient is calculated while avoiding the order jump boundary of the phase shift amount. Features.

  (Operation / Effect) According to this method, it is possible to prevent a calculation error due to the order jump when calculating the phase gradient.

  According to a fifth aspect of the present invention, in the frequency estimation method according to the first or second aspect, the coordinate data is shifted so that the maximum value in the observation data matches the maximum value of the model signal, and the observation data is converted into the model signal. It is characterized by adapting to.

  (Operation / Effect) According to this method, the phase at the coordinate origin is close to zero, and the possibility that the phase value exceeds ± π is reduced. As a result, unwrapping can be eliminated and calculation time can be shortened.

  According to a sixth aspect of the present invention, in the frequency estimation method according to any one of the third to fifth aspects, the phase gradient calculation method for the phase shift amount is a least-squares method for two or more phase shift amounts. It is characterized in that it is obtained by approximating a linear straight line.

  (Operation / Effect) According to this method, a highly accurate phase gradient can be easily obtained by the calculation of the method of least squares.

According to a seventh aspect of the present invention, in the frequency estimation method according to any one of the first to sixth aspects, the frequency (f) to be obtained is assumed to be a frequency of a sinusoidal function of an assumed arbitrary frequency f _0, and the amount of phase shift The phase gradient for the above is defined as dφ ′ (x) / dx, and is obtained from an equation of f = f ₀ + (dφ ′ (x) / dx) / 2π.

  (Operation / Effect) According to this method, since it is not necessary to use complicated arithmetic processing, the calculation load is reduced and the processing time can be shortened.

An eighth invention is the frequency estimation method according to any one of the first to seventh inventions, wherein the observation data comprises a two-dimensional periodic fringe image, the sine wave function comprises a two-dimensional sine wave image, A frequency estimation method, wherein the frequency (f _x , f _y ) of the two-dimensional periodic fringe image is obtained from the following equation.
f _x = f _x0 + (dφ ′ (x, y) / dx) / 2π
f _y = f _y0 + (dφ ′ (x, y) / dy) / 2π
Here, x and y are the two axes of the orthogonal coordinate system, the frequency in the x-axis direction of the assumed arbitrary sine wave function is f _x0, and the frequency in the y-axis direction of the assumed arbitrary sine wave function F _y0 and the phase gradient in the x-axis direction between the two-dimensional periodic fringe image and the two-dimensional sinusoidal image as dφ ′ (x, y) / dx, and the two-dimensional periodic fringe image and the two-dimensional sine The phase gradient in the y-axis direction with respect to the wave image is dφ ′ (x, y) / dy.

  (Operation / Effect) According to this method, two-dimensional frequency estimation is possible. In particular, the frequency in two directions can be estimated simultaneously in one process. Thus, accurate frequency estimation is possible even when the frequency is near zero. Moreover, it is possible to estimate even if one frequency is zero.

  A ninth invention is characterized in that in the frequency estimation method according to any one of the first to eighth inventions, the estimation calculation is newly repeated with the estimated frequency as the frequency of a sinusoidal function having an arbitrary frequency.

  (Operation and Effect) According to this method, a more accurate frequency can be easily obtained.

(Frequency estimation device)
According to a tenth aspect of the present invention, an acquisition means for acquiring observation data and a sinusoidal function having an assumed arbitrary frequency are adapted to the observation data as a model signal, and a partial phase shift amount between the observation data and the model signal And calculating means for calculating the frequency of the observation data based on the frequency of the model signal and the phase gradient with respect to the phase shift amount.

  (Operation / Effect) According to this configuration, the partial phase shift amount between the observed data and the assumed sine wave function of any frequency is obtained, and the frequency is obtained by using the phase gradient for this phase shift amount. Can be obtained accurately. In this method, since it is not necessary to use complicated arithmetic processing such as Fourier transform that is generally used, the calculation load is reduced and the processing time can be shortened. That is, work efficiency can be improved.

  According to an eleventh aspect of the present invention, in the frequency estimation apparatus according to the tenth aspect of the invention, the calculation of the phase shift amount is obtained by applying partial observation data to a sinusoidal function of an assumed arbitrary frequency by a least square method. It is characterized by.

  (Operation / Effect) According to this configuration, the phase shift amount can be easily obtained by the calculation of the least square method.

  A twelfth invention is characterized in that, in the frequency estimation device according to the eleventh invention, before the phase gradient for the phase shift amount is calculated, phase connection is made in advance at the order jump boundary of the phase shift amount. And

  (Operation / Effect) According to this configuration, calculation errors due to the order jump can be prevented regardless of which point is used when calculating the phase gradient.

  According to a thirteenth aspect, in the frequency estimation device according to the eleventh aspect, when calculating the phase gradient for the phase shift amount, the phase gradient is calculated while avoiding the order jump boundary of the phase shift amount. Features.

  (Operation / Effect) According to this configuration, it is possible to prevent a calculation error due to the order jump when calculating the phase gradient.

  According to a fourteenth aspect, in the frequency estimation device according to the tenth or eleventh aspect, the coordinate origin is shifted so that the maximum value in the observation data matches the maximum value of the model signal, and the observation data is converted into the model signal. It is characterized by adapting to.

  (Operation / Effect) According to this configuration, the phase at the coordinate origin is close to zero, and the possibility that the phase value exceeds ± π is reduced. As a result, unwrapping can be eliminated and calculation time can be shortened.

  A fifteenth aspect of the present invention is the frequency estimation device according to the twelfth or thirteenth aspect of the present invention, wherein the phase gradient calculation method for the phase shift amount is a first-order straight line by least squares method for two or more phase shift amounts. Is obtained by approximation.

  (Operation and Effect) According to this configuration, the phase gradient can be easily obtained by the calculation of the least square method.

According to a sixteenth aspect of the present invention, in the frequency estimation device according to any one of the tenth to fifteenth aspects, the frequency (f) to be obtained is assumed to be a frequency of an assumed arbitrary frequency sine wave function f _0, and the amount of phase shift Where dφ ′ (x) / dx is obtained from the equation of f = f ₀ + (dφ ′ (x) / dx) / 2π.

  (Operation / Effect) According to this configuration, since it is not necessary to use complicated arithmetic processing, the calculation load is reduced and the processing time can be shortened.

According to a seventeenth aspect of the present invention, in the frequency estimation device according to any one of the tenth to sixteenth aspects, the observation data is a two-dimensional periodic fringe image, and the sine wave function is a two-dimensional sine wave image, The frequency (f _x , f _y ) of the two-dimensional periodic fringe image is obtained from the following equation.
f _x = f _x0 + (dφ ′ (x, y) / dx) / 2π
f _y = f _y0 + (dφ ′ (x, y) / dy) / 2π
Here, x and y are the two axes of the orthogonal coordinate system, the frequency in the x-axis direction of the assumed arbitrary sine wave function is f _x0, and the frequency in the y-axis direction of the assumed arbitrary sine wave function F _y0 and the phase gradient in the x-axis direction between the two-dimensional periodic fringe image and the two-dimensional sinusoidal image as dφ ′ (x, y) / dx, and the two-dimensional periodic fringe image and the two-dimensional sine The phase gradient in the y-axis direction with respect to the wave image is dφ ′ (x, y) / dy.

  (Operation / Effect) With this configuration, two-dimensional frequency estimation is possible. In particular, the frequency in two directions can be estimated simultaneously in one process. Thus, accurate frequency estimation is possible even when the frequency is near zero. Moreover, it is possible to estimate even if one frequency is zero.

  According to an eighteenth aspect of the present invention, in the frequency estimation apparatus according to any one of the tenth to seventeenth aspects, the estimated calculation is repeated by using the estimated frequency as a new sinusoidal function frequency.

  (Operation and Effect) According to this configuration, a more accurate frequency can be easily obtained.

(Optical interferometry surface shape measurement method)
According to a nineteenth aspect of the present invention, the light output from the light source irradiates the measurement target surface and the reference surface through the branching unit, and is reflected from both the measurement target surface and the reference surface and reflected by the reflected light returning from the same optical path In the surface shape measurement method for determining the surface height and surface shape of the measurement target surface based on the intensity value of the stripes,
A first step of acquiring an image of interference fringes generated in a state where the reference surface is arranged in an obliquely inclined posture at an arbitrary angle with respect to the traveling direction of light;
A second step of obtaining an interference fringe intensity value of each pixel in the acquired image;
Place on multiple pixels in the screen and use the intensity values of multiple pixels in the neighboring area including that pixel, and the local phase shift between the interference fringe waveform in the area and the assumed sine wave function of arbitrary frequency A third step of obtaining a quantity and estimating a frequency of observation data based on a phase gradient obtained from a phase shift amount in a plurality of pixels;
Placed on the measurement target pixel in the screen, using the intensity value of a plurality of pixels in the neighboring area including the pixel, the interference fringe waveform in the area, and the frequency is the estimated frequency or the previously estimated frequency, and the DC component A fourth process for determining the phase of each pixel from the sinusoidal function assuming that the AC amplitude and phase are constant;
A fifth step of obtaining the surface height of the measurement target surface imaged from the obtained phase of each pixel;
A sixth step of obtaining a surface shape from the obtained surface height of the measurement target surface;
It is provided with.

  (Operation / Effect) According to the method for measuring a surface shape according to the present invention, the reference surface is arranged in an obliquely inclined posture at an arbitrary angle with respect to the light traveling direction, thereby returning the same optical path from the measurement target surface and the reference surface. Interference fringes are generated by reflected light. The intensity value of this interference fringe is obtained in units of pixels, and for each pixel using the expression for obtaining the interference fringe waveform, the intensity value of each pixel and the intensity value of the neighboring pixel for each pixel are used, Assuming that the DC component, AC amplitude, and phase of the interference fringe waveform included in the pixel are equal, the phase of each pixel is obtained. The surface height is obtained from the obtained phase. Conventionally, the interference fringe frequency required for the above expression has been obtained by visually counting the number of fringes in the screen or by Fourier transform, but the former has poor accuracy and the latter has a high calculation load. According to the present invention, local phase shift amounts at a plurality of locations between the assumed frequency sinusoidal function and the actual measurement signal are obtained, and observation data is obtained based on the phase gradient obtained from the phase shift amounts at the plurality of pixels. The surface shape can be measured with high accuracy and low calculation load.

  According to a twentieth aspect, in the surface shape measurement method according to the nineteenth aspect, the frequency of the obtained interference fringe image is estimated using any one of the first to ninth aspects.

  (Function / Effect) According to this method, the frequency can be estimated from the interference fringe image of the measurement target surface accurately and with simple calculation, and the surface shape is accurately measured using the estimated frequency. be able to.

In a twenty-first aspect, the light output from the light source irradiates the measurement target surface and the reference surface through the branching unit, and is reflected from both the measurement target surface and the reference surface and caused by reflected light returning from the same optical path. In the surface shape measuring device for determining the surface height and surface shape of the measurement target surface based on the intensity value of the stripes,
The reference surface is arranged in an obliquely inclined posture at an arbitrary angle with respect to the traveling direction of light,
Imaging means for imaging the measurement target surface by generating interference fringes by reflected light that is irradiated with the light and reflected from the measurement target and the reference surface and returns on the same optical path;
Sampling means for capturing the measured measurement target surface as an interference fringe intensity value for each pixel;
Storage means for storing an interference fringe intensity value group that is the intensity value captured by the sampling means;
The intensity value is read out for each pixel from the intensity value group stored in the storage means, placed on a plurality of pixels in the screen, and the intensity value of a plurality of pixels in a neighboring area including the pixel is used, and interference fringes in that area are obtained. Obtain the local phase shift amount between the waveform and the assumed sine wave function of arbitrary frequency, estimate the frequency of the observation data based on the phase gradient obtained from the phase shift amount in multiple pixels, Using the intensity values of a plurality of pixels in the neighboring area including the pixel, the interference fringe waveform in the area and the frequency are the estimated frequency or the frequency estimated in advance, and the DC component and the AC amplitude And, from the sinusoidal function assumed that the phase is constant, obtain the phase of each pixel, obtain the surface height of the measurement target surface imaged from the obtained phase of each pixel, further, the obtained the A calculating means for calculating the surface shape from the surface height of a constant target surface,
It is provided with.

  (Operation / Effect) According to the surface shape measuring apparatus according to the present invention, the reference surface is arranged in an obliquely inclined posture at an arbitrary angle with respect to the light traveling direction, thereby returning the same optical path from the measurement target surface and the reference surface. Interference fringes are generated by reflected light. The intensity value of this interference fringe is obtained in units of pixels, and for each pixel using the expression for obtaining the interference fringe waveform, the intensity value of each pixel and the intensity value of the neighboring pixel for each pixel are used, Assuming that the DC component, AC amplitude, and phase of the interference fringe waveform included in the pixel are equal, the phase of each pixel is obtained. The surface height is obtained from the obtained phase. Conventionally, the interference fringe frequency required for the above expression has been obtained by visually counting the number of fringes in the screen or by Fourier transform, but the former has poor accuracy and the latter has a high calculation load. According to the present invention, local phase shift amounts at a plurality of locations between the assumed frequency sinusoidal function and the actual measurement signal are obtained, and observation data is obtained based on the phase gradient obtained from the phase shift amounts at the plurality of pixels. The surface shape can be measured with high accuracy and low calculation load.

  According to a twenty-second aspect, in the surface shape measurement apparatus according to the twenty-first aspect, the frequency of the acquired interference fringe image is estimated using any one of the tenth to eighteenth aspects.

  (Function / Effect) According to this configuration, the frequency can be accurately estimated from the interference fringe image of the measurement target surface by simple and simple calculation, and the surface shape is accurately measured using the estimated frequency. be able to.

(Striped projection surface shape measurement method)
In a twenty-third aspect, the light output from the light source is projected onto a measurement target surface via a grating, and the surface height and the surface shape of the measurement target surface are calculated based on the intensity value of interference fringes generated by the measurement target surface. In the surface shape measurement method for obtaining
A first step of acquiring an image of interference fringes on the measurement target surface;
A second step of obtaining an interference fringe intensity value of each pixel in the acquired image;
Place on multiple pixels in the screen and use the intensity values of multiple pixels in the neighboring area including that pixel, and the local phase shift between the interference fringe waveform in the area and the assumed sine wave function of arbitrary frequency A third step of obtaining a quantity and estimating a frequency of observation data based on a phase gradient obtained from a phase shift amount in a plurality of pixels;
Placed on the measurement target pixel in the screen, using the intensity value of a plurality of pixels in the neighboring area including the pixel, the interference fringe waveform in the area, and the frequency is the estimated frequency or the previously estimated frequency, and the DC component A fourth process for determining the phase of each pixel from the sinusoidal function assuming that the AC amplitude and phase are constant;
A fifth step of obtaining the surface height of the measurement target surface imaged from the obtained phase of each pixel;
A sixth step of obtaining a surface shape from the obtained surface height of the measurement target surface;
It is provided with.

  (Operation / Effect) According to the surface shape measuring method according to the present invention, the interference fringes are generated by projecting the lattice fringes onto the measurement target. The intensity value of this interference fringe is obtained in units of pixels, and for each pixel using the expression for obtaining the interference fringe waveform, the intensity value of each pixel and the intensity value of the neighboring pixel for each pixel are used, Assuming that the DC component, AC amplitude, and phase of the interference fringe waveform included in the pixel are equal, the phase of each pixel is obtained. The surface height is obtained from the obtained phase. Conventionally, the interference fringe frequency required for the above expression has been obtained by visually counting the number of fringes in the screen or by Fourier transform, but the former has poor accuracy and the latter has a high calculation load. According to the present invention, local phase shift amounts at a plurality of locations between the assumed frequency sinusoidal function and the actual measurement signal are obtained, and observation data is obtained based on the phase gradient obtained from the phase shift amounts at the plurality of pixels. The surface shape can be measured with high accuracy and low calculation load.

  According to a twenty-fourth aspect, in the surface shape measurement method according to the twenty-third aspect, the frequency of the acquired interference fringe image is estimated using any one of the first to ninth aspects.

  (Function / Effect) According to this method, the frequency can be estimated from the interference fringe image of the measurement target surface accurately and with simple calculation, and the surface shape is accurately measured using the estimated frequency. be able to.

(Stripe projection surface shape measuring device)
In a twenty-fifth aspect of the present invention, light output from a light source is projected onto a measurement target surface via a grating, and the surface height and surface shape of the measurement target surface are calculated based on the intensity value of interference fringes generated by the measurement target surface. In the surface shape measuring device for obtaining
An imaging means for imaging an image of the interference fringes on the measurement target surface;
Sampling means for capturing the measured measurement target surface as an interference fringe intensity value for each pixel;
Storage means for storing an interference fringe intensity value group that is the intensity value captured by the sampling means;
Read the intensity value for each pixel from the intensity value group stored in the storage means,
Place on multiple pixels in the screen and use the intensity values of multiple pixels in the neighboring area including that pixel, and the local phase shift between the interference fringe waveform in the area and the assumed sine wave function of arbitrary frequency The amount of the measured data is estimated, and the frequency of the observation data is estimated based on the phase gradient obtained from the amount of phase shift in a plurality of pixels.
Placed on the measurement target pixel in the screen, using the intensity value of a plurality of pixels in the neighboring area including the pixel, the interference fringe waveform in the area, and the frequency is the estimated frequency or the previously estimated frequency, and the DC component From the sinusoidal function assuming that the AC amplitude and phase are constant, the phase of each pixel is obtained,
Obtain the surface height of the measurement target surface imaged from the phase of the obtained each pixel,
Further, a calculation means for obtaining a surface shape from the obtained surface height of the measurement target surface,
It is provided with.

  (Operation / Effect) According to the surface shape measuring apparatus of the present invention, the interference fringes are generated by projecting the lattice fringes onto the measurement target. The intensity value of this interference fringe is obtained in units of pixels, and for each pixel using the expression for obtaining the interference fringe waveform, the intensity value of each pixel and the intensity value of the neighboring pixel for each pixel are used, Assuming that the DC component, AC amplitude, and phase of the interference fringe waveform included in the pixel are equal, the phase of each pixel is obtained. The surface height is obtained from the obtained phase. Conventionally, the interference fringe frequency required for the above expression has been obtained by visually counting the number of fringes in the screen or by Fourier transform, but the former has poor accuracy and the latter has a high calculation load. According to the present invention, local phase shift amounts at a plurality of locations between the assumed frequency sinusoidal function and the actual measurement signal are obtained, and observation data is obtained based on the phase gradient obtained from the phase shift amounts at the plurality of pixels. The surface shape can be measured with high accuracy and low calculation load.

  According to a twenty-sixth aspect of the invention, in the surface shape measuring apparatus according to the twenty-fifth aspect of the invention, the frequency of the acquired interference fringe image is estimated using any one of the tenth to eighteenth aspects.

  (Function / Effect) According to this configuration, the frequency can be accurately estimated from the interference fringe image of the measurement target surface by simple and simple calculation, and the surface shape is accurately measured using the estimated frequency. be able to.

  The “sine wave function” in the present invention means a sine wave function (sinx), a cosine wave function (cosx), and broadly a periodic function having an arbitrary phase (for example, sin (x + φ)). The same concept applies to the “sine wave image”.

  According to the present invention, there are provided a frequency estimation method, a frequency estimation device, a surface shape measurement method, and a surface shape measurement device that require a low calculation load and a short processing time.

It is a figure which shows schematic structure of the surface shape measuring apparatus which concerns on this embodiment. It is a flowchart which shows the process in a surface shape measuring apparatus. It is a figure which shows the captured image data of a measurement object surface. It is a figure which shows the x-axis direction luminance change of a captured image. It is a figure which shows that the range of (phi) can be specified using the code | symbol information of sin (phi) and cos (phi). It is a figure which shows the measurement result at the time of measuring a steep level difference using the apparatus of this embodiment. It is a figure which shows the observed value and model signal waveform of the frequency estimation which concern on Example 1. FIG. It is a figure which shows the phase of each pixel in the case of FIG. It is the figure which fitted the straight line to FIG. It is a figure which shows an observed value when a presumed frequency is made into an initial value, and a model signal waveform. It is a figure which shows the phase of each pixel in the case of FIG. It is a figure which shows the example (Example 2) of a phase jump avoidance. It is a figure which shows the observation image and model image of frequency estimation which concern on Example 4. FIG. It is a figure which shows the phase of each pixel in the case of FIG. It is the figure which fitted the straight line to the data of FIG. It is a figure which compares the true value image of observation data in Example 4, and an estimated image. It is a figure which shows the observation image and model image of frequency estimation which concern on Example 5. FIG. It is a figure which shows the phase of each pixel in the case of FIG. It is the figure which fitted the straight line to the data of FIG. It is a figure which compares the true value image of observation data in Example 5, and an estimated image. It is a figure which shows the fitting point in Example 4 and Example 5. FIG. FIG. 10 is a diagram for explaining an origin shift mode in a third embodiment. It is a figure for demonstrating the fitting which does not use an origin shift mode.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the present embodiment, a surface shape measuring apparatus that measures the surface height and the surface shape of a measurement object having a substantially flat surface using interference fringes will be described as an example.

  FIG. 1 is a diagram showing a schematic configuration of a surface shape measuring apparatus according to an embodiment of the present invention.

  The surface shape measuring apparatus includes an optical system unit 1 that irradiates a substantially flat measuring object 30 having fine uneven steps on the surface of a semiconductor wafer, a glass substrate, a metal film, or the like with monochromatic light in a specific wavelength band, and an optical system. And a control system unit 2 for controlling the unit 1.

  The optical system unit 1 includes a white light source 10 that is a light source for generating light to irradiate the measurement target surface 30A and the reference surface 15, a collimating lens 11 that converts white light from the white light source 10 into parallel light, and a specific frequency band. A band-pass filter 12 that passes only the monochromatic light, a half mirror 13 that reflects the light that has passed through the band-pass filter 12 in the direction of the measurement object 30, while allowing light from the direction of the measurement object 30 to pass, An objective lens 14 that condenses the monochromatic light reflected by the half mirror 13, a reference light that reflects the monochromatic light that has passed through the objective lens 14 to the reference surface 15, and a measurement light that passes through the measurement target surface 30A. And splitting the reference light reflected by the reference surface 15 and the measurement light reflected by the measurement target surface 30A again to generate an interference fringe. A motor 17, an imaging lens 18 for focusing the reference light measuring light and monochromatic light gathered is configured by a CCD camera 19 for imaging the object surface 30A with the interference fringes. The CCD camera 19 corresponds to the image pickup means of the present invention.

  The white light source 10 is a halogen lamp, for example, and generates white light in a relatively wide frequency band. The white light generated from the white light source 10 is converted into parallel light by the collimating lens 11, becomes monochromatic light in a specific frequency band by the band pass filter 12, and travels toward the half mirror 13.

  The half mirror 13 reflects the parallel light from the collimator lens 11 in the direction of the measurement target 30, while allowing the light returned from the direction of the measurement target 30 to pass therethrough. Monochromatic light in a specific frequency band reflected by the half mirror 13 enters the objective lens 14.

  The objective lens 14 is a lens that condenses incident light toward the measurement object 30 and the reference surface 15. The light condensed by the objective lens 14 reaches the beam splitter 17.

  The beam splitter 17 divides the light collected by the objective lens 14 into reference light reflected by the reference surface 15 and measurement light reflected by the measurement target surface 30A. Further, the reference light and the measurement light reflected on each surface and returning on the same optical path are combined again to generate interference. The light that reaches the beam splitter 17 is divided into reference light reflected by the surface of the beam splitter 17 and measurement light that passes through the beam splitter 17, and the reference light reaches the reference surface 15, and the measurement light is measured. It reaches the target surface 30A.

  The reference surface 15 is attached in a slanting front and back inclined posture with respect to the traveling direction of the reference light. The reference light reflected by the reference surface 15 reaches the beam splitter 17, and the reference light is further reflected by the beam splitter 17.

By attaching the reference surface 15 in a slanting posture in front and back with respect to the traveling direction of the reference light, the arrival distance of the reference light and the distance until the reflected light reaches the CCD camera 19 vary depending on the position of the reflection surface. This is equivalent to moving the reference surface 15 and changing the distance L ₁ between the reference surface 15 and the beam splitter 17.

  The measurement light that has passed through the beam splitter 17 is condensed toward the measurement object 30 and reflected by the measurement object surface 30A. The reflected measurement light reaches the beam splitter 17 and passes through the beam splitter 17.

The reference beam and the measurement beam are combined again by the beam splitter 17. At this time, an optical path difference is generated due to a difference between the distance L ₁ between the reference surface 15 and the beam splitter 17 and the distance L ₂ between the beam splitter 17 and the measurement target surface 30A. The reference light and the measurement light interfere with each other according to this optical path difference. The light in the state where the interference occurs passes through the half mirror 13, is imaged by the imaging lens 18, and enters the CCD camera 19.

  The CCD camera 19 captures an image of the measurement target surface 30A that is projected by the measurement light. At this time, because the reference surface 15 is tilted, an interference fringe that is a spatial variation in luminance due to interference is captured in the captured image of the measurement target surface 30A. The captured image data is collected by the control system unit 2. Further, as will be apparent later, the optical system unit 1 is moved in the x, y, and z axis directions in FIG. 1 to a desired imaging location by the drive unit 24 of the control system unit 2. The CCD camera 19 captures an image of the measurement target surface 30 </ b> A at a predetermined sampling timing, and the image data is collected by the control system unit 2.

  The control system unit 2 includes an overall control of the surface shape measuring apparatus, a CPU 20 for performing predetermined arithmetic processing, various data such as image data sequentially collected by the CPU 20 and arithmetic results in the CPU 20, A memory 21 for storing a program, an input unit 22 such as a mouse or a keyboard for inputting other setting information such as a sampling timing and an imaging area, a monitor 23 for displaying an image of the measurement target surface 30A, and the like according to an instruction from the CPU 20 For example, the optical system unit 1 is driven to move up and down and left and right, and is configured by a computer system including a drive unit 24 configured by a drive mechanism such as a three-axis drive type servo motor. The CPU 20 corresponds to the calculation means in the present invention, and the memory 21 corresponds to the storage means in the present invention.

  The CPU 20 is a so-called central processing unit that controls the CCD camera 19, the memory 21, and the drive unit 24, and based on the image data of the measurement target surface 30 </ b> A including the interference fringes captured by the CCD camera 19. A frequency estimation unit 28, a phase calculation unit 25, a code determination unit 26, and an image data creation unit 27 that perform calculation processing for obtaining the surface height of the object 30 are provided. The processing of the frequency estimation unit 28, the phase calculation unit 25, the code determination unit 26, and the image data creation unit 27 in the CPU 20 will be described in detail later. Further, a monitor 23 and an input unit 22 such as a keyboard and a mouse are connected to the CPU 20, and the operator can observe various operation information displayed on the monitor 23 from the input unit 22. Input. Further, the monitor 23 displays a surface image of the measurement target surface 30A, a concavo-convex shape, and the like as numerical values and images.

  The drive unit 24 is a device that moves, for example, the optical system unit 1 in the x, y, and z axis directions in FIG. 1 to a desired imaging location. The drive unit 24 is configured by a drive mechanism including, for example, a three-axis drive type servo motor that drives the optical system unit 1 in the x, y, and z axis directions according to instructions from the CPU 20. In this embodiment, the optical system unit 1 is operated. However, for example, a table (not shown) on which the measurement object 30 is placed may be changed in three orthogonal directions. Further, there may be two or less moving axes or none.

  Hereinafter, processing performed in the entire surface shape measuring apparatus, which is a characteristic part of the present embodiment, will be described with reference to a flowchart shown in FIG.

  In the present embodiment, the case where the reference surface 15 is tilted as shown in FIG. 1 will be described as an example. In this case, the captured image is as shown in FIG. Further, the surface shape measuring device can select either the unwrapping mode or the origin shift mode. The specific contents will be described later in Examples 2 and 3.

<Step S1> Acquisition of Measurement Data The CPU 20 drives a drive system such as a stepping motor (not shown), and the drive unit 24 moves the optical unit 1 to the imaging region of the measurement object 30. When the imaging position is determined, the optical system unit 1 generates white light from the white light source 10. The white light is converted into monochromatic light (for example, wavelength λ = 600 nm) through the bandpass filter 12 and is irradiated on the measurement object 30 and the reference surface 15.

The CCD camera 19 operates in conjunction with the irradiation of the monochromatic light, and for example, the measurement target surface 30A having the convex portion 30B shown in FIG. 1 is imaged once. Image data of the interference fringes of the measurement target surface 30 </ b> A acquired by this imaging is collected and stored in the memory 21. In other words, the memory 21 stores image data of interference fringes generated by the reflected light from the tilted reference surface 15 and the reflected light reflected by the measurement target surface 30A. At this time, the propagation distance of light reflected by the reference surface 15 (twice L ₁ ) varies regularly at the reflection position on the reference surface 15. Therefore, the height flat portion of the object surface 30A, the propagation distance is reflected back by the object surface 30A reflected light (double L _2), since there is no variation in the measured position by the CCD camera 19 Interference fringes in the captured image appear spatially and regularly in the imaging surface in accordance with the direction and angle of inclination of the reference surface 15. This interference fringe has a difference between the propagation distance of light reflected by the reference surface 15 (twice L ₁ ) and the propagation distance of reflected light reflected by the measurement target surface 30A (twice L ₂ ) by λ / 2 = Appears for one period for every 300 nm.

  On the other hand, as shown in FIG. 1, at the portion where the height of the measurement target surface 30 </ b> A changes, an irregular fringe pattern in which the interference fringes are shifted appears.

  This process corresponds to the first process in the present invention.

<Step S2> Acquisition of Interference Light Intensity Value Group The CPU 20 captures from the image data the intensity value of each pixel captured and stored in the memory 21, that is, the intensity value of the interference light on the measurement target surface 30A. At this time, as shown in FIG. 4, the spatial phase of the interference fringes is shifted (for example, in the x-axis direction in the present embodiment of FIG. 4) at the location where the height of the measurement target surface 30 </ b> A and the convex portion 30 </ b> B changes. It appears as an irregular stripe pattern (refer to the vicinity of the 200th pixel and the vicinity of the 330th pixel in FIG. 4).

  This process corresponds to the second process in the present invention.

<Step S3> Carrier Frequency Estimation The frequency estimation unit 28 of the CPU 20 uses, for a plurality of pixels in the screen of the measurement target surface 30A, intensity values of a plurality of pixels in a neighboring region including the pixel, and interference fringes in the region. A local phase shift amount between the waveform and the assumed sine wave function of an arbitrary frequency is obtained, and the frequency of the observation data is estimated based on a phase gradient obtained from the phase shift amount in a plurality of pixels.

  Specifically, first, the phase at an arbitrary pixel in the screen is obtained by the following method. The intensity value of the interference fringe light in each pixel is expressed by the following equation (1). Here, for ease of explanation, a one-dimensional case in the x-axis direction will be described.

  g (x) = a (x) + b (x) cos {2πfx + φ (x)} (1)

  Here, x represents the position coordinate of the pixel in the x-axis direction, and in particular, the pixel at this x position may be referred to as the target pixel. Further, a (x) is a direct current component included in the interference fringe waveform, b (x) is an alternating current component included in the interference fringe waveform (hereinafter referred to as “alternating current amplitude” as appropriate), f Is the spatial frequency of the interference fringe g (x) in the x-axis direction, and φ (x) is the phase. The frequency f is constant in the screen, and it is assumed that the approximate value is known from the visual count of the number of fringes and the design value of the optical system.

  Next, a method for obtaining a phase from luminance (light intensity) information at two points of a target pixel and a pixel adjacent thereto will be described. Since the adjacent pixels are shifted from the target pixel by a minute distance Δx in the x-axis direction, the light intensity value of the interference fringes is expressed by the following equation (2).

  g (x + Δx) = a (x + Δx) + b (x + Δx) cos {2πf * (x + Δx) + φ (x + Δx)} (2)

  Here, in the present embodiment, since the pitch between the pixel of interest and the adjacent pixel is a minute distance, it is assumed that the DC component, AC amplitude, and phase included in the interference fringe across each pixel are equal, and the following equation ( The relational expressions 3) to (5) are used.

a (x) = a (x + Δx) = a (3)
b (x) = b (x + Δx) = b (4)
φ (x) = φ (x + Δx) = φ (5)
Here, a, b, and φ are constants.

  Assuming the above (3) to (5), the expressions (1) and (2) can be replaced as the following expressions (1a) and (2a).

  g (x) = a + bcos {2πfx + φ} (1a)

  g (x + Δx) = a + bcos {2πf * (x + Δx) + φ} (2a)

  Next, G (x) and G (x + Δx) are defined as the following equations (6) and (7), respectively.

  G (x) = g (x) −a (6)

  G (x + Δx) = g (x + Δx) −a (7)

  Next, the following equations (8) and (9) are obtained by the equations (6) and (7), the equations (1a) and (2a), and the addition theorem of the cos function.

G (x) = bcos (2πfx + φ)
= B {cos (2πfx) cosφ−sin (2πfx) sinφ}} (8)

G (x + Δx) = bcos {2πf * (x + Δx) + φ}
= B [cos {2πf * (x + Δx)} cosφ−sin {2πf * (x + Δx)} sinφ]] (9)

  Next, these equations (8) and (9) are represented by a matrix (10).

なお、Ａは、次のように表される。

A is expressed as follows.

ここで、行列（１０）の左辺からＡの逆行列を掛けて展開することにより、次式（１１）、（１２）が得られる。

Here, the following equations (11) and (12) are obtained by multiplying the left side of the matrix (10) by the inverse matrix of A and expanding it.

これら上記式（１１）、（１２）を利用し、次式（１５）を得ることができる。

By using these equations (11) and (12), the following equation (15) can be obtained.

なお、ｎ′は、整数である。

Note that n ′ is an integer.

  Here, the CPU 20 further includes a code determination unit 26, and the code determination unit 26 refers to the code information of sinφ and cosφ. If this code information is used, the existence range of φ can be expanded from π to 2π from the combination of the codes of sinφ and cosφ. FIG. 5 is a specific diagram for specifying the range of φ with reference to the sign information of sin φ and cos φ as shown in equation (15). Therefore, using the sign information of sinφ and cosφ, equation (15) can be expressed by the following equation (16).

なお、nは、整数である。

Note that n is an integer.

  Therefore, the phase φ can be obtained from Equation (16) from G (x), G (x + Δx) and the spatial frequency f of the interference fringe waveform. Since G (x) and G (x + Δx) are composed of the luminance information g (x) and g (x + Δx) of the pixel and the DC component a of the interference fringe waveform from the equations (6) and (7), g (x ) And g (x + Δx), the direct current component a of the interference fringe waveform, and the spatial frequency f of the interference fringe waveform, φ can be obtained by equation (16). g (x) and g (x + Δx) can be obtained as luminance information of the pixel of the CCD camera 19. a can be obtained by, for example, a method of obtaining the average value of the luminance of all the pixels observed by the CCD camera 19, a method of obtaining the average value of the neighboring pixels of the phase calculation target pixel, or a method of measuring the reflectance in advance. . If luminance information of three or more points is used, the phase can be obtained by solving simultaneous equations with the direct current component a as an unknown numerical value.

  The estimation of the frequency is as follows based on the phase gradient obtained from the phase shift amount in the plurality of pixels by obtaining the phase (hereinafter referred to as phase shift amount) in the plurality of pixels in the screen by the above method. It is carried out.

For ease of explanation, considering the one-dimensional case, the x-axis direction will be described first. It is assumed that the model signal having the frequency f ₀ is fitted (adapted) to the observation data having the true frequency f. In this case, the observation data is g (x) = Acos (2πfx + φ (x))
If the model signal is g ′ (x) = Acos (2πf ₀ x + φ ′ (x)), 2πfx + φ (x) = 2πf ₀ x + φ ′ (x) is established.
Therefore, φ ′ (x) = 2π (f−f ₀ ) x + φ (x) (* 1)
It is.
Here, by taking a linear region in which the value of φ can be regarded as constant and differentiating the equation (* 1) with respect to the x-axis direction, the frequency estimation equation shown in the following equation is obtained.
f = f ₀ + (dφ ′ (x) / dx) / 2π
This frequency estimation equation is based on the phase gradient (dφ ′ (x) / dx) for the partial phase shift amount between the observation data and the model signal and the observation data based on the frequency (f ₀ ) of the model signal. This means that the frequency can be estimated.

  The simplest example using this method is to obtain a phase gradient from each phase at two points, but it is also possible to perform more accurate estimation by applying a straight line to each phase at three or more points.

  This process corresponds to the third process of the present invention.

<Step S4> Calculation of Phase in Pixel Unit Using the frequency obtained in step S3, the phase calculation unit 25 of the CPU 20 sets the phase in each pixel to be calculated on the measurement target surface 30A to the phase described in step S3. Calculate in the same way as the calculation. That is, in the measurement target pixel in the screen, using the intensity values of a plurality of neighboring pixels including the pixel, the interference fringe waveform and the frequency in the region are the estimated frequencies obtained in the previous step, and the direct current component Then, the phase of each pixel is obtained from an AC amplitude and a sinusoidal function assuming that the phase is constant.

  This process corresponds to the fourth process of the present invention.

<Step S5> Calculation of surface height in units of pixels The CPU 20 substitutes the phase φ (x) of the pixel to be calculated calculated from the above equation (16) into the following equation (17) to obtain the height z (x). Ask.

Here, z ₀ is the reference height of the measurement object 30.

  This process corresponds to the fifth process in the present invention.

<Step S6> Completion of calculation for all pixels?
CPU20 repeats the process of step S4-S5 until calculation of a phase and height is complete | finished about all the pixels, and calculates | requires a phase and surface height.

<Step S7> Display of Surface Shape The image data creation unit 27 of the CPU 20 creates a display image of the measurement target surface 30A from the calculated surface height information. Then, based on the information created by the image data creation unit 27, the CPU 20 displays information on the surface height of the measurement object 30 on the monitor 23 as shown in FIG. A three-dimensional or two-dimensional image based on the height information is displayed. The operator can grasp the concavo-convex shape on the surface of the measurement target surface 30A by observing these displays. Thus, the measurement process of the surface shape of the measurement target surface 30A is completed.

  This process corresponds to the sixth process in the present invention.

  As described above, in the process of calculating the intensity value of the interference fringe light for each pixel and the intensity values of a plurality of neighboring pixels from the image data captured by the CCD camera 19, the direct current included in the interference fringe waveform of each pixel is calculated. The simultaneous comparison is performed assuming that the component a (x), the AC amplitude b (x), and the phase φ (x) are equal for each pixel, thereby canceling the DC component and the AC amplitude of the interference fringes in each pixel. be able to.

  According to the embodiment of the present invention, a partial phase shift amount between the observation data and the assumed arbitrary frequency sinusoidal function is obtained, and based on the phase gradient for the phase shift amount, the observation data Estimate the frequency. That is, since it is not necessary to use complicated arithmetic processing such as the Prony method or Fourier transform, the calculation load is reduced and the work efficiency can be improved. In the calculation of the frequency estimation, it is only necessary to obtain the phase of at least two points and obtain the slope of the phase of the two points, and obviously the calculation load can be reduced.

  The present invention is not limited to the embodiment described above, and can be modified as follows.

  That is, in the above embodiment, the height of the measurement target surface 30A is obtained using the intensity value of the interference light of one pixel adjacent to the pixel to be calculated. The height of the measurement target surface 30A may be obtained from a total of three or more pixels by using more than one pixel.

Regarding the frequency estimation in step S3, in the above description, only the x-axis direction has been described, but the above method can be extended to two dimensions. That is, the frequencies in the observation data in the x-axis direction and the y-axis direction are f _x and f _y , the frequencies in the model signal in the x-axis direction and the y-axis direction are f _x0 and f _y0 , respectively, and the observation data is g If (x, y) = A cos (2πf _x x + 2π f _y y + φ (x, y)) and the model signal is g ′ (x, y) = A cos (2πf _x0 x + 2πf _y0 y + φ ′ (x, y)), then 2 In terms of dimensions, the expression corresponding to the expression (* 1) is as follows.
φ ′ (x, y) = 2π (f _x -f _x0 ) x + 2π (f _y -f _y0 ) y + φ (x, y)
... (* 1a)
Here, by taking a plane region in which the value of φ (x, y) can be regarded as constant and differentiating the formula (* 1a) with respect to the x-axis direction and the y-axis direction, the frequency estimation formula shown in the following formula is obtained.
f _x = f _x0 + (dφ ′ (x, y) / dx) / 2π
f _y = f _y0 + (dφ ′ (x, y) / dy) / 2π
Note that dφ ′ (x, y) / dx and dφ ′ (x, y) / dy are phase gradients in the x-axis direction and the y-axis direction, respectively. This frequency estimation formula represents that the frequencies in the x-axis direction and the y-axis direction can be estimated simultaneously using the phases obtained at two or more points with different x and y. This method has a feature that two-dimensional frequency estimation can be performed with high accuracy regardless of the frequency and direction of interference fringes.

  Next, the frequency estimation process performed in step S3 will be specifically described with reference to an example using theoretical data. In the following first and second embodiments, the case of estimating the frequency of a sinusoidal periodic signal using the method of the present invention will be described as an example. In the third and fourth embodiments, a case where the frequency of a periodic fringe image is estimated using the method of the present invention will be described as an example.

  The first embodiment corresponds to the frequency estimation of claims 1, 2, 6, 7, 10, 11, 15 and 16. This example was performed for one dimension in the x-axis direction.

Frequency estimation was performed using a cosine wave signal with a frequency = 0.0100 (/ pixel), a DC component = 1.0000, an amplitude = 1.0000, and an initial phase = 0.0000 created by a computer. FIG. 7 shows the observed value and model signal waveform when the predicted frequency value f _{0 is} 0.0090 (/ pixel). The horizontal axis is the horizontal direction of the image captured by the television camera, and the unit is a pixel. This can be handled in the same way even if the horizontal axis is time and the unit is sec.

  A model signal is fitted to an observation value in the vicinity of a certain point, and the phase at that point is obtained. FIG. 8 shows the phase of each pixel when the number of data used for fitting is 25 and the used data area is sequentially changed in the x-axis direction. It can be said that this phase value represents the “phase shift” between the observed value and the model signal.

  When a straight line is fitted to the data shown in FIG. 8, a phase gradient = 0.628283 is obtained as shown in FIG.

Therefore, the frequency is
f = f ₀ + (dφ ′ (x) / dx) / 2π
= 0.0090 + 0.00628 / 2π
= 0.0100
The correct frequency was obtained.

  When frequency estimation is performed again using this frequency as an initial value, the signal waveform and phase are as shown in FIGS. 10 and 11, and the phase gradient is zero. That is, it was confirmed that the frequency estimation value was correct. In this embodiment, since the initial phase is set to zero, the phase value in FIG. 11 is zero. However, even when the initial phase is not zero, the phase value is constant and the phase gradient is zero. There is no problem in estimation.

  In the first embodiment, the phase calculation is performed for all the pixels. However, in order to obtain the phase gradient, the phase calculation may be performed for at least two pixels.

  The second embodiment relates to frequency estimation when unwrapping is necessary, and corresponds to claims 3, 4, 12, and 13. In this example, it is assumed that the unwrapping mode is selected.

When the difference between the frequency predicted value and the observed frequency is large, the phase gradient increases, and a phase jump occurs as shown by the broken line in FIG. This is because the phase calculation result can be obtained only in the interval of ± π. In this case, the correct phase gradient can be obtained by the following measures.
(1) Method by unwrapping: A phase jump is detected, and 2π is added to or subtracted from the phase value so that the jump is eliminated. The phase after unwrapping is as shown by the solid line in FIG. 12, and a correct phase gradient can be obtained.
(2) Method of reducing phase gradient calculation section: A section that does not include a jump is selected and a gradient is calculated.

  The third embodiment relates to frequency estimation when the origin shift mode is selected, and corresponds to claims 5 and 14. A third embodiment will be described with reference to FIGS. The following points are different from the unwrapping mode. That is, in the origin shift mode, when the frequency is estimated, the coordinate origin is shifted so that the vicinity of the maximum luminance value in the observation data coincides with the maximum value of the model signal as shown in FIG. Fitting is performed, and the phase φ ′ (x, y) of each point is calculated. As a result, the phase φ ′ (x, y) of each point becomes zero near the coordinate origin, as shown in FIG. That is, since the required phase is centered at zero, the possibility of exceeding ± π is reduced. This rough estimation is performed in a plurality of small areas, and the average value of the obtained frequencies is used as an initial value to perform frequency estimation in a wide area. As a result, unwrapping can be eliminated and calculation time can be shortened.

  When the origin shift mode is used, the procedure for eliminating the jump, that is, the procedure for adding / subtracting 2π to the phase value is not required. This corresponds to n = 0 in the equation (16). In equation (16), n wrapping determines n so as not to jump while looking at adjacent pixels, and n is 0, and the origin shift is to limit the phase between −π and + π. I can say that. On the other hand, FIG. 23 shows fitting that does not use the origin shift mode (when unwrapping calculation is required). In the fitting that does not use the origin shift mode, when the frequency is estimated, as shown in FIG. 23A, the fitting is performed in a state where the vicinity of the maximum luminance value in the observation data does not match the maximum value of the model signal. And the phase φ ′ (x, y) of each point may be calculated. In this case, as shown in FIG. 23B, the phase φ ′ (x, y) of each point does not become zero near the coordinate origin, and as a result, the obtained phase exceeds ± π. There is.

  The fourth embodiment relates to frequency estimation for diagonal stripes formed two-dimensionally, and corresponds to claims 8 and 17. Embodiment 4 will be described with reference to FIGS. 13, 14, 15, 16, and 21.

Assuming that the observed value is a signal created by a computer as follows, frequency estimation was performed on this signal. That is, the observed value, the frequency f _{x =} 0.1000 for x-axis direction (/ pixel), the frequency of the y-axis direction f _{y =} 0.1000 (/ pixel), the DC component = 1.0000, amplitude = 1.0000, the initial phase = 0.0000 The cos wave signal. A two-dimensional periodic fringe image (that corresponds to g (x, y)) of this observation value signal is shown in FIG. On the other hand, the model signal is a sinusoidal signal having a frequency predicted value f _x0 = 0.11 (/ pixel) and a frequency predicted value f _y0 = 0.0900 (/ pixel). FIG. 13B shows a two-dimensional sinusoidal image of this model signal (that is, corresponding to g ′ (x, y)).

  A two-dimensional sinusoidal image was fitted to the two-dimensional periodic fringe image, and the phase difference was obtained. FIG. 14 shows the phase difference of each pixel when the number of data used for fitting is 3 × 3 (see FIG. 21) and the use data area is sequentially changed in the x-axis direction and the y-axis direction. It can be said that this phase value represents the “phase shift” between the observed value and the model signal.

  When a straight line is fitted using the method of least squares for each of the x-axis direction and the y-axis direction of the data in FIG. 14, the phase gradient = −0.0628 is obtained in the x-axis direction as shown in FIG. . For the y-axis direction, a phase gradient = 0.0628 is obtained as shown in FIG.

Therefore, the frequency is
f _x = f _x0 + (dφ ′ (x, y) / dx) / 2π
= 0.1100-0.0628 / 2π
= 0.1000
f _y = f _y0 + (dφ ′ (x, y) / dy) / 2π
= 0.0900 + 0.0628 / 2π
= 0.1000
The correct frequency was obtained. As shown in FIG. 16B, the estimated image is a two-dimensional periodic fringe image of the observation value signal shown in FIG. 13A (in order to facilitate the comparison between them, FIG. 13 (A) shows the same image). In the third embodiment, the frequencies in two directions can be estimated simultaneously by one process.

  The fifth embodiment relates to frequency estimation for vertical stripes formed in two dimensions, and corresponds to claims 8 and 17. Embodiment 5 will be described with reference to FIGS. 17, 18, 19, 20, and 21.

Assuming that the observed value is a signal created by a computer as follows, frequency estimation was performed on this signal. That is, the observed value, the frequency f _{x =} 0.1000 for x-axis direction (/ pixel), the frequency of the y axis direction f _{y =} 0.0000 (/ pixel), the DC component = 1.0000, amplitude = 1.0000, the initial phase = 0.0000 The cos wave signal. A two-dimensional periodic fringe image (that corresponds to g (x, y)) of this observation value signal is shown in FIG. On the other hand, the model signal is a sinusoidal signal having a frequency prediction value f _x0 = 0.0900 (/ pixel) and a frequency prediction value f _y0 = 0.0100 (/ pixel). FIG. 17B shows a two-dimensional sinusoidal image of this model signal (ie, corresponding to g ′ (x, y)).

  A two-dimensional sinusoidal image was fitted to the two-dimensional periodic fringe image, and the phase difference was obtained. FIG. 18 shows the phase difference of each pixel when the number of data used for fitting is 3 × 3 (see FIG. 21) and the use data area is sequentially changed in the x-axis direction and the y-axis direction. It can be said that this phase value represents the “phase shift” between the observed value and the model signal.

  When a straight line is fitted using the method of least squares in each of the x-axis direction and the y-axis direction of the data in FIG. 18, the phase gradient = 0.0628 is obtained in the x-axis direction as shown in FIG. For the Y-axis direction, phase gradient = −0.0628 is obtained as shown in FIG.

Therefore, the frequency is
f _x = f _x0 + (dφ ′ (x, y) / dx) / 2π
= 0.0900 + 0.0628 / 2π
= 0.1000
f _y = f _y0 + (dφ ′ (x, y) / dy) / 2π
= 0.0100-0.0628 / 2π
= 0.0000
The correct frequency was obtained. As shown in FIG. 20B, the estimated image is a two-dimensional periodic fringe image of the observation value signal shown in FIG. 17A (in order to facilitate comparison between the two, FIG. 17 (A) shows the same image).

  When frequency estimation is performed again using this frequency as an initial value, the signal waveform and phase are as shown in FIGS. 10 and 11, and the phase gradient is zero. That is, it was confirmed that the frequency estimation value was correct. In Example 4, it was shown that estimation is possible even if the frequency in one of the x-axis direction and the y-axis direction is zero.

DESCRIPTION OF SYMBOLS 1 Optical system unit 2 Control system unit 10 White light source 11 Collimating lens 12 Band pass filter 13 Half mirror 14 Objective lens 15 Reference surface 17 Beam splitter 18 Imaging lens 19 CCD camera 20 CPU
DESCRIPTION OF SYMBOLS 21 Memory 22 Input part 23 Monitor 24 Drive part 25 Phase calculation part 26 Code | symbol determination part 27 Image data creation part 28 Frequency estimation part 30 Measurement object 30A Measurement object surface 30B Convex part of measurement coping surface

Claims (26)

A frequency estimation method for estimating the frequency in periodic observation data such as interference fringes and electrical signals,
Obtaining observation data; and
Fitting a hypothetical arbitrary frequency sinusoidal function as a model signal to the observed data;
Obtaining a partial phase shift amount between the observation data and the model signal;
Calculating a frequency of the observation data based on a frequency of the model signal and a phase gradient with respect to the phase shift amount.   2. The frequency estimation method according to claim 1, wherein the phase shift amount is calculated by applying partial observation data to a sinusoidal function of an assumed arbitrary frequency by a least square method. .   3. The frequency estimation method according to claim 2, wherein phase connection is made in advance at the order jump boundary of the phase shift amount before calculating the phase gradient for the phase shift amount.   3. The frequency estimation method according to claim 2, wherein the phase gradient is calculated while avoiding the order jump boundary of the phase shift amount when calculating the phase gradient for the phase shift amount.   3. The frequency estimation method according to claim 1, wherein the coordinate origin is shifted so that the observation data is adapted to the model signal so that the maximum value in the observation data matches the maximum value of the model signal. Frequency estimation method.   6. The frequency estimation method according to claim 3, wherein the phase gradient calculation method for the phase shift amount is obtained by approximating a linear line by least square method to two or more phase shift amounts. A frequency estimation method characterized by the above. In frequency estimation method according to any one of claims 1 to 6, determined like frequency (f) is the frequency of the sinusoidal function of any frequency which is assumed as f _0, the phase slope of the phase shift amount d.phi ' (X) / dx, and a frequency estimation method characterized by obtaining from an equation of f = f ₀ + (dφ ′ (x) / dx) / 2π. The frequency estimation method according to any one of claims 1 to 7, wherein the observation data includes a two-dimensional periodic fringe image, the sine wave function includes a two-dimensional sinusoidal image, and the two-dimensional period. A frequency estimation method, wherein the fringe image frequency (f _x , f _y ) is obtained from the following equation.
f _x = f _x0 + (dφ ′ (x, y) / dx) / 2π
f _y = f _y0 + (dφ ′ (x, y) / dy) / 2π
Here, x and y are the two axes of the orthogonal coordinate system, the frequency in the x-axis direction of the assumed arbitrary sine wave function is f _x0, and the frequency in the y-axis direction of the assumed arbitrary sine wave function F _y0 and the phase gradient in the x-axis direction between the two-dimensional periodic fringe image and the two-dimensional sinusoidal image as dφ ′ (x, y) / dx, and the two-dimensional periodic fringe image and the two-dimensional sine The phase gradient in the y-axis direction with respect to the wave image is dφ ′ (x, y) / dy.   9. The frequency estimation method according to claim 1, wherein the estimation calculation is repeated by using the estimated frequency as a new sinusoidal function frequency. A frequency estimation device for estimating the frequency in periodic observation data such as interference fringes and electrical signals,
Acquisition means for acquiring observation data;
An assumed sine wave function having an arbitrary frequency is adapted as a model signal to the observation data, a partial phase shift amount between the observation data and the model signal is obtained, and the frequency of the model signal and the phase shift amount And a calculation means for calculating the frequency of the observation data based on the phase gradient of the frequency estimation apparatus.   The frequency estimation apparatus according to claim 10, further comprising a calculation unit that calculates the amount of phase shift by applying partial observation data to a sine wave function of an assumed arbitrary frequency by a least square method. Frequency estimation device.   12. The frequency estimation apparatus according to claim 11, further comprising a calculation unit that performs phase connection at an order jump boundary of the phase shift amount in advance before calculating a phase gradient for the phase shift amount. Estimating device.   13. The frequency estimation apparatus according to claim 12, further comprising an arithmetic unit that calculates the phase gradient while avoiding the order jump boundary of the phase shift amount when calculating the phase gradient for the phase shift amount. Frequency estimation device.   12. The frequency estimation apparatus according to claim 10, wherein the coordinate origin is shifted so that the observation data is adapted to the model signal so that the maximum value in the observation data matches the maximum value of the model signal. Frequency estimation device.   16. The frequency estimation apparatus according to claim 12, wherein the phase gradient calculation means for the phase shift amount is obtained by approximating a linear line by least square method to two or more phase shift amounts. A frequency estimation device comprising a calculation means. The frequency estimation apparatus according to any one of claims 10 to 15, wherein the frequency (f) is a frequency of an assumed arbitrary frequency sinusoidal function f _0, and a phase gradient with respect to a phase shift amount is dφ ′ (x ) / Dx, a frequency estimation apparatus comprising a calculating means for obtaining from the formula f = f ₀ + (dφ ′ (x) / dx) / 2π. 17. The frequency estimation apparatus according to claim 10, wherein the observation data is a two-dimensional periodic fringe image, the sinusoidal function is a two-dimensional sinusoidal image, and the two-dimensional periodic fringe image. The frequency estimation device is characterized in that the frequency (f _x , f _y ) is obtained from the following equation.
f _x = f _x0 + (dφ ′ (x, y) / dx) / 2π
f _y = f _y0 + (dφ ′ (x, y) / dy) / 2π
Here, x and y are the two axes of the orthogonal coordinate system, the frequency in the x-axis direction of the assumed arbitrary sine wave function is f _x0, and the frequency in the y-axis direction of the assumed arbitrary sine wave function F _y0 and the phase gradient in the x-axis direction between the two-dimensional periodic fringe image and the two-dimensional sinusoidal image as dφ ′ (x, y) / dx, and the two-dimensional periodic fringe image and the two-dimensional sine The phase gradient in the y-axis direction with respect to the wave image is dφ ′ (x, y) / dy.   18. The frequency estimation apparatus according to claim 10, further comprising a calculation unit that repeats estimation calculation using the estimated frequency as a frequency of a sinusoidal function having an arbitrary frequency. Based on the intensity value of the interference fringes generated by the reflected light that irradiates the measurement target surface and the reference surface through the branching means with light output from the light source, reflects from both the measurement target surface and the reference surface, and returns on the same optical path In the surface shape measurement method to obtain the surface height and surface shape of the measurement target surface,
A first step of acquiring an image of interference fringes generated in a state where the reference surface is arranged in an obliquely inclined posture at an arbitrary angle with respect to the traveling direction of light;
A second step of obtaining an interference fringe intensity value of each pixel in the acquired image;
From the acquired intensity value of the interference fringes, a third process of estimating the carrier frequency due to the oblique inclination posture of the reference surface;
For each pixel, using the estimated frequency or the frequency estimated in advance and using an expression for obtaining an interference fringe waveform, the intensity value of each pixel and the intensity values of a plurality of neighboring pixels , And assuming that the DC component, AC amplitude, and phase of the interference fringe waveform in these pixels are equal, a fourth process for obtaining the phase of each pixel;
A fifth step of obtaining the surface height of the measurement target surface imaged from the obtained phase of each pixel;
A sixth step of obtaining a surface shape from the obtained surface height of the measurement target surface;
A method for measuring a surface shape, comprising:   The surface shape measurement method according to claim 19, wherein the frequency of the acquired interference fringe image is estimated using the frequency estimation method according to claim 1. Measuring method. Based on the intensity value of the interference fringes generated by the reflected light that irradiates the measurement target surface and the reference surface through the branching means with light output from the light source, reflects from both the measurement target surface and the reference surface, and returns on the same optical path In the surface shape measuring device to obtain the surface height and surface shape of the measurement target surface,
The reference surface is arranged in an obliquely inclined posture at an arbitrary angle with respect to the traveling direction of light,
Imaging means for imaging the measurement target surface by generating interference fringes by reflected light that is irradiated with the light and reflected from the measurement target and the reference surface and returns on the same optical path;
Sampling means for capturing the measured measurement target surface as an interference fringe intensity value for each pixel;
Storage means for storing an interference fringe intensity value group that is the intensity value captured by the sampling means;
The intensity value is read for each pixel from the intensity value group stored in the storage means, the carrier frequency according to the oblique inclination posture of the reference surface is estimated, and the estimated frequency or the frequency estimated in advance is used. Using the intensity value of each pixel and the intensity value of the neighboring pixel for each pixel, and assuming that the DC component, AC amplitude, and phase of the interference fringe waveform included in each pixel are equal, and the interference fringe waveform Obtain the phase of each pixel using the obtained expression, obtain the surface height of the measurement target surface imaged from the obtained phase of each pixel, and further, from the obtained surface height of the measurement target surface A computing means for obtaining a surface shape;
A surface shape measuring apparatus comprising:   The surface shape measuring device according to claim 21, comprising the frequency estimating device according to any one of claims 10 to 16, wherein the surface shape measuring device estimates the frequency of the acquired interference fringe image. Surface shape measurement that calculates the surface height and surface shape of the measurement target surface based on the intensity value of the interference fringes generated by the measurement target surface by projecting a lattice image of the light output from the light source through the lattice onto the measurement target surface In the method
A first step of acquiring an image of interference fringes on the measurement target surface;
A second step of obtaining an interference fringe intensity value of each pixel in the acquired image;
From the acquired intensity value of the interference fringes, a third process of estimating the carrier frequency due to the oblique inclination posture of the reference surface;
For each pixel, using the estimated frequency or the frequency estimated in advance and using an expression for obtaining an interference fringe waveform, the intensity value of each pixel and the intensity values of a plurality of neighboring pixels , And assuming that the DC component, AC amplitude, and phase of the interference fringe waveform in these pixels are equal, a fourth process for obtaining the phase of each pixel;
A fifth step of obtaining the surface height of the measurement target surface imaged from the obtained phase of each pixel;
A sixth step of obtaining a surface shape from the obtained surface height of the measurement target surface;
A method for measuring a surface shape, comprising:   The surface shape measurement method according to claim 23, wherein the frequency of the acquired interference fringe image is estimated using the frequency estimation method according to any one of claims 1 to 9. Measuring method. A surface shape measuring device that projects light from a light source onto a measurement target surface via a grating and obtains the surface height and surface shape of the measurement target surface based on the intensity value of interference fringes generated by the measurement target surface In
An imaging means for imaging an image of the interference fringes on the measurement target surface;
Sampling means for capturing the measured measurement target surface as an interference fringe intensity value for each pixel;
Storage means for storing an interference fringe intensity value group that is the intensity value captured by the sampling means;
The intensity value is read for each pixel from the intensity value group stored in the storage means, the carrier frequency according to the oblique inclination posture of the reference surface is estimated, and the estimated frequency or the frequency estimated in advance is used. Using the intensity value of each pixel and the intensity value of the neighboring pixel for each pixel, and assuming that the DC component, AC amplitude, and phase of the interference fringe waveform included in each pixel are equal, and the interference fringe waveform Obtain the phase of each pixel using the obtained expression, obtain the surface height of the measurement target surface imaged from the obtained phase of each pixel, and further, from the obtained surface height of the measurement target surface A computing means for obtaining a surface shape;
A surface shape measuring apparatus comprising:   The surface shape measuring device according to claim 25, comprising the frequency estimating device according to any one of claims 10 to 18, wherein the surface shape measuring device estimates the frequency of the acquired interference fringe image.

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