JP2006349590A - Three-dimensional measuring device, three-dimensional measuring method and three-dimensional measuring program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a three-dimensional measuring device, capable of removing harmonic waves contained in a deformed lattice fringe image by projecting a binary pattern to a measuring object. <P>SOLUTION: This device comprises: an imaging device 350 taking a plurality of deformed lattice fringe images formed by projecting the binary pattern of contrast to the measuring object; a light intensity acquisition part 310 acquiring a plurality of light intensity functions from the plurality of deformed lattice fringe images; a cosine function calculation part 412 calculating a plurality of cosine functions; a sine function calculation part 421 calculating a plurality of sine functions by multiplying the plurality of light intensity functions by a trigonometric function with a phase difference obtained by subtracting a value of moire phase from 90°; a harmonic wave removing part 411 calculating a real function that is the sum of the plurality of cosine functions and an imaginary function that is the sum of the plurality of sine functions and removing harmonic waves contained in a plurality of sine and cosine functions; and a height calculation part 316 calculating the height of the measuring object from moire phases extracted from the imaginary function and the real function. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a three-dimensional measurement technique, and more particularly to a three-dimensional measurement apparatus, a three-dimensional measurement method, and a three-dimensional measurement program for measuring the height of an object surface.

There is a lattice projection type moire method as a method for measuring the three-dimensional shape of an object to be measured. In the “grid projection type moire method”, first, a lattice pattern having a sinusoidal transmittance distribution is projected onto an object to be measured (see, for example, Non-Patent Document 1). Further, a moire is generated by multiplying the deformed lattice image obtained by projecting the lattice pattern onto the object to be measured by a virtual lattice model in the computer (see, for example, Non-Patent Document 2). However, it is difficult to form a lattice pattern having a sinusoidal transmittance distribution on a mask substrate, and the manufacturing cost is high. Therefore, a simple lattice projection type moire method using a mask substrate provided with a lattice pattern (hereinafter referred to as a binary pattern) having a rectangular transmittance distribution is often employed. It is easy to manufacture a binary pattern on a mask substrate, and the manufacturing cost is low. However, since the grating projection type moire method is premised on the projection of a grating pattern having a sinusoidal transmittance distribution, if a binary pattern is projected onto an object to be measured, the deformation grating image contains harmonics, resulting in a measurement error. was there.
Toru Yoshizawa, “Lattice pattern projection type 3D measurement system”, 3D optics, Volume 1, Optical Technology Communications, 1993, p. 83-99 Junichi Kato and Ichiro Yamaguchi, “Real-time processing of fringe images using phase shift electronic moire”, Sensor Technology, Vol. 12, No. 7, 1992, p. 39-44

  Provided are a three-dimensional measurement apparatus, a three-dimensional measurement method, and a three-dimensional measurement program capable of removing measurement errors based on harmonics contained in a deformed lattice image by projecting a binary pattern onto a measurement object.

  In order to achieve the above object, the first feature of the present invention is: (a) an imaging device that captures a plurality of deformed grid images formed by projecting a binary pattern onto an object to be measured; and (b) a plurality of deformations. A light intensity acquisition unit for acquiring a plurality of light intensity functions from the lattice image, and (c) a moire phase value given to each of the plurality of deformed lattice images by the measured object as a first value, and a plurality of light intensity functions. A cosine function calculator for calculating a plurality of cosine functions by multiplying each of the plurality of light intensity functions by a first trigonometric function having a first value phase difference for each of the The second value is obtained by subtracting the value of, and the plurality of light intensity functions are multiplied by a second trigonometric function having a phase difference of the second value for each of the plurality of light intensity functions. A sine function calculator for calculating the function and (e) the sum of multiple cosine functions Calculating a imaginary part function that is the sum of a real part function and a plurality of sine functions, thereby removing a harmonic contained in each of the plurality of cosine functions and the sine function; and (f) an imaginary part function. And a three-dimensional measurement apparatus including a height calculation unit that calculates the height of the measurement object based on the moire phase extracted from the real part function.

  The second feature of the present invention is that (a) imaging a plurality of deformed lattice images formed by projecting a binary pattern onto an object to be measured, and (b) a plurality of light intensity functions from the plurality of deformed lattice images. And (c) a moiré phase value given to each of the plurality of deformed lattice images by the measured object is a first value, and a phase difference of the first value for each of the plurality of light intensity functions Multiplying each of the plurality of light intensity functions by a first trigonometric function to calculate a plurality of cosine functions, and (d) a value obtained by subtracting the first value from 90 degrees is set as the second value. Multiplying each of the plurality of light intensity functions by a second trigonometric function having a phase difference of a second value for each of the light intensity functions, and (e) a plurality of cosine functions. Real part function that is the sum of imaginary parts and imaginary part that is the sum of multiple sine functions Calculating the function, removing harmonics included in each of the cosine function and sine function, and (f) the moiré phase extracted from the imaginary part function and the real part function, The gist of the present invention is a three-dimensional measurement method including a step of calculating a height.

  A third feature of the present invention is a three-dimensional measurement program for driving and controlling a three-dimensional measurement apparatus that measures the surface shape of the object to be measured. The three-dimensional measurement apparatus uses (a) a binary pattern on the object to be measured. (B) a procedure for acquiring a plurality of light intensity functions from the plurality of modified grid images, and (c) a plurality of modified grid images of the object to be measured. And the first trigonometric function having a phase difference of the first value for each of the plurality of light intensity functions is multiplied by each of the plurality of light intensity functions. And (d) a value obtained by subtracting the first value from 90 degrees is set as the second value, and a second value having a phase difference of the second value with respect to each of the plurality of light intensity functions. Is multiplied by each of the multiple light intensity functions to obtain multiple sine functions. Included in each of the cosine function and sine function by calculating the number and (e) calculating the real part function that is the sum of the cosine functions and the imaginary part function that is the sum of the sine functions. And (f) a three-dimensional measurement program that executes a procedure for calculating the height of the object to be measured based on the moire phase extracted from the imaginary part function and the real part function. The gist.

According to the present invention, it is possible to provide a three-dimensional measurement apparatus, a three-dimensional measurement method, and a three-dimensional measurement program capable of removing a measurement error based on harmonics included in a deformed lattice image by projecting a binary pattern onto a measurement object. It is.

  Embodiments of the present invention will be described below. In the following description of the drawings, the same or similar parts are denoted by the same or similar reference numerals. However, the drawings are schematic. Therefore, specific dimensions and the like should be determined in light of the following description. Moreover, it is a matter of course that portions having different dimensional relationships and ratios are included between the drawings.

  As shown in FIG. 1, the three-dimensional measuring apparatus according to the embodiment of the present invention captures a plurality of deformed lattice images formed by projecting a binary pattern consisting of periodic light and dark on an object to be measured. 350 and a central processing unit (CPU) 400 connected to the imaging device 350. The CPU 400 includes a light intensity acquisition unit 310, a cosine function calculation unit 412, a sine function calculation unit 421, a harmonic removal unit 411, and a height calculation unit 316. The light intensity acquisition unit 310 acquires a plurality of light intensity functions from a plurality of modified lattice images. The cosine function calculating unit 412 sets the moire phase value given to each of the plurality of deformed lattice images by the object to be measured as the first value, and has a first value phase difference with respect to each of the plurality of light intensity functions. A plurality of cosine functions are calculated by multiplying each of the plurality of light intensity functions by one trigonometric function. The sine function calculation unit 421 sets the value obtained by subtracting the first value from 90 degrees as the second value, and sets a plurality of second trigonometric functions having a phase difference of the second value for each of the plurality of light intensity functions. A plurality of sine functions are calculated by multiplying each of the light intensity functions. The harmonic removal unit 411 calculates a real part function that is a sum of a plurality of cosine functions and an imaginary part function that is a sum of a plurality of sine functions, thereby generating a harmonic included in each of the plurality of cosine functions and the sine function. Remove. The height calculation unit 316 calculates the height of the object to be measured based on the moire phase extracted from the imaginary part function and the real part function.

  As shown in FIG. 2, the imaging device 350 includes a light source 10 that irradiates light to the measurement object 5 to be measured, a first lens 11 that converts the light emitted from the light source 10 into parallel light, and parallel light irradiation. Grating 3, the stage 80 on which the object 5 to be measured irradiated with the light transmitted through the grating 3, the second lens 21 for condensing the reflected light from the object 5 to be measured, and the reflected light collected. Spatial filter 23 arranged in the vicinity of the focal point, image sensor 20 that receives reflected light that has passed through spatial filter 23, stage drive unit 42 that moves the arrangement position of stage 80, and grating drive unit that moves the arrangement position of grating 3 With 15.

  Here, a linear light source such as a fluorescent discharge tube, a low-pressure mercury lamp, or a xenon lamp can be used as the light source 10. A cylindrical lens or the like can be used as the first lens 11, and a telecentric lens or the like can be used as the second lens 21. FIG. 3A schematically shows the surface of the grating 3, and the grating 3 has a periodic rectangular transmittance distribution as shown in FIG. 3B. By irradiating the grating 3 with light from the light source 10, a binary pattern consisting of periodic light and dark having a pitch P is projected onto the surface of the object 5 to be measured. A charge coupled device (CCD) camera or the like can be used as the image sensor 20, and the light and darkness of the deformed lattice image formed by the reflected light from the object to be measured 5 is converted into a voltage level by the photoelectric conversion function of the CCD camera. Further, the image sensor 20 transmits a digital image of a deformed lattice image composed of a plurality of pixels arranged in a matrix in the vertical (x) direction and the horizontal (y) direction to the deformed lattice image input unit 309 shown in FIG. To do.

  The CPU 400 further includes an imaging device control unit 200 and a modified grid image input unit 309. The imaging device control unit 200 controls the stage driving unit 42 illustrated in FIG. 2 and the arrangement position of the stage 80 by supplying a control signal and the like to the imaging device 350. Similarly, the grating driving unit 15 is controlled to move the arrangement position of the grating 3 in the periodic pattern direction of the grating 3. Further, the imaging device control unit 200 performs adjustment of the light intensity of the light source 10, control of the shutter speed of the image sensor 20, and the like.

  The deformed grid image input unit 309 shown in FIG. 1 irradiates the grid 3 shown in FIG. 2 arranged at a predetermined position with the light source 10, and the digital image of the measured object 5 captured by the image sensor 20 is a first image This is defined as a deformed lattice image. In addition, the grating 3 is moved by the grating driving unit 15 with respect to the shooting position of the first deformed grating image, and the light and dark pattern on the surface of the object to be measured 5 is moved by an eighth distance of the pitch P. This digital image is defined as a second deformed lattice image. In the same manner, a digital image obtained by sequentially moving the light / dark pattern on the surface of the object to be measured 5 by moving an eighth distance of the pitch P, a third modified lattice image, a fourth modified lattice image, a fifth Are defined as a modified lattice image, a sixth modified lattice image, a seventh modified lattice image, and an eighth modified lattice image, respectively.

The light intensity acquisition unit 310 illustrated in FIG. 1 extracts a plurality of pixels arranged in one column in the x direction from each of the first to eighth modified lattice images formed of a plurality of pixels arranged in a matrix. . Here, each pixel has light intensity data, and the first light intensity function I ₁ (x) of the pixel at the coordinate x extracted from the first deformed lattice image is expressed by the following equation (1). Is done. Similarly, the second light intensity function I ₂ (x) of the pixel at the coordinate x extracted from the second modified lattice image is expressed by the following equation (2) and extracted from the third modified lattice image: The third light intensity function I ₃ (x) of the pixel at the coordinate x is expressed by the following equation (3), and the fourth light intensity function I ₄ (4) of the pixel at the coordinate x extracted from the fourth modified lattice image. x) is expressed by the following equation (4). Further, the fifth light intensity function I ₅ (x) of the pixel at the coordinate x extracted from the fifth modified lattice image is expressed by the following equation (5), and the coordinate x extracted from the sixth modified lattice image: The sixth light intensity function I ₆ (x) of the pixel at is expressed by the following equation (6), and the seventh light intensity function I ₇ (x) of the pixel at the coordinate x extracted from the seventh modified lattice image Is represented by the following equation (7), and the eighth light intensity function I ₈ (x) of the pixel at the coordinate x extracted from the eighth modified lattice image is represented by the following equation (8).

I ₁ (x) = A × {cos (2πx / P + φ (x))-(1/3) cos (3 (2πx / P + φ (x))} + B… (1)
I ₂ (x)
= A × {cos (2πx / P + φ (x) + π / 4)-(1/3) cos (3 (2πx / P + φ (x) + π / 4)} + B (2)
I ₃ (x) = A × {cos (2πx / P + φ (x) + π / 2)-(1/3) cos (3 (2πx / P + φ (x) + π / 2)} + B
=-A × sin (2πx / P + φ (x))-(A / 3) sin (3 (2πx / P + φ (x)) + B… (3)
I ₄ (x)
= A × {cos (2πx / P + φ (x) + 3π / 4)-(1/3) cos (3 (2πx / P + φ (x) + 3π / 4)} + B
=-A × sin (2πx / P + φ (x) + π / 4)-(A / 3) sin (3 (2πx / P + φ (x) + π / 4) + B… (4)
I ₅ (x) = A × {cos (2πx / P + φ (x) + π)-(1/3) cos (3 (2πx / P + φ (x) + π)} + B
=-A × cos (2πx / P + φ (x)) + (A / 3) cos (3 (2πx / P + φ (x)) + B… (5)
I ₆ (x)
= A × {cos (2πx / P + φ (x) + 5π / 4)-(1/3) cos (3 (2πx / P + φ (x) + 5π / 4)} + B
=-A × cos (2πx / P + φ (x) + π / 4) + (A / 3) cos (3 (2πx / P + φ (x) + π / 4) + B… (6)
I ₇ (x)
= A × {cos (2πx / P + φ (x) + 3π / 2)-(1/3) cos (3 (2πx / P + φ (x) + 3π / 2)} + B
= A × sin (2πx / P + φ (x)) + (A / 3) sin (3 (2πx / P + φ (x)) + B… (7)
I ₈ (x)
= A × {cos (2πx / P + φ (x) + 7π / 4)-(1/3) cos (3 (2πx / P + φ (x) + 7π / 4)} + B
= A × sin (2πx / P + φ (x) + π / 4) + (A / 3) sin (3 (2πx / P + φ (x) + π / 4) + B… (8)
Here, A and B are constants, A represents an amplitude, and B represents a bias term. The value A is determined by the optical system such as the first and second lenses 11 and 21 shown in FIG. The value of B is determined by factors such as stray light in addition to the reflectance of the optical system such as a lens and the surface of the object 5 to be measured. φ (x) represents the moiré phase that the measured object 5 gives to each of the first to eighth modified lattice images. In addition, in the formulas (1) to (8), it represents up to the third harmonic. For example, in Equation (1), the first order harmonic A cos (2πx / P + φ (x)) and the third order harmonic-(A / 3) cos (3 (2πx / P + φ (x)) ).

The memory grid storage device 432 shown in FIG. 1 is expressed by the following equations (9) to (16), and each of the memory grid functions S ₁ (x), S ₂ (x) is a trigonometric function having a phase difference of π / 4. , S ₃ (x), S ₄ (x), S ₅ (x), S ₆ (x), S ₇ (x), S ₈ (x).

S ₁ (x) = cos (2πx / P)… (9)
S ₂ (x) = cos (2πx / P + π / 4)… (10)
S ₃ (x) = cos (2πx / P + π / 2) =-sin (2πx / P)… (11)
S ₄ (x) = cos (2πx / P + 3π / 4) =-sin (2πx / P + π / 4)… (12)
S ₅ (x) = cos (2πx / P + π) =-cos (2πx / P)… (13)
S ₆ (x) = cos (2πx / P + 5π / 4) =-cos (2πx / P + π / 4)… (14)
S ₇ (x) = cos (2πx / P + 3π / 2) = sin (2πx / P)… (15)
S ₈ (x) = cos (2πx / P + 7π / 4) = sin (2πx / P + π / 4)… (16)
The cosine function calculation unit 412 multiplies the first light intensity function I ₁ (x) given by the above equation (1) by the memory lattice function S ₁ (x) given by the above equation (9) (17 ) To calculate the first cosine function N ₁ (x). Further, the calculation shown in the following equation (18) is performed by multiplying the second light intensity function I ₂ (x) given by the above equation (2) by the memory lattice function S ₂ (x) given by the above equation (10). To calculate a _second cosine function N ₂ (x). Similarly, the following equation (19) is obtained by multiplying the third light intensity function I ₃ (x) given by the above equation (3) by the memory lattice function S ₃ (x) given by the above equation (11). The calculation and the fourth light intensity function I ₄ (x) given by the above formula ( ₄ ) are multiplied by the memory lattice function S ₄ (x) given by the above formula (12). The calculation and the fifth light intensity function I ₅ (x) given by the above formula ( ₅ ) are multiplied by the memory lattice function S ₅ (x) given by the above formula (13), as shown in the following formula (21) The cosine function calculation unit 412 calculates each of the third cosine function N ₃ (x), the fourth cosine function N ₄ (x), and the fifth cosine function N ₅ (x). Further, the cosine function calculation unit 412 multiplies the sixth light intensity function I ₆ (x) given by the above equation (6) by the memory lattice function S ₆ (x) given by the above equation (14) ( 22) and the following calculation of multiplying the seventh light intensity function I ₇ (x) given by the above formula (7) by the memory lattice function S ₇ (x) given by the above formula (15) ( 23) Multiplying the eighth light intensity function I ₈ (x) given by equation (8) above by the memory lattice function S ₈ (x) given by equation (16) The calculation shown in Equation 24) is performed to calculate each of the sixth cosine function N ₆ (x), the seventh cosine function N ₇ (x), and the eighth cosine function N ₈ (x).

N ₁ (x) = I ₁ (x) × S ₁ (x)
= B × cos (2πx / P)
+ (A / 2) {cos (4πx / P + φ (x)) + cos (φ (x))}
-(A / 6) {cos (8πx / P + 3φ (x)) + cos (4πx / P + 3φ (x))}… (17)
N ₂ (x) = I ₂ (x) × S ₂ (x)
= B × cos (2πx / P + π / 4)
+ (A / 2) {cos (4πx / P + φ (x) + π / 2) + cos (φ (x))}
-(A / 6) {cos (8πx / P + 3φ (x) + π) + cos (4πx / P + 3φ (x) + π / 2)}… (18)
N ₃ (x) = I ₃ (x) × S ₃ (x)
=-B × sin (2πx / P)
-(A / 2) {cos (4πx / P + φ (x))-cos (φ (x))}
-(A / 6) {cos (8πx / P + 3φ (x))-cos (4πx / P + 3φ (x))}… (19)
N ₄ (x) = I ₄ (x) × S ₄ (x)
=-B × sin (2πx / P + π / 4)
-(A / 2) {cos (4πx / P + φ (x) + π / 2)-cos (φ (x))}
-(A / 6) {cos (8πx / P + 3φ (x) + π)-cos (4πx / P + 3φ (x) + π / 2)}… (20)
N ₅ (x) = I ₅ (x) × S ₅ (x)
=-B × cos (2πx / P)
+ (A / 2) {cos (4πx / P + φ (x)) + cos (φ (x))}
-(A / 6) {cos (8πx / P + 3φ (x)) + cos (4πx / P + 3φ (x))}… (21)
N ₆ (x) = I ₆ (x) × S ₆ (x)
=-B × cos (2πx / P + π / 4)
+ (A / 2) {cos (4πx / P + φ (x) + π / 2) + cos (φ (x))}
-(A / 6) {cos (8πx / P + 3φ (x) + π) + cos (4πx / P + 3φ (x) + π / 2)}… (22)
N ₇ (x) = I ₇ (x) × S ₇ (x)
= B × sin (2πx / P)
-(A / 2) {cos (4πx / P + φ (x))-cos (φ (x))}
-(A / 6) {cos (8πx / P + 3φ (x))-cos (4πx / P + 3φ (x))}… (23)
N ₈ (x) = I ₈ (x) × S ₈ (x)
= B × sin (2πx / P + π / 4)
-(A / 2) {cos (4πx / P + φ (x) + π / 2)-cos (φ (x))}
-(A / 6) {cos (8πx / P + 3φ (x) + π)-cos (4πx / P + 3φ (x) + π / 2)}… (24)
As described above, the cosine function calculation unit 412 calculates the memory lattice functions S ₁ (x) to S ₈ for the first term of the first to eighth light intensity functions I ₁ (x) to I ₈ (x). First to eighth cosine functions N ₁ (x) to N ₈ (x) are calculated by multiplying the first trigonometric functions having a phase difference of φ (x) among (x). Here, as shown in the equation (17), the first cosine function N ₁ (x) is the moire component (A / 2) cosφ (x) and the fundamental harmonic B × cos that is the fundamental wave (2πx / P), 2nd harmonic (A / 2) cos (4πx / P + φ (x))-(A / 6) cos (4πx / P + 3φ (x)), and 4th harmonic Wave- (A / 6) cos (8πx / P + 3φ (x)). Further, as shown in the equations (18) to (24), the second to eighth cosine functions N ₂ (x) to N ₈ (x) are also moiré components, and the first, second, and fourth order. Including harmonics.

The sine function calculation unit 421 multiplies the first light intensity function I ₁ (x) given by the above equation (1) by the memory lattice function S ₃ (x) given by the above equation (11), The first sine function O ₁ (x) shown in the following equation (25) is calculated. Further, the calculation shown in the following equation (26) is performed by multiplying the second light intensity function I ₂ (x) given by the above equation (2) by the memory lattice function S ₄ (x) given by the above equation (12). To calculate the _second sine function O ₂ (x). Similarly, the following expression (27) is obtained by multiplying the third light intensity function I ₃ (x) given by the above expression (3) by the memory lattice function S ₅ (x) given by the above expression (13). The following equation (28) is calculated and multiplied by the memory lattice function S ₆ (x) given by the above equation (14) to the fourth light intensity function I ₄ (x) given by the above equation (4). The calculation and the fifth light intensity function I ₅ (x) given by the above formula (5) are multiplied by the memory lattice function S ₇ (x) given by the above formula (15), and the following formula (29) is shown. The sine function calculation unit 421 calculates the third sine function O ₃ (x), the fourth sine function O ₄ (x), and the fifth sine function O ₅ (x). Further, the sine function calculation unit 421 multiplies the sixth light intensity function I ₆ (x) given by the above expression (6) by the memory lattice function S ₈ (x) given by the above expression (16) ( (30) and the seventh light intensity function I ₇ (x) given by equation (7) above is multiplied by the memory lattice function S ₁ (x) given by equation (9) below ( The calculation shown in Equation 31) and the eighth light intensity function I ₈ (x) given in Equation (8) above are multiplied by the memory lattice function S ₂ (x) given in Equation (10) below ( The sixth sine function O ₆ (x), the seventh sine function O ₇ (x), and the eighth sine function O ₈ (x) are calculated by performing the calculation shown in the equation (32). :
O ₁ (x) = I ₁ (x) × S ₃ (x)
=-B × sin (2πx / P)
-(A / 2) {sin (4πx / P + φ (x))-sin (φ (x))}
+ (A / 6) {sin (8πx / P + 3φ (x))-sin (4πx / P + 3φ (x))}… (25)
O ₂ (x) = I ₂ (x) × S ₄ (x)
=-B × sin (2πx / P + π / 4)
-(A / 2) {sin (4πx / P + φ (x) + π / 2)-sin (φ (x))}
+ (A / 6) {sin (8πx / P + 3φ (x) + π)-sin (4πx / P + 3φ (x) + π / 2)}… (26)
O ₃ (x) = I ₃ (x) × S ₅ (x)
=-B × cos (2πx / P )
+ (A / 2) {sin (4πx / P + φ (x)) + sin (φ (x))}
+ (A / 6) {sin (8πx / P + 3φ (x)) + sin (4πx / P + 3φ (x))}… (27)
O ₄ (x) = I ₄ (x) × S ₆ (x)
=-B × cos (2πx / P + π / 4)
+ (A / 2) {sin (4πx / P + φ (x) + π / 2) + sin (φ (x))}
+ (A / 6) {sin (8πx / P + 3φ (x) + π) + sin (4πx / P + 3φ (x) + π / 2)}… (28)
O ₅ (x) = I ₅ (x) × S ₇ (x)
= B × sin (2πx / P)
-(A / 2) {sin (4πx / P + φ (x))-sin (φ (x))}
+ (A / 6) {sin (8πx / P + 3φ (x))-sin (4πx / P + 3φ (x))}… (29)
O ₆ (x) = I ₆ (x) × S ₈ (x)
= B × sin (2πx / P + π / 4)
-(A / 2) {sin (4πx / P + φ (x) + π / 2)-sin (φ (x))}
+ (A / 6) {sin (8πx / P + 3φ (x) + π)-sin (4πx / P + 3φ (x) + π / 2)}… (30)
O ₇ (x) = I ₇ (x) × S ₁ (x)
= B × cos (2πx / P )
+ (A / 2) {sin (4πx / P + φ (x)) + sin (φ (x))}
+ (A / 6) {sin (8πx / P + 3φ (x)) + sin (4πx / P + 3φ (x))}… (31)
O ₈ (x) = I ₈ (x) × S ₂ (x)
= B × cos (2πx / P + π / 4)
+ (A / 2) {sin (4πx / P + φ (x) + π / 2) + sin (φ (x))}
+ (A / 6) {sin (8πx / P + 3φ (x) + π) + sin (4πx / P + 3φ (x) + π / 2)}… (32)
As described above, the sine function calculation unit 421 performs the memory lattice functions S ₁ (x) to S ₈ for the first term of the first to eighth light intensity functions I ₁ (x) to I ₈ (x). The first to eighth sine functions O ₁ (x) to O ₈ (x) are respectively multiplied by the second trigonometric functions having a phase difference of (π / 2-φ (x)) among (x). Is calculated. Here, as shown in the equation (25), the first sine function O ₁ (x) includes (A / 2) sinφ (x) that is a moire component and the first-order harmonic that is a fundamental wave − B × sin (2πx / P), 2nd harmonic-(A / 2) sin (4πx / P + φ (x))-(A / 6) sin (4πx / P + 3φ (x)), and 4th order (A / 6) sin (8πx / P + 3φ (x)). Further, as shown in the equations (26) to (32), each of the second to eighth sine functions O ₂ (x) to O ₈ (x) also has a moire component, a first order, a second order, and a fourth order. Including harmonics.

The harmonic removal unit 411 is represented by the following equation (33) that takes the sum of the _{first to} eighth cosine functions N ₁ (x) to N ₈ (x) given by the above equations (17) to (24), respectively. Calculation is performed to calculate the real part function R (x). The harmonic removal unit 411 calculates the real part function R (x), thereby obtaining the first, second, and fourth order included in the first to _eighth cosine functions N ₁ (x) to N ₈ (x). Remove harmonics. :
R (x) = N ₁ (x) + N ₂ (x) + N ₃ (x) + N ₄ (x) + N ₅ (x) + N ₆ (x) + N ₇ (x) + N ₈ ( x)
= 4A cosφ (x) (33)
Further, the harmonic removal unit 411 takes the sum of the _{first to} eighth sine functions O ₁ (x) to O ₈ (x) given by the above expressions (25) to (32), respectively, to the following expression (34): The imaginary function J (x) is calculated by performing the calculation shown in FIG. The harmonic removal unit 411 calculates the imaginary part function J (x), and thereby includes the first, second, and fourth order included in the first to _eighth sine functions O ₁ (x) to O ₈ (x). Remove harmonics. :
J (x) = O ₁ (x) + O ₂ (x) + O ₃ (x) + O ₄ (x) + O ₅ (x) + O ₆ (x) + O ₇ (x) + O ₈ ( x)
= 4A sinφ (x) (34)
The phase extraction unit 413 extracts the moire phase φ (x) by dividing the imaginary part function J (x) by the real part function R (x) and taking its arc tangent as shown in the following equation (35). . :
φ (x) = tan ^-1 (J (x) / R (x))… (35)
The height calculation unit 316 converts the unit system of the moire phase φ (x) and calculates the height function H (x) of the measured object 5 shown in FIG. Here, if the angle between the direction perpendicular to the stage 80 and the traveling direction of the parallel light transmitted through the grating 3 is θ, the measurement range of the imaging device 350 is given by P / tanθ, and P / tanθ is 2π. Is equivalent to Therefore, by substituting the moire phase φ (x) into the following equation (36), the unit system is converted, and the height function H (x) that gives the height of the measured object 5 at the coordinate x is calculated. :
H (x) = (φ (x) / 2π) × P / tanθ… (36)
The CPU 400 is further connected to a data storage device 331, a program storage device 330, an input device 340, and an output device 341. The data storage device 331 sequentially stores the calculation results by the CPU 400. The program storage device 330 stores an operating system that controls the CPU 400. As the data storage device 331 and the program storage device 330, for example, a recording medium for recording a program such as a semiconductor memory, a magnetic disk, an optical disk, a magneto-optical disk, and a magnetic tape can be used. As the input device 340, for example, a keyboard, a mouse, a voice device, or the like can be used. As the output device 341, a printer, a liquid crystal display (LCD), a CRT display, or the like can be used.

  Next, a three-dimensional measurement method according to an embodiment of the present invention will be described with reference to the flowchart of FIG. Note that the calculation results by the CPU 400 shown in FIG. 1 are sequentially stored in the data storage device 331.

 (a) First, in step S90, the lattice 3 and the measured object 5 used for the three-dimensional measurement shown in FIG. 2 are prepared. The object to be measured 5 is placed on the stage 80. Next, in step S91, a control signal is sent from the imaging device control unit 200 shown in FIG. 1 to the stage drive unit 42 shown in FIG. 2, and the stage 80 is moved to a place where the three-dimensional measurement of the measured object 5 is suitably performed. Further, a control signal is sent from the imaging device control unit 200 to the light source 10 to adjust the light intensity of the light emitted from the light source 10. Proceeding to step S92, measurement conditions for performing three-dimensional measurement are set. The setting of measurement conditions refers to a setting for automatically detecting a place where the measured object 5 does not exist and deleting data at that place.

 (b) In step S93, light is emitted from the light source 10 toward the first lens 11. The light incident on the first lens 11 becomes parallel light and enters the grating 3. The parallel light transmitted through the grating 3 forms a periodic bright and dark binary pattern having a pitch P on the surface of the object 5 to be measured. Here, a control signal is sent from the imaging device control unit 200 to the image sensor 20, and the image sensor 20 opens the shutter and captures a deformed lattice image formed by the light reflected from the measured object 5. Next, a control signal is sent from the imaging device control unit 200 to the grating driving unit 15, and by moving the grating 3, a periodic light / dark binary pattern having the pitch P of the surface of the object to be measured 5 is converted to the pitch P. Is moved in the direction of the periodic pattern of the binary pattern by a distance of 1/8 of the distance, and a new deformed lattice image is captured. Further, the movement of the lattice 3 and the imaging of the deformed lattice image are repeated to obtain a total of eight deformed lattice images.

(c) The acquired eight modified lattice images are sequentially taken into the modified lattice image input unit 309 shown in FIG. 1 in step S94, and the first modified lattice image, the second modified lattice image, and the third modified lattice image, respectively. They are defined as a modified lattice image, a fourth modified lattice image, a fifth modified lattice image, a sixth modified lattice image, a seventh modified lattice image, and an eighth modified lattice image. Next, in step S100, the light intensity acquisition unit 310 calculates the _{first to} eighth light intensity functions I ₁ (x) shown in the above equations (1) to (8) from the first to eighth modified lattice images. Extract ~ I ₈ (x).

(d) In step S201, the cosine function calculation unit 412 receives the first to eighth light intensity functions I ₁ (x) to I ₈ (x) from the light intensity acquisition unit 310. Further, the cosine function calculation unit 412 reads out each of the memory lattice functions S ₁ (x) to S ₈ (x) shown in the equations (9) to (16) from the memory lattice storage device 432. Next, the cosine function calculation unit 412 includes the memory lattice functions S ₁ (x) to S ₈ (x) for each of the first to eighth light intensity functions I ₁ (x) to I ₈ (x). The first to eighth cosine functions N ₁ (x) to N ₈ (x) shown in the above equations (17) to (24) are calculated by multiplying those having a phase difference of φ (x). Here, the first to eighth cosine functions N ₁ (x) to N ₈ (x) include moire components and first, second, and fourth harmonics.

(e) In step S202, the sine function calculation unit 421 receives each of the first to eighth light intensity functions I ₁ (x) to I ₈ (x) from the light intensity acquisition unit 310. Further, the sine function calculation unit 421 reads each of the memory grid functions S ₁ (x) to S ₈ (x) shown in the above equations (9) to (16) from the memory grid storage device 432. Next, the sine function calculation unit 421 includes the memory lattice functions S ₁ (x) to S ₈ (x) for each of the first to eighth light intensity functions I ₁ (x) to I ₈ (x). By multiplying the phase difference by (π / 2-φ (x)), the first to eighth sine functions O ₁ (x) to O ₈ (x ) Is calculated. Here, the first to eighth sine functions O ₁ (x) to O ₈ (x) include moire components and first-order, second-order, and fourth-order harmonics.

(f) In step S203, the harmonic removal unit 411 receives the first to eighth cosine functions N ₁ (x) to N ₈ (x) from the cosine function calculation unit 412. The harmonic removal unit 411 performs the calculation shown in the above equation (33) that takes the sum of the _{first to} eighth cosine functions N ₁ (x) to N ₈ (x), and calculates the real part function R (x). . By calculating the real part function R (x), first, second, and fourth harmonics included in the first to _eighth cosine functions N ₁ (x) to N ₈ (x) are removed. The Next, in step S204, the harmonic removing unit 411 receives the first to eighth sine functions O ₁ (x) to O ₈ (x) from the sine function calculating unit 421. The harmonic removal unit 411 performs the calculation shown in the above equation (34) that takes the sum of the _{first to} eighth sine functions O ₁ (x) to O ₈ (x), and calculates the imaginary part function J (x). . By calculating the imaginary part function J (x), the first, second, and fourth harmonics included in the first to _eighth sine functions O ₁ (x) to O ₈ (x) are removed. The

  (d) In step S205, the phase extraction unit 413 receives the real part function R (x) and the imaginary part function J (x) from the harmonic removal unit 411. Next, as shown in the above equation (35), the phase extraction unit 413 divides the imaginary part function J (x) by the real part function R (x) and takes its arc tangent to obtain the moire phase φ (x). Extract. In step S206, the height calculation unit 316 receives the moire phase φ (x) from the phase extraction unit 413. Thereafter, the height calculation unit 316 calculates the height function H (x) at the coordinate x of the measured object 5 shown in FIG. 1 based on the moire phase φ (x) as shown in the above equation (36), The three-dimensional measurement method according to the embodiment ends.

According to the three-dimensional measuring apparatus and the three-dimensional measuring method according to the embodiment of the present invention described above, the transmittance distribution of the grating 3 is sinusoidal as shown in FIGS. 3 (a) and 3 (b). Even in the case where a light and dark binary pattern is projected on the surface of the object 5 to be measured, the first to eighth cosine functions N ₁ (x) to N _{1 in} step S203 and step S204 shown in FIG. The first and higher harmonics included in ₈ (x) and the first to eighth sine functions O ₁ (x) to O ₈ (x) are removed, resulting in the first and higher harmonics. Measurement errors can be eliminated.

Here, the relationship between the number of deformed lattice images acquired in step S93 and the order of harmonics removed in steps S203 and S204 will be described with reference to FIG. As shown in the above equation (1), when the first light intensity function I ₁ (x) is represented by a function including up to the third harmonic, the first harmonic as shown in the above equation (9). The first cosine function expressed by the above equation (17), which is a moiré with the memory lattice function S ₁ (x) including only the wave, is a moire component (A / 2) sinφ (x), Includes 2nd and 4th harmonics. Since the moiré component (A / 2) sinφ (x) is necessary to calculate the height of the measured object 5 shown in FIG. 1, only the first, second, and fourth harmonics need to be removed. . Therefore, in order to remove the fourth-order harmonics first, the equation (18) including the fourth-order harmonics having a phase difference of π with respect to the fourth-order harmonics included in the equation (17) is required. . When the phase of the fourth harmonic is shifted by π, the phase of the first harmonic is shifted by π / 4, and the phase of the second harmonic is shifted by π / 2.

  After removing the 4th harmonic, remove the 2nd harmonic. By removing the fourth-order harmonics, the second-order harmonics having a phase difference of π / 2 with respect to the second-order harmonics included in the formula (17) appear in the formula (18). In order to remove the total of the 2nd order harmonics included in (17) and (18), the 2nd order harmonics with a phase difference of π with respect to the 2nd order harmonics included in (17) Equation (19) including harmonics and Equation (20) including second harmonics having a phase difference of π with respect to the second harmonics included in Equation (18) are required. At this point, the four cosine functions (17) to (20) are required. When the phase of the second harmonic included in equation (17) is shifted by π, the phase of the first harmonic is shifted by π / 2 as shown in equation (19), and 2 included in equation (18). When the phase of the next harmonic is shifted by π, the phase of the first harmonic is shifted by 3π / 4 with respect to the first harmonic included in equation (17) as shown in equation (20).

Finally, remove the first harmonic. By removing the 2nd and 4th harmonics, the 3rd primary with phase differences of π / 4, π / 2, and 3π / 4, respectively, with respect to the 1st harmonic contained in Equation (17) The harmonics of (18) to (20) appear. In order to remove a total of four first-order harmonics included in Equations (17) to (20), the first-order harmonics with a phase difference of π with respect to the first-order harmonics included in Equation (17) Included in Eq. (21), which includes harmonics, and Eq. (22), which includes first-order harmonics with a phase difference of π with respect to the first-order harmonics included in Eq. (18), and (19) Equation (23) including the first harmonic with a phase difference of π with respect to the first harmonic, and the first harmonic with a phase difference of π with respect to the first harmonic included in the equation (20). Equation (24) including waves is required. Note that the second and fourth harmonics newly generated in the equations (18) to (24) cancel each other. Therefore, when the first light intensity function I ₁ (x) is represented by a function including up to the third harmonic, in order to remove the first and higher harmonics included in the equation (17), (16) The seven cosine functions given by Equation (24) are required. Therefore, the first to eighth light intensity functions I ₁ (x) to I ₈ (x) shown in the equations (1) to (8) can be acquired by capturing eight deformed lattice images in step S93. Necessary. Note that the first and higher harmonics included in the first to _eighth sine functions O ₁ (x) to O ₈ (x) given by the equations (25) to (32) are also the first to eighth cosine functions. Since it is canceled and removed in the same manner as the first and higher harmonics included in N ₁ (x) to N ₈ (x), the description is omitted.

Next, a case where the first light intensity function I ₁ (x) is expressed by a function including up to the fifth harmonic will be described with reference to FIG. When the first light intensity function I ₁ (x) is expressed by a function including up to the fifth harmonic, the first light intensity function I ₁ (x) is a moiré component, and the first, third, and fifth orders. Of harmonics. Thus, the first cosine function, which is a moiré with the memory lattice function S ₁ (x) containing only the first harmonic, will contain the first, second, fourth, and sixth harmonics. . Therefore, in order to remove the 6th harmonic contained in the first cosine function, a new cosine function including a 6th harmonic having a phase difference of π is required. When the phase of the 6th harmonic is shifted by π, the phase of the 1st harmonic is shifted by π / 6, the phase of the 2nd harmonic is shifted by π / 3, and the phase of the 4th harmonic is 2π / 3 shift.

  After removing the 6th harmonic, remove the 4th harmonic. By removing the sixth-order harmonic, a new fourth-order harmonic having a phase difference of 2π / 3 with respect to the fourth-order harmonic included in the first cosine function is generated. In order to remove two fourth-order harmonics, a cosine function including a fourth-order harmonic having a phase difference of π with respect to a fourth-order harmonic included in the first cosine function and a phase difference of 5π A new cosine function including the 4th harmonic of / 3 is required. At this point, four cosine functions are needed. When the phase of the fourth-order harmonic included in the first cosine function is shifted by π, the phase of the first-order harmonic is shifted by π / 4, and the phase of the second-order harmonic is shifted by π / 2. When the phase of the 4th harmonic contained in the first cosine function is shifted by 5π / 3, the phase of the 1st harmonic is shifted by 3π / 4, and the phase of the 2nd harmonic is shifted by 5π / 6. .

  After removing the 4th harmonic, remove the 2nd harmonic. By removing the 6th and 4th harmonics, the phase differences are π / 3, π / 2, and 5π / 6, respectively, for the 2nd harmonic contained in the first cosine function. Three new second harmonics are generated. Therefore, in order to remove the four second-order harmonics, the phase differences are π, 4π / 3, 3π / 2, and 11π / 6, respectively, with respect to the second-order harmonics included in the first cosine function. Four more cosine functions are needed, including the next harmonic. At this point, 8 cosine functions are needed. When the phase of the second harmonic contained in the first cosine function is shifted by π, 4π / 3, 3π / 2, and 11π / 6, the phase of the first harmonic is π / 2, 2π / 3, respectively. , 3π / 4, and 11π / 12 shifts.

Finally, remove the first harmonic. By removing the second-order, fourth-order, and sixth-order harmonics, the phase difference is π / 6, π / 4, 5π / 12, respectively, with respect to the first-order harmonics included in the first cosine function. Seven new first-order harmonics are generated: π / 2, 2π / 3, 3π / 4, and 11π / 12. Therefore, in order to remove the eight first-order harmonics, the phase differences for the first-order harmonics included in the first cosine function are π, 7π / 6, 5π / 4, 17π / 12, 3π, respectively. Eight more cosine functions are required, including the first harmonics of / 2, 5π / 3, 7π / 4, and 23π / 12. At this point, 16 cosine functions are needed. Note that the second, fourth, and sixth harmonics included in the cosine function newly generated to remove the first harmonic are canceled out. Accordingly, when the first light intensity function I ₁ (x) is expressed by a function including up to the fifth harmonic, 16 cosine functions are required. Therefore, it is necessary to capture 16 deformed lattice images in step S93.

As a result, the number of types of harmonics of the cosine function, for example, primary to a cosine function, secondary, and order if three harmonics of harmonics are included 4, are 2 ³ Eight deformed grid images are required. Further, primary to a cosine function, secondary, fourth, and if four harmonics sixth-order harmonics are included, it is necessary to 16 sheets of deformable grating image is two ^4. The same applies when the number of types of harmonics included in the cosine function is five or more, and when n types of harmonics are included in the cosine function, 2 ⁿ deformed lattice images are required.

Next, in step S90 of FIG. 4, a flat mirror is arranged as the object to be measured 5 on the stage 80 shown in FIG. 2, and in step S93, the first deformed grating image shown in FIG. A specific example when the second to eighth modified lattice images are captured will be described. In step S201, the memory lattice function S ₁ (x) given in (9) above becomes a lattice as shown in FIG. 8 when imaged. In this case, FIG. 9 is an image of the moire phase φ (x) calculated in step S205, and FIG. 10 is a cross-sectional view in the AA direction. On the other hand, FIG. 11 shows an image of the moire phase φ (x) calculated when only four deformed lattice images are captured, and FIG. 12 shows a cross-sectional view in the AA direction. Furthermore, FIG. 13 is an image of the moire phase φ (x) calculated when the second to eighth modified lattice images are captured but only one type of memory lattice function is prepared, and is shown in the AA direction. A cross-sectional view is shown in FIG. As shown in FIG. 12, when only four deformed lattice images are captured, the error component due to the third harmonic included in the light intensity function is superimposed on the moire phase φ (x), so noise is present in the measurement result. appear. Further, when only one type of memory lattice function is prepared as shown in FIG. 14, the phase jump due to the harmonics becomes severe and measurement is impossible. On the other hand, according to the three-dimensional measurement apparatus and the three-dimensional measurement method according to the embodiment, the third-order included in each of the first to eighth light intensity functions I ₁ (x) to I ₈ (x) Since the error component caused by the harmonics is removed, three-dimensional measurement with less noise and high accuracy is possible as shown in FIG.

(Modification)
In the description of the memory grid storage device 432 illustrated in FIG. 1, it has been described that the memory grid functions S ₁ (x) to S ₈ (x) represented by the formulas (9) to (16) are stored. The memory lattice function S ₅ (x) differs from the memory lattice function S ₁ (x) in the equation (9) only in sign. Further, the memory lattice function S ₆ (x) in the equation (14) differs from the memory lattice function S ₂ (x) in the equation (10) only in sign, and the memory lattice function S ₇ (x) in the equation (15) is (11 Only the sign differs from the memory lattice function S ₃ (x) in Expression (16), and the memory lattice function S ₈ (x) in Expression (16) differs from the memory lattice function S ₄ (x) in Expression (12) only in sign. Therefore, the memory grid storage device 432 may store only the memory grid functions S ₁ (x) to S ₄ (x) given by the equations (9) to (12).

In this case, the cosine function calculation unit 412 calculates each of the fifth to eighth cosine functions N ₅ (x) to N ₈ (x) by the following equations (37) to (40), and the sine function calculation unit 421 Each of the third to sixth sine functions O ₃ (x) to O ₆ (x) may be calculated by the following equations (41) to (44).

N ₅ (x) = I ₅ (x) × (-S ₁ (x))… (37)
N ₆ (x) = I ₆ (x) × (-S ₂ (x))… (38)
N ₇ (x) = I ₇ (x) × (-S ₃ (x))… (39)
N ₈ (x) = I ₈ (x) × (-S ₄ (x))… (40)
O ₃ (x) = I ₃ (x) × (-S ₁ (x))… (41)
O ₄ (x) = I ₄ (x) × (-S ₂ (x))… (42)
O ₅ (x) = I ₅ (x) × (-S ₃ (x))… (43)
O ₆ (x) = I ₆ (x) × (-S ₄ (x))… (44)
Furthermore, the three-dimensional measuring method according to the embodiment is not limited to the order shown in FIG. For example, after step S100, the process proceeds to step S202 to calculate the _{first to} eighth sine functions O ₁ (x) to O ₈ (x), and after calculating the imaginary part function J (x) in step S204, step S201 is performed. Step S203 and Step S205 may be proceeded to.

(Other embodiments)
As described above, the present invention has been described according to the embodiment. However, it should not be understood that the description and drawings constituting a part of this disclosure limit the present invention. From this disclosure, various alternative embodiments, examples and operational techniques should be apparent to those skilled in the art. For example, the phase extraction unit 413 shown in FIG. 1 divides the imaginary part function J (x) by the real part function R (x) and takes the arctangent thereof to obtain the moiré phase φ ( It was explained that x) was extracted. In contrast, a database in which the relationship between the imaginary part function J (x), the real part function R (x), and the moire phase φ (x) is created in advance, and the imaginary part function J (x) and the real part function R is created. The moire phase φ (x) may be derived by referring to the database when (x) is calculated. Further, the above-described three-dimensional measurement method can be expressed as a series of processes or operations connected in time series. Therefore, in order to execute the three-dimensional measurement method in the computer system, the three-dimensional measurement method shown in FIG. 4 can be realized by a computer program product that specifies a plurality of functions performed by a processor or the like in the computer system. Here, the computer program product refers to a recording device or a recording medium that can be inputted to and outputted from a computer system such as the program storage device 330 shown in FIG. The recording medium includes a memory device, a magnetic disk device, an optical disk device, and other devices capable of recording other programs. Therefore, the present invention is limited only by the invention specifying matters in the scope of claims reasonable from this disclosure.

It is a block diagram of the three-dimensional measuring apparatus which concerns on embodiment of this invention. 1 is a schematic diagram of an imaging apparatus according to an embodiment of the present invention. It is a mimetic diagram of a lattice concerning an embodiment of the invention. It is a flowchart which shows the three-dimensional measuring method which concerns on embodiment of this invention. It is a table | surface (the 1) for demonstrating the three-dimensional measuring method which concerns on embodiment of this invention. It is a table | surface (the 2) for demonstrating the three-dimensional measuring method which concerns on embodiment of this invention. It is a deformation | transformation lattice image which concerns on embodiment of this invention. It is an image of the memory lattice function according to the embodiment of the present invention. It is a surface shape image of the to-be-measured object which concerns on embodiment of this invention. It is a cross-sectional profile of the surface shape image of the to-be-measured object which concerns on embodiment of this invention. It is the surface shape image (the 1) of the to-be-measured object which concerns on a prior art. It is a cross-sectional profile (the 1) of the surface shape image of the to-be-measured object which concerns on a prior art. It is the surface shape image (the 2) of the to-be-measured object which concerns on a prior art. It is a cross-sectional profile (the 2) of the surface shape image of the to-be-measured object which concerns on a prior art.

Explanation of symbols

3 ... Lattice
5 ... Object to be measured
10 ... Light source
11 ... 1st lens
15 ... Lattice drive unit
20… Image sensor
21 ... Second lens
23 ... Spatial filter
42… Stage drive unit
80 ... Stage
200 ... Imaging device controller
309 ... Deformed grid image input unit
310 ... Light intensity acquisition unit
316… Height calculator
330 ... Program storage device
331 ... Data storage device
340 ... Input device
341 ... Output device
350 ... Imaging device
400 ... CPU
411 ... Harmonic wave removal unit
412: Cosine function calculator
413 ... Phase extraction unit
421 ... Sine function calculator
432 ... Memory grid storage device

Claims (9)

An imaging device that captures a plurality of deformed lattice images formed by projecting a binary pattern onto an object to be measured;
A light intensity acquisition unit that respectively acquires a plurality of light intensity functions from the plurality of deformed lattice images;
A first moire phase value given to each of the plurality of deformed lattice images by the measured object is a first value, and a first triangle having a phase difference of the first value with respect to each of the plurality of light intensity functions. A cosine function calculating unit that multiplies each of the plurality of light intensity functions by a function to calculate a plurality of cosine functions;
A value obtained by subtracting the first value from 90 degrees is defined as a second value, and a second trigonometric function having a phase difference of the second value for each of the plurality of light intensity functions is defined as the plurality of light intensity. A sine function calculator that calculates each of the functions and calculates a plurality of sine functions;
By calculating a real part function that is the sum of the plurality of cosine functions and an imaginary part function that is the sum of the plurality of sine functions, harmonics included in each of the plurality of cosine functions and sine functions are removed. A wave removal unit;
A three-dimensional measurement apparatus comprising: a height calculation unit that calculates a height of the object to be measured based on the moire phase extracted from the imaginary part function and the real part function.   The three-dimensional measurement apparatus according to claim 1, wherein each of the plurality of deformed lattice images has a phase difference different by 45 degrees.   3. The three-dimensional measurement apparatus according to claim 1, wherein the number of the plurality of deformed lattice images is equal to a power of 2 with the number of harmonics as an index. Capturing a plurality of deformed lattice images formed by projecting a binary pattern onto the object to be measured;
Obtaining each of a plurality of light intensity functions from the plurality of modified lattice images;
A first moire phase value given to each of the plurality of deformed lattice images by the measured object is a first value, and a first triangle having a phase difference of the first value with respect to each of the plurality of light intensity functions. Multiplying each of the plurality of light intensity functions by a function to calculate a plurality of cosine functions;
A value obtained by subtracting the first value from 90 degrees is defined as a second value, and a second trigonometric function having a phase difference of the second value for each of the plurality of light intensity functions is defined as the plurality of light intensity. Multiplying each of the functions to calculate a plurality of sine functions;
Calculating a real part function that is a sum of the plurality of cosine functions and an imaginary part function that is a sum of the plurality of sine functions, thereby removing harmonics included in each of the plurality of cosine functions and the sine function. When,
Calculating the height of the object to be measured based on the moiré phase extracted from the imaginary part function and the real part function.   5. The three-dimensional measurement method according to claim 4, wherein each of the plurality of modified lattice images has a phase difference different by 45 degrees.   6. The three-dimensional measurement method according to claim 4, wherein the number of the plurality of modified lattice images is equal to a power of 2 with the order of the harmonics as an index.   7. The three-dimensional measurement method according to claim 4, wherein the step of acquiring the plurality of modified lattice images includes a procedure of moving the binary pattern at equal intervals.   8. The step of calculating the height of the object to be measured includes a procedure of dividing the imaginary part function by the real part function and taking an arc tangent. 3D measurement method. A three-dimensional measurement program for driving and controlling a three-dimensional measurement apparatus for measuring the surface shape of an object to be measured.
A procedure for imaging a plurality of deformed lattice images formed by projecting a binary pattern onto the object to be measured;
Obtaining each of a plurality of light intensity functions from the plurality of deformed lattice images;
A first moire phase value given to each of the plurality of deformed lattice images by the measured object is a first value, and a first triangle having a phase difference of the first value with respect to each of the plurality of light intensity functions. Multiplying each of the plurality of light intensity functions by a function to calculate a plurality of cosine functions;
A value obtained by subtracting the first value from 90 degrees is defined as a second value, and a second trigonometric function having a phase difference of the second value for each of the plurality of light intensity functions is defined as the plurality of light intensity. Multiply each of the functions to calculate multiple sine functions;
A procedure for removing harmonics included in each of the plurality of cosine functions and the sine function by calculating a real part function that is the sum of the plurality of cosine functions and an imaginary part function that is the sum of the plurality of sine functions. When,
A program for calculating a height of the object to be measured based on the moire phase extracted from the imaginary part function and the real part function.