JP7215719B2 - Method and apparatus for measuring out-of-plane displacement distribution and three-dimensional shape of measurement object - Google Patents

Description

Application of Article 30, Paragraph 2 of the Patent Law (1) ICEM18 program (cover, page 14), presentation materials (2) 60th Lecture on Structural Strength program (cover, excerpt from August 3), collection of lecture papers (cover , table of contents excerpt, P265-267), presentation material (3) 2018 Japan Society for Precision Engineering Autumn Meeting Scientific Lecture Proceedings (cover, table of contents 1/4, 567-568), poster (4) 13th ISEM'18 program ( Cover, P10, 13), Proceedings, Presentation Materials (5) ISOT2018 Program (Cover, P1-2, P28), Extended Abstract Book (Cover, P132, P141-142), Presentation Materials (6) ICPE2018 Program (Cover , P20-23), Lecture Proceedings, Presentation Materials (7) M&M2018 Mechanics of Materials Conference Program (Cover, P17-18), Poster, Lecture Proceedings PS-85-87

The present invention relates to a method and apparatus for measuring out-of-plane displacement distribution and three-dimensional shape of an object using interference fringes having a light-dark distribution in the optical axis direction.

Non-contact three-dimensional shape measurement is in wide-ranging demand in manufacturing, medical, civil engineering, and clothing fields. Especially for objects with large curved surfaces such as sheet metal processed products and press processed products, 3D measurement by pattern projection, which can measure 3D distribution without contact, is effective as a method that can measure and inspect in a short time. is. As conventional grid projection methods, the methods and apparatuses shown in Non-Patent Document 1 and Non-Patent Document 2 have been developed. Patent Document 1 and Non-Patent Document 3 disclose a technique capable of measuring a minute displacement with a resolution of about 1 millimeter from a position several tens of meters away from the object to be measured.

JP 2007-093576 A

C. Quan, et al., "Shape measurement of small objects using LCD fringe projection with phase shifting," Opt. Commun. 189, (2001) 21. M. Schaffer, et al.,“Coherent two-beam interference fringe projection for highspeed three-dimensional shape measurements,”Appl. Opt. 52, (2013) 2306. Tetsushi Uebo, Nami Murata, Measurement of minute displacement by standing wave radar, Proc.

However, in the techniques disclosed in Non-Patent Document 1 and Non-Patent Document 2, it is necessary to increase the distance between the light source and the camera when trying to obtain information in the out-of-plane direction (normal direction of the surface). Therefore, miniaturization of the measurement system is difficult. In particular, when interference fringes are used, the resolution is too small, on the order of sub-micrometers, so that it is not suitable for measuring large structures. In addition, the techniques disclosed in Patent Document 1 and Non-Patent Document 3 measure only one point on the surface of the object to be measured, and cannot measure the distribution of displacement on the surface of the object to be measured.
SUMMARY OF THE INVENTION Accordingly, an object of the present invention is to provide a method for measuring the distribution of displacement in the out-of-plane direction of an object located relatively far away with the light projecting side and the light receiving side arranged substantially coaxially, and to use the method. to provide the equipment.

The invention according to claim 1 of the present application is a measurement method in which interference fringes are projected onto the surface of an object, and the reflected light of the projected interference fringes is captured by an imaging means, wherein the interference fringes can be irradiated from three directions. Based on the principle of interference by light waves of interference, three-beam interference fringes consisting of regions in which interference fringes appear and regions in which interference fringes do not appear are formed in the irradiation direction of light emitted from three directions, and are formed on the surface of the object. This measurement method measures the displacement or the three-dimensional shape of the object by imaging fringes formed by three-beam interference fringes.
The invention according to claim 2 is a three-beam measuring device that projects interference fringes on the surface of an object and captures the reflected light of the projected interference fringes with imaging means, wherein a light source that emits coherent light and 3-beam forming means for forming three coherent light waves from the coherent light and projecting 3-beam interference fringes on the surface of the object; imaging means for receiving reflected light from the surface of the object; means for measuring the displacement or the three-dimensional shape of the object based on fringes formed on the surface of the object imaged by the three-beam interference fringes.
The invention according to claim 3 is the three-beam measurement device according to claim 2, further comprising a grating plate that forms moire fringes from the three- beam interference fringes.
The invention according to claim 4 is the three-beam measuring apparatus according to claim 3, further comprising means for determining the amplitude or power of the moire fringes by a phase analysis method.
The invention according to claim 5 further comprises phase shift means for shifting the phase of one of the three coherent light waves to shift the phase of the fringe pattern of the three-beam interference fringes in the light exit direction. 5. The three-beam measuring device according to any one of 2 to 4 .

According to the present invention, it is possible to provide a method for measuring the distribution of displacement in the out-of-plane direction of an object to be measured located relatively far away with the light projecting side and the light receiving side arranged substantially coaxially, and an apparatus using the method. .

FIG. 2 is a conceptual diagram for explaining a grating projection method using three-beam interference; It is a figure explaining generation|occurrence|production of the interference fringe by 3 light beams. It is an example of an optical system that implements the measurement method of the present invention. It is a figure explaining a spatial fringe analysis method. It is an example of an optical system for optically obtaining a fringe pattern in the depth direction. It is an example of an optical system for realizing the phase shift method in the present invention. It is an optical system model for simulation. It is a figure explaining the interference fringe of three-beam interference calculated from Formula 7. FIG. FIG. 9 is a diagram for explaining the amplitude of a fringe pattern in the depth direction obtained by applying the spatial fringe analysis method to FIG. 8; It is a figure explaining the phase-shifted interference fringe. It is a photograph figure which shows the optical system at the time of experiment. 1 is a conceptual diagram of an experimental optical system; FIG. It is a figure which shows a photography result. It is a figure which shows an experimental optical system and a measurement target object. It is a figure which shows the interference fringe image|photographed with the camera. 13 is an amplitude distribution diagram of the interference fringes of FIG. 12; FIG. It is a figure explaining the amplitude distribution which smoothed 9x9 pixels. It is a figure explaining the fringe pattern of the depth direction which phase-shifted. It is a figure explaining the phase of a depth direction fringe pattern. It is a figure explaining the phase of the smoothed depth direction fringe pattern. FIG. 10 is a diagram showing an experimental optical system during shape measurement; FIG. 10 is a diagram showing a phase image when the reference plane is 5.0 mm; It is a figure which shows the phase difference image at the time of a reference plane being 5.0 mm and 0.0 mm. It is a figure explaining the phase difference in each position of a plane object. FIG. 10 is a diagram showing a metal plate tilted at 60°; FIG. 10 is a diagram showing a phase distribution obtained by measuring a metal plate tilted at 60°; FIG. 5 is a diagram illustrating shape profiles of metal plates tilted at 60° and 45°; FIG. 11C is a diagram for explaining the phase distribution when the object shown in FIG. 11-4 is measured; Figure 11-5 illustrates the shape profile of the object shown in Figure 11-4; FIG. 2 illustrates a typical optical system for implementing the method of the present invention with spherical waves when (a) three mirrors are used and (b) arbitrary shaped mirrors are used. It is a figure explaining the optical model (xz plane) used by simulation. It is a figure explaining the result of the spherical wave simulation in xz plane. It is a figure explaining the optical model (xz plane) used by simulation. It is a figure explaining the result of the spherical wave simulation in xy plane. It is a figure explaining the example of the typical optical system in the case of using an optical fiber. It is a schematic diagram in the case of performing a phase shift in an optical system using an optical fiber.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
(1) Outline of this measurement method When trying to obtain information on displacement in the out-of-plane direction (normal direction of the surface) of the object to be measured using the grid projection method, it is necessary to increase the distance between the light source and the camera. , it is difficult to miniaturize the measurement system. Moreover, especially when interference fringes are used, the resolution is too small, on the order of sub-micrometers, so that it is not suitable for measuring large structures with large areas.

In the three-beam interferometer according to the present invention, by superimposing the light beams from the two-beam interferometers, an intensity change appears to form an interference fringe pattern along the optical axis direction (light projection direction). For this reason, the striped pattern in the optical axis direction directly obtains information on the three-dimensional shape and displacement of the measurement object in the out-of-plane direction without tilting the camera to capture an image of the measurement object or performing interpolation or coordinate conversion. be able to.

Therefore, the measurement accuracy is not affected by the positional relationship between the light source and the camera, eliminating the need for camera alignment. Furthermore, distant objects can be measured while the measuring device is kept compact. This measurement method can be widely applied to the non-contact inspection of the surface of a large structure having a relatively large surface area.

(2) Shape Measurement Principle of the Present Invention FIG. 1 is a diagram showing the concept of a grid projection method using three-beam interference. The measurement method of the present invention is a lattice projection method in which a lattice fringe pattern having an intensity distribution in the optical axis direction (projection direction of the three light beams) is obtained by three-beam interference. As shown in FIG. 1, a measurement object (Object) is irradiated with three light beams from a light source. The three luminous fluxes are luminous fluxes directed toward the measurement object from substantially the same direction when viewed from the measurement object, and the luminous fluxes are irradiated to the measurement object from substantially coaxial directions. Interference fringes appear on the surface of the object to be measured. A camera captures an image of the interference fringes formed on the surface of the object to be measured. Although the camera is coaxial with the light beam from the light source in FIG. 1, the camera and light source need not be coaxial.

In this measurement method, the shape of the object in the out-of-plane direction appears as a pattern due to interference, such as the contour lines shown in FIG. This striped pattern can be directly imaged by a camera. In addition, with the light source and the camera arranged substantially coaxially (almost in the same direction with respect to the object to be measured), the out-of-plane displacement or three-dimensional shape of the surface of the object to be measured located far from the light source and camera can be measured. can be measured. Image data captured by the camera is processed by a computer (not shown) to obtain the shape and displacement of the object to be measured.

(3) Interference fringes due to three-beam interference When two collimated lights (E0, E1) are caused to interfere, interference fringes are generated in a direction perpendicular to the optical axis. At this time, the interval d _s of one cycle of the interference fringes can be expressed by Equation (1).

Here, λ is the wavelength of the laser light source used, and θ ₁ is the angle between E 0 and E 1 . Also, when θ ₁ ≈0, Equation 1 can be expressed by Equation 2.

Next, consider the case of three-beam interference including the third light wave E2.
Assume that the angles formed by E0 and E1, and between E0 and E2 are θ1 _and θ2, respectively, as shown in _FIG . At this time, when the interference fringes generated by E0 and E1 and the interference fringes generated by E0 and E2 are superimposed, if _θ1 = θ2, as shown in _FIG . Interference fringes with intensity distribution are produced. The interval _dL of one period of interference fringes having an intensity distribution in the optical axis direction can be expressed by Equation 3-1.

Equation 3-1 can be expressed by Equation 2 from the relationship of Equation 1.

Here, if θ1≈0 and θ2≈0, then tan θ ₁ =θ ₁ and tan θ ₂ =θ ₂
Therefore, Formula 3-2 becomes Formula 3-3.

Also, when θ ₁ =θ ₂ ≈0, Equation 3 can be expressed as Equation 4 in the same way as Equation 2.

Thus, the three-beam interference can generate interference fringes having an intensity distribution in the optical axis direction. By projecting the lattice pattern of the interference fringes onto the object to be measured, it is possible to directly obtain information on the three-dimensional shape in the depth direction with respect to the optical axis and the displacement of the surface of the object to be measured in the out-of-plane direction.

FIG. 3 shows an example of an optical system that implements the measurement method of the present invention. The measurement unit includes a laser as a light source, a collimating lens for collimating the laser beam, and a half mirror for reflecting the collimated beam in the directions of mirrors 0, 1 and 2. The measurement unit further includes a camera that receives reflected light from the object to be measured. A camera has a lens and an image sensor. A laser beam emitted from a laser light source is collimated by a collimating lens. The collimated laser light is reflected by the half mirrors in the directions of mirror 0, mirror 1, and mirror 2. FIG. Mirrors 0, 1, and 2 are used to split the laser beam from the laser light source into three beams.

The three laser beams reflected by the mirrors 0, 1, and 2 are applied to the object to be measured via the half mirror. A pattern of contour lines is formed by the interference fringes on the surface of the object to be measured. The camera captures contour fringes due to interference fringes formed on the surface of the object to be measured by receiving reflected light from the object to be measured.

(4) Acquisition of fringe pattern in depth direction (optical axis direction, i.e. light projection direction) Interference fringes due to light waves are superimposed on each other. At this time, the interference fringes in the depth direction are moire fringes in which the interference fringes due to these two light waves overlap. In the moire fringes, fine two-wave interference fringes strongly appear in areas where constructive interference occurs. Conversely, fine interference fringes of two light waves appear weakly in a region where destructive interference occurs. Therefore, by calculating the amplitude or power of the interference fringes obtained by the camera, only the fringe pattern in the depth direction along the optical axis can be obtained.

Two methods of analytically obtaining the amplitude of the interference fringes of light flux interference and optically obtaining the amplitude will be described below.
(4-1)
First, the spatial fringe analysis method (Yasuhiko Arai, Shunsuke Yokoseki, Expo Shiraki, Asaharu Yamada, Two-dimensional spatial fringe analysis method using CCD image sampling technology, Optics, 25-1, (1995) 42.) Analytically obtaining a fringe pattern in the depth direction using
FIG. 4 is a diagram explaining the spatial fringe analysis method. As described above, the fringe pattern in the depth direction appears depending on the intensity of the interference fringes of E 0 and E 1 and the intensity of the interference fringes of E 0 and E 2 . If the pixel pitch of the camera is of the same order as the fine interference fringes, the pixel structure of the camera becomes the reference lattice in the spatial fringe analysis method, resulting in moire fringes. Also, moire fringes are generated by thinning out an image with an arbitrary number of pixels in the x or y direction. At this time, the phase of moire fringes changes by changing the pixel position where thinning is started.

By utilizing this fact, phase shifting is performed a plurality of times within one period of the moire fringes, so that a plurality of phase-shifted moire fringe images can be obtained. At this time, by acquiring three or more phase-shifted moiré fringe images, it is possible to obtain the amplitude or power/phase of the moiré fringes. The amplitude of the moire fringes can be obtained by Equation (5).

Here, A is the amplitude of moiré fringes, N is the number of moiré fringes, and k is an integer (0, 1, 2, 3, . . . , N−1).
The amplitude of the moire fringes is a constant multiple of the amplitude of the fringe pattern in the depth direction. So far, we have described the method of analytically obtaining the amplitude of the fringe pattern in the depth direction using the spatial fringe analysis method.

(4-2)
Next, a method for optically obtaining the amplitude of the fringe pattern in the depth direction will be described. In the spatial fringe analysis method, the pixel structure of the camera served as a reference grid to generate moire fringes. For optical acquisition, a Ronchi ruling or grating plate is used as a reference grating. A schematic diagram of a representative optical system at this time is shown in FIG.

The light wave (interference fringes) reflected by the object to be measured is imaged on the installed grating plate via the lens. At this time, an image of the interference fringes is formed on the grating plate, so that moire fringes are generated on the grating plate. The moire fringes are captured by a camera. Also, by directly moving the grating plate, the phase of the moire fringes is shifted. As in the case of the spatial fringe analysis method, the amplitude of the moire fringes can be obtained by acquiring the images of the moire fringes that are phase-shifted three or more times and performing the calculation of Equation (5).

(5) Calculation of the phase of the fringe pattern in the depth direction by phase shift In this measurement method, in order to obtain the shape and displacement distribution in the out-of-plane direction, it is necessary to obtain the phase of the fringe pattern in the depth direction of the optical axis. . Here, in this measurement method, the phase shift method (E. Kim, et al., “Profilometry without phase unwrapping using multi-frequency and four-step phase-shift sinusoidal fringe We describe an optical system and a calculation method for obtaining the phase of the fringe pattern in the depth direction using projection,” Opt. Express 17, 7818 (2009)).

Generally, in the field of digital holography using the two-beam interferometer described in the above-mentioned E. Kim, et al. to shift the phase of the light wave. This retardation is then achieved by using a phase shifter composed of mirrors or glass plates or polarizers.

In the measuring method according to the present invention, the same effect can be obtained by shifting any one of the three optical paths. FIG. 6 shows a representative optical system for realizing the phase shift method in this measurement method. In FIG. 6, by moving the mirror 0 among the three beams, a phase shifter is provided in the central optical path (E ₀ ) to realize phase delay. At this time, due to the phase delay of the central optical path, the light and dark positions of the aforementioned fringe pattern in the depth direction shift in the x-direction or the y-direction. In the phase shift method, in order to obtain the phase, it is necessary to acquire a fringe pattern that is shifted at equal intervals three times or more in one cycle of the fringes. Therefore, it is sufficient to acquire three or more stripe patterns in the depth direction in which the light and dark patterns are shifted at equal intervals. The phase distribution in the fringe pattern can be calculated by applying Equation 6 to the acquired plurality of depth direction fringe patterns.

Here, θ is the phase of moiré fringes, N is the number of moiré fringes, and k is an integer (0, 1, 2, 3, . . . , N−1).

(6) Effects of Embodiments of the Present Invention (6-1) When measuring the three-dimensional shape and displacement distribution of an object to be measured using the grating projection method, the intensity of the interference fringes increases based on the principle of three-beam interference. Interference fringes varying along the optical axis can be directly projected.
(6-2) A phase-shifted three-beam interference fringe can be obtained by adding a phase shift mechanism in the measuring device and appropriately delaying the phase of an arbitrary optical path out of the three optical paths.
(6-3) By performing fringe analysis on the plurality of phase-shifted three-beam interference fringes obtained in (6-2), the amplitude distribution of the plurality of phase-shifted fringe patterns in the depth direction can be obtained.
(6-4) The phase distribution of the fringe patterns in the depth direction is obtained by performing calculations for converting the amplitude distributions of the plurality of fringe patterns in the depth direction obtained in (6-3) into phases.
(6-5) By analyzing the phase distribution of the fringe pattern in the depth direction obtained in (6-4), the shape and displacement of the object in the depth direction can be obtained.
(6-6) A measurement system having a spatial resolution of sub-millimeter order and a wide measurement range in the depth direction can be constructed.
(6-7) A distant measurement target object can be measured with the light source and the camera arranged substantially coaxially.
(6-8) Due to (6-7), the size of the measuring device can be easily reduced.

(7) Example (7-1) Numerical Analysis As an example, numerical analysis was performed to confirm an interference pattern that changes in the optical axis direction caused by the interference of three light beams. Numerical analysis was also conducted to confirm that the interference pattern that changes in the direction of the optical axis also shifts when the phase is shifted.

FIG. 7 shows the optical model used in this analysis. Table 1 shows the parameters used. The intensity distribution I(x,z) on the xz plane can be expressed by Equation (7).

Here, A0, A1 and A2 are the intensities of E0, E1 and E2, b1 is the coordinate of E1, and b2 is the coordinate of E2.

A simulation is performed using Equation 7 below.
FIG. 8 shows interference fringes of three-beam interference obtained by Equation (7). FIG. 9 shows the power component distribution of FIG. 8 calculated by the spatial fringe analysis method. Here, the x-axis is horizontal with respect to the optical axis, and the z-axis is the depth direction.

The decimation number in the spatial fringe analysis method was set to 10 along the x direction. The pitch of the fringe pattern in the depth direction can be analytically obtained from Equation 5, and is 6.00 mm for this parameter. In FIGS. 8 and 9, one period of the interference fringes is 100 pixels. Since the pixel size is 0.06 mm, the actual pitch of the fringe pattern in the depth direction is 6.00 mm. This agrees with Equation 6 and the results calculated from the parameters. Therefore, it was confirmed that interference fringes in the depth direction were correctly generated.

Next, the case of shifting the phase of any one of the three light beams will be described. In this simulation, the case of shifting the phase of E0 among E0, E1, and E2 shown in FIG. 7 is analyzed, but the phase of any beam may be shifted. At this time, the interference fringes of the two beams generated by E0 and E1 and by E0 and E2 change with the phase shift of E0. Ultimately, the pattern in the optical axis direction due to the interference of the three light beams is generated by superimposing the interference fringes of the two light beams in two directions, so it is considered that it changes in the same way. 10(a) and 10(b) show patterns due to the interference of the three beams when the phase of E0 is shifted.

The simulation was performed with 640×480 pixels, of which 640×120 pixels are shown in FIG. The phase shift amounts Δφ of E0 are set to 0, π/4, π/2, 3π/4, and π, respectively. In addition, the white crosses in the figure are arranged so that the patterns varying in the direction of the optical axis weaken each other. Looking at FIG. 10, it can be seen that the interference pattern appearing along the optical axis moves along the optical axis at regular intervals (50 pixels each on the image) as the E0 phase shifts. It was also confirmed that the interference fringes moved by one period when the phase of E0 was just shifted by π.

(7-2) Experiment In order to confirm patterns appearing in the depth direction without image processing, a moire pattern is generated using Ronchi ruling.
The laser beams divided into three are irradiated on the object so as to interfere with each other. This is imaged by a lens placed on the object side, and a Ronchi ruling is installed at the imaging position. By photographing the image formed on the Ronchi ruling with a camera, moire fringes appear due to two patterns with different pitches, the interference fringes and the Ronchi ruling. Moiré fringes appear in areas where fine interference fringes due to interference between two lasers are visible, and moiré fringes do not appear in areas where fine interference fringes do not appear.

In the above-mentioned methods, the distance between the interference fringes was small, and it was difficult to confirm the pattern appearing in the depth direction without image processing. By photographing, fringes with a larger pitch than the interference fringes obtained by the above-described method will appear.

Since the amplitude of the moiré fringes obtained at this time is the same as the amplitude of the original interference fringes, the amplitude distribution of the original interference fringes can be obtained by obtaining the amplitude distribution of the moiré fringes. It is considered possible to confirm the pattern in the depth direction without image processing.

FIG. 11-1 is a photograph showing the optical system during the experiment. FIG. 11-2 is a conceptual diagram of the experimental optical system. FIG. 11-3 is a diagram showing the imaging result. Table 2 is a table showing the parameters of the experiment.

The lines of the Ronchi ruling are reflected on the whole, but there are stripes that appear at different angles and pitches from the Ronchi ruling. These are moire fringes.
Since the moire fringes appear as fine interference fringes and Ronchi ruling, moiré fringes appear and disappear at the same intervals as when the interval in the depth direction is obtained from the amplitude distribution.
By photographing the moire fringes, we were able to confirm the pattern appearing in the depth direction without image processing.

Furthermore, in another experiment, a fringe pattern in the depth direction was generated by three-beam interference, and an experiment was conducted to confirm that it was the same as the numerical analysis. The optical system used in the experiment is shown in FIG. 11-4. Table 3 shows each experimental condition during the experiment. A laser with a wavelength of 532 nm was used as the light source.

Moreover, it is confirmed by experiments that the phase shift of the interference pattern that changes in the direction of the optical axis can be performed by the phase shift. The light source is a DDS (Diode Direct SHG) laser with a wavelength of 532 nm. 2010) 54.) was used.

A beam emitted from the laser was split into three by three mirrors. These mirrors were placed with a slight rotation so that the split beams interfered on the object. The camera was equipped with a lens with a focal length of 150 mm and was placed next to the mirror. The interval between interference patterns appearing in the direction orthogonal to the optical axis direction can be obtained from Equation (2).

FIG. 12 shows the interference fringes photographed by the camera. In this image, there are portions where fine interference fringes are visible and portions where they are not visible, and it can be seen that results similar to the simulation results shown in FIG. 8 are obtained. As a result, it was confirmed that an interference pattern varying in the optical axis direction appeared due to the interference of the three light beams. As in the simulation result shown in FIG. 8, this photographed image also has a low contrast between regions W and B, so the spatial fringe analysis method is used to obtain the amplitude distribution of fine interference fringes. The results are shown in FIG.

However, with only this processing, there are bright spots even within region B due to the influence of speckles. Therefore, a smoothing process is performed to reduce the influence of this point. FIG. 14 shows the result of smoothing FIG. 13 by 9×9 pixels. It can be confirmed that the area W and the area B appear at regular intervals. By obtaining the amplitude distribution, it was possible to obtain the change in the intensity distribution appearing in the optical axis direction as a light-dark pattern. A ruler placed on the object was photographed to obtain the interval of the interference pattern appearing in the optical axis direction, and the size of one pixel was calculated from the scale of the ruler.

As a result of the measurement, the spacing of the interference patterns appearing on the object was 7.0 mm. Since the surface of the projecting object has an inclination of 40°, the spacing of the interference patterns along the optical axis is 5.4 mm. Since this value is almost the same as the result of the simulation performed with the same parameters, it was confirmed that an interference pattern that varies in the optical axis direction appeared due to the laser interference of the three beams.

Next, the change in the projection pattern due to the interference of the three light fluxes when the phase of Mirror 0 in FIG. 11-4 is shifted will be confirmed. Mirror 0 shifts the phase by translating the mirror in the out-of-plane direction using a piezo stage. It has been confirmed by simulation that the amount of phase shift required for the pattern to move by one period is π. The phase shift amount of is π/2, which is half of this.

Since the experiment uses a light source with a wavelength of 532 nm, the necessary phase shift amount is 133.5 nm. Since it is desired to set the shift amount Δφ of the pattern by π/2, one shift amount is 33 nm, which is π/8 of the wavelength of the light source. FIG. 15 shows the amplitude distribution obtained from the photographed pattern. Looking at FIG. 15, it can be confirmed that the interference pattern in the optical axis direction moves with the phase shift of Mirror 0 .

Further, FIG. 16 shows the phase distribution of the fringe pattern in the depth direction obtained by the phase shift method. Since the amplitude distribution shown in FIG. 13 has a lot of noise due to speckles, a lot of noise appears in the phase image as well. Therefore, the phase distribution was obtained by the phase shift method from the smoothed amplitude image (FIG. 14). The pixels used for smoothing in this case are 31×31 pixels. FIG. 17 shows the phase obtained by performing the phase shift method after performing the smoothing process. Since the speckle disappeared, the phase distribution of the depth direction fringe pattern appeared clearly.

Next, the pattern with the phase shift applied to the planar object is photographed, and calibration is performed. FIG. 18 shows the optical system used to create the reference plane. The plane object was moved by 0.5 mm from 0.0 to 5.0 mm. The phase at each position was determined, and the phase difference from the phase at 0.0 mm was determined. A phase image and a phase contrast image at a displacement of 5.0 mm are shown in Figs. 19 and 20, respectively. FIG. 21 shows a graph showing the relationship between the displacement and the change in phase by obtaining the average value of each phase difference on one line. The slope of this approximate straight line was 1.2 rad/mm. Accordingly, the displacement can be obtained using Equation (8).

Also, the z-coordinate can be obtained from Equation (9).

Next, shape measurement is performed using the coated metal plate. The size of the metal plate used is 100 mm×10 mm. The sample is placed at an angle to the optical axis, and the displacement in the direction of the optical axis is determined from the change in phase at this time. Measurement was performed with the sample tilted at 60° and 45°. Fig. 22 shows the sample when set at 60°. FIG. 23 shows the obtained phase, and FIG. 24 shows the shape profile obtained based on FIG.

From the slope of the approximate straight line obtained, the measurement result of the object set at 60.0° was 60.6°, and the measurement result of the object set at 45.0° was 45.2°. We were able to obtain the measurement results at almost the same angle as the installed angle.

Subsequently, the plane portion and the oblique portion of the sample shown in FIG. 11-4(c) are photographed at the same time, and shape measurement is performed in the same manner as for the flat plate. The obtained phase image is shown in FIG. 25, and the shape profile is shown in FIG. From the measurement results, it was confirmed that the diagonal part and the flat part can be measured at the same time. The inclination of the oblique part (y = 3.0 to 4.9) was 40.7° and the inclination of the flat part (y = 1.0 to 3.0) was 86.4°.
The angle between the two surfaces of the measurement sample was 127.1° against the angle of 130° between the two surfaces of the measurement sample, which is close to the angle of the measurement sample. Speckle noise is considered to have a large effect on the variation in measurement results in these measurements.

(8) Enlargement measurement method of horizontal measurement area using spherical wave (8-1) Measurement principle of the present invention In the optical system (see FIG. 3) described so far, laser light is collimated by a collimating lens. , it is difficult to increase the measurement range in the lateral direction of the optical axis.
Therefore, in the measuring method according to the present invention described below, the object is irradiated with the laser beam as a spherical wave instead of as a parallel beam. Here, the horizontal direction refers to a plane perpendicular to the direction in which the intensity distribution fluctuates in the fringe pattern in the depth direction.

As a result, the incident light spreads and reaches the object to be measured, so that the irradiated area becomes large. FIG. 27 shows an optical system for realizing this. As can be seen from FIG. 27, the laser light is not parallel light but expanded light expanding in the direction of the optical axis, so the reflected light from each mirror also irradiates the object as a spherical wave.

At this time, as described above, the laser light, which is a spherical wave, spreads while propagating and reaches the object to be measured. Therefore, compared with the case of parallel light, the measurement area in the horizontal direction orthogonal to the optical axis direction becomes larger. FIG. 27 shows an optical system for analytically obtaining a fringe pattern in the depth direction from the interference fringes obtained with a spherical wave by a fringe analysis method. It is also possible to optically generate a fringe pattern in the depth direction in advance.

Further, in this case, it is also possible to use a mirror of any shape designed so that the incident light, which is a spherical wave, similarly overlaps and interferes on the object to be measured (see FIG. 27(b)). In this case, the optical system can be constructed with a single mirror.

(8-2) Simulation-Based Example In the following, a simulation performed to confirm that the method can also be implemented with spherical waves will be described. Table 4 shows the parameters used in the simulation, and FIG. 28 shows the optical model for this simulation. The amplitude distribution on the xz plane of the light wave within the analysis area of FIG. 28 can be expressed by Equation 10.

Here, A0, A1, and A2 are the intensities of Beam0, Beam1, and Beam2, b1 is the x-coordinate of Beam1, and b2 is the x-coordinate of Beam2.

FIG. 29 shows interference fringes on the xz plane when spherical waves are used. It can be seen that interference fringes appear as in the case of parallel light. In addition, it can be seen that the intensity of interference fringes also appears as moire fringes in the depth direction. Therefore, even in the case of spherical waves, it can be seen that a fringe pattern in the depth direction can be obtained in the same way as with parallel light.

In addition, in order to confirm the three-dimensional appearance of the interference fringes in detail, the amplitude distribution of the interference fringes on the xy plane at each depth (z) position was obtained. The parameters used in the simulation in this case are shown in Table 5, and the optical model is shown in FIG. What is the amplitude distribution on the xy plane of the light wave within the analysis area of FIG. It can be expressed by Equation 11.

where D is the z-direction distance from Beam0 to the observation point.
Here, the analysis was performed by changing the z-position to be analyzed from 750 mm to 755 mm by 1 mm.
FIG. 31 shows the amplitude distribution of interference fringes on the xy plane at each z position obtained by simulation. It can be seen that the intensity of the interference fringes changes periodically as the measurement plane is moved in the z direction.

Also, in FIG. 29, it can be seen that the pattern appears only in the y direction because moire fringes do not occur at the z position corresponding to the region where the interference fringes are weakened. When the amplitude distribution of moiré fringes (the fringe pattern in the depth direction) is obtained, the distribution in the y direction only disappears. Thus, even in the case of spherical waves, it is possible to perform the method of the present invention in the same way as with parallel light. Further, as described above, when this technique is executed with a spherical wave that spreads the incident light on the object to be measured, the measurement area in the horizontal direction can be expanded.
So far, we have discussed the case of an optical system that uses a beam splitter and three mirrors, arbitrarily shaped mirrors designed to interfere, to produce three beams from a single laser.

(8-3) Simplification of Optical System Using Optical Fibers An optical system using optical fibers instead of a beam splitter, three mirrors, and arbitrary-shaped mirrors designed to interfere will be described below. 32(a) and 32(b) show schematic diagrams of an optical system that implements the present invention using optical fibers.

In this optical system, first, a laser beam is coupled to an optical fiber. Alternatively, commercially available fiber-out lasers can also be used. Then, the fiber splitter splits the light wave into three optical fibers. Then, the object to be measured is irradiated with the light wave emitted from the branched optical fiber. At this time, the light waves emitted from each optical fiber interfere with each other because they are originally the same laser light source.

Therefore, the same effect as in the case of creating a three-beam optical system using a beam splitter and three mirrors can be obtained, and the optical fiber has less spatial restrictions, so the measurement unit can be made smaller. Furthermore, since the laser beam can be emitted through an optical fiber, there is no need to insert the laser main body into the measurement unit, which makes it possible to significantly reduce the size of the measurement unit. Since the light wave emitted from the optical fiber is normally a spherical wave, another advantage is that the method using the above spherical wave can be easily applied.

The divergence angle of light emitted from a fiber is determined by the core system of the fiber. In order to obtain a desired divergence angle, a lens may be arranged at the fiber output end as shown in FIG. 32(b). This makes it possible to generate a spherical wave with an arbitrary divergence angle even when using an arbitrary fiber.

Consider the case where phase shift is performed in an optical system using optical fibers. An optical system in that case is shown in FIG. A phase shift can be easily performed by attaching a fiber-based phase shifter to any one of the three branched optical fibers. Here, as shown in FIG. 33(b), even in this case, a spherical wave having an arbitrary divergence angle can be generated by arranging a lens at the fiber output end.

In the case of FIG. 33, a phase shift is applied to the central optical fiber. In this way, even an optical system using an optical fiber can perform phase shift, so that phase analysis of a fringe pattern in the depth direction can be performed. Also, since fiber optic based phase shifters are generally small, the size of the measurement unit can be kept small. Parameters such as the core system of the optical fiber can be determined by designing the optical system such as the wavelength of the light source used and the distance to the object.

0 mirror 1 mirror 2 mirror

Claims (5)

In a measurement method in which interference fringes are projected onto the surface of an object and the reflected light of the projected interference fringes is captured by an imaging means,
Based on the principle of interference by coherent light waves irradiated from three directions, the interference fringes are three-beam interference fringes consisting of regions where interference fringes appear and regions where interference fringes do not appear in the irradiation direction of light irradiated from three directions. formed,
A measurement method for measuring the displacement or the three-dimensional shape of the object by imaging fringes formed by the three-beam interference fringes formed on the surface of the object. In a three-beam measurement device that projects interference fringes on the surface of an object and captures the reflected light of the projected interference fringes with imaging means,
a light source that emits coherent light;
three-beam forming means for forming three coherent light waves from the coherent light from the light source and projecting three-beam interference fringes on the surface of the object;
imaging means for receiving reflected light from the surface of the object;
means for measuring the displacement or three-dimensional shape of the object based on fringes formed by the three-beam interference fringes formed on the surface of the object imaged by the imaging means;
A three-beam measuring device with 3. The three-beam measuring device according to claim 2, comprising a grating plate that forms moire fringes from the three- beam interference fringes. 4. The three-beam measuring device according to claim 3, further comprising means for determining the amplitude or power of said moire fringes by a phase analysis method. phase shift means for phase-shifting one of the three coherent light waves to shift the phase of the fringe pattern of the three-beam interference fringes in the direction of light emission;
The three-beam measuring device according to any one of claims 2 to 4.

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