JP2010256192A - Shape measuring method and shape measuring device by phase shift method, complex amplitude measuring method, and complex amplitude measuring device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a shape measuring method and a device or the like capable of measuring the shape of a measuring object with high measurement accuracy, even when having disturbance vibration or air fluctuation. <P>SOLUTION: This shape measuring device includes: a branching device 6 for branching a coherent light flux 11 emitted from a light source 1, and irradiating a measuring object 7 and a reference mirror 8 therewith; a driving device 20 generating relative motion between the measuring object 7 and the reference mirror 8; a superimposing device 6 for forming an interference fringe by superimposing object light 12 reflected by the measuring object 7 on reference light 13 reflected by the reference mirror 8; an imaging device 10 for acquiring continuously-imaged data acquired by imaging the interference fringe continuously; and a calculation device 21 for calculating a three-dimensional shape of the measuring object 7 from the continuously imaged data. By modulating each frequency of the object light 12 and the reference light 13 by relative motion according to a Doppler effect, the calculation device 21 acquires a phase shift spectrum from a spectrum of a frequency difference between both lights, and calculates the three-dimensional shape of the measuring object 7 from the phase shift spectrum and the continuously imaged data. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a shape measuring method, a shape measuring device, a complex amplitude measuring method, and a complex amplitude measuring device using a phase shift method. More specifically, the present invention relates to a shape measuring method and apparatus that can satisfactorily measure the shape of an object to be measured and a method and apparatus that can perform complex amplitude measurement with high accuracy even when disturbance or the like occurs.

  In phase shift interferometry, object light reflected by a subject (also referred to as an object to be measured) and reference light reflected by a reference mirror are superimposed, and the resulting interference fringes are recorded and acquired by an imaging device such as a CCD camera. This is a technique for measuring the shape of a three-dimensional object using a phase shift method as an analysis method for the obtained data. The phase shift method is a technique for acquiring three or more interference fringe images by changing the phase of the reference light by a certain amount, and extracting only the complex amplitude information of the object to be measured by calculation. The shape can be calculated. Further, by dividing the reference light into three or more regions having different phases, it is also possible to obtain information on the object to be measured from one acquired image.

  Digital holography, on the other hand, superimposes the object light reflected by the object to be measured and the reference light reflected by the reference mirror, records the generated interference fringes with an imaging device such as a CCD camera, and uses the computer to generate the diffracted light. This is a technique for obtaining a three-dimensional object shape by simulating. However, the simulated diffracted light includes unnecessary 0th-order light and −1st-order light in addition to the 1st-order light, and it is necessary to remove them. Here, the 0th order light is a reference light component, the primary light is an object light component from the object to be measured, and the −1st order light is a component of its conjugate wave.

  In recent years, phase shift digital holography that applies a phase shift method to digital holography has attracted attention as a three-dimensional measurement technique such as object displacement measurement and shape measurement. In conventional phase shift interferometry and phase shift digital holography, a reference mirror mounted on a movable stage is moved minutely, and the phase of the reference light is changed by π / 2. A method of creating a subject image or a digital hologram is used. Note that the difference between phase shift interferometry and digital holography is whether or not the subject and the camera are in an imaging relationship.

  Non-Patent Document 1 below proposes a technique for measuring the shape of an object using phase shift interferometry. FIG. 7 is an experimental configuration diagram described in the same document. A symbol M1 in FIG. 7 represents a device under test whose shape is slightly deformed from a plane, and a symbol M2 represents a reference mirror having a planar shape. In the measuring apparatus shown in FIG. 7, the shape of the DUT M1 is measured based on the planar shape of the reference mirror M2. In FIG. 7, light emitted from a laser is expanded by two lenses L1 and L2, and is divided into two lights by a beam splitter (BS). One light is reflected by the beam splitter (BS) and irradiates the object to be measured M1, and the other light passes through the beam splitter (BS) and enters the reference mirror M2.

  The light reflected by the object to be measured M1 (this light is called “object light”) returns to the original optical path, a part of which passes through the beam splitter (BS) and the lens L3, and enters the photo detector. To do. At this time, the lens L3 forms an image of the object to be measured M1 on a photo detector. On the other hand, the light reflected by the reference mirror M2 (this light is referred to as “reference light”) also returns to the original optical path, a part of which is reflected by the beam splitter (BS), and passes through the lens L3 in the same manner as the object light. Then, it is incident on a photo detector. At this time, the object beam and the reference beam overlap to form an interference fringe as illustrated in FIG. If the DUT M1 is also in the same plane as the reference mirror M2, the formed interference fringes are straight lines at equal intervals (for example, pitch P). However, it can be seen that the interference fringes shown in FIG. 8 are slightly deformed as represented by δ (deformation amount). The shape error of the object can be calculated from the deformation amount.

  When measuring the shape error with the naked eye, first measure the stripes. The relationship between the average pitch P and the average spatial frequency f representing the fringe density (the number of interference fringes per unit length) can be written as the following equation (a). Here, assuming that the object to be measured M1 is deformed by ε from the plane, the object light reflected by the object to be measured M1 is shifted in phase by an amount corresponding to 2ε with respect to the reference light. Let φ be the phase difference between the object beam and the reference beam. When the interference fringes are displaced by exactly one fringe, the phase difference φ between the object beam and the reference beam is 2π. At this time, when the phase difference φ is expressed using the deformation amount δ of the interference fringes, the following equation (b) is obtained. On the other hand, when the wavelength of the laser beam is λ, the relationship between the deformation amount ε and the phase difference φ can be written as the following equation (c). That is, if the deformation amount δ of the measurement object M1 is measured from the interference fringes and the phase difference φ is obtained, the deformation amount ε can be obtained, and the shape measurement of the measurement object M1 can be performed.

  In the conventional shape measurement, the phase difference φ is automatically obtained by image processing and arithmetic processing. For example, in the following Non-Patent Document 1, the interference fringe intensity distribution can be expressed by the following formula (1 ′), and when the Fourier transform calculation is performed on the interference fringe intensity distribution by the following formula (2 ′), the spatial frequency of the interference fringes Information including f and the phase difference φ is supposed to be obtained. When the following expressions (5 ′) and (6 ′) are calculated, the phase difference φ is obtained, and the deformation amount ε is obtained from the above expression (c).

  The following Patent Documents 1 to 3 and the like have been proposed for vibration-resistant interferometers that are unlikely to be affected by external vibrations or air disturbances near the object to be measured.

  For example, Patent Document 1 below provides a device that quantitatively evaluates an error caused by a disturbance to a measurement value in measurement using an optical interferometer, and based on the result, provides an apparatus in which the measurement error is less than an allowable value. To do. Specifically, a disturbance measuring device and a measuring device using the measured value give a phase difference that changes in a sawtooth shape between the object light and the reference light in the interference optical system. By measuring the phase difference using a sinusoidal change and sampling the phase difference at a constant frequency, it is possible to evaluate the frequency characteristics of the amount of error caused by the disturbance to the measurement value. It is. This measuring device divides the interference light into two light beams, provides openings at positions corresponding to different parts of the measured object with each light beam, and measures the phase difference between the interference light beams that have passed through the openings, thereby measuring disturbance. It is possible to evaluate the spatial distribution of the error amount given to the value. Based on the result, the frequency of the sawtooth phase difference necessary for achieving the measurement accuracy is determined.

  Patent Document 2 below relates to an interferometer that improves the measurement accuracy of the surface shape and surface accuracy of an aspheric lens. Specifically, a means for dividing a coherent light beam emitted from the same light source into a reference wave and a test wave, a wavefront forming means for forming a wavefront corresponding to the measurement surface of the test object in the reference wave, and the above Superimposing means for superimposing the reference wave and the test wave, imaging means for observing interference fringes formed via the superimposing means, and surface shape and surface accuracy of the measurement surface by taking in output data of the imaging means The wavefront forming means includes a phase control element capable of arbitrarily modulating the phase of the reference wave applied to the surface to be measured. There has been proposed an interferometer that analyzes output data of the imaging means based on a phase modulation amount by a phase control element.

  Patent Document 3 below relates to a vibration-resistant interferometer suitable for measuring the surface shape of an optical member or the like that requires a highly accurate measurement result. Specifically, the coherent light is irradiated to the reference surface on the reference plate and the test surface on the subject, and interference fringes due to the reference light from the reference surface and the object light from the test surface are observed on the observation surface. An interference fringe forming means formed above, a light detection means for detecting a local light quantity of the interference fringe image disposed at a predetermined position on the observation surface, and an optical path difference between the reference light and the object light. The vibration applying means for applying a predetermined vibration to any member in the optical path of the interference fringe forming means, and the vibration applying means so as to reduce the change in the amount of light detected by the light detecting means. There has been proposed a vibration-resistant interferometer provided with a control means for controlling the vibrations.

Guanming Lay and Toyohiko Yatagai, “Use of the fast Fourie transform method for analyzing linear and equispaced Fizeau fringes”, Applied Optics, Vol.33, No.25, 5935-5940 (1994)

JP 2004-150965 A JP 2001-174233 A Japanese Patent Laid-Open No. 8-114412

  In the prior art described in Non-Patent Document 1, when there is disturbance vibration or air fluctuation, the optical path length from the laser to the photodetector relatively changes between the object light and the reference light. When the interference fringes fluctuate due to such changes, it is impossible to distinguish whether the fluctuation of the interference fringes is due to shape deformation or disturbance, and the measurement accuracy is significantly reduced. Therefore, high-accuracy measurement has a problem that an expensive and large-sized device is required to block disturbance, and operability is deteriorated.

  Further, since the pitch P of the interference fringes can be obtained with higher accuracy as the number of interference fringes increases, the accuracy of the spatial frequency f obtained by Fourier expansion increases. However, since the number of pixels of the image captured by the photodetector is limited, the resolution per pixel is limited. Therefore, the calculated resolution of the required phase difference φ is reduced. As described above, the measurement accuracy is limited by the number of pixels of the photodetector.

  Also, with the conventional phase shift method that moves the movable stage by a certain amount, it is difficult to measure objects with dynamic changes because the measurement accuracy decreases and the time delay occurs due to disturbances such as minute vibrations of the optical system. There is also the problem of being.

  Further, in the phase shift method obtained by spatially dividing a plurality of images from one image without using a movable stage, the resolution is lowered because the number of pixels of the divided images is reduced.

  The present invention has been made to solve the above problems, and its purpose is to enable measurement of the shape of an object to be measured with high measurement accuracy even when there are disturbance vibrations and air fluctuations. The object is to provide a shape measuring method and a shape measuring apparatus. Another object of the present invention is to provide a complex amplitude measuring method and a complex amplitude measuring apparatus by a phase shift method using the Doppler effect.

  The shape measuring method according to the present invention for solving the above-described problem is that the coherent light beam emitted from the same light source is branched to irradiate the object to be measured and the reference mirror, and the object light reflected by the object to be measured and the A method of superimposing the reference light reflected by the reference mirror and measuring the shape of the object to be measured from the obtained interference fringe data, causing a relative movement between the object to be measured and the reference mirror, Continuous imaging data is obtained by continuously imaging the intensity distribution of the interference fringes changed by the relative motion, and the object light and the reference light are modulated by modulating the frequencies of the object light and the reference light by the Doppler effect. A phase shift spectrum converted from a frequency difference spectrum into a phase shift amount is obtained, and a three-dimensional shape of the object to be measured is measured from the phase shift spectrum and the continuous imaging data.

  In the shape measuring method according to the present invention, the relative movement between the object to be measured and the reference mirror is generated by moving the object to be measured or the reference mirror in parallel with the optical axis of the irradiation light.

  In the shape measuring method according to the present invention, the three-dimensional measurement of the object to be measured is performed by applying a Doppler phase shift method to the intensity distribution of the interference fringes and extracting a complex amplitude of the obtained primary light. .

  In the shape measuring method according to the present invention, the sampling frequency of the interference fringes is more than twice the frequency difference between the object light and the reference light.

  The shape measuring apparatus according to the present invention includes a light source, a branching device that divides a coherent light beam emitted from the light source and irradiates the object to be measured and the reference mirror, and the object to be measured and the reference mirror. A driving device that causes relative movement between the driving device, a superimposing device that forms an interference fringe by superimposing the object light reflected by the object to be measured and the reference light reflected by the reference mirror, and imaging for imaging the interference fringe And a calculation device that calculates a three-dimensional shape of the object to be measured from the continuous imaging data, and the calculation device modulates the frequencies of the object light and the reference light by the Doppler effect by the relative motion. Thus, a phase shift spectrum obtained by converting the spectrum of the frequency difference between the object beam and the reference beam into a phase shift amount is obtained, and the three-dimensional shape of the object to be measured is calculated from the phase shift spectrum and the continuous imaging data. Characterized in that it.

  In the shape measuring apparatus according to the present invention, the drive device causes the object to be measured or the reference mirror to move in parallel with the optical axis of the irradiation light to cause relative movement.

  In the shape measurement apparatus according to the present invention, the calculation apparatus applies a Doppler phase shift method to the intensity distribution of the interference fringes, extracts a complex amplitude of the obtained primary light, and extracts 3 of the object to be measured. Calculate the dimensional shape.

  In the shape measuring apparatus according to the present invention, the imaging apparatus sets the sampling frequency of the interference fringes to more than twice the frequency difference between the object light and the reference light.

  The complex amplitude measurement method according to the present invention divides a coherent light beam emitted from the same light source, irradiates the object to be measured and the reference mirror, and reflects the object light reflected by the object to be measured and the reference mirror. A method of measuring the complex amplitude of the object light from the obtained interference fringe data, wherein a relative motion is generated between the object to be measured and the reference mirror, and the relative motion The intensity distribution of the interference fringes changed by the above is continuously imaged to obtain continuous imaging data, and the frequency difference between the object light and the reference light is modulated by modulating the frequency of the object light and the reference light by the Doppler effect. A phase shift spectrum converted into a phase shift amount from the spectrum is obtained, and a complex amplitude of the object light is measured from the phase shift spectrum and the continuous imaging data.

  A complex amplitude measuring apparatus according to the present invention includes a light source, a branching device that divides a coherent light beam emitted from the light source and irradiates the measured object and the reference mirror, and the measured object and the reference mirror. A driving device that causes relative movement between the driving device, a superimposing device that forms interference fringes by superimposing the object light reflected by the object to be measured and the reference light reflected by the reference mirror, and the interference fringes continuously. An imaging device that obtains continuous imaging data by imaging, and a calculation device that calculates a complex amplitude of the object light from the continuous imaging data, wherein the calculation device calculates the object light and the reference light by the relative motion; A frequency shift is modulated by the Doppler effect to obtain a phase shift spectrum converted from a spectrum of a frequency difference between the object light and the reference light into a phase shift amount, and from the phase shift spectrum and the continuous imaging data, And calculating a complex amplitude of the object light.

  According to the present invention, the drive device that generates relative motion between the object to be measured and the reference mirror continuously captures the intensity distribution of the interference fringes changed by the relative motion to obtain continuous imaging data, By modulating the frequency of the object light and the reference light by the Doppler effect, a phase shift spectrum obtained by converting the spectrum of the frequency difference between the object light and the reference light into a phase shift amount is obtained. This phase shift spectrum shows the respective signal strengths when the phase shift method is performed with a certain phase shift amount, and there is a phase shift amount that is not affected by disturbance. As a result, the three-dimensional shape of the object to be measured and the complex amplitude of the object light can be measured from the phase shift spectrum and the obtained continuous imaging data. According to such a measurement means, measurement with high measurement accuracy is possible even when there is disturbance vibration or air fluctuation.

  In particular, in the present invention, a phase shift is generated by modulating the angular frequency of the object light and / or the reference light by the Doppler effect by relatively moving the object to be measured and the reference mirror, and the object light and the reference light A phase shift method for extracting information of only the primary light from a phase shift spectrum converted from a frequency difference spectrum into a phase shift amount is applied. That is, since only the complex amplitude of the primary light can be extracted from the continuous imaging data of the interference fringes obtained by changing the phase of the object light and / or the reference light, the 0th order conventionally included in the simulated diffracted light. It is possible to remove light and minus first-order light and to minimize the influence of external vibrations on the reproduced image. Specifically, for example, when a phase shift is generated by moving the reference mirror, a reconstructed image from which the 0th-order light and the −1st-order light are removed can be obtained, and the phase shift is caused by vibration of the optical system. Is generated, a reproduced image is obtained by adding both the −1st order light component and the primary light component. If such a phase shift method according to the present invention is used for three-dimensional measurement of an object to be measured, measurement accuracy can be remarkably improved even when there is disturbance vibration or air fluctuation, and an expensive large-sized apparatus. Is also unnecessary, and the problem of poor operability does not occur.

It is the schematic which shows the optical system which concerns on this invention. It is explanatory drawing until a phase shift spectrum is obtained from the intensity distribution of interference fringes. It is a phase shift spectrum when the reference mirror is moved at a constant speed. It is a phase shift spectrum when an optical system is vibrated. It is the reproduction | regeneration image obtained in FIG. It is the reproduction | regeneration image obtained in FIG. It is an experiment block diagram described in the nonpatent literature 1. It is an example of the interference fringe obtained by the experimental system of FIG.

  Hereinafter, a shape measuring method and apparatus, and a complex amplitude measuring method and apparatus according to the present invention will be described in detail with reference to the drawings.

[Shape measuring method and shape measuring apparatus]
In the shape measuring method according to the present invention, as shown in FIG. 1, the coherent light beam 11 emitted from the same light source 1 is branched, irradiated to the measured object 7 and the reference mirror 8, and reflected by the measured object 7. A method of superimposing the object light 12 and the reference light 13 reflected by the reference mirror 8 and measuring the shape of the object 7 to be measured from the obtained interference fringe data, between the object 7 and the reference mirror 8. The relative motion of the interference fringes changed by the relative motion is continuously imaged to obtain continuous imaging data, and the frequencies of the object beam 12 and the reference beam 13 are modulated by the Doppler effect. A phase shift spectrum converted into a phase shift amount from the spectrum of the frequency difference between the object beam 12 and the reference beam 13 is obtained, and the three-dimensional shape of the DUT 7 is measured from the phase shift spectrum and the continuous imaging data.

  Further, as shown in FIG. 1, the shape measuring apparatus 1 according to the present invention branches a light source 1 and a coherent light beam 11 emitted from the light source 1 and irradiates the measured object 7 and the reference mirror 8. 6, a driving device 20 that causes relative movement between the DUT 7 and the reference mirror 8, and the object light 12 reflected by the DUT 7 and the reference light 13 reflected by the reference mirror 8 are overlapped. A superimposing device 6 that forms interference fringes; an imaging device 10 that continuously images the interference fringes to obtain continuous imaging data; and a calculation device 21 that calculates a three-dimensional shape of the object 7 to be measured from the continuous imaging data; Have The calculation device 21 then converts the frequency difference between the object light 12 and the reference light 13 into a phase shift spectrum from the spectrum of the frequency difference between the object light 12 and the reference light 13 by modulating the frequency of the object light 12 and the reference light 13 by the Doppler effect. And the three-dimensional shape of the DUT 7 is calculated from the phase shift spectrum and the continuous imaging data.

(Shape measurement)
The method and apparatus of the present invention relating to shape measurement will be described in detail using the shape measuring apparatus 30 shown in FIG.

  The type of the light source 1 is not particularly limited. For example, a He-Ne laser having a wavelength of 632.8 nm is used. The coherent light beam 11 emitted from the laser light source 1 passes through a neutral density (ND) filter 2, passes through a collimator including a lens 3, a spatial filter 4, and a lens 5, and is expanded into parallel light. Become. The parallel light is split into two lights by a beam splitter 6 (also referred to as a branching device 6).

  One of the divided light beams is reflected 90 ° upward on the paper surface and travels toward the object 7 to be measured, while the other light is transmitted as it is and travels toward the reference mirror 8. The light traveling toward the object to be measured 7 is reflected by the surface thereof to become object light 12. On the other hand, the light directed to the reference mirror 8 is also reflected on the surface thereof to become the reference light 13. The object beam 12 and the reference beam 13 return to the beam splitter 6 again and overlap. The overlapping object beam 12 and reference beam 13 form an interference fringe, go downward in the drawing, and are imaged by a continuous imaging camera 10 (also referred to as an imaging device).

  In the shape measuring apparatus 30, the type of the light source 1 is not limited to the He—Ne laser, and may be a gas laser or a semiconductor laser with high coherence. Both the neutral density filter 2 and the spatial filter 4 are arbitrarily provided as necessary. The spatial filter 4 cuts unnecessary light such as ghost light and reflected light. The beam splitter 6 in which the object light 12 and the reference light 13 overlap functions as a branching device, but also functions as a superimposing device in the above.

  In the example of FIG. 1, since the drive device 20 is provided in the reference mirror 8, the angular frequency of the reference light 13 is modulated by the Doppler effect by moving the reference mirror 8 relative to the object 7 to be measured. ing. In the example of FIG. 1, the reference mirror 8 is moved, but the DUT 7 may be moved. Examples of the drive device 20 include a drive device using a DC motor as a drive source, a drive device using a piezo element as a drive source, and a drive device using a stepping motor as a drive source.

  The relative motion in this case may be moved by providing the driving device 20 on one of the measured object 7 and the reference mirror 8 or may be moved arbitrarily by providing the driving device 20 on both. . Further, the movement may be a constant speed or a non-constant irregular (non-uniform, random) speed as long as the movement is performed in a direction parallel to the optical axis. When both the DUT 7 and the reference mirror 8 are moved, it is preferable that the respective speeds are different. Such relative movement is performed by the driving device 20 attached to the DUT 7 or the reference mirror 8, but the irregular speed may be irregular performance derived from the driving device 20. .

  The object 7 to be measured, which is an object for shape measurement, is not particularly limited, and examples thereof include a plane mirror, a concave mirror, and a diffractive optical element. The shape and size of the DUT 7 that can be preferably applied is preferably, for example, a size of about several millimeters square to several centimeters square and having an uneven surface having a wavelength of the illumination laser beam. In the examples described later, five hundred yen coins are measured experimentally. In addition, the measurement range of unevenness can be adjusted by combining a multi-wavelength method of illuminating with a plurality of laser beams having different wavelengths.

  As the reference mirror 8, it is preferable to use a plane mirror whose surface roughness is sufficiently smaller than the surface unevenness of the object 7 to be measured.

  The continuous imaging camera 10 (imaging device 10) is connected to a computer 21 (calculation device 21) and performs arithmetic processing on the captured interference fringe data (image data). As the continuous imaging camera 10, a CMOS camera capable of high-speed imaging is preferably used, but other cameras may be used and are not particularly limited. The imaging speed of the continuous imaging camera 10 will be described later.

  In the present invention, the drive device 20 that generates relative motion between the DUT 7 and the reference mirror 8 continuously captures the intensity distribution of the interference fringes changed by the relative motion to obtain continuous image data. The frequency of the object light 12 and the reference light 13 is modulated by the Doppler effect, thereby obtaining a phase shift spectrum converted from the frequency difference spectrum of the object light 12 and the reference light 13 into the phase shift amount. This phase shift spectrum shows the respective signal strengths when the phase shift method is performed with a certain phase shift amount, and there is a phase shift amount that is not affected by disturbance. As a result, the three-dimensional shape of the DUT 7 can be measured from the phase shift spectrum and the continuous imaging data obtained. Similarly, the complex amplitude of the object light 12 can be measured. According to such a measurement means, measurement with high measurement accuracy is possible even when there is disturbance vibration or air fluctuation.

(Doppler phase shift method)
Next, the Doppler phase shift method will be described.

As shown in FIG. 1, when irradiated with plane wave to the reference mirror 8 and the object 7 to be measured, the complex amplitude U _R of the complex amplitude U _O and reference light 13 of the object beam 12 on the imaging surface of the continuous imaging camera 10 The following equations (1) and (2) are obtained.

Here, A _O , φ _O , ω _O , A _R , φ _R , and ω _R are the amplitude, phase, and angular frequency of the object beam 12 and the amplitude, phase, and angular frequency of the reference beam 13, respectively. If the object 7 to be measured is moving at a speed _{v O = (v O, x} , v O, y, v O, z), subjected to frequency modulation by the Doppler effect. At that time, the frequency is considered to vary depending on the traveling direction of the plane wave. The angular frequency of the object beam 12 can be expressed as in Expression (3) by the Doppler effect.

Here, ω _O , c, v _O , and k are the angular frequency of incident light, the speed of light, the magnitude of v _O , and the magnitude of k, respectively. When the moving speed of the DUT 7 is sufficiently smaller than the speed of light, the equation (4) is obtained.

  Similarly, the angular frequency of the reference beam 13 is expressed by Equation (5).

Here, v _R = (v _{R, x} , v _{R, y} , v _{R, z} ) is a moving velocity vector of the moved reference mirror 8. When the interference fringes of the object beam 12 and the reference beam 13 are continuously recorded by the continuous imaging camera 10, the time-dependent digital hologram is expressed by Equation (6).

  When this is subjected to time Fourier transform, Equation (7) is obtained. Equation (8) is the phase difference between the object light 12 and the reference light 13 that does not include a phase shift due to the Doppler effect, that is, the phase of the wavefront of the object light 12.

  Here, a and b are arbitrary functions with respect to ω, and have a relationship of Expression (9). Equation (10) is the angular frequency difference between the object beam 12 and the reference beam 13 due to the Doppler effect.

Here, when the frequency difference Δω / 2π between the object beam 12 and the reference beam 13 is smaller than ½ of the sampling frequency of the continuous imaging camera 10, the second term of the above equation (7) is The term and the third term can be separated. Here, when ω = ω ₁ and other than the second term is 0, equation (7) becomes equation (11).

Here, since A _R a (ω) and b (ω) −φ _R are spatially constant, the complex amplitude of the object light 12 can be extracted by the above equation (11).

  As described above, the Doppler phase shift method proposed in the present invention can be applied even when the phase of the reference beam 13 is arbitrarily changed. The resulting phase difference between the object beam 12 and the reference beam 13 due to disturbance is regarded as a phase shift that takes into account the Doppler effect of light. When the continuous imaging camera 10 is used, the complex amplitude of the object light 12 that is a constant phase shift amount component can be extracted from the state of vibration by capturing the state of vibration. Therefore, according to the Doppler phase shift method proposed in the present invention, it can be applied to an optical system for interference measurement that is resistant to vibration, and a shape measuring method, apparatus, and phase measuring method and apparatus according to the present invention can be obtained. it can.

  Next, algorithms for obtaining a phase shift spectrum and for obtaining a reproduced image from the obtained phase shift spectrum will be described.

  FIG. 2 is an explanatory diagram for obtaining a phase shift spectrum from the intensity distribution of interference fringes imaged by a continuous imaging camera. FIG. 2A is a diagram showing the time variation of the obtained interference fringe intensity obtained by analyzing the interference fringes continuously captured at high speed by the continuous imaging camera 10 constituting the apparatus of FIG. When the intensity at a position where there is an interference fringe obtained in FIG. 2A is subjected to time Fourier transform, it can be expressed as a frequency spectrum shown in FIG. The frequency spectrum obtained in FIG. 2B is converted into a phase shift amount by “phase shift amount = −angular frequency difference Δω due to Doppler effect / sampling frequency” to obtain the phase shift spectrum shown in FIG. It is done.

By detecting the peak position appearing in the phase shift spectrum thus obtained and applying the following equation (12) to each pixel of the continuously photographed image, 1 in the phase shift amount indicated by the peak position of the phase shift spectrum. The complex amplitude U _O ′ of the next light can be extracted. In the following equation (12), N is the number of samplings, Δt is the sampling period, and φ _s is the phase shift amount indicated by the peak position. Further, since the spatial frequency pattern obtained by performing spatial Fourier transform on the interference fringe intensity also changes with time due to the Doppler effect, the phase shift spectrum in the spatial frequency pattern may be obtained.

  Interference fringes generated by superimposing the object beam 12 and the reference beam 13 are recorded as a digital hologram on the imaging surface of the continuous imaging camera 10 that is an image sensor. The intensity and phase pattern of the recorded digital hologram can be reproduced by calculating the complex diffraction pattern of the digital hologram. However, the diffraction pattern of the digital hologram includes 0th-order light and conjugate image (−1st-order light) in addition to the image of the object 7 to be measured.

  In the conventional normal phase shift algorithm, the reference mirror 8 is moved by the driving device 20, the phase of the reference light 13 is shifted by a certain amount every time, and unnecessary using three or more obtained image data. Ingredients are removed. In the aforementioned Non-Patent Document 1, a phase shift algorithm for an arbitrary phase shift amount is proposed. In the method proposed in this document, if the phase shift amount changes with time due to disturbances such as vibration of the optical system and air flow, an error is caused.

  On the other hand, in the method of the present invention, the device to be measured 7 and the reference mirror 8 are relatively moved by the driving device 20 (the reference mirror 8 is moved in Example 1 described later), and the light Doppler is moved. Unnecessary components are removed by the phase shift algorithm using the effect. Therefore, the resultant phase difference between the object light 12 and the reference light 13 due to disturbance is regarded as a phase shift that takes into account the Doppler effect of light, and the state of vibration is determined by using a high-speed continuous imaging camera as the imaging device 10. It can be captured based on a lot of data. As a result, only the complex amplitude of the first-order light can be extracted from the phase shift spectrum, and data from which error data due to disturbances such as zero-order light and −1st-order light is removed can be extracted. Therefore, the optical system of interference measurement resistant to vibration can be obtained, and can be suitably used as a shape measuring method / apparatus.

  When a phase shift occurs due to unintentional vibration applied to the optical system, a reproduced image is obtained by adding both components of the −1st order light and the 1st order light. If the phase shift method according to the present invention is used for three-dimensional measurement of an object to be measured, the measurement accuracy can be remarkably improved even when there are disturbance vibrations and air fluctuations. It becomes unnecessary and the problem of deterioration in operability does not occur.

  Specifically, for example, when the reference mirror 8 is relatively moved, the optical path length of the reference light 13 changes with time. Accordingly, the phase difference between the reference beam 13 and the object beam 12 also changes. The expression representing the intensity of the interference fringes is a function of time t as well as x and y of the two-dimensional image. At this time, each time the reference mirror 8 moves slightly, an interference fringe image is taken with the continuous imaging camera 10 (photodetector 10) and is taken into the calculation device 10 (computer 10). A periodic change in the intensity of the object beam 12 from the point is input to the computer.

  When the object to be measured 7 is not a flat surface and each point is deformed, the time for the object light 12 reflected at the center and the periphery of the object to be measured 7 to reach the photodetector 10 is different. Therefore, the phase of light is different. At this time, when the computer 10 performs a time Fourier transform such that the periodic fluctuation of the interference intensity at each point is expressed by the above equation (7) and further calculates the result of diffraction integration, the intensity distribution and phase of the original object light 12 are calculated. Is required. That is, the same function as the image reproduction by the hologram is obtained.

  Next, the relationship between the disturbance frequency component and the frame rate (sampling frequency) of the continuous imaging apparatus will be described.

  If there is no disturbance and the movable stage that relatively moves the reference mirror 8 can maintain a constant speed, the frame rate (the number of images that can be acquired per unit time: sampling frequency) is not limited, and an arbitrary camera can be used. Therefore, if the camera 10 having a large frame rate is used, measurement can be performed in a short time. However, it is preferable that the frame rate of the camera 10 is high when non-uniformity occurs in relative motion or unintended external vibration is applied.

  For example, a certain time waveform can be decomposed into frequency components by Fourier transformation, but due to the Doppler effect, the time variation of the interference fringes occurs in relation to the frequency difference between the object beam 12 and the reference beam 13. At this time, if the frequency difference is constant, there is only one frequency component when the time waveform is decomposed by the frequency component. The complex amplitude of the frequency component includes the amplitude and phase information of the object beam 12. Actually, an image is acquired at every time step and discrete Fourier transform is performed by a computer. Whether the frequency can be accurately decomposed is determined by the Nyquist theorem, the sampling frequency is the frequency of the maximum frequency component included in the time waveform. Must be greater than twice. When the frequency difference between the object light 12 and the reference light 13 is constant, if the frequency difference is ½ or more of the sampling frequency, it may be recognized as another frequency. However, amplitude and phase information is maintained as the different frequency components. Therefore, when the frequency difference between the object beam 12 and the reference beam 13 is constant, the Nyquist limit does not cause an error. Note that the sampling time must be greater than the reciprocal (period) of the required frequency. On the other hand, when the Nyquist theorem is not satisfied, it is recognized as a frequency different from the actual frequency, but a sampling time corresponding to the cycle is required. In addition, it is desirable that the number of sampling points per cycle of the frequency component less than ½ of the sampling frequency is greater than “the number of included frequency components × 2”.

  Here, it is assumed that the error is caused by the case where the sign of the frequency difference between the object beam 12 and the reference beam 13 is not constant. The frequency difference code is determined by the sign of the relative velocity between the object 7 to be measured and the reference mirror 8. In the case of translational movement (when moving in one direction parallel to the optical axis), the sign is constant, but the vibration motion ( In the case of movement in two directions parallel to the optical axis), the signs are switched. The + side and − side of the phase shift spectrum are in the relationship between the + (−) primary light component and the − (+) primary light component, and the + 1st order light component and the −1st order light component are respectively in the phase shift spectrum. Whether it appears on the side is determined by the sign of the frequency difference. If the signs are switched, the + 1st order light component and the −1st order light component come out on the same side, but if the translational relative motion is caused simultaneously with the vibration, the frequency component corresponding to the translational relative motion is not obtained. It is possible to prevent the code from being changed. Thereby, a frequency component satisfying at least the Nyquist theorem and a frequency component due to translational motion can be separated. Note that frequency components that do not satisfy Nyquist's theorem are dispersed in other frequency components, and may overlap with frequency components of translational motion. Therefore, the higher the sampling frequency, the more accurately the frequency component due to the disturbance can be taken in, and the overlap with the frequency component corresponding to the translational motion can be reduced.

  Hereinafter, the present invention will be described in more detail with reference to examples.

[Example 1]
FIG. 3 is a phase shift spectrum when the reference mirror 8 is moved at a constant speed (1 × 10 ⁻⁵ m / s) using the apparatus 30 of FIG. On the other hand, FIG. 4, using the device 30 shown in FIG. 1, along with moving the reference mirror 8 at a constant rate ^{(1 × 10 -5 m / s} ), an optical system applying vibration deliberately to the device 30 It is a phase shift spectrum when it is vibrated. 5 is an example of the reproduced image obtained in FIG. 3, and FIG. 6 is an example of the reproduced image obtained in FIG.

In Example 1, the wavelength of the laser light source 1 is 632.8 nm, the frame rate of the continuous imaging camera 10 is 500 fps (which means the same as the sampling frequency 500 Hz), and a movable stage using a DC motor is used as the driving device 20. The set speed of the movable stage is 1 × 10 ⁻⁵ m / s. Actually, when the movable stage moves toward the beam splitter 6 side, when viewed from the reference light 13 reflected from the reference mirror 8, it seems to move at a double speed, so the speed is 2 × 10 ^{−. 5} m / s. Since the frequency difference at this time is “speed / wavelength”, it is 31.6 Hz. If this is converted into a phase difference (phase shift amount), it is “angular frequency difference / sampling frequency”, so that it becomes 0.40 rad. Therefore, FIG. 3 has a spectrum peak around 0.40 rad, and FIG. 4 also has a spectrum signal around 0.40 rad.

  FIG. 4 shows the result of intentionally applying vibration to the device 30, but spectral components not shown in FIG. 3 appear from end to end of the graph. Therefore, in the obtained reproduced image, FIG. 6 is more noisy than FIG. Such noise can be solved by using a camera that can capture images at a higher speed than the continuous imaging camera 10 having a frame rate of 500 fps used here. In addition, as shown in FIG. 4, when the spectrum component has come out to the end, the frequency component more than the Nyquist limit is disperse | distributed to the whole spectrum, and it has a state with a little more noise component.

  In this embodiment, the continuous imaging camera 10 with a frame rate of 500 fps is used. However, if a continuous imaging camera with a small frame rate (for example, several tens of fps) is used, the phase spectrum after conversion has noise as shown in FIG. It becomes difficult to judge whether or not the complex amplitude of the measured object 7 can be reproduced in the demonstration experiment. Therefore, it is preferable to use a photodetector that can obtain continuous imaging data faster than the frequency of disturbance vibration.

  In this way, even when disturbance vibrations or air fluctuations are applied, noise due to disturbance vibrations and the original periodic signal can be separated by time Fourier transform, and a highly accurate shape that is not easily affected by disturbances Measurement can be performed.

1 Light source (laser)
2 Neutral filter 3 Lens 4 Spatial filter 5 Lens 6 Beam splitter (branching device, superimposing device)
7 Object to be measured 8 Reference mirror 9 Neutral density filter 10 Continuous imaging camera (imaging device)
DESCRIPTION OF SYMBOLS 11 Coherent light beam 12 Object light 13 Reference light 20 Drive apparatus 21 Computer (calculation apparatus)
30 Shape measuring device

Claims (10)

Interference obtained by diverging coherent light beams emitted from the same light source and irradiating the object to be measured and the reference mirror, superimposing the object light reflected by the object to be measured and the reference light reflected by the reference mirror A method for measuring the shape of an object to be measured from fringe data,
A relative motion is generated between the object to be measured and the reference mirror, and the intensity distribution of the interference fringes changed by the relative motion is continuously imaged to obtain continuous imaging data, and the object light and the reference By modulating the frequency of light by the Doppler effect, a phase shift spectrum converted from the spectrum of the frequency difference between the object beam and the reference beam into a phase shift amount is obtained, and the phase shift spectrum and the continuous imaging data are used to obtain the phase shift spectrum. A shape measuring method, comprising measuring a three-dimensional shape of a measurement object.   The shape measurement method according to claim 1, wherein the relative movement between the object to be measured and the reference mirror is generated by moving the object to be measured or the reference mirror in parallel with the optical axis of the irradiation light.   The shape according to claim 1 or 2, wherein the three-dimensional measurement of the object to be measured is performed by applying a Doppler phase shift method to the intensity distribution of the interference fringes and extracting a complex amplitude of the obtained primary light. Measuring method.   The shape measuring method according to claim 1, wherein a sampling frequency of the interference fringes is more than twice a frequency difference between the object light and the reference light. A light source, a branching device that divides the coherent light beam emitted from the light source and irradiates the object to be measured and the reference mirror, and a driving device that causes relative movement between the object to be measured and the reference mirror; A superimposing device that forms interference fringes by superimposing the object light reflected by the object to be measured and the reference light reflected by the reference mirror; and an imaging device that continuously captures the interference fringes to obtain continuous imaging data. A calculation device for calculating a three-dimensional shape of the object to be measured from the continuous imaging data,
The calculation device obtains a phase shift spectrum converted from a spectrum of a frequency difference between the object light and the reference light into a phase shift amount by modulating the frequency of the object light and the reference light by the Doppler effect by the relative motion. Then, a shape measuring apparatus for calculating a three-dimensional shape of the object to be measured from the phase shift spectrum and the continuous imaging data.   The shape measuring apparatus according to claim 5, wherein the driving device causes the object to be measured or the reference mirror to move in parallel with the optical axis of the irradiation light to cause relative movement.   The calculation device applies a Doppler phase shift method to the intensity distribution of the interference fringes, extracts a complex amplitude of the obtained primary light, and calculates a three-dimensional shape of the object to be measured. 6. The shape measuring apparatus according to 6.   The shape measuring apparatus according to claim 5, wherein the imaging apparatus sets a sampling frequency of the interference fringes to more than twice a frequency difference between the object light and the reference light. Interference obtained by diverging coherent light beams emitted from the same light source and irradiating the object to be measured and the reference mirror, superimposing the object light reflected by the object to be measured and the reference light reflected by the reference mirror A method of measuring a complex amplitude of the object light from fringe data,
A relative motion is generated between the object to be measured and the reference mirror, and the intensity distribution of the interference fringes changed by the relative motion is continuously imaged to obtain continuous imaging data, and the object light and the reference A phase shift spectrum obtained by converting a spectrum of a frequency difference between the object light and the reference light into a phase shift amount by modulating a frequency of light by a Doppler effect is obtained, and the object is obtained from the phase shift spectrum and the continuous imaging data. A method for measuring a complex amplitude, comprising measuring a complex amplitude of light. A light source, a branching device that divides a coherent light beam emitted from the light source and irradiates the object to be measured and a reference mirror, a drive device that causes relative movement between the object to be measured and the reference mirror, and A superimposing device that forms interference fringes by superimposing the object light reflected by the object to be measured and the reference light reflected by the reference mirror; an imaging device that continuously images the interference fringes to obtain continuous imaging data; A calculation device for calculating a complex amplitude of the object light from the continuous imaging data;
The calculation device obtains a phase shift spectrum converted from a spectrum of a frequency difference between the object light and the reference light into a phase shift amount by modulating the frequency of the object light and the reference light by the Doppler effect by the relative motion. And calculating a complex amplitude of the object light from the phase shift spectrum and the continuous imaging data.

Images