JP6193546B2 - Three-dimensional position measuring method, velocity measuring method, three-dimensional position measuring device and velocity measuring device - Google Patents

Description

  The present invention relates to a method and apparatus for measuring the three-dimensional position of an object using digital holography technology, and to a method and apparatus for measuring the velocity of an object in three dimensions.

Measuring the three-dimensional position of particles is necessary, for example, when visualizing the flow of a fluid or measuring changes in flow velocity or density distribution of particles floating in the fluid in real time. Numerous methods have been developed for flow visualization, but a typical method is to visually observe the flow of smoke by flowing a fine mist of smoke into the fluid. . The Schlieren method is used as a flow visualization method using an optical method, and the laser Doppler velocity measurement method (Laser Doppler Velocimetry, LDV) and particle image velocity measurement method (Particle Image Velocimetry, PIV) are used as flow velocity measurement methods. Are known.
A technique for observing the movement of particles in three dimensions has also been developed, one of which is stereo PIV. Patent Document 1 discloses an example of a stereo PIV. Here, two cameras are used to observe the three-dimensional movement of particles using the principle of triangulation.

  On the other hand, with the recent increase in sensitivity of video cameras using solid-state imaging devices such as CCDs and higher performance of personal computers (hereinafter referred to as PCs), holograms of objects are recorded with video cameras, and three-dimensional images of objects are recorded. Digital holography technology for reproducing by calculation on a PC has been developed. Digital holography technology is applied to particle image velocimetry and is called digital holographic PIV.

  Patent Document 2 discloses an example of a holographic PIV. In Patent Document 2, a fluid is caused to flow in a flow path formed of a transparent glass tube, and tracer particles are mixed therein. The laser is irradiated to the flow path, the laser transmitted through the flow path is received by the CCD, and the light scattered by the tracer particles is captured by the CCD. On the CCD, scattered light and non-scattered light interfere with each other, and interference fringes are imaged by the CCD. By performing a predetermined calculation process on the interference fringe data (hologram data), an image of each tracer particle is reproduced. As the image is reproduced, the three-dimensional position of each tracer particle is determined. Of the three dimensions, two dimensions (X, Y) are orthogonal coordinates of a plane parallel to the imaging surface of the CCD, and the remaining one is the Z-axis direction perpendicular to the imaging surface. The Z-axis direction is the direction of the reproduction distance set during image reproduction.

In Patent Document 2, a plurality of positions are set as positions in the Z-axis direction, and the coordinates of the tracer particles are specified by examining changes in luminance values while reproducing an image at each position. Then, the three-dimensional velocity vector of the tracer particle is obtained by specifying the three-dimensional position of the tracer particle at two times with a predetermined time difference. In Patent Document 2, the processing speed is increased by dividing three-dimensional image data obtained by calculating hologram data, for example, in the X-axis direction and the Z-axis direction and performing parallel processing on a plurality of PCs.
In addition, Non-Patent Document 1, pages 199 to 205, discloses a digital holographic PIV. Here, an in-axis type and an off-axis type digital holographic PIV are disclosed. Non-Patent Document 2 discloses a stereo digital holographic PIV using two cameras.

JP 2010-243309 A JP 2005-315850 A

The Visualization Society of Japan, “PIV Handbook” (Morikita Publishing, July 20, 2002) Shunsuke Imamura and Ko Ikeda, “Stereo digital holographic PIV in the microscopic area” (Journal of Visualization Information Society Vol.31 Suppl. No.1 (July 2011), 317-320)

  As explained in Non-Patent Document 1, PIV by photography takes a position measurement by recording optical amplitude, whereas digital holographic PIV records interference fringes as hologram data. For this reason, in the digital holographic PIV, photographing with a deep depth of field can be performed, and a three-dimensional position measurement with a wider depth is possible.

Such characteristics are applicable not only to PIV but also to general three-dimensional position measurement by digital holography. However, it cannot be said that each technique disclosed so far fully utilizes the characteristics of digital holography in three-dimensional position measurement.
The invention of the present application has been made in consideration of such a technical background, and by providing a three-dimensional position measurement technique that makes better use of the characteristics of digital holography, digital holography in various fields of three-dimensional position measurement is provided. The purpose is to further develop the application of.

In order to solve the above problem, the invention according to claim 1 of the present application includes an irradiation step of irradiating an object with coherent light emitted from a light source,
An imaging process in which object light that is light from an object irradiated with coherent light and coherent light that does not include object information are guided to an image sensor, and interference fringes due to the two lights are imaged by the image sensor,
A recording step of recording the imaged interference fringes as hologram data;
A three-dimensional position measuring method having a specific step of identifying a three-dimensional position of an object from hologram data,
One dimension of the three-dimensional position is the direction of the reproduction distance, which is the separation distance between the imaging surface and the reproduction surface of the image sensor,
The specific process calculates the reproduction of the image of the object while changing the reproduction distance with respect to the recorded hologram data, acquires wavefront data as complex amplitude data as a result of the reproduction calculation, and is included in the acquired wavefront data Including the operation of identifying the position of the object in the direction of the reproduction distance with respect to the reference plane set at a location different from the reproduction plane based on the phase information;
The position in the direction of the reproduction distance in the identification process is determined based on the reproduction distance when the shape of the image that changes due to the difference in the reproduction distance becomes a shape assumed to be obtained when reproduced at the correct reproduction distance. Based on the configuration.
In order to solve the above-mentioned problem, the invention according to claim 2 has a sample data acquisition step of acquiring sample data in the configuration of claim 1 , and the sample data is reproduced at the correct reproduction distance. It is the wavefront data of the image of the shape assumed to be obtained when
Judgment that the shape is obtained when played back at the correct playback distance is made by comparing each wavefront data acquired while changing the playback distance with the sample data, and whether the correlation between the two is greater than the reference value It has a configuration that it is performed depending on why.
In order to solve the above-mentioned problem, the invention according to claim 3 is known in the configuration of claim 2 with respect to a sample object in which the sample data can be regarded as having the same size and shape as the object and the same refractive index. The imaging process and the recording process are performed at the imaging distance as in the case of the object, and the wavefront data is obtained by performing the reproduction calculation from the recorded hologram data.
In order to solve the above problem, the invention according to claim 4 is the configuration according to claim 2 , wherein the sample data includes the size and shape of the object, the refractive index of the object, and a medium around the object. The data is obtained by calculation according to the refractive index.
In order to solve the above-described problem, the invention according to claim 5 is the configuration according to any one of claims 1 to 4 , wherein the specifying of the position in the direction of the reproduction distance in the specifying step is the wavefront of the entire image of the object. It is configured to be performed based on data.
In order to solve the above problem, the invention according to claim 6 is the structure according to any one of claims 1 to 5 , wherein the wavefront data includes amplitude information.
The identifying step includes an operation of identifying a position in the direction of the reproduction distance based on the phase information and then confirming whether an object exists at the position based on the amplitude information. .
In order to solve the above problem, according to a seventh aspect of the present invention, in the configuration according to any one of the first to sixth aspects, the imaging step is configured to convert the object light into image side telecentric, object side telecentric, or both side telecentric. It has a configuration in which the imaging optical system guides the imaging device to take an image.
In order to solve the above problem, according to an eighth aspect of the present invention, in the structure according to any one of the first to seventh aspects, the object is a spherical object formed of a material transparent to the coherent light. It has a configuration that there is.
In order to solve the above-mentioned problems, the invention according to claim 9 has a structure in which the object is a unicellular organism, a living cell, or a cultured cell in the configuration of any of claims 1 to 7 .
In order to solve the above problem, the invention according to claim 10 is a velocity measurement method using the three-dimensional position measurement method according to any one of claims 1 to 9 ,
The irradiation step is a step of irradiating the object with the coherent light at a first time and irradiating the coherent light at a second time after a predetermined time from the first time,
The recording step is a step of recording the interference fringes imaged at the first and second times as hologram data,
The specifying step is a step of specifying the three-dimensional position of the object at each first and second time from each hologram data,
A speed measuring step for obtaining a speed vector of the object based on the identified three-dimensional position at each time;
In order to solve the above problem, the invention according to claim 11 is a velocity measuring method using the three-dimensional position measuring method according to any one of claims 1 to 8 ,
The object is tracer particles mixed in the fluid flowing through the flow path,
The irradiation step is a step of irradiating the tracer particles with the coherent light at a first time and irradiating the coherent light at a second time after a predetermined time from the first time,
The recording step is a step of recording the interference fringes imaged at the first and second times as hologram data,
The specifying step is a step of specifying the three-dimensional position of the tracer particle at each first and second time from each hologram data,
It has the structure of having the speed measurement process which calculates | requires the velocity vector of tracer particle | grains based on the identified three-dimensional position of each time.

In order to solve the above problems, the invention according to claim 12 is
A light source that emits coherent light;
An image sensor;
Guide and emit coherent light to the object, guide the object light from the irradiated object to the image sensor, and guide the coherent light not including object information to the image sensor as the reference light. An optical system that causes the image sensor to pick up interference fringes by causing interference, and
A storage unit for storing the interference fringes captured by the image sensor as hologram data;
A three-dimensional position measurement apparatus comprising an arithmetic processing unit that specifies a three-dimensional position of the object from the hologram data by calculation,
One dimension of the three-dimensional position is the direction of the reproduction distance, which is the separation distance between the imaging surface and the reproduction surface of the image sensor,
The arithmetic processing unit performs a reproduction calculation of the image of the object while changing the reproduction distance with respect to the stored hologram data, and acquires wavefront data that is complex amplitude data as a result of the reproduction calculation. Based on the phase information included, it specifies the position of the object in the direction of the reproduction distance relative to the reference plane set at a location different from the reproduction plane,
The arithmetic processing unit determines the position in the direction of the reproduction distance based on the reproduction distance when the shape of the image that changes due to the difference in the reproduction distance is assumed to be obtained when the image is reproduced at the correct reproduction distance. Is specified.
In order to solve the above-mentioned problem, the invention according to claim 13 is the configuration of claim 12 , wherein the storage unit stores sample data, and the sample data is reproduced at the correct reproduction distance. Is the wavefront data of the image that is supposed to be obtained,
The arithmetic processing unit compares each wavefront data acquired while changing the reproduction distance and the sample data, and when the correlation between the two is greater than or equal to a reference value, when the reproduction is performed at the correct reproduction distance, It has a configuration in which it is determined that the shape is assumed to be obtained.
Further, in order to solve the above-mentioned problem, the invention according to claim 14 is known in the configuration of claim 13 with respect to a sample object in which the sample data can be regarded as having the same size and shape as the object and the same refractive index. The wavefront data obtained by performing reproduction calculation on the hologram data obtained by photographing the interference fringes in the same manner as the object at the imaging distance.
In order to solve the above problem, according to a fifteenth aspect of the present invention, in the configuration of the thirteenth aspect , the sample data includes the dimensional shape of the object, the refractive index of the object, and a medium around the object. The data is obtained by calculation according to the refractive index.
In order to solve the above problem, according to a sixteenth aspect of the present invention, in the configuration according to any one of the twelfth to fifteenth aspects, the arithmetic processing unit is configured to determine the direction of the reproduction distance based on the wavefront data of the entire image of the object. It has the structure that it specifies what position.
In order to solve the above problem, the invention according to claim 17 is the structure according to any one of claims 12 to 16 , wherein the wavefront data includes amplitude information.
The arithmetic processing unit identifies a position in the direction of the reproduction distance based on the image reproduction result based on the phase information, and then confirms whether an object exists at the position based on the image reproduction result based on the amplitude information. It has the structure of being based on.
In order to solve the above problem, an invention according to claim 18 is the structure according to any one of claims 12 to 17 , wherein the optical system includes an imaging optical system that guides the object light to the imaging element. The imaging optical system is configured to be image side telecentric, object side telecentric, or both side telecentric.
In order to solve the above problem, according to a nineteenth aspect of the present invention, in the structure according to any one of the twelfth to eighteenth aspects, the object is a spherical one formed of a material transparent to the coherent light. It has a configuration that there is.
In order to solve the above-mentioned problem, the invention according to claim 20 uses the three-dimensional position measuring device according to any one of claims 12 to 19 to measure a three-dimensional velocity vector of the object. Because
The coherent light source and the optical system irradiate the object with the coherent light at a first time and the coherent light at a second time after a predetermined time from the first time. ,
The imaging element is for imaging the interference fringes at the first and second times,
The storage unit stores the interference fringes imaged at the first and second times as hologram data, respectively.
The arithmetic processing unit specifies a three-dimensional position of the object at each first and second time from each hologram data, and obtains a velocity vector of the object according to the specified three-dimensional position at each time. It has the structure of.
In order to solve the above-mentioned problem, the invention according to claim 21 has the structure according to claim 20 , wherein the object is a tracer particle mixed in a fluid flowing in a flow path.

As described below, according to the method of claim 1 or the apparatus of claim 12 of the present application, the three-dimensional position, particularly the position in the direction of the reproduction distance, is specified based on the phase information. The position is specified based on the data of a wider area. For this reason, highly accurate three-dimensional measurement can be performed.
According to the second or thirteenth aspect of the invention, in addition to the above effects, the position is specified based on the high degree of correlation between the reproduced image data and the sample data, so that the specification is easy.
According to the invention described in claim 3 or 14 , in addition to the above effect, the sample data is obtained by performing the same photographing and reproduction calculation on the sample object. The position can be measured with high accuracy.
Further, according to the invention of claim 4 or 15 , in addition to the above effect, the sample data is obtained by calculation. Therefore, even when an object having a large variation in shape and refractive index is targeted, Sample data can be created so as not to reduce the accuracy of position measurement.
According to the invention described in claim 5 or 16 , in addition to the above effect, the position is specified by using the entire wavefront of the reproduced image of one object, so the effect of improving accuracy is remarkable.
According to the invention described in claim 6 or 17 , in addition to the above effect, the filter processing is performed by the amplitude information, so that the occurrence of an error that erroneously specifies the position where the object does not exist is suppressed. In this respect, more accurate three-dimensional position measurement can be performed.
According to the invention described in claim 7 or 18 , in addition to the above effect, the object light is guided to the image sensor by the image side telecentric, object side telecentric or both side telecentric imaging optical system, so that the reproduction distance is obtained. The work of specifying the position in the direction can be facilitated, or by increasing the depth of field, it is possible to target a wide measurement space in the depth direction.
According to the invention described in claim 8 or 19 , in addition to the above effect, the object is a spherical object formed of a material transparent to coherent light, so that it is easy to specify the position in the direction of the reproduction distance. is there. In addition, since the viewing angle when imaging an object can be small, the depth of field can be increased, and a wide measurement space in the depth direction can be targeted.
According to the ninth aspect of the invention, it is possible to measure the three-dimensional position of a unicellular organism, a living cell or a cultured cell while obtaining the effect of any of the first to seventh aspects.
According to the invention of claim 10 or 20 , the three-dimensional velocity vector of the object can be measured while obtaining the effect of any of claims 1 to 9 or the effect of any of claims 12 to 19. .
According to the invention of claim 11 or 21 , the three-dimensional velocity vector of the tracer particles can be measured while obtaining the effect of any one of claims 1 to 8 or the effect of claim 20 .

1 is a schematic diagram of a three-dimensional position measuring apparatus according to a first embodiment of the present invention. It is the perspective schematic which showed the principle of the three-dimensional position measurement using digital holography. It is the figure which showed typically about the difference between the method of embodiment and the method of patent document 2. FIG. It is the schematic shown about specification of the position of the reproduction | regeneration distance direction in the three-dimensional position measuring method of embodiment. It is the schematic shown about the 1st example of the acquisition method of sample data. It is the schematic shown about the 2nd example of the acquisition method of sample data. It is the figure which showed about the experiment which specified the position of the reproduction | regeneration distance direction by sample data based on actual data. It is the perspective view shown typically about the specific process in the method of embodiment. It is the schematic shown about the filter process by amplitude information. It is the flowchart shown about the outline of a position specific program. It is the schematic shown about the telecentricity of the imaging optical system 4 in the apparatus of FIG. It is the schematic of the principal part of the three-dimensional position measuring apparatus which concerns on 2nd embodiment of this invention. It is the isometric view schematic shown about embodiment of invention of the speed measuring method.

Next, modes for carrying out the present invention (hereinafter referred to as embodiments) will be described.
FIG. 1 is a schematic diagram of a three-dimensional position measuring apparatus according to the first embodiment of the present invention. The apparatus shown in FIG. 1 is an apparatus that measures the three-dimensional position of an object using a digital holography technique. This apparatus includes a coherent light source 1, an image sensor 2, optical systems 3, 4, and 5, and a computer 6.

As the coherent light source 1, a laser oscillator is used. For example, a HeNe laser oscillator having a wavelength of 632.8 nm, a ruby laser oscillator having a wavelength of 694 nm, or the like is used. As the image sensor 2, a CCD having a number of pixels that covers a sufficient area with a sufficiently fine pixel pitch is used.
As the optical system, an irradiation optical system 3 that guides and emits light from the coherent light source 1 to the object S, and an imaging optical system 4 that guides the light (object light) from the irradiated object S to the imaging device 2. A reference light optical system 5 that guides coherent light not including object information to the image sensor 2 as reference light is provided. “Object information” is a term that assumes that the wavefront of coherent light changes according to the properties (shape, refractive index, etc.) of the object when the object is irradiated with coherent light. It is a term meaning object information that can be expressed by. For example, when an object image is reproduced by a wavefront as described later, the shape of the object is “object information”. When the transmittance distribution in the object is obtained from the wavefront, the transmittance distribution is “object information”. Coherent light that does not include such object information (in this embodiment, coherent light that has not passed through an object) is used as reference light.

  The apparatus of this embodiment is an apparatus for realizing PTV (Particle Tracking Velocimetry) which is a kind of PIV as described later. Therefore, the object S that is the measurement target of the three-dimensional position is a plurality of tracer particles mixed in the fluid 100 flowing through the flow path. The flow path is formed of a tube 101 made of a material such as glass or acrylic that sufficiently transmits coherent light. As shown in FIG. 1, the irradiation optical system 3 guides light from the coherent light source 1 and irradiates an object (tracer particle) S in the tube 101.

  In principle, it is possible to use separate light sources for object light and reference light, but using separate light sources makes it possible to sufficiently align the wavelength and phase (make it coherent). difficult. For this reason, the light from one coherent light source 1 is divided and used. That is, as shown in FIG. 1, an extraction beam splitter 51 is provided on the optical path of the irradiation optical system 3, and a part of the light is extracted as reference light. Further, the reference light can be extracted from the object light. Specifically, there are two methods. One is that the light after object diffraction is separated into two by a beam splitter and then passed through a spatial filter that combines a Fourier transform lens and a pinhole on one side, thereby coherent light with missing object information. Is used as a reference light (this will be described later). The other is that, as disclosed in International Publication No. 2008/123408, a Fourier transform lens and a micro semi-transparent mirror are similarly arranged on the optical path of the light after object diffraction, and the zero-order light component of the object diffraction light Is used as a reference beam.

  In the present embodiment, light transmitted through the tube 101 enters the image sensor 2. This light includes object light. The object light is diffracted light from the object (tracer particle) S irradiated with the coherent light. However, the object light is reflected by the object S in the case where the coherent light is scattered by the object S (scattered light). There is a case of the emitted light (reflected light) and a case of the light emitted through the object S (transmitted light). The object is to capture the light from the object S, image the interference fringe with the reference light and measure the position, and the object light may be any case. Scattered light, reflected light, and transmitted light may be indistinguishable, and even if they cannot be distinguished, there is no problem as long as position measurement is possible. In the present embodiment, the tracer particles that are the object S are formed of a transparent material such as acrylic, and therefore the object light is mainly transmitted light.

As shown in FIG. 1, the imaging optical system 4 is provided between the tube 101 and the imaging device 2. In this embodiment, the interference fringes obtained while enlarging and projecting the object S are recorded as hologram data. For this reason, the imaging optical system 4 includes an objective lens 41 and an imaging lens 42. As shown in FIG. 1, the image sensor 2 is arranged so that the imaging surface is perpendicular to the optical axis of the imaging optical system 4.
An integrating beam splitter 52 is provided on the optical path between the imaging lens 42 and the image sensor 2. The reference light optical system 5 guides the reference light extracted by the extraction beam splitter 51 to the integration beam splitter 52 by the mirror 53 and makes it incident on the image sensor 2 together with the object light.

  The reference light optical system 5 is configured to allow the reference light to be incident on the image sensor 2 in an off-axis manner. The off-axis means that the reference light is incident with an angle with respect to the object light instead of the same incident angle as the object light. Specifically, the mirror 53 is provided with an off-axis drive mechanism 54. The off-axis drive mechanism 54 is a mechanism that changes the mirror 53 from a 45 ° angle with respect to the optical axis to a state inclined by a predetermined angle.

  As shown in FIG. 1, the irradiation optical system 3 and the reference light optical system 5 are provided with beam expanders 31 and 55, and the coherent light is expanded and used in a light beam of a necessary size. It is supposed to be. In each of the beam expanders 31 and 55, spatial filters 32 and 56 for noise removal are arranged as necessary.

  The computer 6 performs three-dimensional position measurement of the object by performing arithmetic processing on the data sent from the image sensor 2. The computer 6 includes a CPU as an arithmetic processing unit 61, a storage unit 62, a printer, a display, and the like as an output unit. The image pickup device 2 is connected to the computer 6 via an interface, and interference fringe data picked up by the image pickup device 2 is stored in the storage unit 62 of the computer 6 as hologram data.

  In the present embodiment, the recording of the hologram is to store the captured interference fringe data in the storage unit 62 of the computer 6 as hologram data. The storage unit 62 is a storage such as a memory or a hard disk. In addition, the computer 6 is installed with a reproduction calculation program for performing reproduction calculation described later, a position specifying program for specifying a three-dimensional position from the reproduction calculation result, and the like, which can be executed by the arithmetic processing unit 61. .

A method for measuring the three-dimensional position of an object using such a three-dimensional position measuring apparatus will be described below. The following description is also a description of an embodiment of the invention of the three-dimensional position measurement method, and is also a description of the arithmetic processing unit 61.
FIG. 2 is a schematic perspective view showing the principle of three-dimensional position measurement using digital holography. When reproducing an image by numerical calculation, it is necessary to specify a hologram surface and a reproduction surface. The hologram surface is a surface on which the hologram exists, but here, the position of the imaging surface of the imaging device 2 is assumed. Usually, in order to simplify the calculation, the reproduction surface is parallel to the hologram surface as shown in FIG.

  The hologram data output from the image sensor 2 is a light intensity signal (light intensity distribution) in each pixel. Therefore, as shown in FIG. 2, the hologram data 21 can be defined as g (x, y). However, as described above, the hologram data 21 is interference fringes (partially enlarged in FIG. 2 and indicated by reference numeral 22) formed by the object light and the reference light, and the pattern of the interference fringes 22 is g ( x, y). As shown in FIG. 2, in order to simplify the calculation, the reproduction surface is an XY plane that shares the hologram surface with the Z axis. The distance D between the hologram surface and the reproduction surface is a reproduction distance that is an important parameter in the reproduction calculation.

式１において、λは再生光の波長、ｋは波数である。式１に対し、式２に示すフレネル近似を適用して代入すると、式３が得られる。

式３において、積分をフーリエ変換であるとみなして変形すると、式４が得られる。

式４において、Ｆのカッコ内はフーリエ変換であることを示す。ｘやｙは、撮像面の各ピクセルからの出力値であり、離散フーリエ変換をすることでＧ（Ｘ，Ｙ）が得られる。式４からも解るように、データＧ（Ｘ，Ｙ）は、再生面における各点の光情報を複素数の形式で表現したもの（複素振幅データ）である。従って、途中の計算を省略すると、このデータＧ（Ｘ，Ｙ）は、以下の式５で表現されることになる。

As an example, a case where reproduction is performed at a distance of Fresnel diffraction using Fourier transform will be described. Let r be the distance from one point on the hologram surface to one point on the playback surface. x and y are coordinates on the hologram surface, and X and Y are coordinates on the reproduction surface.
The complex amplitude distribution on the reproduction surface can be expressed as Equation 1 according to Kirchhoff's diffraction integral equation.

In Equation 1, λ is the wavelength of the reproduction light, and k is the wave number. If the Fresnel approximation shown in Formula 2 is applied and substituted into Formula 1, Formula 3 is obtained.

In Equation 3, if the integral is regarded as a Fourier transform and transformed, Equation 4 is obtained.

In Equation 4, the parentheses of F indicate Fourier transform. x and y are output values from each pixel on the imaging surface, and G (X, Y) is obtained by performing a discrete Fourier transform. As can be seen from Equation 4, the data G (X, Y) is a representation of the optical information of each point on the reproduction surface in the form of a complex number (complex amplitude data). Therefore, if the calculation in the middle is omitted, this data G (X, Y) is expressed by the following Equation 5.

Thus, the result of the reproduction calculation is complex amplitude data at each point on the reproduction surface, and the pitch depends on the pitch (pixel pitch) of the hologram data 21 that is the original data. In digital holography, when an image is reproduced with amplitude information, | A | ² at each coordinate point is calculated from Equation 5 and output. When an image is reproduced with phase information, a deviation angle φ at each coordinate point is calculated and output. The output is an amplitude value distribution (amplitude value map) and a phase value distribution (phase value map) on the playback surface. When this is visualized by some method, an image of the target object is displayed in it. Will appear.

Now, when the three-dimensional position of the object is specified using the result of such reproduction calculation, the two dimensions out of the three dimensions are the X axis and the Y axis in the reproduction calculation. In FIG. 1, a certain reference plane is set for the pipe 101 (for example, a vertical plane). As shown in FIG. 2, the image pickup device 2 is arranged with high accuracy so that the image pickup surface is parallel to the reference plane. As a result, the reproduction surface is also parallel to the reference surface. If a reference point (reference point) in the reference plane is set, the position in the XY direction of the image on the reproduction plane can be specified in relation to the reference point.
In the present embodiment, the object S is a tracer particle and is spherical. Therefore, when the image can be correctly reproduced, whether it is an amplitude reproduction image or a phase reproduction image, it has a circular outline. Therefore, the center position of the circle can be specified as the position in the XY direction.

  Assuming that the position in the XY direction can be specified in this way, the problem is in the Z-axis direction. The Z-axis direction is the direction of the reproduction distance D as can be seen from FIG. When specifying the position in the Z-axis direction, as shown in FIG. 2, the image reproduction is repeated several times while changing the reproduction distance, and the position in the Z-axis direction is specified according to the reproduction distance when the reproduction was most correctly performed. . That is, when the objective lens is not used (same magnification), the reproduction distance when the reproduction is most correct is equal to the distance between the position where the object is located and the imaging surface. Accordingly, if a certain reference surface is provided in the tube 101 in the Z-axis direction, and the position of the hologram surface (the image pickup surface of the image pickup device 2) with respect to the reference surface is set as known data, the position of the object in the Z-axis direction is also determined. It was able to be identified.

For example, as shown in FIG. 2, it is assumed that reproduction is most correctly performed at a certain reproduction distance D. In this case, if the distance between the reference surface and the hologram surface is d ₁ and the distance between the object S and the hologram surface is d ₂ , the distance d ₂ is equal to D. Therefore, the object S is d ₁ from the reference surface. It is located at a position from the hologram surface by −D. When an objective lens is used, the ratio d ₂ : D varies depending on the magnification, but the basic principle is the same.

  Thus, what becomes a problem when specifying the position in the Z-axis direction is what makes “most correctly reproduced”. With respect to this point, Patent Document 2 describes “the value of Z at which the luminance value reaches a peak” (paragraph 0022). That is, Patent Document 2 observes a change in luminance in a reproduced image while changing the reproduction distance, and specifies the position in the Z-axis direction based on the reproduction distance when the luminance has a peak. Since the luminance value is the light intensity, that is, the amplitude, it can be said that Patent Document 2 measures the three-dimensional position using the amplitude information among the results of the reproduction calculation.

On the other hand, in the present embodiment, unlike the disclosure of Patent Document 2, the three-dimensional position is specified using the phase information in the result of the reproduction calculation. Hereinafter, this point will be described.
As described above, in digital holography, the result of reproduction calculation is obtained as complex amplitude data on the reproduction surface. It can be said that the wavefront data of light from the object is reproduced as it is. The method of Patent Document 2 uses only amplitude information among such wavefront data. In a sense, only a part of the result of the reproduction calculation is used, and the characteristics of the digital holography technology are not fully utilized. In the present embodiment, the result of the reproduction calculation is regarded as a wavefront (this is an inherent characteristic of digital holography), and a determination is made according to the state of the wavefront. Judgment based on the state of the wavefront inevitably means that phase information that is not used in Patent Document 2 is used in the result of reproduction calculation.

The above point will be described in more detail with reference to FIG. FIG. 3 is a diagram schematically showing the difference between the method of the embodiment and the method of Patent Document 2.
As shown in FIG. 3, the object S is irradiated with coherent light L that is a plane wave. Wavefront of the coherent light L is disturbed by the object S, from the object S, the shape and surface state of the object S, the object light is emitted by the wavefront W ₁ which changes according to the refractive index. Then, the object light interferes with the reference light on the imaging surface to form a hologram, and an image is reproduced by performing calculation processing on the hologram. Reproducing the resulting image is a complex amplitude data, as described above, it expresses the wavefront W ₁ on the object (i.e., playing). Assuming that the reproduced wavefront is W ₂ , the method of Patent Document 2 focuses on only the luminance value (amplitude information) in the data of the wavefront W ₂ of this reproduced image, and “ This is a method of “reproduced”. As shown in FIG. 3, this is based on only the sharpness of the rising edge of the luminance value ΔI of the reproduced image portion of only the amplitude information obtained from the fringe image (paragraph 0011 of Patent Document 2). It is equivalent to the method of judging.

On the other hand, the method of the present embodiment is a method of directly utilizing the wavefront W ₂ of the reproduced image. More specifically, the method of the present embodiment utilizes the fact that the shape of the reproduced image changes according to the reproduction distance when the phase information is extracted from the wavefront data and the image is reproduced. It can be assumed in advance what shape the image will be when reproduced at the correct reproduction distance. Therefore, based on the assumption, the position is specified by the reproduction distance when the correct shape is obtained.
To be more specific, in this embodiment, assuming wavefront Ws that would be obtained if it is correctly reproduced, comparing the wavefront Ws, the wavefront W ₂ which is actually obtained. Then, when the correlation between the two becomes the highest, it is assumed that “the most correctly reproduced”. The data of “the wavefront Ws assumed to be obtained when correctly reproduced” is hereinafter referred to as sample data.

  The superiority or inferiority due to such a difference in method is obvious. That is, in Patent Document 2, only luminance value information is extracted from the reproduction result, and only a very small area of the reproduced image, which is a fringe image portion, is extracted and judged, whereas in the present embodiment, reproduction processing is performed. The result is taken as a wavefront to the last, and is judged by the wavefront. Judgment based on the wavefront means judgment based on the three-dimensional shape of the object and judgment based on a wider area.

  In the position measurement by such an optical method, the influence of noise due to slight foreign matter existing in the optical system or readout noise by the image sensor is unavoidable, and a considerable amount of noise is included in the reproduction result. In this case, since the method of Patent Document 2 does not make a judgment based on the wavefront, if noise (for example, speckle noise) that causes a peak in luminance value is mixed for some reason, it directly leads to a misperception of the position in the reproduction distance direction. End up. Further, as in Patent Document 2, if only a small part of the area is captured and judged, the SN ratio (that is, the ratio of the amount of noise to the amount of information that is the basis of judgment) is poor, and the accuracy of judgment is reduced. Easy to do. On the other hand, in the method according to the present embodiment, the determination is made based on the parameter corresponding to the shape of the object called the wavefront. In addition, since the determination is based on a wider area, the influence of mixed noise is relatively small (the SN ratio is high). In this respect as well, the accuracy of determination is further increased. That is, the position specifying accuracy in the Z-axis direction is increased.

The method of this embodiment having the above advantages will be described in more detail with reference to FIG. FIG. 4 is a schematic diagram illustrating the specification of the position in the reproduction distance direction in the three-dimensional position measurement method of the embodiment.
In this embodiment, transparent spherical particles are targeted as the object S in order to facilitate the evaluation of the correlation with the sample data. Since the object S is transparent, the object light is mainly transmitted light as described above.

As shown in FIG. 4, the coherent plane wave L in transparent object S is incident, plane wave L distorted according to the refractive index n ₂ of the refractive index n ₁ and the object S in the medium. At this time, if n ₂ > n ₁ , the speed of the light decreases as it enters the object S. Therefore, when the light passes through the object S as shown in FIG. The wavefront of this transmitted light is due to the action of the transparent and spherical object S resembling a lens (hereinafter, this action is referred to as the lens effect), and the wavefront gradually contracts as shown in FIG. However, it spreads through a certain condensing point.

Here, consider the wavefront W ₁ immediately after the plane wave is transmitted through the object S as a reference, hereinafter referred to as a reference wavefront. The position of the reference wavefront W _1, the position of the object S. Further, as shown in FIG. 4, a distance between the reference wavefront W ₁ and the hologram surface to as d. If, when carrying out the regenerating a little shorter regeneration distance than d, than the position of the reference wavefront W ₁ it means that had regenerated a little at a position before (position closer to the hologram plane), the wave front of the regenerated , decreases the size of the overall than the reference wavefront W _1, the radius of curvature becomes smaller. In addition, in the case of performing the play in a little long playback distance than d, than the position of the reference wavefront W ₁ it means that had to play a little bit position of the back (a position far from the hologram surface), wavefront play , a little curvature radius is larger than the reference wavefront W _1. Therefore, if an image is reproduced while changing the reproduction distance, and the reproduction distance at the time when it is determined that the obtained wavefront size and shape match W ₁ is specified, the position of the object in the Z-axis direction can be specified accordingly. It ’s done.

  Next, sample data in the above method will be described. For sample data, two different acquisition methods are possible. One is a method in which a sample object is actually photographed, hologram data is recorded, and a result of reproduction calculation is used as sample data. FIG. 5 shows this method, and is a schematic diagram showing a first example of a sample data acquisition method.

In the above example, all the tracer particles mixed into the fluid in the tube 101 are all made of the same material and have the same particle size. Accordingly, one tracer particle is taken out as the sample object So, and the interference pattern is imaged by irradiating the coherent light L in the same medium to obtain hologram data. At this time, as shown in FIG. 5, in order to set the position to a known fixed position, imaging is performed by placing the sample object So on a transparent plate 102 such as a petri dish. The plate 102 is accurately arranged at a predetermined position in relation to the image sensor 2.
A value obtained by subtracting the particle size from the separation distance between the plate 102 and the image pickup device 2 is the photographing distance d. The reproduction distance is set to the same distance as this distance, and the reproduction calculation is performed. Thereby, sample data is obtained. As the plate 102, a plate having a refractive index as close as possible to the refractive index of the medium around the object is used.

従って、標本データの波面Ｗ_ｓは、屈折率差を考慮し、式７で表される。

As another method, sample data can be obtained by calculation without performing imaging. FIG. 6 shows this, and is a schematic diagram showing a second example of the sample data acquisition method.
As described above, when the object transparent spherical reference wavefront W ₁ by the lens effect is hemispherical wavefront. Size and curvature of the reference wavefront W _1, the refractive index n ₁ of the _medium, the refractive index n ₂ of the _object, if known particle size of the material φ is can be obtained by calculation. That is, a hemispherical surface having a diameter of φ can be expressed by the following Equation 6 (the lowest point of the hemisphere is the origin).

Therefore, the wavefront W _{s of the} sample data is expressed by Expression 7 in consideration of the refractive index difference.

The result confirmed by actual data that the position in the reproduction distance direction can be specified based on the sample data as described above will be described. FIG. 7 is a diagram illustrating an experiment in which the position in the reproduction distance direction is specified based on sample data based on actual data.
In the experiment shown in FIG. 7, a transparent spherical particle (refractive index: 1.59) made of polystyrene having a particle size of 25 μm was floated in water and irradiated with a HeNe laser having a wavelength of 632.8 nm to photograph a hologram. Then, reproduction calculation was performed while changing the reproduction distance to 130 mm, 140 mm, and 150 mm, phase information was extracted from the complex amplitude data, and a phase value map was obtained. FIG. 7 is a graph showing the distribution of phase values in a certain direction of the reproduction surface (XY plane). The horizontal axis represents the position on the reproduction surface, and the vertical axis represents the phase value converted into a position in the Z-axis direction. That is, it is represented as a line (wavefront) connecting points having the same phase value. FIG. 7 shows a phase value distribution when D = 130 mm is a reproduction distance 130 mm, a phase value distribution when D = 140 mm is a reproduction distance 140 mm, and a phase value distribution when D = 150 mm is a reproduction distance 150 mm. .

In FIG. 7, wavefronts at respective reproduction distances are shown superimposed. As shown in FIG. 7 (1), as the reproduction distance is shortened, the radius of curvature of the wavefront becomes smaller (that is, the shape changes). This is due to the lens effect described above. Generally speaking, the shape of the wavefront when a plane wave is disturbed by an object depends on the shape of the object on the surface of the object, but the shape of the wavefront changes during the subsequent propagation process. To do.
In FIG. 7B, sample data is added to the data of (1). In this example, the sample data was acquired by the calculation method shown in FIG. As shown in FIG. 7B, in this example, the wavefront when the reproduction distance is 140 mm is closest to the sample data (highest correlation). Therefore, in this example, it can be determined that “the most correctly reproduced” is achieved at the reproduction distance of 140 mm.

Next, a method for specifying the three-dimensional position of an object from the sample data obtained by any of the above methods will be described with reference to FIG. FIG. 8 is a perspective view schematically showing a specific step in the method of the embodiment.
First, as shown in FIG. 8A, reproduction calculation is performed while changing the reproduction distance, and as a result, phase value maps M ₁ , M ₂ , M ₃ ... Are obtained. Since the coherent plane wave is irradiated and the imaging surface of the imaging device 2 is arranged in parallel with the wavefront, the wavefront is not disturbed and the phase is constant when no object is present. Where the object is present, the wave front is disturbed and the phase is different, so that it appears as images... G ₃₁ , G ₃₂ , G ₃₃ . In FIG. 8, the image is made (visualized) for easy understanding, but actually the data is processed with the phase value (numerical value) as it is, and the image is made as shown in FIG. It's not the above process.

In order to facilitate understanding of the phase value maps M ₁ , M ₂ , M ₃ ,... Obtained for each reproduction distance (Z = Z ₁ , Z = Z ₂ , Z = Z ₃ ,. If they are arranged side by side, an example is shown in FIG. In the phase value map (three-dimensional reproduction space) arranged as shown in FIG. 8 (2), it is confirmed that a reproduced image exists at the same position in the XY directions. That is, the reproduced image G ₁₁ , the reproduced image G ₂₁ , and the reproduced image G ₃₁ are located at substantially the same position in the XY direction. Three of the reproduced image G ₁₂ , the reproduced image G ₂₂ , and the reproduced image G ₃₂ are also located at substantially the same position in the XY direction. Further, the reproduced image G ₁₃ , the reproduced image G ₂₃ , and the reproduced image G ₃₃ are also located at substantially the same position in the XY direction. Each image at the same position in the XY directions is assumed to be a reproduced image for one object. However, in each set of reproduced images, the shape is not the same even if the positions in the XY directions are the same. That is, the radius of curvature of each set of reproduced images becomes smaller as the reproduction distance becomes shorter.

As described above, the correlation between the reproduction images G _{11 to} G ₃₃ on each reproduction plane and the sample data is evaluated, and data having a correlation higher than the reference value is left as data. Then, the data whose correlation is less than the reference value is reset to zero. To reset to zero is to make the phase value the same as the phase value of the part other than the image (background phase value). As a result, the image at that location disappears as shown in FIG.

When performing such processing with respect to the wavefront of the hemispherical surfaces of all of the reproduction image, as shown in FIG. 8 (3), the three-dimensional space, is high than a predetermined correlation reproduction image of the sample data G ₃₂ , G ₂₁ and G ₁₃ remain. These reproduced images G ₃₂ , G ₂₁ , and G ₁₃ are reproduced images determined to have been reproduced at the correct reproduction distance, and their positions indicate the positions of the respective objects (tracer particles). Therefore, in each reproduced image G ₃₂ , G ₂₁ , G ₁₃ , the coordinates of the center in the XY direction are obtained and specified as the position in the XY direction, and the position in the Z-axis direction is specified according to the reproduction distance from which the reproduced image is obtained. . Thereby, the three-dimensional position of each object has been identified.

  Note that the reference value is appropriately determined in consideration of the pitch when the reproduction calculation is performed by changing the resolution and reproduction distance of the imaging optical system 4. Setting a higher reference value results in a more accurate measurement, but if there is no reconstructed image that exceeds the reference value at all, there is no object even though there is an object. If the reference value is set too low, two positions for one object may be specified. In consideration of this, the reference value is appropriately determined.

  In the present embodiment, the three-dimensional position of the object is specified according to the phase information in this way, but amplitude information is also used in an auxiliary manner in order to further improve measurement accuracy. Specifically, each reproduced image shown in FIG. 8 (3) (each reproduced image whose correlation with the sample data is determined to be equal to or higher than the reference value) is collated with the reproduced image based on the amplitude information, noise, etc. It is checked whether it is error data caused by the error. If the error data is determined from the amplitude information, the reproduced image data is reset to zero and handled as no object (tracer particle) at that position. In other words, it is a filtering process based on amplitude information.

FIG. 9 is a schematic diagram illustrating filtering processing based on amplitude information. When performing filter processing, amplitude information is extracted from the result of reproduction calculation, and an amplitude value map at each reproduction distance is obtained. Then, for each reproduced image of the phase information shown in FIG. 8 (3) (reproduced image determined to reproduce each object at the correct position), the three-dimensional position is identified as described above, and the identification is performed. The amplitude value at the coordinate of the three-dimensional position (hereinafter referred to as the specified coordinate) is referred to.
Specifically, if certain specified coordinates are Xn, Yn, and Zn, an amplitude value map at a reproduction distance of Z = Zn is read. Then, as shown in FIG. 9, a rectangular reference area including the specified coordinates is set in the amplitude value map of Z = Zn. That is, areas of Xn ± Δx and Yn ± Δy are set. The sizes of Δx and Δy are assumed to be sufficiently larger than the assumed size of the reproduced image.

  Then, image processing for checking the contrast ratio is performed on the data in the reference area, and it is determined whether or not the contrast ratio is a certain level or more. For example, the maximum and minimum amplitude values are compared to determine whether they are above a certain level, or whether the angle of the rising edge of the amplitude value (image outline) is above a certain level. Or If the contrast ratio is above a certain level, it is confirmed by the amplitude information that an object is present at that position, so that the identification result based on the phase information can be adopted as it is. If the contrast ratio is less than a certain value, depending on the amplitude information, it could not be confirmed that the object was present at that position. Therefore, the specific result based on the phase information is determined to be an error caused by some noise. Is done. Therefore, in this case, the specific result is reset to zero (there is no object at that position). In the method of the present embodiment, such a filtering process based on the amplitude information is performed, and only the finally reconstructed image is obtained as a three-dimensional position measurement result.

Next, a part related to software among the three-dimensional position measuring apparatus in which the above method is performed will be described. As described above, the apparatus includes the computer 6, and the various processes described above are executed by various programs installed in the computer 6.
As various programs, a reproduction calculation program that performs reproduction calculation on one hologram data and obtains complex amplitude data at each reproduction distance, a phase information extraction program that obtains a phase value map at each reproduction distance from each complex amplitude data, An amplitude information extraction program that obtains an amplitude value map at each reproduction distance from complex amplitude data, specifies a three-dimensional position based on each phase value map, and performs a filtering process based on the amplitude information, and a formal three-dimensional position specification result A location specifying program is installed.

  The reproduction calculation program performs discrete Fourier transform and the like for image reproduction, and is not particularly different from ordinary digital holography. Therefore, detailed description is omitted. Since reproduction calculation is performed while changing the reproduction distance, an initial value of the reproduction distance, an end value of the reproduction distance, and a pitch for changing the reproduction distance are passed as arguments to the reproduction calculation program. For example, when measuring the three-dimensional position of an object in a space of 50 × 50 × 50 (mm), since the depth is 50 mm, the reproduction distance needs to be changed over a 50 mm range. In this case, for example, the initial value of the reproduction distance is 100 mm, the final value is 150 mm, and the change pitch is 10 mm. In this example, the reproduction calculation is repeated six times, and six complex amplitude data sets are obtained for one hologram data (one shot).

  The phase information extraction program and the amplitude information extraction program are basically the same as in the case of image reproduction in normal digital holography. The phase information extraction program sequentially reads each data set of complex amplitudes, calculates a declination from the complex amplitude at each point, and outputs a phase value map. The number of phase value maps is output as many as the number of complex amplitude data sets (the number obtained by changing the reproduction distance). In the above example, six phase value maps are output. The amplitude information extraction program also sequentially reads each data set of complex amplitudes, calculates the square of the absolute value of the amplitude from the complex amplitude at each point, and outputs an amplitude value map. Similarly, the number of amplitude value maps is the number of times the reproduction distance is changed. The phase value map and the amplitude value map are stored in the storage unit 62 for later processing.

As described above, the position specifying program specifies a three-dimensional position from the phase value map of each reproduction distance. FIG. 10 is a flowchart showing an outline of the position specifying program.
As illustrated in FIG. 10, the position specifying program reads the first phase value map from the storage unit 62. The first is, for example, a phase value map when the above-described reproduction distance is an initial value. Then, the phase value map is subjected to data processing, and an area of a portion that is considered as an image of each object is set. That is, if there is an area where the phase value has changed greatly, a rectangular area including the area is set. Then, the data of the rectangular area is compared with the sample data as described above, and the correlation is evaluated. If the correlation is greater than or equal to the reference value, it is determined that the image is an image that is correctly reproduced, and the center coordinates of the image are stored in a memory variable as an indication of the position of the specified object (specified coordinates). To do.

  A specific example of the method of checking the correlation is, for example, by sequentially comparing the phase value of each coordinate of the portion seen as an image with the phase value of the same coordinate in the standard data, and taking the difference, and averaging the difference over the entire coordinate A method is conceivable in which a value is calculated and a determination is made based on whether the average value is within a reference value. The differences may be summed and a determination may be made based on whether the sum is within a reference value.

  The above processing is repeated for one phase value map, and each three-dimensional coordinate is stored as a specified coordinate separately in a memory variable, and then the next phase value map is read. The next phase value map is a phase value map obtained by changing the reproduction distance by a predetermined pitch. The same processing is repeated for the next phase value map, the three-dimensional coordinates of the portion of the reproduced image having a certain correlation or more are specified, and the coordinates are stored in a memory variable.

  When the three-dimensional coordinates are specified and stored in the memory variables for all the phase value maps, the program next performs a filtering process with the amplitude information. That is, as shown in FIG. 10, each specified coordinate is sequentially read from the memory variable, and an amplitude value map having the coordinate is read from the storage unit 62. Then, as described above, a rectangular reference area is set, and it is determined whether or not the contrast ratio is greater than a certain value. If not, the error data is reset to zero. When the filtering process is completed for all specified coordinates, the position specifying program ends.

  According to the three-dimensional position measurement method or apparatus of the above-described embodiment, the three-dimensional position, particularly the position in the reproduction distance direction, is specified based on the phase information. For this reason, whether or not the reproduced image is at the correct position is determined according to the three-dimensional shape of the object, and is determined based on a wider area. For this reason, a more accurate determination can be made, and a highly accurate three-dimensional position can be specified. In particular, in this embodiment, since the determination is made using the entire wavefront of the reproduced image of one object, this effect is remarkable.

In this embodiment, when the three-dimensional position is specified based on the phase information, the filtering process is performed using the amplitude information. For this reason, the occurrence of an error that erroneously specifies a position where no object exists is suppressed, and in this respect, more accurate three-dimensional position measurement can be performed.
Note that the use of the phase information is determined by the wavefront, but it is not always necessary to use the entire wavefront of the reproduced image. For example, in the semi-arc-shaped phase reproduction image shown in FIG. 7, the determination can also be made by checking the correlation with the sample data for the half area (¼ arc) on one side from the lowest point. Even in this case, the measurement can be performed with sufficiently high accuracy as compared with the determination of the peak of the luminance value as in Patent Document 2. However, it is a matter of course that the measurement with higher accuracy can be performed by using the wavefront data of the entire reproduced image.

  Further, the point that the object that is the object of measurement is spherical has an effect that the calculation is easy when the sample data is obtained by calculation. If the object is not spherical but has a complicated shape, the calculation for obtaining the sample data may be complicated. In this case, the method shown in FIG. A method for obtaining specimen data by performing imaging in advance may be adopted.

  Note that the method of obtaining sample data by calculation is advantageous when there is a large variation in objects in terms of dimensions and refractive index. If the variation of the object is large in terms of dimensions and refractive index (when the standard deviation is large), or if the selected sample object has a large deviation value, the measurement accuracy will be reduced. In the case of obtaining sample data by calculation, there is no such problem because a sample object is assumed to have an average shape and refractive index. In some cases, the size and refractive index of a considerable number of objects may be examined in advance, and the size and refractive index of the sample object may be determined by a statistical method.

  Further, the point that the object S is transparent and the object light is transmitted light has an advantage that a wide measurement space can be targeted in the depth direction. When a hologram is recorded by scattered light instead of transparent objects (tracer particles) as in the conventionally known PIV, it is necessary to shoot with a wider viewing angle than when using transmitted light. In this case, it is necessary to use a lens having a large NA, and it becomes difficult to increase the depth of field. For this reason, it becomes difficult to ensure a wide measurement space in the depth direction. Generally speaking, when recording a hologram with transmitted light and measuring a three-dimensional position, a narrower viewing angle is sufficient compared to scattered light. Therefore, it is advantageous in securing a wide measurement space in the depth direction.

  In addition, the point which the object S is transparent and spherical makes the said merit more remarkable. That is, if the object is spherical, the correlation with the sample data can be determined based on the state where the wavefront gradually contracts due to the lens effect as described above. As can be seen from FIG. 4, the viewing angle of the imaging optical system 4 may be narrower for such observation. Therefore, the effect of deepening the depth of field by using a lens having a small NA is remarkable.

  In the method and apparatus of the present embodiment, the imaging optical system 4 is a telecentric optical system. For this reason, highly accurate three-dimensional position measurement can be performed more easily. This point will be described with reference to FIG. FIG. 11 is a schematic diagram showing the telecentricity of the imaging optical system 4 in the apparatus of FIG. A telecentric optical system generally refers to an optical system in which the principal ray can be regarded as being parallel to the principal axis. In particular, as shown in FIG. 11 (1), an optical system in which the principal ray can be regarded as parallel to the optical axis on both the object side and the image side is called double-sided telecentric. Such a double-sided telecentric optical system can be achieved by making the position of the image-side focal point of the objective lens 41 coincide with the position of the object-side focal point of the imaging lens 42 (confocal).

  In order to easily perform highly accurate three-dimensional position measurement, image side telecentric is particularly important. As shown in FIG. 11 (2), when an image is taken with the image sensor 2 via an optical system that is not telecentric on the image side, it is inevitable that the image is distorted. In this case, it becomes difficult to distinguish whether the distortion of the obtained reproduced image is caused by the incorrect reproduction distance as described above or whether the optical system is not telecentric. The distortion caused by non-telecentric advance what distortions examines whether occurring keep making data for correction, by in terms of correcting the reproduced image it necessary to perform contrast or the like of the sample data described above There is. For this reason, trying to specify a highly accurate three-dimensional position is a complicated and difficult task. If the image side telecentric as in this embodiment, there is no such problem.

  In addition, as shown in FIG. 11 (2), if the object side telecentric is not used, the lateral magnification is different, and the dimensional shape of the image changes depending on the position of the object. For this reason, it becomes difficult to compare with the above-described sample data, and an error in which it is determined that the image reproduced at the correct reproduction distance is not correct is likely to occur. In this embodiment, since the object side is also telecentric, there is no such problem, and highly accurate three-dimensional position measurement can be performed stably. The merit of recording a hologram with transmitted light and measuring the three-dimensional position has been described above. However, in order to increase the depth of field, an object-side telecentric optical system is advantageous, and the measurement space in the depth direction is advantageous. The effect of increasing the value becomes more remarkable.

Next, another embodiment of the three-dimensional position measurement method and apparatus of the present invention will be described. FIG. 12 is a schematic view of the main part of the three-dimensional position measuring apparatus according to the second embodiment of the present invention.
In the embodiment shown in FIG. 1, the light from the coherent light source 1 is extracted by the extraction beam splitter 51 and used as the reference light. However, as described above, the reference light can be extracted from the object light. The apparatus of the second embodiment shown in FIG. 12 is this type of apparatus.

  More specifically, in the reference light optical system 5 in this embodiment, an extraction beam splitter 57 is provided at a position where the object light is incident. Then, as shown in FIG. 12, a Fourier transform lens 581, a pinhole plate 582, and a collimator lens 583 are provided on one of the optical paths branched by the extraction beam splitter 57. The pinhole plate 582 is disposed so that the pinhole is positioned at the image side focal point of the Fourier transform lens 581.

  A lens also allows light to pass through a finite area and has a diffraction phenomenon. As is well known, when the screen is placed at the image-side focal position of the lens, the same state as when diffracted light is projected onto the screen at infinity is obtained, and a Fraunhofer diffraction image is obtained. Since this diffraction image is the same as the Fourier transform, it is called a Fourier transform action by a lens or a Fourier transform lens. Also in this embodiment, a Fraun-Hofer diffraction image by the Fourier transform lens 581 is obtained on the pinhole plate 582, and its distribution corresponds to Fourier transform. At this time, light having a low spatial frequency is distributed in the vicinity of the optical axis, and light having a high spatial frequency is distributed at a position away from the optical axis. This is the same as the principle of the spatial filter.

In FIG. 12, when a plane wave (parallel light) L ₁ is irradiated onto an object S (here, tracer particles), diffracted light (object light) L ₂ is emitted from the object S. As shown schematically in FIG. 12, the wavefront of the plane wave L ₁ is disturbed by the object S, the object beam L _2, not disturbed and the light wave is disturbed depending on the shape and the refractive index or the like of the object S Light included. That is, even the object light L _2, a wavefront of light transmitted through the homogeneous part of the object S holds almost the same shape as the original plane wave. Such object light L ₂ is divided by the beam splitter 57, and one of the divided light beams reaches the pinhole plate 582 through the Fourier transform lens 581. The light whose wave front is disturbed has a high spatial frequency and is therefore distributed at a location away from the optical axis. Therefore, by arranging the pinhole plate 582 as shown in FIG. 12, light having a high spatial frequency is removed, and light having only a low spatial frequency (here, a spherical wave) L ₃ is obtained. Light high spatial frequencies, an optical wavefront is disturbed by the object S, because it is light, which may represent the object information, the spherical wave L ₃ would that light which does not include the object information. The spherical wave L ₃ is converted into parallel light L ₄ by the collimator lens 583 and integrated with the other object light L ₅ by the beam splitter 59. Then, the parallel light L ₄ and the object light L ₅ are superimposed on each other and enter the image sensor 2 in a state of interference. Even when such a reference light optical system 5 is used, interference fringes can be similarly obtained and hologram data can be recorded.

Next, each embodiment of the invention of the speed measuring method and the invention of the speed measuring device will be described. FIG. 13 is a schematic perspective view showing an embodiment of the invention of the speed measuring method.
The embodiment of the velocity measuring method is a method of performing the three-dimensional position measurement by the above-described method at two times and obtaining the velocity vector of the tracer particle based on the time difference. Presence of an object (tracer particles), for example, three positions as shown in FIG. 13 (1) was confirmed at a certain time t _1, the three-dimensional position is identified as P ₁ to P _3. Furthermore, at t ₂ after Δt, it is assumed that the presence of an object is confirmed at three locations as shown in FIG. 13B, and the three-dimensional positions are specified as P ₁ ′ to P ₃ ′.

  At this time, for each object imaged at two times, correspondence is made as to which reproduced image corresponds to the reproduced image of the same object. Several methods are known for the correspondence. For example, when the rough direction and velocity of the fluid flow in the tube 101 are known, the region where the tracer particles can exist after Δt seconds accordingly. And the reproduced image whose position is specified in the region after Δt seconds is associated with the same particle. In addition, after associating each reproduced image with 1: 1, if there is a pair in which the direction of the velocity vector is different from the limit as compared with the other pairs, the correspondence of the pair is associated as an error. Correction may be performed to correct it. Using these known methods as necessary, the three-dimensional positions specified at two times are associated with each other to obtain a spatial distribution of the three-dimensional velocity vector.

  An embodiment of the velocity measuring device can be realized by adding a velocity measuring program to the computer 6 and installing it in any of the above-described embodiments of the three-dimensional position measuring device. After reading the measurement result of the three-dimensional position at two times from the storage unit 62 and performing the above-described association, each velocity vector is obtained based on the vector between the paired coordinates and the time difference. Programmed like so.

  Note that the speed measurement device includes a control unit that controls the image sensor 2 and the coherent light source 1 in order to cause the image sensor 2 to perform imaging at the two times. For example, a laser as coherent light is used as a pulse, and the cycle of the pulse is made to coincide with the time difference between the two times. Then, imaging is performed by the imaging device 2 in synchronization with the pulse period. At this time, the frame frequency of the image sensor 2 and the laser pulse may be synchronized so that photographing at one time is performed in exactly one frame.

Since the speed measurement method and the speed measurement apparatus use the three-dimensional position measurement method and apparatus according to any one of the above-described embodiments, the speed vector can be measured based on the measurement result of the accurate three-dimensional position. it can.
The merit that the tracer particle is a transparent spherical shape has been described above. In particular, when the liquid flow is measured by PIV, the tracer particle is a polystyrene particle having a specific gravity close to 1 from the viewpoint of following the flow of the particle. Commonly used. Resin particles such as polystyrene are readily available as transparent particles, and this is also advantageous.

The three-dimensional position measuring method and apparatus of the present invention can be used for measuring the three-dimensional positions of various objects in addition to the tracer particles in the PIV described above. For example, it can be used for observation of single-cell organisms such as Chlamydomonas and Paramecium, biological cells such as cancer cells, blood cells and sperm, and cultured cells such as yeast. In this case, in the case of measuring a three-dimensional position in water, in addition to counting the number in a three-dimensional space, it is also possible to measure a three-dimensional velocity vector from the measured three-dimensional position between two times.
In each of the above-described embodiments, the imaging optical system 4 is disposed on the side opposite to the side on which the irradiation optical system emits coherent light, and the transmitted light is mainly incident on the imaging element 2 as object light. In some cases, light is used as object light. The image pickup device 2 is arranged on the same side as the side on which the coherent light is irradiated, and a reflected beam is taken out and made incident on the image pickup device 2 using a beam splitter or the like as necessary.

In the above description, it is explained that the processing is performed in the state of numerical data without imaging the reproduced image when specifying the three-dimensional position. However, the numerical data may be processed after imaging, and after the three-dimensional position is specified. Of course, an imaged reproduced image may be output.
In each of the above embodiments, the position in the Z-axis direction is specified by the image based on the phase information, and the position in the XY direction is also specified at the center position of the image. However, the position in the XY direction is specified by the image based on the amplitude information. You can go. That is, if the coordinates specified by the phase information are Xn, Yn, Zn, the amplitude value map of Z = Zn is read, and the amplitude reproduction image is reproduced at a position including the coordinates of (Xn, Yn). After confirmation, the center of the amplitude reproduction image may be obtained and set as the position in the XY direction.

The determination of “whether or not playback was performed at the correct playback distance” is performed by checking the correlation with the sample data in each of the above-described embodiments, but there may be other methods. For example, with respect to each wavefront data obtained while changing the reproduction distance, it is conceivable to calculate a characteristic part of the shape of the image by calculation and judge based on the value. In the above-described example, the curvature of the arc is calculated for each obtained wavefront data, and it can be determined that “reproduced at the correct reproduction distance” when the value is close to the reference value.
Further, in the above description, the method of checking the correlation with the sample data is exemplified by the method based on the numerical value (the method of comparing the phase values themselves), but there may be a method of comparing the images. For example, one image obtained while changing the reproduction distance may be overlaid with an image based on sample data, and the correlation may be checked based on the amount of the overlapped portion.

  One of the major features of digital holography is that the hologram is digital data, and data transfer and copying are easy. Accordingly, there is a case where hologram data is transferred to a place different from the photographing place, reproduction calculation is performed, and a three-dimensional position is measured. In addition, a program for performing reproduction calculation and position specification is implemented as a program on the server, and the position may be measured by sending data from the computer to which the image sensor 2 is connected to the server.

DESCRIPTION OF SYMBOLS 1 Coherent light source 2 Imaging device 3 Irradiation optical system 4 Imaging optical system 5 Reference light optical system 6 Computer 61 Arithmetic processing unit 62 Storage unit

Claims (21)

An irradiation step of irradiating an object with coherent light emitted from a light source;
An imaging process in which object light that is light from an object irradiated with coherent light and coherent light that does not include object information are guided to an image sensor, and interference fringes due to the two lights are imaged by the image sensor,
A recording step of recording the imaged interference fringes as hologram data;
A three-dimensional position measuring method having a specific step of identifying a three-dimensional position of an object from hologram data,
One dimension of the three-dimensional position is the direction of the reproduction distance, which is the separation distance between the imaging surface and the reproduction surface of the image sensor,
The specific process calculates the reproduction of the image of the object while changing the reproduction distance with respect to the recorded hologram data, acquires wavefront data as complex amplitude data as a result of the reproduction calculation, and is included in the acquired wavefront data Including the operation of identifying the position of the object in the direction of the reproduction distance with respect to the reference plane set at a location different from the reproduction plane based on the phase information;
The position in the direction of the reproduction distance in the identification process is determined based on the reproduction distance when the shape of the image that changes due to the difference in the reproduction distance becomes a shape assumed to be obtained when reproduced at the correct reproduction distance. A three-dimensional position measurement method, characterized in that the method is performed based on the above. A sample data acquisition step of acquiring sample data, the sample data is wavefront data of an image of a shape assumed to be obtained when reproduced at the correct reproduction distance;
Judgment that the shape is obtained when played back at the correct playback distance is made by comparing each wavefront data acquired while changing the playback distance with the sample data, and whether the correlation between the two is greater than the reference value The three-dimensional position measuring method according to claim 1 , wherein the three-dimensional position measuring method is performed depending on whether or not. The specimen data is reproduced from the recorded hologram data by performing an imaging process and a recording process in the same manner as the object at a known imaging distance for a specimen object that can be regarded as having the same size and shape and the same refractive index as the object. 3. The three-dimensional position measuring method according to claim 2 , wherein the wavefront data is obtained by calculation. 3. The three-dimensional image according to claim 2 , wherein the sample data is data obtained by calculation according to a dimension and shape of the object, a refractive index of the object, and a refractive index of a medium around the object. Position measurement method. The specific position of the reproduction distance in a particular process, three-dimensional position measuring method according to claim 1 to 4, characterized in that is performed based on wavefront data of the entire image of the object. The wavefront data includes amplitude information;
The identifying step includes an operation of identifying a position in the direction of the reproduction distance based on the phase information and then confirming whether an object is present at the position based on the amplitude information. The three-dimensional position measuring method according to any one of claims 1 to 5 . The imaging process, the object beam, the image-side telecentric to any one of claims 1 to 6, characterized in that the object-side telecentric or double telecentric imaging optical system is a step of imaging is guided to the image sensor The three-dimensional position measuring method described. An object is three-dimensional position measuring method according to any one claims 1 to 7, characterized in that the spherical formed of a material transparent to the coherent light. The three-dimensional position measurement method according to any one of claims 1 to 7 , wherein the object is a unicellular organism, a living cell, or a cultured cell. A speed measuring method using the three-dimensional position measuring method according to any one of claims 1 to 9,
The irradiation step is a step of irradiating the object with the coherent light at a first time and irradiating the coherent light at a second time after a predetermined time from the first time,
The recording step is a step of recording the interference fringes imaged at the first and second times as hologram data,
The specifying step is a step of specifying the three-dimensional position of the object at each first and second time from each hologram data,
A speed measurement method comprising a speed measurement step of obtaining a speed vector of the object based on a specified three-dimensional position at each time. A speed measuring method using the three-dimensional position measuring method according to any one of claims 1 to 8,
The object is tracer particles mixed in the fluid flowing through the flow path,
The irradiation step is a step of irradiating the tracer particles with the coherent light at a first time and irradiating the coherent light at a second time after a predetermined time from the first time,
The recording step is a step of recording the interference fringes imaged at the first and second times as hologram data,
The specifying step is a step of specifying the three-dimensional position of the tracer particle at each first and second time from each hologram data,
A speed measuring method comprising a speed measuring step for obtaining a speed vector of a tracer particle based on a specified three-dimensional position at each time. A light source that emits coherent light;
An image sensor;
Guide and emit coherent light to the object, guide the object light from the irradiated object to the image sensor, and guide the coherent light not including object information to the image sensor as the reference light. An optical system that causes the image sensor to pick up interference fringes by causing interference, and
A storage unit for storing the interference fringes captured by the image sensor as hologram data;
A three-dimensional position measurement apparatus comprising an arithmetic processing unit that specifies a three-dimensional position of the object from the hologram data by calculation,
One dimension of the three-dimensional position is the direction of the reproduction distance, which is the separation distance between the imaging surface and the reproduction surface of the image sensor,
The arithmetic processing unit performs a reproduction calculation of the image of the object while changing the reproduction distance with respect to the stored hologram data, and acquires wavefront data that is complex amplitude data as a result of the reproduction calculation. Based on the phase information included, it specifies the position of the object in the direction of the reproduction distance relative to the reference plane set at a location different from the reproduction plane,
The arithmetic processing unit determines the position in the direction of the reproduction distance based on the reproduction distance when the shape of the image that changes due to the difference in the reproduction distance becomes a shape that is assumed to be obtained when reproduced at the correct reproduction distance. A three-dimensional position measuring apparatus characterized by specifying Sample data is stored in the storage unit, the sample data is wavefront data of an image assumed to be obtained when reproduced at the correct reproduction distance,
The arithmetic processing unit compares each wavefront data acquired while changing the reproduction distance and the sample data, and when the correlation between the two is greater than or equal to a reference value, when the reproduction is performed at the correct reproduction distance, 13. The three-dimensional position measuring apparatus according to claim 12 , wherein it is determined that the shape assumed to be obtained is obtained. The specimen data is reproduced and calculated with respect to the hologram data obtained by photographing the interference fringes in the same manner as the object at a known imaging distance with respect to the specimen object that can be regarded as having the same size and shape and the same refractive index as the object. The three-dimensional position measurement apparatus according to claim 13 , wherein the wavefront data is acquired by performing the step. The three-dimensional position according to claim 13 , wherein the sample data is data obtained by calculation according to the size and shape of the object, the refractive index of the object, and the refractive index of a medium around the object. measuring device. 16. The three-dimensional position measurement apparatus according to claim 12 , wherein the arithmetic processing unit specifies a position in a reproduction distance direction based on wavefront data of the entire image of the object. The wavefront data includes amplitude information;
The arithmetic processing unit identifies a position in the direction of the reproduction distance based on the image reproduction result based on the phase information, and then confirms whether an object exists at the position based on the image reproduction result based on the amplitude information. The three-dimensional position measurement apparatus according to claim 12 , wherein the three-dimensional position measurement apparatus is performed based on the determination. Wherein the optical system, the object beam includes an optical system for imaging for guiding the imaging element, an optical imaging system, 12 through claim, wherein the image-side telecentric, and an object-side telecentric or both-side telecentric The three-dimensional position measuring apparatus according to any one of 17 . The three-dimensional position measurement apparatus according to claim 12 , wherein the object is a spherical object formed of a material transparent to the coherent light. A velocity measuring device for measuring a three-dimensional velocity vector of the object using the three-dimensional position measuring device according to any one of claims 12 to 19 ,
The coherent light source and the optical system irradiate the object with the coherent light at a first time and the coherent light at a second time after a predetermined time from the first time. ,
The imaging element is for imaging the interference fringes at the first and second times,
The storage unit stores the interference fringes imaged at the first and second times as hologram data, respectively.
The arithmetic processing unit specifies a three-dimensional position of the object at each first and second time from each hologram data, and obtains a velocity vector of the object according to the specified three-dimensional position at each time. A speed measuring device characterized by that. 21. The velocity measuring device according to claim 20 , wherein the object is a tracer particle mixed in a fluid flowing in a flow path.

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