Patent Publication Number: US-9411146-B2

Title: Observation device

Description:
TECHNICAL FIELD 
     The present invention relates to a device for observing an image of an object. 
     BACKGROUND ART 
     Use of a phase shift method described in non-patent literature 1 or 2 has been known as a technology of observing an image of an object to obtain a three-dimensional image of the object. In an observation device according to the phase shift method, light with a wavelength of which is emitted from a light source divided in two light components, one of which permeates the object and becomes object light and the other one of which becomes reference light, so as to take a two-dimensional image made by an interference between the object light and the reference light. An optical path length of the reference light is eccentric by λ/4 so that four two-dimensional images are taken, a specified arithmetic is performed for the four two-dimensional images so as to obtain two-dimensional complex amplitude, and then a three-dimensional amplitude image and a three-dimensional phase image of the object are obtained from a plurality of complex amplitude images to be obtained from each direction of light incident to the object. 
     Further, a Hilbert transform method described in a non-patent literature 3 has been known as a technology of obtaining a complex amplitude image from one captured image. 
     CITATION LIST 
     Non-Patent Literature
     [Non-Patent Literature 1] Wonshik Choi, “Tomographic phase microscopy,” Nature Methods—4, 717-719 (2007).   [Non-Patent Literature 2] Niyom Lue, “Synthetic aperture tomographic phase microscopy for 3D imaging of live cells in translational motion,” OPTICS EXPRESS, 16, 16240, (2008)   [Non-Patent Literature 3] Takahiro Ikeda, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” OPTICS LETTERS, 30, (2005)   

     SUMMARY OF INVENTION 
     Technical Problem 
     In the observation device using the phase shift method described in the non-patent literature 1 or 2, it is required that the object is in a stationary state while four two-dimensional images are obtained. In order to obtain an image of a moving object, it is required to obtain the four two-dimensional images by using an optical detector having a high frame rate and capable of taking image at a high speed during a term in which the object is regarded as being in the stationary state. However, the optical detector capable of taking the image at a high speed is expensive, or has a small number of pixels and low spatial resolution. Further, since an exposure time is at most within a period in which the object is regarded as being stationary, in view of an aspect of SN, image quality is decreased and sensitivity is low. When the Hilbert transform described in the non-patent literature 3 is used, further, the spatial resolution is deteriorated by about ¼, so that the image quality is decreased. 
     The present invention has been made to solve the above-mentioned problems in the prior art, and an aspect of the present invention is to provide an observation device capable of obtaining an image of a moving object even though an optical detector of which a reading speed per pixel is low is used. 
     Solution to Problem 
     In accordance with an aspect of the present invention, an observation device is provided. The observation device includes: a light source section for emitting light to a moving object from multiple directions; a detection section for being disposed on a predetermined plane such that scattered light having an identical scattering angle from among scattered light generated by the object upon irradiation with the light by the light source enters at an identical position, and when a direction perpendicular to a moving direction of the object is defined as a first direction and a direction parallel with the moving direction of the object is defined as a second direction, outputting data temporally changing at a frequency corresponding to an amount of Doppler shift of light that reaches at each position on the predetermined plane, for each position in the first direction and the second direction, at each times; an arithmetic operation section for performing a one-dimensional Fourier transform with respect to time variables, for data having a position in the first direction on the predetermined plane, a position in the second direction on the predetermined plane, and a time as variables, and extracting data having an identical incident angle relative to the object from the Fourier-transformed data, on the basis of Doppler Effect; and an optical system for receiving a light emitted from the light source and splitting the received light in front of the object in two light components so as to yield first light and second light, modulating the first light or the second light with a modulator, and then causing a heterodyne interference between the first light and the second light on the predetermined plane. 
     In the observation device of the present invention, the light is emitted by the light source section to the moving object from multiple directions, and the moving object emits scattered light. The scattered light is subjected to an amount of Doppler shift according to the scattering direction. Among the scattered lights passing through a predetermined optical system, the scattered light with an identical scattering angle is received at an identical position of the detection section. The detection section outputs data temporally changing at a frequency corresponding to an amount of Doppler shift of light that reached at each position on a predetermined plane, for each position in the first direction and the second direction, at each times. A one-dimensional Fourier transform with respect to time is performed, for data having a position in first-direction on the predetermined plane, a position in the second-direction on the predetermined plane, and a time as variables by the arithmetic operation section, and extracts data having an identical incident angle relative to the object from the Fourier transformed data, on the basis of the Doppler effect. According to this configuration, since it is possible to extract data with the same incident angle for the object by using the Doppler Effect, it is unnecessary to photograph an image of the object at plural times within a period when the object is regarded as being stationary. Accordingly, it is possible to obtain the image of the moving object even though the optical detector of which the reading speed per pixel is low is used. 
     Further, the arithmetic operation section may extract data of a plane surface satisfying following Equation (1) from the Fourier transformed data,
 
[Equation (1)]
 
ω−Ω=α y +β sin θ 0   (1)
 
in which ω is a time frequency of the Fourier transformed data, Ω is a modulation frequency, y is a position in the second direction of the detection section, θ 0  is an incident angle, and α and β are constant. In this case, by Equation (1) the data having the identical angle for the object can be extracted from the one dimensional Fourier transformed data on the time variable, based on the Doppler Effect. In the Equation (1), the objet moves at a velocity V so as to cause the Doppler Effect, and it is expressed that a certain relation is present between the time frequency ω and the position y, based on the Doppler Effect.
 
     The observation device further includes a condensing lens interposed between the object and the detection section, and the arithmetic operation section may extract data of the surface satisfying following Equation (2) from the Fourier transformed data, 
                   [     Equation   ⁢           ⁢     (   2   )       ]                             ω   -   Ω     =         2   ⁢   π   ⁢           ⁢   V     λ     ⁡     [       sin   ⁡     (       tan     -   1       ⁡     (     y     f   Y       )       )       -     sin   ⁢           ⁢     θ   0         ]               (   2   )               
in which ω is a time frequency of the Fourier transformed data, Ω is a modulation frequency of the modulator, V is a moving velocity of the object, λ is a wavelength of the light emitted by the light source section, y is a position in the second direction of the detection section, f Y  is a focal distance in the second direction of the condensing lens, and θ 0  is the incident angle.
 
In this case, by Equation (2) the data having the identical angle for the object can be accurately extracted from the one dimensional Fourier transformed data on the time variable, based on the Doppler Effect.
 
     Further, the observation device further includes a condensing lens interposed between the object and the detection section, and the light receiving surface of the detection section is disposed on a surface in which a Fresnel diffraction image of the object is formed in the first direction and a Fraunhofer diffraction image of the object is formed in the second direction by the condensing lens. The arithmetic operation section may include a first Fourier transform section for performing the one dimensional Fourier transform with respect to a time variable, a second Fourier transform section for performing a one dimensional Fourier transform with respect to the first direction, a diagonal cut section for extracting data having an identical incident angle for the object based on the Doppler Effect, and a secondary phase division section for dividing a secondary phase which is a value determined by a position at which the detection section is disposed. In this case, an incident angel dependence complex amplitude image can be appropriately obtained. 
     The observation device further includes a condensing lens interposed between the object and the detection section, and the light receiving surface of the detection section is disposed on a surface in which a Fraunhofer diffraction image of the object is formed in the first direction and a Fraunhofer diffraction image of the object is formed in the second direction by the condensing lens. The arithmetic operation section may include a first Fourier transform section for performing the one dimensional Fourier transform with respect to a time variable, and a diagonal cut section for extracting data having an identical incident angle for the object based on the Doppler Effect. In this case, an incident angel dependence complex amplitude image can be appropriately obtained. 
     The observation device further includes a condensing lens interposed between the object and the detection section, and the light receiving surface of the detection section is disposed on a surface in which an image of the object is formed in the first direction and a Fraunhofer diffraction image of the object is formed in the second direction by the condensing lens. The arithmetic operation section may include a first Fourier transform section for performing a one dimensional Fourier transform with respect to a time variable, a second Fourier transform section for performing a one dimensional Fourier transform with respect to the first direction, and a diagonal cut section for extracting data having an identical incident angle for the object based on the Doppler Effect. In this case, an incident angel dependence complex amplitude image can be appropriately obtained. 
     The observation device further includes a condensing lens interposed between the object and the detection section, in which the condensing lens is a fθ lens and the arithmetic operation section may extract data of the surface satisfying following Equation (3) from the Fourier transformed data, 
                   [     Equation   ⁢           ⁢     (   3   )       ]                             ω   -   Ω     =         2   ⁢   π   ⁢           ⁢     V   Y       λ     ⁡     [       sin   ⁡     (     y     f   Y       )       -     sin   ⁢           ⁢     θ   0         ]               (   3   )               
in which ω is a time frequency of the Fourier transformed data, Ω is a modulation frequency of the modulator, V Y  is a moving velocity of the object the a second direction, λ is a wavelength of the light emitted by the light source section, y is a position in the second direction of the detection section, f Y  is a focal distance of the second direction of the condensing lens, and θ 0  is an incident angle.
 
In this case, by Equation (3) the data having an identical angle for the object can be accurately extracted from the one dimensional Fourier transformed data with respect to a time variable, based on the Doppler Effect.
 
     The observation device further includes an illumination lens which receives the light emitted from the light source section and then emits the light diverged or converged in the second direction, the illumination lens being disposed between the light source section and the object. In this case, the light can be emitted to the object from multiple directions. 
     The observation device further includes a velocity detection section for detecting the moving velocity of the object, in which the arithmetic operation section may perform a correction in a velocity change of the object while performing the one dimensional Fourier transform with respect to a time variable based on the velocity of the object detected by the velocity detection section. 
     Further, an emission of the light to the object may be performed by an optical arrangement of a transmitted illumination, or an emission of the light to the object may be performed by an optical arrangement of a reflection illumination. 
     Further, the light source section may be a light source for generating light of a single longitudinal mode, or for generating broadband light. Further, the light source section may be a mode-locked laser. 
     Advantageous Effects of Invention 
     According to the present invention, it is possible to obtain the image of the object even though the optical detector of which the reading speed per pixel is low is used. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a view illustrating a principle of acquiring an image of an object by means of an observation device in accordance with an embodiment; 
         FIG. 2( a )  is a view illustrating an incident angle of incident light L 0 , and  FIG. 2( b )  is a view illustrating a scattering angle θ of scattered light generated by an object  2 ; 
         FIG. 3  is a view illustrating the incident light L 0  scattered by the object  2  which is viewed from a direction of ξ axis; 
         FIG. 4  is a view illustrating a sequence of acquiring an incident angle dependence complex amplitude image by means of a phase shift method according to the conventional art; 
         FIG. 5  is a view illustrating a sequence of acquiring an incident angle dependence complex amplitude image in the observation device  1  according to a first embodiment; 
         FIG. 6  is a view illustrating a configuration of the observation device  1  according to the first embodiment; 
         FIG. 7( a )  is a side view illustrating an illumination lens  20  which is viewed from a Y axial direction, and  FIG. 7( b )  is a side view illustrating the illumination lens  20  which is viewed from an X axial direction; 
         FIG. 8  is a view illustrating a configuration of a condensing lens  30  according to the first placement example; 
         FIG. 9  is a view schematically illustrating lights incident to a detection section  50  by interposing the condensing lens  30 ; 
         FIG. 10  is a view schematically illustrating an appearance of scattered lights caused by incident lights with three incident angles, which are incident to the detection section  50 ; 
         FIG. 11  is a block diagram illustrating a configuration of an arithmetic operation section  60  according to the first placement example; 
         FIG. 12  is a view illustrating an example of an interference strength image i acquired by the detection section  50 ; 
         FIG. 13  is a view schematically illustrating a frequency dependence complex amplitude image a; 
         FIG. 14  is a view schematically illustrating the complex amplitude image a of  FIG. 13 , which is viewed from an X axial direction; 
         FIG. 15  is a view illustrating a configuration of a condensing lens  30 A according to a second placement example; 
         FIG. 16  is a block diagram illustrating a configuration of an arithmetic operation section  60 A according to the second placement example; 
         FIG. 17  is a view illustrating a configuration of a condensing lens  30 B according to a third placement example; 
         FIG. 18  is a block diagram illustrating a configuration of an arithmetic operation section  60 B according to the third placement example; 
         FIG. 19  is a view illustrating amplitude images of the frequency dependence complex amplitude image a with respect to each frequency; 
         FIG. 20  is a view illustrating phase images of the frequency dependence complex amplitude image a with respect to each frequency; and 
         FIG. 21  is a view illustrating the amplitude image of the incident angle dependence complex amplitude image A and the phase image of the incident angle dependence complex amplitude image A, in which the amplitude image is shown on the left and the phase image is shown on the right. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, an embodiment of the present invention will be described in detail with reference to the accompanying drawings. Identical reference numerals denote the same or similar structural elements in the description of the drawings, and a duplicated description will be omitted. 
     An observation device in the present embodiment acquires an image of an object by using a Doppler shift effect induced when light is emitted to a moving object, and particularly by using a certain relation between an incident direction of light incident to the object and an amount of Doppler shift. Firstly, a principle of acquiring the image of the object by means of the observation device of the present embodiment will be described with reference to  FIG. 1 . 
       FIG. 1  is a view illustrating a principle of acquiring the image of the object by means of the observation device according to the present embodiment. In  FIG. 1 , ξ-η coordinate system, x-y coordinate system, and u-v coordinate system are shown. All of ξ axis, a η axis, an x axis, a y axis, an u axis and a v axis are perpendicular to an optical axis of a condensing lens  30 . The ξ axis and the x axis are parallel with each other. The η axis and the y axis are parallel with each other. An object  2  to be observed is present on a ξ-η plane surface. The condensing lens  30  is present on an x-y plane surface. Further, a back focal plane of the condensing lens  30  is identical to a u-v plane surface. A distance between the ξ-η plane surface and the x-y plane surface is d. The distance between the x-y plane surface and the u-v plane surface is identical to a focal distance f of the condensing lens  30 . In this specification, the ξ axial direction, the x axial direction, the X axial direction and a first direction are parallel with one another, and the η axial direction, the y axial direction, the Y axial direction and a second direction are parallel with one another. 
     The object  2  moves in a −η direction on the ξ-η plane surface, and light L 0  with different incidence angles is emitted to the object  2 . Scattered lights L 1 , L 2  and L 3  generated by emitting the light L 0  to the object  2  propagate in multiple directions, and are subjected to a Doppler shift by the movement of the object  2 . The scattered light L 1  with a vector component of a scattering direction identical to a movement direction of the object  2  has an increasing optical frequency. The scattered light L 2  having no vector component of the scattering direction identical to the movement direction of the object  2  has an unchanged optical frequency. The scattered light L 3  with a vector component of a scattering direction opposite to a movement direction of the object  2  has a decreasing optical frequency. These scattered lights L 1 , L 2  and L 3  arrive at the u-v plane surface through the condensing lens  30 . 
       FIG. 2( a )  is a view illustrating an incident angle of the incident light L 0 , and  FIG. 2( b )  is a view illustrating a scattering angle of the scattered light L by means of the object  2 . As shown in  FIG. 2( a ) , in order to express the incident angle of the incident light L 0 , two parameters of an elevation angle θ 0  and an azimuthal angle φ 0  need to be described. A point light source imaginarily disposed in the object  2  is an origin of the ξ-η-ζ coordinate system. With respect to the origin, an angle between a vector of an incident direction of the incident light L 0  and the ζ axis is referred to as the elevation angle θ 0 , and an angle between a projection vector of the vector of the incident direction to the ξ η plane and the ξ axis is referred to as the azimuthal angle θ 0  Further, an angle between the projection vector of the incident light L 0  to the η-ζ plane and the ζ axis is defined as θ 0 ′. Similarly, as shown in  FIG. 2( b ) , an angle between a direction vector of the scattered light L from the point light source and the ζ axis is defined as an elevation angle θ, and an angle between a projection vector of the scattered directional vector to a ξ-η plane surface and the ξ axis is defined as an azimuthal angle φ. Further, an angle between a projection vector of the scattered light L to the η-ζ plane and the ζ axis is defined as θ′. 
       FIG. 3  is a view illustrating an appearance of the incident light L 0  scattered by the object  2  which is viewed from a direction of a ξ axis. In  FIG. 3 , a unit incident vector of the incident light L 0  is defined as s 0 , and a unit scattering vector of the scattered light L is expressed by s. 
     When light with a frequency of ω 0  is emitted to the object  2  moving at a velocity vector V, the frequency of scattering waves generated in the object  2  is changed by a Doppler shift frequency ω d  which is expressed by Equation (4) due to a Doppler effect. In Equation (4), a unit incident vector of the incident light for the object  2  is defined as s 0 , and a unit scattering vector indicating a scattering direction of the scattered wave generated in the object  2  is defined as s. In Equation (4), λ is a wavelength of light. Equation (4) indicates that an amount of the Doppler shift ω d  is proportional to a scalar product of (s−s 0 ) and a velocity vector V of a moving object. In Equation (4), a frequency transition by an inner product term (ω d1 =−(2π/λ)s 0 ·V) of a unit incident vector s 0  and a velocity vector V is called a first Doppler Effect. Further, a frequency transition by an inner product term (ω d2 =(2π/λ)s·V) of a unit scattered vector s and a velocity vector V is called a second Doppler Effect. In this case, an optical frequency of the scattered light caused by the object  2  is affected by an incident vector component and a scattering directional vector component as follows. That is, the incident light with the incident vector component in a direction identical to a moving direction of the object  2  has a low optical frequency of the scattered light generated in the object  2  by the first Doppler Effect. The incident light with the incident vector component in a direction opposite to the moving direction of the object  2  has a high optical frequency of the scattered light generated in the object  2  by the first Doppler Effect. The incident light without the incident vector component in a direction parallel with the moving direction of the object  2  is not affected by the first Doppler Effect and has an unchanged optical frequency of the scattered light generated in the object  2 . The scattered light with the vector component in a scattering direction identical to the moving direction of the object  2  has a high optical frequency due to the second Doppler Effect. The scattered light with the vector component in a scattering direction opposite to the moving direction of the object  2  has a low optical frequency due to the second Doppler Effect. The scattered light with the scattered vector component in a direction parallel without the moving direction of the object  2  is not affected by the second Doppler Effect and has an unchanged optical frequency of the scattered light generated in the object  2 . 
     
       
         
           
             
               
                 
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     In Equation (4), if the velocity V and the unit scattering vector s are constant, it will be known that the Doppler shift frequency ω d  of a diffraction wave observed at a certain position corresponds to the unit incident vector s 0  one to one. As described above, the complex amplitude image of waves of the Doppler shift frequency ω d  depends on the incident angle θ 0  of incident waves. 
     It is known that a three dimensional amplitude image and a three dimensional phase image may be obtained from the complex amplitude image, in which the incident angle θ 0  is used as a variable (hereinafter, referred to as an incident angle dependence complex amplitude image), by using an X ray CT algorithm or a diffractive tomography algorithm. Therefore, if the incident angle dependence complex amplitude image may be obtained, the three dimensional amplitude image and the three dimensional phase image can be obtained. Hereinafter, a comparison of a sequence of acquiring the incident angle dependence complex amplitude image in the observation device according to the embodiment of the present invention with a sequence of acquiring an incident angle dependence complex amplitude image by a phase shift method will be described in order to help in understanding the present invention. 
       FIG. 4  is a view illustrating a sequence of acquiring the incident angle dependence complex amplitude image according to the conventional phase shift method. In  FIG. 4 , a longitudinal axis of a graph indicates a position of the object, and a cross axis of the graph denotes a time. An arrow mark shown at an upper portion of  FIG. 4  indicates an imaging timing. It is regarded that the object moves at a constant velocity in a specific direction. In the phase shift method, for the object moving at a time t 1 , an image of the object is imaged by plural pieces within a time when it is regarded that the object does not move, and interference strength images of the plural pieces of the images are acquired. In the phase shift method, at this time, the complex amplitude image in which the position of the object is used as a variable (hereinafter, referred to as a position dependence complex amplitude image) is acquired by making the interference strength image interfere with the reference light in which an optical length is changed by λ/4. Since the object moves at the constant velocity, meanwhile, the position dependence complex amplitude image may be a complex amplitude image in which a time is used as a variable. Such a position dependence complex amplitude image is acquired at a desired time interval by plural pieces (see t 1 , t 2  and t 3  of  FIG. 4 ). In a synthetic aperture tomography, a complex amplitude image in which a frequency is used as a variable (hereinafter, referred to as a frequency dependence complex amplitude image) is acquired by performing a one dimensional Fourier transform with respect to a time variable t to the position dependence complex amplitude image obtained at each time. Then, the incident angle dependence complex amplitude image is acquired by using the relation between the frequency m and the incident angle θ 0 . 
     In the phase shift method, as described above, for the moving object, it is necessary that the object is imaged by plural pieces within a time when it is regarded that the object does not move, so as to acquire A plurality of the interference strength images. If the object such as a cell and the like is made to flow in a flow cytometer, the cell moves at several meters/second. If laser light with a wavelength of 633 nm is emitted to a cell which has a diameter of 10 μm and moves at 1 m/second and the cell is photographed by using an objective lens with NA=0.45 (twenty-times magnification), a diffraction limit of the objective lens is estimated to be about 0.9 μm. For this reason, it is necessary to restrain a blur caused by the movement of the object up to 0.9 μm. Accordingly, if only strength image of the object is acquired, a photographing of the object must be completed within 0.9 μm/1 m/s=0.9 μs. If one piece of the complex amplitude image is acquired from four pieces of interference images, on the other hand, it is necessary to restrain a phase precision of the complex amplitude image up to 1/100. Therefore, a time interval of the four continuous pieces of the interference images is estimated from 0.633 μm/1 m/s/0.45/100 to 10-8 seconds. For this reason, in the phase shift method, under this condition, it is necessary to acquire the interference strength image by using a two-dimensional optical detector with a frame rate of about 100 MHz. However, it is difficult to obtain the two-dimensional optical detector with a super high-speed and pixels. 
     With respect to this,  FIG. 5  is a view illustrating a sequence of acquiring the incident angle dependence complex amplitude image in the observation device according to the embodiment of the present invention. Similarly to  FIG. 4 , in  FIG. 5 , a longitudinal axis of a graph indicates a position of the object, and a cross axis of the graph denotes a time. An arrow mark shown at an upper portion of  FIG. 5  indicates an imaging timing. It is regarded that the object moves at a constant velocity in a desired direction. In the observation device according to the present embodiment, for the object moving at a time t 1 , an image of the object is taken by one piece within a time when it is regarded that the object does not move, and one interference strength image is acquired. This interference strength image is acquired at a desired time interval by plural times (see t 1 , t 2  and t 3  of  FIG. 5 ). Then, the frequency dependence complex amplitude image is acquired by performing the one dimensional Fourier transform with respect to a time variable t to the interference strength image obtained at each time, without performing an operation of calculating the position dependence complex amplitude image from the position dependence interference strength image. In turn, the incident angle dependence complex amplitude image is obtained from the frequency dependence complex amplitude image by using a certain relation between the Doppler shift frequency w and the incident angle θ 0 . As described above, in the observation device according to the present embodiment, since the object is photographed by one piece within a time when it is regarded that the object does not move, the incident angle dependence complex amplitude image with a high precision can be obtained although the two dimensional optical detector with a high frame rate is not used. Hereinafter, the configuration of the observation device according to the present invention will be described. 
     First Embodiment 
     First Placement Example 
     An observation device  1  according to the present embodiment acquires an incident angle dependence complex amplitude image of an object  2  based on the principle described above.  FIG. 6  is a view illustrating a configuration of the observation device  1  according to the first embodiment. As shown in  FIG. 6 , the observation device  1  of the present embodiment includes a light source section  10 , an illumination lens  20 , a beam splitter HM1, a condensing lens  30 , a beam splitter HM2, a modulation section  40 , a mirror M1, a mirror M2, a detection section  50  and a arithmetic operation section  60 . 
     The light source section  10  emits light through the illumination lens  20  to the moving object in multiple directions so that a Doppler effect is induced in the light. The light source section  10  is, for example a HeNe laser light source, and outputs light (optical frequency ω 0 ), which is emitted to an object  2 , as parallel light. The beam splitter HM1 inputs the light output from the light source section  10  in front of the object  2 , splits the light into two light components, i.e., first light and second light, outputs the first light to the illumination lens  20 , and outputs the second light to the modulation section  40 . 
     The illumination lens  20  receives the light output from the beam splitter HM1, and emits the light, which has multiple directions in the Y axial direction and a fixed direction in the X axial direction, to the object  2 . A cylindrical lens is used as the illumination lens  20 .  FIG. 7  is a view illustrating an example of the illumination lens  20 , in which  FIG. 7( a )  is a side view illustrating the illumination lens  20  viewed in the Y axial direction, and  FIG. 7( b )  is a side view illustrating the illumination lens  20  viewed in the X axial direction. A dotted line shown in  FIG. 7  denotes an appearance of an image formation of light by means of the illumination lens  20 . f LS2  of  FIG. 7  indicates a focusing distance of the illumination lens  20 . As shown in  FIG. 7 , the illumination lens  20  has a surface with a curvature disposed in parallel with the Y axial direction and a surface without the curvature disposed in parallel with the X axial direction. Light which is parallel light in the X axial direction and is convergent light in the Y axial direction is emitted to the object  2  by means of the illumination lens  20 . In result, the light is emitted from multiple directions in the Y axial direction to the object  2 . In  FIG. 7 , further, a cylindrical lens of a convex lens is shown as the illumination lens  20 , but a cylindrical lens of a concave lens may be used as the illumination lens  20 . In this case, light which is the parallel light in the X axial direction and divergent light in the Y axial direction is emitted to the object  2 . The incident vector s 0  of the convergent light or the divergent light to be output by means of the illumination lens  20  is preferably present in an identical plane S 0 . The plane surface S 0  is a surface formed by a moving direction of the object  2  and the optical axis ζ. Further, the observation device  1  of the embodiment may have no illumination lens  20 , and light which is the parallel light in the X axial direction and the convergent light or the divergent light in the Y axial direction may be emitted from the light source section  10 . 
     The modulation section  40  includes a first modulator  41  and a second modulator  42 . The first modulator  41  and the second modulator  42  are, for example, acousto-optic device. The first modulator  41  diffracts the light output from the light source section  10  through a first modulation signal so as to output the diffracted light to the second modulator  42 . The second modulator  42  diffracts the light output from the first modulator  41  through a second modulation signal so as to output the diffracted light to the mirror M1. The light output from the second modulator  42  is reflected by the mirrors M1 and M2 in sequence, and is output to the beam splitter HM2. On the other hand, the modulator  40  may be disposed in a light path of the first light. 
     A frequency of the first modulation signal provided to the first modulator  41  is slightly different from a frequency of the second modulation signal provided to the second modulator  42 . For example, the first modulation frequency is 40 MHz, and the second modulation frequency is 40.000010 MHz. Therefore, a difference Ω between them is 10 Hz. The first modulation signal and the second modulation signal are sine waves, respectively. Further, the modulation section  40  must not be constituted of two modulators such as the first modulator  41  and the second modulator  42 . That is, the modulator  40  may have a function of performing a frequency transition of the optical frequency by a desired frequency Ω (hereinafter, referred to as a modulation frequency Ω), and the modulation section  40  may be constituted of one modulator, or three or more modulators. 
     The condensing lens  30  inputs scattered waves generated in the object  2  by an emission of the light output from the illumination lens  20 , so as to form a Fresnel diffraction image in the X axial direction and a Fraunhofer diffraction image in the Y axial direction on a light receiving surface of the detection section  50 . The condensing lens  30  outputs the light to the beam splitter HM2. The configuration of the condensing lens  30  is shown in  FIG. 8 .  FIG. 8( a )  is a side view illustrating the condensing lens  30  which is viewed from the Y axial direction, and  FIG. 8( b )  is a side view illustrating the condensing lens  30  which is viewed from the X axial direction. A dotted line shown in  FIG. 8  denotes an appearance of an image formation of light by means of the condensing lens  30 . As shown in  FIG. 8 , the condensing lens  30  includes four lenses such as a lens OB, a lens LS1, a lens LS2 and a lens LS3. 
     The lens OB is an objective lens which has a numerical aperture NA=0.45 with twenty-times magnification. A back focal plane of the lens OB is referred to as FP. The lens LS1 is a lens which has no curvature in the X axial direction and has a curvature in the Y axial direction. The lens LS2 is a lens which has a curvature in the X axial direction but has no curvature in the Y axial direction. The lens LS3 is a lens which has no curvature in the X axial direction but has a curvature in the Y axial direction. The Y axial directions of the lenses LS1 and LS3 form a 4f optical system. The 4f optical system is an optical system in which a back focal plane of the lens LS1 is identical to a previous focal plane of the lens LS3, and an image on the previous focal plane of the lens LS1 is formed on the back focal plane of the lens LS3. The lens LS2 is disposed on a plane different from the back focal plane of the lens LS1 and different from the front focal plane of the lens LS3. As shown in  FIG. 8( a ) , with respect to the X axial direction, the condensing lens  30  forms not the Fraunhofer diffraction image surface or the image formation surface but a Fresnel diffraction image surface on the light receiving surface of the detection section  50  through the lens LS2 by using the light output from the lens OB. As shown in  FIG. 8( b ) , further, with respect to the Y axial direction, the condensing lens  30  forms the Fraunhofer diffraction surface on the receiving light surface of the detection section  50  by making the light output from the back focal plane of the lens OB be parallel light through the lens LS1 and converging the parallel light through the lens LS3. By interposing the condensing lens  30  between the object  2  and the detection section  50 , the light among the scattered lights from the object  2 , which has a different incident angle θ 0  and an identical scattered angle θ′, is condensed at a point of the light receiving surface of the detection section  50 . 
     The beam splitter HM2 introduces the light (object light) arrived from the condensing lens  30  and the light (reference light) arrived from the modulation section  40  by interposing the mirror M1 and M2 into the light receiving surface of the detection section  50 , and makes both lights to be subjected to a heterodyne interference on the light receiving surface of the detection section  50 . The frequency of the light output from the modulation section  40  and incident to the light receiving surface of the detection section  50  corresponds to ω 0 +Ω. The Ω is a difference frequency between the first modulation frequency and the second modulation frequency. The object light and the reference light are subjected to the heterodyne interference on the light receiving surface of the detecting section  50 , and the detecting section  50  observes interference beat signals of the object light and the reference light. 
     The detection section  50  is disposed on a predetermined plane such that scattered light having an identical scattering angle enters at an identical position, and outputs data temporally changing at a frequency corresponding to an amount of Doppler shift of light that reaches at each position on the predetermined plane, for each position in the first direction and the second direction, at each times. The detection section  50  is a two-dimensional optical detector which detects the light arrived at the light receiving surface thereof and outputs a signal corresponding to the detected light, through a pixel configuration arranged in parallel in the X axial direction and the Y axial direction. The receiving surface of the detection section  50  is disposed on a surface where the Fresnel diffraction image of the object  2  is formed in the first direction by the condensing lens  30 , and the Fraunhofer diffraction image of the object  2  is formed in the second direction. Here, a direction which is parallel within the plane surface S 0  and perpendicular to a Z axis is defined as a u direction, and a direction which is parallel within the plane surface S 0  and perpendicular to the u direction is defined as a v direction. Further, an axis perpendicular to the X axis and the Y axis is defined as the Z axis. 
       FIG. 9  is a view schematically illustrating lights incident to the detection section  50  by interposing the condensing lens  30 . In  FIG. 9 , with respect to the Y axis direction, the object  2  is disposed on the previous focal plane of the condensing lens  30 , and the light receiving surface of the detection section  50  is disposed on the back focal plane of the condensing lens  30 . 
       FIG. 9( a )  is a view illustrating an appearance of scattered lights L 1 , L 2  and L 3  which are formed at the object  2  by the incident light and are incident to the detection section  50 , by paying attention to the incident light of which the incident angle θ 0  is −ψ. If the object  2  moves in a −Y axial direction, the incident light L 0  with an incident vector component of a direction opposite to the moving direction of the object  2  has a high optical frequency (ω d1 =δ) of the scattered light caused by the object  2  by means of the first Doppler Effect. The object  2  scatters the light subjected to the first Doppler Effect. The scattered light L 1  which has no scattering directional vector component in a direction parallel with the moving direction of the object  2  is not subjected to the second Doppler Effect (ω d2 2=0). Therefore, in the optical frequency of the scattering light L 1 , only a frequency transition by the first Doppler Effect is observed (ω d =δ+0=δ). The scattered light L 2  with the vector component in a scattering direction opposite to the moving direction of the object  2  has a low optical frequency due to the second Doppler Effect (ω d2 =−δ). Therefore, the optical frequency of the scattered light L 2  is not changed by the first Doppler Effect and the second Doppler Effect (ωd=δ−δ=0). The scattered light L 3  with the vector component in a scattering direction opposite to the moving direction of the object  2  is subjected to the frequency modulation by the Doppler shift and has a low optical frequency (ω d2 =−2δ). Therefore, the optical frequency of the scattered light L 3  is lowered by the first Doppler Effect and the second Doppler Effect (ω d =δ−2δ=−δ). These scattered lights L 1 , L 2  and L 3  arrive at positions P 1 , P 2  and P 3  of each detection section  50  through the condensing lens  30 . 
       FIG. 9( b )  is a view illustrating an appearance of the scattered lights L 1 , L 2  and L which are formed by the incident light in the object  2  and are incident to the detection section  50 , by paying attention to the incident light of which the incident angle θ 0  is 0. If the object  2  moves in a −Y axial direction, the incident light L 0  with no an incident vector component of a direction parallel with the moving direction of the object  2  is not subjected to the first Doppler Effect and has an optical frequency of the scattered light, which is caused by the object  2 , identical to the incident light (ω d1 =0). The object  2  scatters the light which is not subjected to the first Doppler Effect. The scattered light L 1  with the vector component in a scattering direction identical to the moving direction of the object  2  is subjected to the frequency modulation by the Doppler shift and has a high optical frequency (ω d2 =+δ). Therefore, the optical frequency of the scattered light L 1  gets higher by the first Doppler Effect and the second Doppler Effect (ω d =0+δ=+δ). The scattered light L 2  having no vector component of the scattering direction parallel to the movement direction of the object  2  has an unchanged optical frequency (ω d2 =0). Therefore, the optical frequency of the scattered light L 2  is not changed by the first Doppler Effect and the second Doppler Effect (ω d =0−0=0). The scattered light L 3  with the vector component in a scattering direction opposite to the moving direction of the object  2  is subjected to the frequency modulation by the Doppler shift and has a low optical frequency (ω d2 =−δ). Therefore, the optical frequency of the scattered light L 3  is lowered by the first Doppler Effect and the second Doppler Effect (ω d =0−δ=−δ). These scattered lights L 1 , L 2  and L 3  arrive at positions P 2 , P 3  and P 4  of each detection section  50  through the condensing lens  30 . 
       FIG. 9( c )  is a view illustrating an appearance of the scattered lights L 1 , L 2  and L 3  which are formed by the incident light in the object  2  and are incident to the detection section  50 , by paying attention to the incident light of which the incident angle θ 0  is ψ. If the object  2  moves in a −Y axial direction, the incident light L 0  with an incident vector component of a direction identical to the moving direction of the object  2  has a lower optical frequency (ω d1 =−δ) than the incident light caused by the object  2  by means of the first Doppler effect. The object  2  scatters the light subjected to the first Doppler Effect. The scattered light L 1  with the vector component in a scattering direction identical to the moving direction of the object  2  is subjected to the frequency modulation by the Doppler Effect and has a high optical frequency (ω d2 =2δ). Therefore, the optical frequency of the scattered light L 1  gets higher by the first Doppler Effect and the second Doppler Effect (ω d =δ+2δ=δ). The scattered light La with the vector component in a scattering direction identical to the moving direction of the object  2  has a high optical frequency modulated by the Doppler Effect (ω d2 =δ). Therefore, the optical frequency of the scattered light L 2  is not changed by the first Doppler Effect and the second Doppler Effect (ω d =−δ+δ=0). The scattered light L 3  having no vector component of the scattering direction parallel to the movement direction of the object  2  has an unchanged optical frequency (ω d2 =0). Therefore, the optical frequency (ω d =−δ+0=−δ) of the scattered light L 3  is lowered by the first Doppler Effect and the second Doppler Effect. These scattered lights L 1 , L 2  and L 3  arrive at positions P 3 , P 4  and P 5  of detection section  50  respectively through the condensing lens  30 . 
     At positions P n  (n=1˜5) of the detection section  50 , a signal in which a frequency is transited by a frequency ω d  by the Doppler Effect of the scattered lights L 1 , L 2  and L 3  with reference to a frequency Ω is observed as an interference beat signal. The amplitude and the phase (i.g., complex amplitude value) of each scattered angle are obtained by recording the interference beat signal for a predetermined period and calculating the amplitude and the phase of the interference beat signal. 
       FIG. 10  is a view schematically illustrating an appearance of the scattered lights caused by the incident lights with three incident angles θ 0 =−ψ, 0, ψ, which are incident to the detection section  50 . Although the scattered lights with different angles θ′ are formed for each incident angle θ 0 , in  FIG. 10 , the scattered lights L 1 , L 2  and L 3  with a specific scattered angle θ′ are shown. The scattered lights L 1 , L 2  and L 3  with an identical scattered angle θ′ arrive at the same position P 2  by interposing the condensing lens  30 . These scattered lights L 1 , L 2  and L 3  are subjected to different frequency transitions by the Doppler Effect, respectively, because they have different incident angles θ 0 . In result, the frequencies of the scattered lights L 1 , L 2  and L 3  are different from one another. Accordingly, although the scattered lights caused by the incident lights with different incident angles θ 0  arrive at the same pixel of the detection section  50 , the frequencies can be distinguished from the frequency transition of the scattered lights by the Fourier transform and the like, thereby extracting a signal at each incident angle. 
     As described above, the lights among the scattered lights from the object  2 , which have a different incident angle θ 0  and the same scattered angle θ′, are converged by means of the condensing lens  30  at a point (x, y) of the light receiving surface of the detection section  50 . Here, the point (x, y) is a coordinate of a pixel of the detection section  50  established as parallel in two-dimensions. That is, the scattered angle θ of the scattering light observed at the point (x, y) is a fixed value. Further, since the scattered light caused by the object  2  is subjected to the frequency transition of the frequency ω d  in Equation (4), the interference strength detected at the point (x, y) through an optical heterodyne interference measurement is changed to the frequency ω d . Because the scattered light caused by different incident angles θ 0  arrives at the point (x, y), beat signals overlapped different frequencies subjected to the frequency transition according to the incident angle θ 0  are observed at the point (x, y). If the Fourier transform with respect to a time variable t is performed for these beat signals, the Doppler shift frequency ω d  involved in the beat signals can be known. Since the scattered angle θ of Equation (4) is a fixed value at the point (x, y), a specific relation between the Doppler shift frequency (ad and the incident angle θ 0  is present as shown in Equation (5). Therefore, the complex amplitude image at the incident angle can be obtained by a simple transform. Further, V Y  is a Y axial component of a velocity of the object, and a modulation frequency Ω is set to 0 for a brief description. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       5 
                       ) 
                     
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           ω 
                           d 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               2 
                               ⁢ 
                               π 
                             
                             λ 
                           
                           ⁢ 
                           
                             
                               ( 
                               
                                 s 
                                 - 
                                 
                                   s 
                                   0 
                                 
                               
                               ) 
                             
                             · 
                             V 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               2 
                               ⁢ 
                               π 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 V 
                                 Y 
                               
                             
                             λ 
                           
                           ⁢ 
                           
                             ( 
                             
                               
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   θ 
                                   ′ 
                                 
                               
                               - 
                               
                                 sin 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   θ 
                                   0 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Further, when a maximum incident angle is defined as θ 0max  and a maximum light receiving scattering angle is defined as θ max , a maximum Doppler shift frequency Bw can be expressed by Equation (6). In Equation (6), λ is a wavelength of the incident light, and V is a velocity of the object. Accordingly, the Doppler shift frequency band becomes 2Bw. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       6 
                       ) 
                     
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     B 
                     w 
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         π 
                       
                       λ 
                     
                     ⁢ 
                     
                        
                       V 
                        
                     
                     ⁢ 
                     
                       ( 
                       
                         
                            
                           
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               θ 
                               
                                 0 
                                 ⁢ 
                                 max 
                               
                             
                           
                            
                         
                         + 
                         
                            
                           
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               θ 
                               max 
                             
                           
                            
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     In the embodiment, a projective incident angle θ 0 ′ to a Y-Z plane is identical to the incident angle θ 0  because the incident unit vector so has no an X axial component. If the unit incident vector so has an X axial component, the projective incident angle θ 0 ′ is substituted for θ 0  of Equation (5). 
     The arithmetic operation section  60  performs a one-dimensional Fourier transform with respect to a time variable for a data having a position in first-direction on the predetermined plane, a position in the second-direction on the predetermined plane, and a time as variables and extracting data having an identical incident angle on the basis of the Doppler effect from the Fourier-transformed data. 
     As shown in  FIG. 11 , the arithmetic operation section  60  includes a first Fourier transform section  61 , a diagonal cut section (extraction section)  62 , a second Fourier transform section  64  and a second phase division section  63 . The first Fourier transform section  61  performs one dimensional Fourier transform with respect to the time variable for the interference strength image acquired by the detection section  50 . The diagonal cut section  62  extracts data having the same incident angle from the one dimensional Fourier transformed data on the basis of the Doppler Effect. The second Fourier transform section  64  performs the one dimensional Fourier transform with respect to a variable x for the data output from the diagonal cut section  62 . The second phase division section  63  divides the data output from the second Fourier transform section  64  by a second phase H(x). On the other hand, the first Fourier transform section  61 , the diagonal cut section  62 , the second Fourier transform section  64  and the secondary phase division section  63  may be disposed in a desired sequence by replacement with one another while the secondary phase division section  63  is disposed in the rear of the second Fourier transform section  64 . 
     The interference strength image acquired by the detection section  50  is shown as i (x, y; η). In  FIG. 12 , an example of the interference strength image i (x, y; η) acquired by the detection section  50  is shown. In the example of  FIG. 12 , a circular opening with a diameter of 25 μm, which moves at a velocity of 10 μm/s is used as the object  2 . Further, a CCD camera to output images of 180 sheets with 640×128 pixels and a size of one pixel of 7.4×7.4 μm is used as the detection section  50 . In the interference strength image i (x, y; η) shown in  FIG. 12 , it may be known that a distance of interference fringes varies from a number 1 to a number 7. 
     If the object  2  moves at a velocity V, the position of the object  2  may be indicated by η=Vt. Here, t is a time. The interference strength image i (x, y; η) may be shown as i (t, x, y) because the object  2  moves at a constant velocity. The first Fourier transform section  61  obtains a frequency dependence complex amplitude image a (ω, x, y) by performing the Fourier transform with respect to a time variance t for the interference strength image i (t, x, y). Here, ω is a time frequency.  FIG. 13  schematically shows the frequency dependence complex amplitude image a (ω, x, y) obtained by the Fourier transform.  FIG. 14  is a view illustrating the complex amplitude image a of  FIG. 13 , which is viewed from an X axial direction. As shown in  FIGS. 13 and 14 , because an X-Y plane surface is arranged in parallel with the paper surface for the X axial direction, the frequency dependence complex amplitude image will be described in two-dimensions of −Y planes surface for a brief description. 
     The scattering angle θ′ in Equation (5) is a value determined based on a physical arrangement of the object  2 , the condensing lens  30  and the detection section  50 , and is a constant value during a measurement. If a focal distance of the Y axial direction of the condensing lens  30  is f Y , the scattering angle θ′ is expressed by Equation (7) using the focal distance f Y  of the condensing lens  30  and the light receiving coordinate (x, y) when the back focal plane of the Y axial direction of the condensing lens  30  is identical to the light receiving surface of the detection section  50 .
 
[Equation (7)]
 
θ′=tan −1 ( y/f   Y )  (7)
 
     Here, since f Y  is already known, the scattering angle θ′ is a projective scattering angle determined by only a variable y. If the scattering angle θ′ of Equation (7) is substituted for Equation (5) and a heterodyne frequency Ω is evaluated, a time frequency ω output from the first Fourier transform section  61  is expressed by Equation (8) as follows. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       8 
                       ) 
                     
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     ω 
                     - 
                     Ω 
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           Y 
                         
                       
                       λ 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           y 
                           
                             f 
                             Y 
                           
                         
                         - 
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             0 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In Equation (8), if α=2πV y /(λf Y ), and β=−2πV y /λ, Equation (8) will be expressed like Equation (1) as follows. That is, Equation (1) is a linear function of y and ω. In Equation (1), in the case that a term of β sin θ 0  is constant, the complex amplitude value is a complex amplitude value in the light receiving surface when light is emitted to the object at a fixed incident angle θ 0 .
 
[Equation (1)]
 
ω−Ω=α y +β sin θ 0   (1)
 
     The diagonal cut section  62  extracts a plane surface satisfying Equation (1) from the frequency dependence complex amplitude image a (ω, x, y). As described above, the image extracted by the diagonal cut section  62  is an incident dependence complex amplitude image A (θ 0 , x, y).  FIGS. 13 and 14  schematically show the mathematical operation. Referring to  FIGS. 13 and 14 , an inclined surface indicated by a dotted line is the incident angle dependence complex amplitude image A (θ 0 , x, y) extracted by the diagonal cut section  62 . The incident angle dependence complex amplitude image A (θ 0 , x, y) is extracted so as to traverse a direction of a frequency ω and a Y axial direction for the plural sheets of complex amplitude images a (ω, x, y). As shown in  FIG. 14 , element data of the incident angle dependence complex amplitude image A (θ 0 , x, y) becomes element data of a linear function in a ω-Y plane surface as expressed in Equation (1). 
     Equations (1) and (8) induced from Equations (5) and (7) make sin θ′ approximate to θ′ and θ′ approximate to y/f Y . By using the approximation, the incident angle dependence complex amplitude image A (θ 0 , x, y) becomes a flat surface. If the approximation is not used, the incident angle dependence complex amplitude image A (θ 0 , x, y) becomes a curved surface. 
     Further, with respect to the approximation of θ′ to y/f Y , the approximation value can be close to a true value by using a fθ lens in the Y axial direction of the condensing lens  30 . In the case that a focal distance is f and incident light with angle θ reaches a position y of a back focal plane of a lens from a previous focal point, a conventional lens may indicate a relation of an incident angle θ and a position y as y=f tan θ while the fθ lens indicates the relation as y=fθ. In this case, the diagonal cut section  62  extracts a flat surface satisfying Equation (3) from the frequency dependence complex amplitude image a (ω, x, y). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ( 
                       3 
                       ) 
                     
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     ω 
                     - 
                     Ω 
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           V 
                           Y 
                         
                       
                       λ 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           sin 
                           ⁡ 
                           
                             ( 
                             
                               y 
                               
                                 f 
                                 Y 
                               
                             
                             ) 
                           
                         
                         - 
                         
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             θ 
                             0 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     In the placement example, the light receiving surface of the detection section  50  is arranged on a surface in which the Fresnel diffraction image of the object  2  is formed in the X axial direction and the Fraunhofer diffraction image of the object  2  is formed in the Y axial direction. When the detection section  50  is disposed on the Fresnel diffraction image surface, the image is blurred so that the secondary phase H(x) is shown. In the placement example, accordingly, the secondary phase H(x) is shown in the X axial direction. 
     After performing one dimensional Fourier transform with respect to a variable x for the incident angle dependence complex amplitude image A (θ 0 , x, y) obtained by the diagonal cut section  62 , the secondary phase division section  63  divides the incident angle dependence complex amplitude image A (θ 0 , x, y) by the secondary phase H(x). Herewith, the secondary phase division section  63  obtains the complex amplitude image from the complex amplitude image obtained in the placement example, such as a case that the light receiving surface of the detection section  50  is arranged on a surface in which the Fraunhofer diffraction image of the object  2  is formed in the X axial direction and the Fraunhofer diffraction image of the object  2  is formed in the Y axial direction. The secondary phase H(x) is a value determined by the position where the detection section  50  is disposed. The secondary phase H(x) is expressed by Equation (9). In Equation (9), γ is a constant.
 
[Equation (9)]
 
 H ( x )=exp(γ x   2 )  (9)
 
     The secondary phase division section  63  performs one dimensional Fourier transform with respect to a variable x for the incident angle dependence complex amplitude image A (θ 0 , x, y) obtained by Equation (1), and divides the incident angle dependence complex amplitude image A by the secondary phase H(x) of Equation (9) so as to obtain the incident angle dependent complex amplitude image A without a blur. As described above, the observation device  1  of the placement example obtains the incident angle dependence complex amplitude image A. 
     Second Placement Example 
     In turn, a second placement example of the embodiment will be described. In the second placement example, the light receiving surface of the detection section  50  is arranged on a surface in which the Fraunhofer diffraction image of the object  2  is formed in the X axial direction and the Fraunhofer diffraction image of the object  2  is formed in the Y axial direction. On this account, in the present placement example, a condensing lens  30 A is prepared instead of the condensing lens  30  of the first placement example. Further, in the present placement example, an arithmetic operation section  60 A is prepared instead of the arithmetic operation section  60  of the first placement example. Other configurations are identical to those in the first placement example. Hereinafter, only differences from the first placement example will be described, and the description of identification to the first placement example will be omitted. 
       FIG. 15  shows the condensing lens  30 A employed to the placement example. The condensing lens  30 A inputs scattered waves generated in the object  2  by an emission of the light output from the illumination lens  20 , so as to form an image, which is a Fraunhofer diffraction image in an X axial direction and a Fraunhofer diffraction image in an Y axial direction, on a light receiving surface of the detection section  50 .  FIG. 15(A)  is a side view illustrating the condensing lens  30 A which is viewed from the Y axial direction, and  FIG. 15(B)  is a side view illustrating the condensing lens  30  which is viewed from the X axial direction. A dotted line shown in  FIG. 15  denotes an appearance of an image formation of light by means of the condensing lens  30 A. As shown in  FIG. 15 , the condensing lens  30 A includes three lenses such as a lens OB, a lens LS1 and a lens LS3. 
     The lens OB is an objective lens which has a numerical aperture NA=0.45 with twenty-times magnification. A back focal plane of the lens OB is referred to as FP. The lens LS is a lens which has a curvature in the X axial direction and the Y axial direction. The lens LS3 is a lens which has a curvature in the X axial direction the Y axial direction. As shown in  FIG. 15(A) , with respect to the X axial direction, the condensing lens  30 A forms the Fraunhofer diffraction image on the receiving light surface of the detection section  50  by making the light output from the back focal plane of the lens OB be parallel light through the lens LS1 and converging the parallel light through the lens LS3. As shown in  FIG. 15(B) , further, with respect to the Y axial direction, the condensing lens  30 A forms the Fraunhofer diffraction image on the receiving light surface of the detection section  50  by making the light output from the back focal plane of the lens OB be parallel light through the lens LS1 and converging the parallel light through the lens LS3. By interposing the condensing lens  30  between the object  2  and the detection section  50 , the light among the scattered lights from the object  2 , which has a different incident angle θ 0  and an identical scattering angle θ′, is condensed at a point of the light receiving surface of the detection section  50 . 
     A detection section is disposed on a predetermined plane such that scattered light having the identical scattering angle θ′ enters at an identical position, and outputs a data temporally changing at a frequency corresponding to an amount of Doppler shift of light that reaches at each position on a predetermined plane, for each position in the first direction and the second direction, at each times. 
     As shown in  FIG. 16 , the arithmetic operation section  60 A includes the first Fourier transform section  61  and the diagonal cut section  62 . However, arithmetic operation section  60 A does not include the second Fourier transform section  64  and the secondary phase division section  63 . In the present placement example, the light receiving surface of the detection section  50  is disposed on a surface in which the Fraunhofer diffraction image of the object  2  is formed in the X axial direction and the Fraunhofer diffraction image of the object  2  is formed in the Y axial direction. When the detection section  50  is disposed on the Fraunhofer diffraction image, the lenses LS1 and LS3 constituting the lens  30 A optically perform one dimensional Fourier transform with respect to the variable x through an operation of a lens having a curvature in the X axial direction, and also the secondary phase H(x) becomes 1. In the placement example, further, it is unnecessary to perform the one dimensional Fourier transform with respect to the variable x by means of the secondary Fourier transform section  64 . Moreover, it is unnecessary to divide the secondary phase H(x) by means of the secondary phase division section  63 . 
     The incident angle dependence complex amplitude image A (θ 0 , x, y) obtained in the present placement example is identical to the incident angle dependence complex amplitude image A which has no blur and is obtained by dividing incident angle dependence complex amplitude image A (θ 0 , x, y) obtained by Equation (1) in the first placement example by the secondary phase H(x) of Equation (9). That is, in the second placement example, an effect by the secondary phase division section  63  is obtained by the optical operation of the condensing lens  30 A. On the contrary, in the first placement example, it may be said that the secondary phase division section  63  implements the optical operation of the lens  30 A of the second placement example through an arithmetic operation. 
     Third Placement Example 
     In turn, a third placement example of the embodiment will be described. In the third placement example, the light receiving surface of the detection section  50  is disposed on a surface in which the image of the object  2  is formed in the X axial direction and the Fraunhofer diffraction image of the object  2  is formed in the Y axial direction. On this account, in the present placement example, a condensing lens  30 B is provided instead of the condensing lens  30  of the first placement example and the condensing lens  30 A of the second placement example. Further, in the present placement example, an arithmetic operation section  60 B is provided instead of the arithmetic operation section  60  of the first placement example and the arithmetic operation section  60 A of the second placement example. Other configurations are identical to those of the first placement example and the second placement example. Hereinafter, only differences from the first placement example and the second placement example will be described, and the description of identification to the first placement example and the second placement example will be omitted. 
       FIG. 17  shows the condensing lens  30 B employed to the present placement example. The condensing lens  30 B inputs scattered waves generated in the object  2  by an emission of the light output from the illumination lens  20 , so as to form an image, which is an objective image of the object  2  in an X axial direction and a Fraunhofer diffraction image in an Y axial direction, on a light receiving surface of the detection section  50 .  FIG. 17(A)  is a side view illustrating the condensing lens  30 B which is viewed from the Y axial direction, and  FIG. 17(B)  is a side view illustrating the condensing lens  30 B which is viewed from the X axial direction. A dotted line shown in  FIG. 17  denotes an appearance of an image formation of light by means of the condensing lens  30 B. As shown in  FIG. 17 , the condensing lens  30 B includes four lenses such as a lens OB, a lens LS1, a lens LS2 and a lens LS3. 
     The lens OB is an objective lens which has a numerical aperture NA=0.45 with twenty-times magnification. A back focal plane of the lens OB is defined as FP. The lens LS1 is a lens which has no curvature of the X axial direction and has a curvature of the Y axial direction. The lens LS2 is a lens which has a curvature of the X axial direction but has no curvature of the Y axial direction. The lens LS3 is a lens which has no curvature of the X axial direction but has a curvature of the Y axial direction. The lens LS2 is disposed on a back focal plane of the lens LS1 and the previous focal plane of the lens LS3. As shown in  FIG. 17(A) , with respect to the X axial direction, the condensing lens  30 B forms the objective image on the receiving light surface of the detection section  50  by making the light output from the back focal plane of the lens OB be parallel light through the lens LS2. As shown in  FIG. 17(B) , further, with respect to the Y axial direction, the condensing lens  30 B forms the Fraunhofer diffraction image on the receiving light surface of the detection section  50  by making the light output from the back focal plane of the lens OB be parallel light through the lens LS1 and converging the parallel light through the lens LS3. By interposing the condensing lens  30 B between the object  2  and the detection section  50 , the light among the scattered lights from the object lens  2 , which has the different incident angle θ 0  and the identical scattering angle θ′, is condensed at a point of the light receiving surface of the detection section  50 . 
     As shown in  FIG. 18 , the arithmetic operation section  60 B further includes a second Fourier transform section  64  in addition to the first Fourier transform section  61  and the diagonal cut section  62 . The second Fourier transform section  64  performs the one-dimensional Fourier transform with respect to a variable x for the data output from the first Fourier transform section. The first Fourier transform section  61  and the diagonal cut section  62  have the same function as those in the first placement example. On the other hand, the first Fourier transform section  61  and the second Fourier transform section  64  may be changed in their position and disposed in a desired sequence. That is, in the third placement example, it may be said that an operation of the second Fourier transform section  64  in the arithmetic operation section  60 B implements an optical operation in the X axial direction of the condensing lens  30 A in the second placement example through an arithmetic operation. 
       FIGS. 19, 20 and 21  show a complex amplitude image obtained by an observation device of the present placement example. In  FIGS. 19, 20 and 21 , a circular opening with a diameter of 25 μm, which moves at a velocity of 10 μm/s, is used as the object  2 . Further, a CCD camera to output images of 180 sheets with 640×128 pixels and a one pixel size of 7.4×7.4 μm is used as the detection section  50 .  FIG. 19  shows an amplitude image of a frequency dependence complex amplitude image a (ω, x, y) calculated by the arithmetic operation section  60 B for each frequency (number 1 to number 6).  FIG. 20  shows a phase image of the frequency dependence complex amplitude image a (ω, x, y) calculated by the arithmetic operation section  60 B for each frequency (number 1 to number 6). In  FIGS. 19 and 20 , a transverse axis is defined as an X axis, and a longitudinal axis is defined as a Y axis. 
       FIG. 21  shows an incident angle dependence complex amplitude image A (θ 0 , x, y) obtained by extracting a plane surface satisfying Equation (1) from the frequency dependence complex amplitude image a (ω, x, y) of  FIGS. 19 and 20  by means of the diagonal cut section  62 .  FIG. 21( a )  shows the incident angle dependence complex amplitude image A in the case that an incident angle θ 0 =0.7 mrad,  FIG. 21( b )  shows the incident angle dependence complex amplitude image A in the case that the incident angle θ 0 =0 mrad, and  FIG. 21( c )  shows the incident angle complex amplitude image A in the case that the incident angle θ 0 =−0.7 mrad. In the left side of  FIGS. 21( a ), 21( b ) and 21( c ) , an amplitude image of the incident angle dependence complex amplitude image A is shown, and in the right side of the  FIGS. 21( a ), 21( b ) and 21( c ) , a phase image of the incident angle dependence complex amplitude image A is shown. In  FIG. 21 , a transverse axis is defined as an X axis, and a longitudinal axis is defined as a Y axis. 
     In the observation device  1  of present embodiment, when light is emitted to a moving object  2  from multiple directions by means of a light source section  10  and an illumination lens  20 , the moving object  2  scatters light. The scattered light is subjected to an amount of Doppler shift which corresponds to a scattering angle θ′. The scattered light among the scattered lights, which has the identical scattering angle θ′, is received at the same position on the detection section  50 . The detection section  50  outputs data temporally changing at a frequency ω d  that corresponds to an amount of Doppler shift of light that has arrived at each positions on a the light receiving surface, for each position in the first direction and the second direction, at each times. The arithmetic operation section  60  performs a one-dimensional Fourier transform with respect to time is, for data having a position in first-direction on the predetermined plane, a position in the second-direction on the predetermined plane, and a time as variables, and extracts data having the identical incident angle θ 0  relative to the object from the Fourier transformed data, on the basis of the Doppler effect. According to this configuration, since it is possible to extract data with the same incident angle θ 0  for the object by using the Doppler Effect, it is unnecessary to take an image of the object  2  at plural times within a period when the object  2  is regarded to be stopped. Therefore, when the detection section  50  in which a reading speed per pixel is low is used, it is possible to obtain the image of the moving object  2 . 
     Second Embodiment 
     In the first embodiment, the diagonal cut section  62  extracts a plane surface satisfying Equation (1) so as to obtain the incident angel dependence complex amplitude image A (θ 0 , x, y). In the second embodiment, the diagonal cut section  62  has a configuration identical to that of the first embodiment except that it extracts a plane different from that in the first embodiment. Hereinafter, a difference between the first embodiment and the second embodiment will be described, and identical aspects of the second embodiment to the first embodiment will be omitted. 
     Equations (1) and (8) induced from Equations (5) and (7) make sin θ′ approximate to θ′ and θ′ approximate to y/f Y . By using the approximation, the incident angle dependence complex amplitude image A (θ 0 , x, y) becomes a flat surface. Further, Equations (1) and (8) are formulas established in the condensing lenses  30 ,  30 A and  30 B satisfying the Abbe sine condition for the Y axial direction. On this account, if the condensing lenses  30 ,  30 A and  30 B satisfying the Abbe sine condition are used instead of the approximation, the incident angle dependence complex amplitude image A (θ 0 , x, y) becomes a flat surface. In the diagonal cut section  62  of the present embodiment, two approximations are not applied, and the incident angle dependence complex amplitude image a (θ 0 , x, y) is obtained by following Equation (2) which is an exact formula of Equations (1) and (8). 
     
       
         
           
             
               
                 
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     Equation (2) which is the exact formula is not a linear function, differently from Equations (1) and (8) which are approximation. However, the incident angle dependence complex amplitude image A with a high precision can be obtained by extracting the incident angle dependence complex amplitude image A (θ 0 , x, y) from a surface S satisfying Equation (2). 
     Modification 
     In the observation device  1  of the present embodiment, when the velocity of the object  2  is changed, a frequency modulation in a Doppler signal occurs, and an image of the object  2  which is finally obtained expands and contracts in a flowing direction. In order to correct these expansions and contractions, it is preferred that the observation device  1  of the present embodiment further includes a velocity detecting section for detecting a moving velocity of the object  2 . Further, it is preferred that the arithmetic operation section  60  performs a correction related to the velocity change of the object  2  in one dimensional Fourier transform of a time direction based on the velocity of the object  2  detected by the velocity detecting section. A photography timing of the velocity detecting section  50  may be set based on the velocity of the object  2  detected by the velocity detecting section. 
     Any type of velocity detecting section may be used as the velocity detecting section. However, the moving velocity of the object  2  can be obtained only by detecting a frequency of a signal at a position, where scattered light arrives at on the back focal plane of the condensing lens  30 , by using a relation between the moving velocity and the amount of the Doppler shift. In this case, the velocity detection section may detect light, which is diverged from light directed from a beam splitter HM2 to the detection section  50 , on the Fourier plane. On the other hand, the velocity detection section may detect light at a pixel independently installed on some portion of the light receiving surface of the detection section  50 . The pixel preferably has a size corresponding to an area having a resolution of the moving velocity induced from the relation of the moving velocity V of the object  2  and the Doppler frequency ω d . 
     In the observation device  1  of the present embodiment, in the second embodiment, light among the light L 0  emitted to the object  2  (zero order light), which is not scattered by the object  2 , is condensed at a point of the detection section  50 . When the zero order light arrives at the light receiving surface of the detection section  50 , a quality of signal obtained by the detection section  50  is deteriorated. Accordingly, a neutral density filter may be installed in order to decrease the zero order light such that all the zero order light does not arrive at the light receiving surface of the detection section  50 . Alternately, light having a beam-cross section in which the zero order light hardly occurs may be emitted to the object  2 . It is preferred to correct strength non-uniformity by evaluating strength to the light arriving at the detection section  50  when the object  2  is not present between the light source section  10  and the detection section  50 . 
     In the above description, the embodiment in which the image of the object of the light source is acquired by a transmitted illumination has been mainly described. However, it is apparent that the image of the object may be acquired by a reflected illumination (epi-illumination) or an ultra-illumination. As a light source, use of light in a single longitudinal mode is appropriate, but the light source is not limited thereto. For example, information on a depth of a phase object may be acquired by using light of a broadband. Moreover, it is appropriate that light in which a phase relation between wavelength components is constant is used as broadband light. For example, a mode-locked laser may be used as such a light source. 
     REFERENCE SIGN LIST 
       1  . . . observation device,  2  . . . object,  10  . . . light source section,  20  . . . illumination lens,  30 ,  30 A,  30 B . . . condensing lens,  40  . . . modulation section (modulator),  50  . . . detection section,  60 ,  60 A,  60 B . . . arithmetic operation section,  61  . . . first Fourier transform section,  62  . . . diagonal cut section (extraction section),  63  . . . secondary phase division section,  64  . . . second Fourier transform section.