WO2015156379A1

WO2015156379A1 - Image processing unit and control method for image processing unit

Info

Publication number: WO2015156379A1
Application number: PCT/JP2015/061182
Authority: WO
Inventors: Kentaro Nagai; Soichiro Handa
Original assignee: Canon Kabushiki Kaisha
Priority date: 2014-04-10
Filing date: 2015-04-03
Publication date: 2015-10-15
Also published as: JP2015205174A

Abstract

An image processing unit that extracts phase information from a two-dimensional periodic pattern image, the device comprises an acquisition unit that acquires the pattern image; a first transform unit that transforms the pattern image into a two-dimensional spatial frequency domain image; an extraction unit that extracts a peak of a spectrum included in the spatial frequency domain image and a surrounding region thereof; and a second transform unit that acquires a phase image by transforming the extracted image to a real space, a transform which is inverse to the transform performed by the first transform unit, wherein the extraction unit extracts a region such as to include a first-order spectrum and one or more secondary spectra.

Description

DESCRIPTION

Title of Invention

IMAGE PROCESSING UNIT AND CONTROL METHOD FOR IMAGE PROCESSING UNIT

Technical Field

[0001] The present invention relates to an image processing unit that acquires phase information from a two-dimensional pattern image.

Background Art

[0002] A method for detecting a phase shift

occurring due to interference of electromagnetic waves is known as a method for measuring the shape of a material with a high accuracy. In a measurement method using a phase, an object is irradiated with light with a uniform wavefront (that is, coherent light) to generate interference. The interference fringe thus generated includes information relating to changes of an incident light wavefront (changes in phase) caused by a difference in phase from a

fraction to several tenths of a wavelength.

Therefore, phase changes can be acquired by measuring the interference fringe. A device for measurements based on such a method is called a phase

interferometer, and such a device is capable of precise measurements, for example, such as measurements of slight unevenness on a lens surface.

[0003] In particular, X-ray phase imaging has recently attracted much attention among the

measurement methods using interference. With the X- ray phase imaging, changes in an optical path length occurring when X rays are transmitted by an object are detected by phase interference and converted into an image. The advantage of the X-ray phase imaging is that because the absorbance of X rays inside the object is not converted into an image, by contrast with the conventional methods, the exposure dose can be reduced when the object is a living body.

[0004] A Talbot interferometer using X-rays is an example of a X-ray phase imaging apparatus (see Non- Patent Literature 1) . Where X-rays radiated from a X-ray source are transmitted by an object, the phase of the X-rays changes. Further, where the X-rays transmitted by the object pass through a grating having a periodic pattern (called a diffraction grating), an interference pattern is formed at a position at a predetermined distance called a Talbot distance. The X-ray Talbot interferometer measures the aforementioned change of the incident light wavefront by analyzing changes in the interference pattern (referred to hereinbelow as "first interference pattern") which are caused by the presence of the object.

[0005] The pattern period of the diffraction grating is determined by the device length and wavelength of the incident light, and when the incident light is X-rays, the pattern period is usually of an order of several microns. The

interference fringes generated by the diffraction grating also have a period of an order of several microns. As a result, the fringes cannot be detected with the resolution of the usual X-ray detector. For this reason, a shielding grading of the same or substantially the same period as the first

interference pattern is arranged at a position where the first interference pattern is to be formed, and part of the first interference pattern is shielded. As a result, a second interference pattern (moire) with a period of about several hundreds of microns is generated. By detecting this moire with an X-ray detector, it is possible to measure indirectly the changes in the first interference pattern.

A method in which the shielding grating

(absorption grating) with an adjusted period is arranged with the same orientation as the first interference pattern and a method in which the shielding grating is turned are used to generate the moire. The moire generated by the former method is called "enlarged moire", and the moire generated by the latter method called "rotated moire".

[0006] Meanwhile, since information acquired by the X-ray detector is the intensity distribution of X- rays, information on the inside^' of the object cannot be obtained unless the intensity distribution is returned to phase information.

A Fourier transform method is one of the methods for retrieving (recovering) a differential phase from moire. Where a moire image is Fourier transformed, a spectral peak appears at a position corresponding to a carrier frequency. Accordingly, a constant range surrounding the spectral peak is cut out and inverse Fourier transform is performed with respect to the cut-out region. As a result, the differential phase can be recovered.

Patent Literature 1 discloses an invention that relates to such a technique and provides a device that recovers a differential phase by transforming a two-dimensional moire image into a spatial frequency domain image, cutting out data around a spectrum matching the carrier frequency, and subjecting the data to inverse Fourier transform.

Citation List Patent Literature

[0007] Patent Literature 1: Japanese Patent

Application Publication No. 2011-153969.

Non Patent Literature

[0008] Non Patent Literature 1: Itoh,H.et al. Two- dimensional grating-based X-ray phase-contrast

imaging using Fourier transform phase retrieval,

Optics Express 19, 3339(2011) .

Summary of Invention

Technical Problem

[0009] The size of the cut-out region affects the spatial resolution when phase information is

recovered. More specifically, the spatial resolution increases as the 'cut-out range is expanded. However, where other spectral peaks or side lobes enter the cut-out range, artefacts are admixed to the recovered phase image. Therefore, unlimited increase of the cut-out range is impossible. The, resultant problem is that the increase in spatial resolution is limited.

[0010] The present invention has been created to resolve the problem inherent to the conventional techniques, and it is an objective of the present invention to increase spatial resolution in an interferometer that retrieve phase information from a periodic pattern.

Solution to Problem

[0011] The present invention in its one aspect provides an image processing unit that extracts phase information from a two-dimensional periodic pattern image, the unit comprises an acquisition unit that acquires the pattern image; a first transform unit that transforms the pattern image into a two- dimensional spatial frequency domain image; an extraction unit that extracts a peak of a spectrum included in the spatial frequency domain image and a surrounding region thereof; and a second transform unit that acquires a phase image by transforming the extracted image to a real space, wherein the

extraction unit extracts a region such as to include a first-order spectrum and one or more secondary spectra.

[0012] The present invention in its another aspect provides a control method for an image processing unit that extracts phase information from a two- dimensional periodic pattern image, the method comprises a first transform step for transforming the pattern image into a two-dimensional spatial

frequency domain image; an extraction step for extracting a peak of a spectrum included in the

spatial frequency domain image and a surrounding region thereof; and a second transform step for

acquiring a phase image by transforming the extracted image to a real space, wherein in the extraction step, a region is extracted such as to include a first- order spectrum and one or more secondary spectra.

[0013] The present invention in its another aspect provides an image processing unit that extracts phase information from a two—dimensional periodic pattern image, the unit comprises a first acquiring unit that acquires a pattern image; and a second acquiring unit that acquires phase information by windowed

Fourier transforming the pattern image, wherein a window function used in the windowed Fourier

transform is obtained by inverse Fourier transforming a filter function that extracts a region such as to include a first-order spectrum and one or more

secondary spectrum from a two-dimensional spatial frequency image obtained by transforming the pattern image .

Advantageous Effects of Invention

[0014] According to the present invention, spatial resolution can be increased in an interferometer that recovers phase information from a periodic pattern. Further features of the present invention will become apparent from the following description of exemplary embodiments with reference to the attached drawings .

Brief Description of Drawings

[0015] FIG. 1 is a schematic diagram of an imaging apparatus according to an embodiment.

FIGS. 2A to 2E illustrate a procedure for

acquiring a phase with a Fourier transform method.

FIGS. 3A to 3D illustrate results obtained when phase retrieval is performed by using the

conventional example.

FIGS. 4A to 4D illustrate the results obtained when phase retrieval is performed in the embodiment.

FIGS. 5A to 5C compare the conventional example with the embodiment .

FIG. 6 is a processing flowchart diagram of the imaging apparatus according to the embodiment.

Description of Embodiments

[0016] (System Configuration)

An embodiment of the present invention is

explained hereinbelow in detail with reference to the drawings . FIG. 1 depicts the configuration of an imaging apparatus 1 according to the present embodiment. The imaging apparatus 1 is a Talbot X-ray phase imaging device provided with an X-ray source 110, a

diffraction grating 120, a shielding grating 130, an X-ray detector 140, a computational unit 150, and an image display device 160.

In the present embodiment, an object 210, which is a measurement object, is disposed between the X- ray source 110 and the diffraction grating 120, but the object may be also disposed between the

diffraction grating 120 and the shielding grating 130.

[0017] The X-ray source 110 is a ray source for generating X-rays to be radiated onto the object 210. The radiated X-rays fall on the diffraction grating 120 after passing through the object.

The diffraction grating 120 is means (optical element) for causing the diffraction of the X-rays transmitted by the object. The diffraction grating ■is of a phase type in which a diffraction pattern is arranged with a predetermined period. An amplitude- type diffraction grating (in other words, a shielding grating) can be also used instead of the phase-type diffraction grating. The X-rays diffracted by the diffraction grating 120 form a pattern image

(interference image 310) in which bright portions and dark portions are arranged side by side in the arrangement direction at a predetermined distance called a Talbot distance. In FIG. 1, the reference symbol L2 represents the Talbot distance.

The interference image generated by the

diffraction grating 120 is referred to hereinbelow as a first interference pattern.

[0018] The period of the first interference pattern generated by the interference of X-rays is usually about several microns to ten odd microns and cannot be directly detected by detectors that are typically used. Accordingly, the shielding grating 130 which has a grating period same as or slightly different from that of the first interference pattern is disposed at the Talbot distance and a second

interference pattern is generated. In the shielding grating 130, transparent portions and non-transparent portions are arranged alternately. As a result, part of X-rays is shielded. As a consequence, a moire is generated and the period of the first interference pattern can be enlarged to several tens of

micrometers or more (or without a limit) .

The generated second interference pattern is detected by the X-ray detector 140. The X-ray

detector 140 is means for acquiring the intensity distribution of X-rays in a plane (detection plane) . The resolution of the X-ray detector is usually about several tens of square micrometers, but since the moire is generated, the first interference pattern can be measured indirectly.

The period of the second interference pattern can be determined, as appropriate, with consideration for the phase retrieval method used and the size of the detection plane of the X-ray detector 140. In the present embodiment, it is preferred that the period of the second interference pattern be equal to or greater than a two-fold pixel size and equal to or less than the range of the detection plane of the X- ray detector 140.

[0019] The relationship between the interference pattern and the internal information on the object is explained hereinbelow.

In the present embodiment, the object 210 is disposed between the X-ray source 110 and the

diffraction grating 120. Since X-rays typically have high transmissivity , where an object, mainly a living body, is irradiated, the X-rays are mostly

transmitted thereby, but shifted by phase according to the elemental composition and density of the substance through which the rays are transmitted.

This change i phase affects the arrangement of the first interference pattern. Therefore, the second interference pattern generated by the shielding grating 130 is also distorted.

[0020] In the present embodiment, the computational unit 150 acquires the distortions, which have thus been generated, by retrieving the differential

information on the phase from the second interference pattern. The internal information on the object is acquired by comparing with the case in which the object is not present. The acquired internal

information is outputted as image information to the image display device 160.

Further, in the present embodiment, the

computational unit 150 is a computer, but the

computational function may be also realized by FPGA or ASIC, or a combination thereof.

[0021] (Method for Acquiring Phase Image)

The conventional method for retrieving a

differential phase image from the acquired second interference pattern is explained hereinbelow. The interference pattern generated by the grating (in the present embodiment, the second interference pattern) is referred to hereinbelow as "fringe pattern".

In the present invention and in the present description, when a term "phase image" is merely used, the term indicates both a differential phase image, and an undifferentiated phase image (the same image obtained by integrating differential phase■ information, which is also referred to as an integral phase image ) .

Likewise, when a term "phase information" is merely used, the term indicates both differential phase information, and undifferentiated phase

information (the same information obtained by

integrating differential phase information, which is also referred to as integral phase information) .

In the Talbot interferometer, a phase shift method or a Fourier transform phase retrieval method

(Fourier transform method) can be used to retrieve the differential phase image, but in the present^' example, the Fourier transform method is explained. Further, in the present example, the case is

explained in which the fringe pattern is generated using a two-dimensionally arranged grating. With such a configuration, a bidirectional (X-axis

direction and Y-axis direction) differential phase image is acquired by one-shot X-ray irradiation.

[0022] FIGS. 2A to 2E illustrate the process of acquiring a phase image by the Fourier transform method. Where a fringe pattern is subjected to

Fourier transform, a spatial frequency domain image

(spectral pattern) corresponding to the period of the fringe pattern can be obtained. FIG. 2A presents the shape of the object which is used in the explanation of the present embodiment. The object has a pyramidal shape, and FIG. 2A is a top view of the pyramid taken from the apex thereof. FIG. 2B is an image representing a fringe patter before the phase is recovered.

[0023] The intensity I(x, y) of the fringe pattern can be represented by Expression (1) .

[Formula 1]

I(x, y) = a(x, y)(l + b, (x, y)cos[> (x,y) + (ox l + b₂ (x, y) cos[P₂ (x,y) + ay])

Expression (1) For the sake of simplicity, in the present example, the fringe directions are arranged along the X-axis and Y-axis directions. Here, x and y are integers representing pixel coordinates. Further, a is the intensity of the transmitted X-rays, b_x and Pi represent the amplitude and phase relating to the fringe pattern in the x direction, and b2 and P₂.

represent the amplitude and phase relating to the fringe pattern in the y direction. Here, co is a value representing the spatial frequency of the fringe; ω = π / 2. Thus, in this case, a fringe with a four-pixel period is assumed.

[0024] Information (bi and Pi) on the fringe

pattern in the X-axis direction does not necessarily represent information relating to the differential phase in the X-axis direction, and information (b₂ and P2) on the fringe pattern in the Y-axis direction does not necessarily represent information relating to the differential phase in the y-axis direction. Whether the (bi and Pi) or (b₂ and P₂) includes phase information relating to an X differential or includes phase information relating to an Y differential depends on the method used for acquiring the second interference pattern.

[0025] An approach to acquiring a fringe pattern in the Talbot interferometer can be generally classified into two methods, namely, a method using an enlarged moire and a method using a rotated moire.

The method using an enlarged moire is

specifically a method in which a moire a generated by shifting the period of the shielding grating 130 itself with respect to the period of the self-image of the diffraction grating 120 while aligning the pattern period direction of the self-image created by the diffraction grating 120 and the pattern period direction of the shielding grating 130.

[0026] The method using a rotated moire is

specifically a method in which a moire is generated by shifting the pattern period direction of the self- image created by the diffraction grating 120 and the pattern period direction of the shielding grating 130. Thus, the diffraction grating and the shielding

grating are arranged at mutually different angles.

It goes without saying that the two methods may be combined.

[0027] Where the method using a rotated moire is used to rotate the moire, the mutual arrangement of the first-order spectrum including X-di f fe rent ia 1 information and the first-order spectrum including Y- differential information changes. However, in the present invention and in the present description, the method using a rotated moire is assumed to include a method in which rotation and enlargement are combined together, and the rotated pattern is assumed to

include the moire formed by the method in which

rotation and enlargement are combined. In other words, the first-order spectrum including X- differential information is present outside the X- axis on the XY plane, and the first-order spectrum including Y-dif ferent ial information is present

outside the Y-axis on the XY plane.

Therefore, the spectrum including differential information in the Y-axis direction can be disposed on the X axis, and the spectrum including

differential information in the X-axis direction can be disposed on the Y axis. In the present embodiment, an example is explained in which the spectrum including differential information in the Y-axis direction can be disposed on the X axis, and the spectrum including differential information in the X- axis direction can be disposed on the Y axis, but the spectra are not necessarily always present exactly on the X axis and Y axis. The feature of setting the spectrum including differential information in the X- axis direction to be closer to the Y axis than to the X axis and setting the spectrum including

differential information in the Y-axis direction to be closer to the X axis than to the Y axis does not depart from the spirit of the present invention.

[0028] FIG. 2C depicts an image (referred to

hereinbelow as "Fourier image") obtained by taking a logarithm of an absolute value of the spectral

pattern after Fourier transform. In the present example, nine spectral peaks are present on the plane. In this case, to simplify the explanation, the fringe pattern represented by Expression 1 is used therefor. Thus, nine spectral peaks are arranged in a square shape with the sides parallel to the X axis and Y axis. Each spectral peak and the surrounding region thereof will be simply referred to hereinbelow as " spectrum" . [0029] In FIG. 2C, the spectrum positioned in the center is a zero-order spectrum. The four spectra (depicted by point lines) which are the closest to · the zero-order spectrum are primary spectra. The four spectra positioned on the outermost side are secondary spectra.

Where one of those primary spectra is extracted using a filter function, pasted on a separate

frequency space, as depicted in FIG. 2D, and

subjected to inverse Fourier transform, an

information of an image such as depicted in FIG. 2E can be obtained. The image thus obtained represents the phase of X-rays that have been transmitted by the obj ect .

[0030] A method for cutting out a Fourier image is explained hereinbelow. Where a Fourier image is cut out by the conventional method, it is necessary to set a filter function such as not to include a

spectrum (at least the peak of the spectrum; the bottom of the spectrum can be present) outside the spectrum which is to be cut out. This is done so to prevent artefacts from being mixed with the acquired image due to the inclusion of an neighboring spectrum.

[0031] FIGS. 3A to 3D depict an example of phase retrieval performed by the conventional technique.

With the conventional technique, the filter function is set such as not to include the adjacent spectra, as depicted in FIGS. 3A and 3B. A Hann function F represented by Expression (2) is an example of such a filter function.

Formula 2]

Expression (2) [0032] Here, k_x and k_y stand for coordinates on a wave number space in which spacing in the x and y directions is represented by equal number of pixels of the image within a range from - π to π . The range of those coordinates matches the range of the drawing depicted in FIG. 2C. Further, k_x0 and k_y0 stand for central coordinates of the Hann window, and σ is a width of the Hann window.

Where a window such as depicted in FIGS. 3A and 3B is set, σ is taken as the distance to the nearest spectrum, that is, σ = π/2, in order to prevent the peak of the neighboring spectrum from being included in the cut-out range. As a result, the differential phase images such as depicted in FIGS. 3C or FIG. 3D can be acquired. An integrated phase image can be acquired by performing integration by using the differential phase images in the X-axis direction and Y-axis direction that have thus been acquired. [0033] Where the filter function is enlarged by a factor of two, Expression (3) is obtained. Where the wave number space with a range from - π to π is spread, a periodic boundary condition is used.

[Formula 3

^F(k_x,k_y) =

Expression ( 3 ) [0034] The filter function in the present

embodiment is explained hereinbelow.

In the present embodiment, a spectrum on the Y axis is cut out to acquire differential information in the X-axis direction, and in this case, the filter function is set such that the width in the X-axis direction becomes larger than the width in the Y-axis direction. Likewise, a spectrum on the X axis is cut out to acquire differential information in the Y-axis direction, and in this case, the filter function is set such that the width in the Y-axis direction

becomes larger than the width in the X-axis direction

Such filter functions are graphically

represented by solid lines in FIGS. 4A and 4B. More specifically, the filter function corresponding to FIG. 4A is represented by Expression (4), and the filter function corresponding to FIG. 4B is

represented by Expression (5) .

[Formula 4]

Expression

Formula 5]

Expression (5) [0035] As a result, the filter function becomes non-isotropic . Further, the filter function for acquiring phase information in the Y-di f ferent ial direction, which is located on the^' X axis, and the filter function for acquiring phase information in the X-different ial direction, which is located on the

Y axis, become different functions. In addition, since the range of the filter function is enlarged, two spectra represented by dot lines, from among the four secondary spectra, are included in the

respective ranges cut out by the filter functions.

[0036] FIGS. 4C and 4D illustrate the results obtained in acquiring differential phase images in the X-axis and Y-axis directions by performing filtering with the above-described functions. It follows from above that the phase of the fringe is recovered although the secondary spectra are included

[0037] Further, FIGS. 5A and 5B illustrate the comparison of enlarged edge portions in the

conventional technique and the present embodiment. The comparison result indicates that the edge portion is sharper in the present embodiment.

FIG. 5C depicts a modulation transfer function (MTF) calculated from the edge portion. In the graph in FIG. 5C, the transfer intensity is plotted against the ordinate and the frequency is plotted against the abscissa. This figure means that the spatial

resolution increases as the graph spreads in the lateral direction. This graph also, demonstrates that the spatial resolution has increased over that in the conventional example.

[0038] The reason why such processing can be performed is explained below.

Where Fourier transform is performed, phase information included in a fringe is localized close a spectral peak on the wave number space. Therefore, with the Fourier transform method, phase information is acquired by cutting out the surroundings of the spectral peak and then performing inverse Fourier transform. The cut-out surface area in this case needs to be small in order to avoid interference from the neighboring spectrum.

[0039] However, since high-frequency information for increasing the special resolution is present at a position separated from the spectral peak, where the cut-out surface area is decreased, only an image with a low spatial resolution can be obtained. For this reason, the cut-out surface area has conventionally been set as large as possible within a range in which the interference from the neighboring spectrum could be avoided.

However, the research conducted by the inventors clearly demonstrates that where a Fourier image is cut out, it is actually not necessary to avoid all of the spectra different from the spectrum which is to be cut out. More specifically, a phase can be recovered even when a secondary spectrum is included in the effective cut-out range. Thus, the cut-out range can be of a non-isotropic shape such as a rectangle or an ellipse including a secondary

spectrum, rather than of an isotropic shape such as a square or a circle as in the conventional technique. In the present embodiment, where a phase is thus recovered, by increasing the cut-out range in a certain direction, it is possible to increase the spatial resolution with respect to this direction. When the Fourier image is thus cut out such as to include the secondary spectrum, it is preferred that a second interference pattern be formed by using the rotated moire because the increase in artefacts can be better reduced. than when the second interference pattern is formed using only the enlarged moire, and the spatial resolution can be increased. The spatial resolution can be increased because the secondary spectrum has a differential phase component in the Y direction and X direction as a result of using the rotated moire.

[0040] In the example depicted in FIG. 2C, the spatial resolution in the Y-axis direction is

increased by taking as a center a first-order

spectrum relating to the differential phase in the Y direction, which is positioned on the X axis, and including the secondary spectra located before and after the center into the cut-out range. Further, the spatial resolution in the X-axis direction is increased by taking a first-order spectrum on the Y axis as a center and including secondary spectra located before and after the center into the cut-out range.

[0041] In the present embodiment, a spectrum having differential information relating to the Y-axis direction can be made to be present as a first-order spectrum on the X axis or within a range of ±45 degrees therefrom by generating a rotated moire by using the shielding grating 130. Further, a spectrum having differential information relating to the X- axis direction can be made to be present as a first- order spectrum on the Y axis or within a range of ±45 degrees therefrom. As a result, differential

information relating to both the X-axis direction and the Y-axis direction can be acquired in a single measurement cycle.

The differential information relating to each axial direction which is thus obtained by cutting out the Fourier image such as to include also a secondary spectrum has a spatial resolution higher than that of the differential information obtained by cutting out the Fourier image such that only a first-order

spectrum is included. Therefore, where the phase image is integrated, the spatial resolutions in the X-axis and Y-axis directions supplement each other, and therefore a phase integrated image with increased spatial resolution can be obtained.

[0042] Where the function such as represented by Expression (2) is used as a filter function, the effective range in a cut-out process can be defined by taking a location, in which the output value of the filter function is zero, as a boundary.

Meanwhile, a function having an unlimited spread, sich as the Gaussian function represented by

Expression (6) may be also used as the filter

function. In such a case, a location in which the output value of the function becomes sufficiently small (for example, equal to or less than 1% of the central maximum value) may be taken as the boundary of the cut-out range. Furthermore, for example, a position at a distance of 3σ from the center may be taken as a boundary and the area on the inner side with respect to the boundary may be taken as the effective range.

In either case, a filter function such that the peaks of the first-order spectrum and secondary spectrum of the object are included in the cut-out range may be set. By setting such a filter function, it is possible to cut out simultaneously the

information (principal information) with a low

spatial resolution which is present close to the first-order spectrum and also high-spatial-resolution information (information for increasing the spatial resolution) which is present close to the secondary spectrum .

[Formula 6]

Expression (6)

[0043] (Processing Flowchart)

A processing flowchart for realizing the above described functions is explained hereinbelow.

FIG. 6 is a flowchart of processing performed the imaging apparatus 1 according to the present embodiment. The processing is started by a user's operation (for example, an operation of imaging) .

[0044] Initially, in step Sll, the X-ray source 110 generates X-rays and irradiates the object 210. The emitted X-rays are transmitted by the object, pass through the diffraction grating 120 and the shielding grating 130 and then fall on the X-ray detector 140.

Then, in step S12, the X-ray detector 140

acquires the intensity distribution of the X-rays on the detection plane. The acquired intensity

distribution is transmitted to the computational unit 150.

[0045] Then, in step S13, the computational unit 150 transforms the acquired X-ray intensity

distribution into a two-dimensional spatial frequency domain image (Fourier image) by Fourier transform.

In the subsequent step S14, the computational unit 150 cuts out part of the Fourier image by the above-described method using a filter function. In this case, two regions, namely, a region for

acquiring differential information relating to the X- axis direction and a region for acquiring

differential information relating to the Y-axis direction, are cut out.

[0046] Then, in step S15, the computational unit 150 pastes a plurality of cut-out regions on a separate frequency space and performs inverse Fourier transform thereof. As a result, an information of a differential phase image in the X-axis direction and a differential phase image in the Y-axis direction can be acquired.

Finally, in step S16, the computational unit 150 performs integration by using the respective the information of differential phase images and acquires an integrated phase image. The acquired information of integrated phase image is subjected to image processing and then outputted to the image display device 160.

[0047] As explained hereinabove, in the imaging device according to the present embodiment, a non- isotropic cut-out range such that includes one or more spectra inclusive of a secondary spectrum is set when cutting out the peak of a first-order spectrum included in the Fourier image and the vicinity of the peak. As a result, only spatial resolution can be increased without generating artefacts.

[0048] (Variation Example)

The above-described embodiment is but an example illustrating the present invention, and the present invention can be implemented by performing

appropriate changes or using appropriate combinations, without departing from the spirit of the invention. For example, the present invention can be implemented as an imaging apparatus including at least part of the abovement ioned processing, and can be also implemented as an image processing unit that

generates an integrated phase image on the basis of the inputted interference image, without using means (interference image detection device) for detecting an interference image. Further, the invention can be also implemented as a method for controlling an image processing unit or a program that causes an image processing unit to execute the control method. The above-mentioned processing steps or means can be also implemented in random combinations, provided that no technical contradiction arises. In the present invention and present description, the imaging apparatus is not limited to a device for imaging information on an object, provided that it is a device capturing an image of a periodic pattern.

Further, the image processing unit is not limited to a device that forms an image, provided that it is a device acquiring information which is different from information inputted using intensity information on a periodic pattern.

[0049] In the embodiment, a Talbot-type X-ray phase imaging device is explained by way of example, but the phase image acquisition method according to the present invention may be also applied to a

differential interferometer of another type, provided that a phase change induced by interference is

generated and this phase change is acquired. Further, the light to be used for measurements is not limited to X-rays, and electromagnetic waves of any

wavelength may be used.

[0050] In the example explained in the embodiment, one first-order spectrum and two secondary spectra are included in the cut-out range, but any cut-out range may be used, provided that one first-order spectrum and one or more secondary spectra are

included .

Further, in the explanation of the embodiment, a window function is used as a cut-out function, but any function may be used, provided that a

predetermined region of a two-dimensional Fourier image can be cut out .

[0051] Further, in the explanation of the

embodiment, a two-dimensional spatial frequency

domain image is acquired by Fourier transforming a pattern image, but methods other than Fourier

transform may be used, provided that a two- dimensional spatial frequency domain image can be acquired. Moreover, in the explanation of the

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ppeerrffoorrmmeedd bbyy wwiinnddoowweedd FFoouurriieerr ttrraannssffoorrmm iinnsstteeaadd ooff ssuucchh pprroocceessssiinngg..

[[00005522]] TThhee wwiinnddoowweedd FFoouurriieerr ttrraannssffoorrmm iiss ttrraannssffoorrmm ddeeffiinneedd bbyy EExxpprreessssiioonn ((77)) .. IInn EExxpprreessssiioonn ((77)) ,, gg((xx,,yy)) iiss rreeffeerrrreedd ttoo aass aann oorriiggiinnaall ffuunnccttiioonn,, aanndd ww((xx,,yy)) iiss rreeffeerrrreedd ttoo aass aa wwiinnddooww ffuunnccttiioonn,, aanndd,,

SS (( xxii ,, yyii ,, kk '' _xx,, kk ¹¹ _yy )) iiss tthhee rreessuulltt oobbttaaiinneedd bbyy tthhee

wwiinnddoowweedd FFoouurriieerr ttrraannssffoorrmm..

[[FFoorrmmuullaa 77]]

SS(( ,, ,,

EExxpprreessssiioonn ((77))

TThhiiss wwiinnddoowweedd FFoouurriieerr ttrraannssffoorrmm mmaayy bbee

rreepprreesseenntteedd bbyy EExxpprreessssiioonn ((88)) ..

[[FFoorrmmuullaa 88]]

Expression (8)

[0053] Here, the calligraphy font F is an operator indicating Fourier transform, and the superscript -1 indicates an inverse Fourier transform. Further, the symbol of * indicates convolution integration.

Further, G(k_x,k_y) indicates Fourier transform of the original function g(x,y), and (k_x,k_y) indicates Fourier transform of the window function w(x,y) .

Expression (8) is derived by using the

characteristics of convolution and Fourier transform indicated in Expression (9) .

[Formula 9]

ifg(^x _>y)f(^x'-^x _> ^~y)dxdy = g(x,y) * f(x,y)

5[g(x,y)exp[-ia_xx-ia_yy =G(k_x+a_x,k_y+a_y) Expression ₍9₎

[0054] The windowed Fourier transform indicated by Expression (8) is equivalent to Fourier transforming the function g, subsequently moving a first-order spectrum to origin, and subsequently multiplying the result by Fourier transform of the window function.

Namely, when the filter functions F(k_x,k_y) used in the embodiment is associated to W(k_x,k_y) and when I(x,y) is associated to g(x,y), the final line of Expression (8) is equivalent to the result obtained by multiplying Fourier transform of I by the filter function F and subsequently performing inverse

Fourier transform. This is equivalent to the processing of Steps S13-S15 in FIG. 6. Namely, Steps S13-S15 in the

embodiment can be replaced by windowed Fourier

transform. Specifically, windowed Fourier transform may be performed by using the result obtained by inverse Fourier transforming the filter function F explained in the embodiment as a window function w (x, y ) .

In a case where phase retrieval is performed by using windowed Fourier transform, a shape of a window function can be changed for each region on an image. In doing so, noise can be decreased from the

conventional level and/or spatial resolution can be improved. Further, by combining different methods, such synergistic effects can be obtained.

[0055] As mentioned above, the filter function F in the present embodiment cuts out a region such as to include a first-order spectrum and one or more

secondary spectrum in a two-dimensional Fourier image.

In a case where windowed Fourier transform is performed, a pattern period and a period direction are obtained in advance, and a peak location in a two-dimensional Fourier image is predicted based on the obtained pattern period and the period direction, and a cut out region of a filter function may be set based on the prediction results. The pattern period and the period direction can be theoretically obtained from a configuration of an imaging device (configuration of an optical element and arranging method thereof, etc.), or may be obtained by imaging a pattern image in a state in which an object is not arranged.

In a case of a differential interferometer, since changes of a peak location in a two-dimensional Fourier image caused by an object are small, a peak location can be predicted without considering the effects of the object.

[0056] The imaging apparatus according to the present invention may be also configured separately form the X-ray source or electromagnetic wave source and may be configured to enable imaging in

combination with the X-ray source or electromagnetic wave source. Further, the imaging apparatus

according to the invention may be a device that acquires a differential phase image and does not necessarily include means for generating an

integrated phase image or means for displaying information on the inside of the object.

[0057] The present invention can be also

implemented with a computer (or a device such as CPU and MPU) of a system or an apparatus that realizes the aforementioned functions of the embodiment by reading and executing a program which has been

recorded in a storage device. Further, the present invention can be also implemented by a method

including a step executed by a computer of a system or an apparatus that realizes the aforementioned functions of the embodiment by reading and executing a program which has been recorded in a storage device.

For this purpose, the program is, for example, provided to the computer through a network or from recording media of a variety of types that can serve as the abovement ioned storage device (in other words, computer-readable storage medium that holds data non- temporarily) . Therefore, the computer (inclusive of a device such as CPU and MPU), the program (inclusive of a program code and a program product) , and a

computer-readable storage medium that holds data non- temporarily are all also included in the scope of the present invention.

[0058] While the present invention has been

described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such

modifications and equivalent structures and functions. This application claims the benefit of Japanese Patent Application No. 2014-081270, filed on April 10, 2014, which is hereby incorporated by reference

herein in its entirety.

Reference Signs List

[0059] 110: X-ray source, 120: Diffraction grating, 130: Shielding grating, 140: X-ray detector, 150:

Computational unit, 160: Image display device

Claims

1. An image processing unit that extracts phase information from a two-dimensional periodic pattern image, the unit comprising:

an acquisition unit that acquires the pattern image ;

a first transform unit that transforms the pattern image into a two-dimensional spatial

frequency domain image;

an extraction unit that extracts a peak of a spectrum included in the spatial frequency domain image and a surrounding region thereof; and

a second transform unit that acquires a phase image by transforming the extracted image to a real space

, wherein

the extraction unit extracts a region such as to include a first-order spectrum and one or more secondary spectra.

2. The image processing unit according to claim 1, wherein the transforming the extracted image to the real space is performed by a transform which is inverse to the transform performed by the first transform unit respect to the extracted image.

3. The image processing unit according to claim 1 or 2, wherein

the extraction unit extracts a plurality of regions including a spectrum having differential information relating to an X-axis direction and a spectrum having differential information relating to a Y-axis direction.

4. The image processing unit according to claim 3, wherein

the extraction unit extracts regions that have non-isot ropic shapes and mutually different shapes.

5. The image processing unit according to any one of claims 1 to 4, wherein

the pattern image is an image in which the spectrum including differential information relating to a Y-axis direction is arranged in a range of +45 degrees from an X axis and the spectrum including differential information relating to an X-axis direction is arranged in a range of ±45 degrees from a Y axis in the spatial frequency domain image resulting from the transform performed by the first transform unit.

6. The image processing unit according to any one of claims 1 to 5, wherein

the extraction unit applies a window function to the spatial frequency domain image, and by taking, as a boundary, a location at which an output value of the window function becomes zero, or a location at which the output value is at a predetermined ratio to a maximum value, extracts an interior of the boundary.

7. The image processing unit according to claim 6, wherein

the window function is a Gaussian function.

8.. The image processing unit according to any one of claims 1 to 7, wherein

the pattern image is an image generated by an interference detection device that forms an

interference pattern, which is formed by causing interference of electromagne ic waves radiated toward an object, and detects the interference pattern with a detector.

9. An imaging apparatus comprising:

an interference image detection device

including: a diffraction grating that diffracts electromagnetic waves radiated toward an object;

a absorption grating that shields periodically part of electromagnetic waves that have passed through the diffraction grating; and

a detector that detects an intensity distribution, in a plane, of electromagnetic waves that have passed through the absorption grating; and the image processing unit according to any one of claims 1 to 7.

10. The imaging apparatus according to claim 9, wherein

the absorption grating is such that an array direction of the grating is inclined within a -range of ±45 degrees with respect to an array direction of the diffraction grating.

11. A control method for an image processing unit that extracts phase information from a two- dimensional periodic pattern image, the method comprising:

a first transform step for transforming the pattern image into a two-dimensional spatial

frequency domain image; an extraction step for extracting a peak of a spectrum included in the spatial frequency domain image and a surrounding region thereof; and

a second transform step for acquiring- a phase image by transforming the extracted image to a real space

, wherein

in the extraction step, a region is extracted such as to include a first-order spectrum and one or more secondary spectra.

12. A program for causing a computer to execute the steps of the control method for an image

processing unit according to claim 11.

13. An image processing unit that extracts phase information from a two—dimens iona 1 periodic pattern image, the unit comprising: a first acquiring unit that acquires a pattern image; and a second acquiring unit that acquires phase information by windowed Fourier transforming the pattern image, wherein a window function used in the windowed Fourier transform is obtained by inverse Fourier transforming a filter function that extracts a region such as to include a first-order spectrum and one or more secondary spectrum from a two-dimensional spatial frequency image obtained by transforming the pattern image.