JP5258504B2 - Phase grating used in X-ray phase imaging and manufacturing method thereof, X-ray phase contrast image imaging apparatus using the phase grating, and X-ray computed tomography system - Google Patents

Description

  The present invention relates to a phase grating used for X-ray phase imaging and a manufacturing method thereof, an X-ray phase contrast image imaging apparatus using the phase grating, and an X-ray computed tomography system.

Conventionally, an X-ray fluoroscopic image technique for obtaining a contrast image using a difference in X-ray absorption ability has been studied.
However, since the X-ray absorption ability becomes smaller as the light element becomes, there is a problem that a sufficient contrast cannot be expected for a living soft tissue or soft material.
Therefore, in recent years, imaging methods for generating contrast based on the amount of X-ray phase change have been studied. One X-ray phase imaging method using this phase contrast is an imaging method using Talbot interference.

FIG. 10 shows a configuration example of the Talbot interferometry.
For imaging by Talbot interferometry, a spatially coherent X-ray source 13, a phase-type diffraction grating (hereinafter referred to as a phase grating) 15 for periodically modulating the phase of X-rays, and a detector 17 Is at least necessary.
The spatially coherent X-rays are those in which the X-ray intensity distribution after passing through the phase grating 15 reflects the shape of the phase grating 15.
When the phase of the X-ray transmitted through the phase grating is periodically modulated and a phase grating having a phase difference of π / 2 is used, the distance from the phase grating is (n−1 / 2) × (d ² / Λ)
A high-contrast light / dark periodic image appears at the position of and at the periphery thereof.
Here, d is the pitch of the phase grating 15, λ is the X-ray wavelength, and n is an integer.
In the present specification, the pitch of the phase grating refers to the period of the linear structures arranged periodically and in parallel at the fixed intervals in the phase grating.
Moreover, in this specification, the linear structure arrange | positioned in parallel periodically with a fixed space | interval is defined as a striped structure part.
Therefore, the phase grating has a structure constituted by such a diffraction grating in which linear stripe-like structure portions parallel to each other are periodically arranged at regular intervals.
These will be described more specifically. The pitch of the phase grating is, as shown in the schematic diagram of the phase grating in FIG. 9, between a certain stripe structure and the adjacent stripe structure. Indicates the distance C between the central portions, or indicates the distance C ′ between the end faces of the lattices.
Further, the width of the striped structure portion is the length of the striped structure portion in the direction perpendicular to the direction of transmission of the X-ray shown by A in FIG. 9 (on the short side of the striped structure portion). Length).
Further, the height (thickness) of the striped structure portion is the length of the striped structure portion (the length of the striped structure portion) in the same direction as the X-ray transmission direction indicated by B in FIG. Side length).
Further, the gap in the striped structure portion indicates the interval between the striped structure portion and the striped structure portion indicated by D in FIG.

In this way, a phenomenon in which a light / dark periodic image having the same period as the pitch of the phase grating is formed at a specific distance from the phase grating is the Talbot effect.
As shown in FIG. 10, when the subject 14 is placed in front of the phase grating, the irradiated X-rays are refracted by the subject 14.
Therefore, a phase image of the subject 14 can be obtained by detecting a light / dark periodic image formed by X-rays that are refracted through the subject 14.
However, since the bright / dark periodic image has the same pitch as the phase grating, an X-ray image detector with high spatial resolution is required for direct detection.
In such a case, it is possible to use an absorption grating 16 that is made of a material that absorbs X-rays and has a sufficient thickness.
If the absorption grating 16 is arranged at a position where a light / dark periodic image is formed, moire fringes are generated due to the overlap of the light / dark periodic image and the absorption grating 16.
That is, the information on the phase shift can be observed by the detector 17 as a deformation of the moire fringes.

By the way, when miniaturizing the imaging device for X-ray phase contrast images, it is desirable to form the bright and dark periodic images as close as possible to the phase grating 15.
As one of the methods for shortening the distance from the phase grating 15 to the light / dark periodic image in this way, it is possible to reduce the pitch of the phase grating 15.

However, if the pitch of the phase grating 15 is to be reduced, the width A and the gap D in the striped structure portion must be reduced.
Therefore, the aspect ratio defined by the thickness (height) B in the striped structure portion / the gap D in the striped structure portion or the thickness (height) B in the striped structure portion / the width A in the striped structure portion. Becomes large and difficult to manufacture.
For example, when Si is used as the material of the phase grating 15, the thickness necessary for shifting the phase of 20 keV X-rays by π is about 29.2 μm.
Further, when the slit-like phase grating 15 is manufactured, it is required to manufacture it with a pitch of about 2 μm, that is, an opening width of 1 μm, depending on the required resolution. At this time, the aspect ratio is about 30, and it is difficult to produce a large-area diffraction grating.

For this reason, in Patent Document 1, a diffraction grating having a substantially high aspect ratio is manufactured by stacking using partial gratings having a low aspect ratio.
Specifically, as shown in FIG. 11, the height of the projected ridges is increased by stacking the sub-lattices 18 having a low aspect ratio that can be easily manufactured in the vertical direction, and the aspect ratio A high diffraction grating is manufactured.
US Patent Application Publication No. 2007/0183579

As described above, according to the conventional example of Patent Document 1, by stacking the low-aspect-ratio partial grating 18, the height of the apparent protrusion is increased, and a diffraction grating having a high-aspect ratio is manufactured. doing.
By using a multi-layered phase grating as in Patent Document 1, it is possible to shorten the distance between the phase grating and the light / dark periodic image as compared with a single-layer phase grating.
However, in Patent Document 1, when the partial gratings are stacked, the distance is set by setting the thickness of the partial grating to a predetermined thickness in relation to the X-ray intensity distribution in the plane parallel to the phase grating. Nothing is said about shortening.

In view of the above problems, the present invention sets the thickness of the striped structure portion of the diffraction grating constituting the phase grating to a predetermined thickness in relation to the X-ray intensity distribution in a plane parallel to the phase grating. By
It is an object of the present invention to provide a phase grating used for X-ray phase imaging and a method for manufacturing the same, which can reduce the distance between the phase grating and the light / dark periodic image. Another object of the present invention is to provide an X-ray phase contrast image imaging apparatus using the above phase grating and an X-ray computed tomography system having the imaging apparatus.

The present invention provides a phase grating used for X-ray phase imaging and a manufacturing method thereof, an X-ray phase contrast image imaging apparatus using the phase grating, and an X-ray computed tomography system configured as follows.
The present invention is a phase grating for modulating the phase of X-rays ,
Striped structure of multiple is configured by arranged periodic manner, comprises a first diffraction grating and second diffraction grating,
The plurality of striped structures of the first and second diffraction gratings have a width in a direction perpendicular to a direction through which X-rays pass and a thickness in the same direction as the direction through which the X-rays pass.
The thickness of the striped structure is such that the phase is shifted by a necessary amount with respect to the transmitted X-rays so that the X-ray intensity distribution in a plane parallel to the phase grating has a predetermined intensity. Set,
The width and spacing of the plurality of striped structure portions of the first diffraction grating are equal to the width and spacing of the plurality of striped structure portions of the second diffraction grating,
In the periodic direction in which the plurality of striped structure portions of the first and second diffraction gratings are arranged ,
Each of the plurality of stripe-like structure of the second diffraction grating, to have a 1/4 pitch shifting are stacked in the structure for each of a plurality of stripe-like structure of the first diffraction grating Features.
Also, a phase grating that modulates the phase of the X-ray of the present invention,
The phase shift amount is Aπ (where 0 <A <1) with respect to the transmitted X-ray.
The phase grating that modulates the phase of the X-ray of the present invention includes a wherein said plurality of width of banded structure is equal to the periodically arranged plurality of striped structure spacing between To do .
Also, a phase grating that modulates the phase of the X-ray of the present invention,
Wherein the first diffraction grating is formed on one surface of the base plate,
Wherein the second diffraction grating are made form the other surface side of the front Kimoto plate.
According to another aspect of the present invention, there is provided an X-ray phase contrast image capturing apparatus including any of the phase gratings described above and a detector that detects X-rays transmitted through the phase grating .
The X-ray computed tomography system of the present invention is characterized by having the above-described imaging device for X-ray phase contrast images.
Moreover, the manufacturing method of the phase grating used for the X-ray phase imaging of the present invention is as follows:
A step of laminating a first diffraction grating and a second diffraction grating configured by periodically arranging a plurality of striped structure portions;
The plurality of striped structures of the first and second diffraction gratings have a width in a direction perpendicular to a direction through which X-rays pass and a thickness in the same direction as the direction through which the X-rays pass.
The width and spacing of the plurality of striped structure portions of the first diffraction grating are equal to the width and spacing of the plurality of striped structure portions of the second diffraction grating,
The laminating step includes
In the periodic direction in which the plurality of striped structure portions of the first and second diffraction gratings are arranged,
The first diffraction grating and the first diffraction grating so that each of the plurality of striped structure portions of the second diffraction grating is shifted by ¼ pitch with respect to each of the plurality of stripe structure portions of the first diffraction grating. A second diffraction grating is stacked.

According to the present invention, the distance from the phase grating where the X-ray intensity distribution in the plane parallel to the phase grating is maximum or second is shortened as compared with the case of the single-layer phase grating. A phase grating and a manufacturing method thereof can be realized.
In addition, according to the present invention, it is possible to realize an X-ray phase contrast image imaging apparatus using the phase grating and an X-ray computed tomography system having the imaging apparatus.

Next, an embodiment of the present invention will be described.
FIG. 1 is a diagram illustrating a configuration example of a phase grating used for X-ray phase imaging in which two layers of line diffraction gratings are shifted and stacked on each other.
In FIG. 1, 1 is an X-ray, 2 is a diffraction grating of the first layer, and 3 is a diffraction grating of the second layer.
The phase grating of the present embodiment has a two-layer linear diffraction grating composed of linear stripe structures parallel to each other and arranged periodically in a line at regular intervals. The striped structure portions are stacked and shifted in the periodic direction in which they are arranged.
In the present embodiment, in a phase grating in which such a plurality of diffraction gratings are stacked,
The thickness of the striped structure is set to a thickness that shifts the phase by a necessary amount with respect to the transmitted X-ray so that the X-ray intensity distribution in a plane parallel to the phase grating has a predetermined intensity. A set configuration example will be described.

In this embodiment, the striped structure portion in the diffraction grating has a width in a direction perpendicular to a direction in which X-rays are transmitted and a thickness in the same direction as the direction in which the X-rays are transmitted.
The striped structure is formed to have a thickness that shifts the phase by Aπ with respect to the transmitted X-ray. However, 0 <A <1.
When the two-layer linear diffraction grating is stacked, as shown in FIG. 1, the second diffraction grating 3 (second diffraction grating) is connected to the first layer with respect to incident X-rays. The diffraction grating 2 (first diffraction grating) is laminated with a quarter pitch shift in the periodic direction.
The X-ray 1 enters from the direction perpendicular to the substrate. Incident X-rays have a portion that passes through the Aπ shift portion of the diffraction grating by one layer, a portion that passes by two layers, and a portion that does not pass through.

At this time, as shown in FIG. 2, the transmitted X-rays form a region 6 through which the X-rays pass without phase change, a region 5 having a phase difference Aπ, and a region 4 having a phase difference 2Aπ.
Here, FIG. 3 shows a simulation result regarding the relationship between the position where the intensity of the X-ray transmitted through the laminated phase grating is maximum and second, and the phase shift amount of the diffraction grating.
Here, the phase shift amount is an amount by which the phase of X-rays transmitted during a single diffraction grating layer (one diffraction grating layer) changes.
For example, in the phase grating shown in FIGS. 1 and 2, the phase shift amount is Aπ.
Further, the width and gap of the striped structure portion in the phase grating are equal, and the laminated phase gratings are shifted from each other by a quarter pitch in the periodic direction.
Note that the horizontal axis of FIG. 3 indicates the amount of X-ray phase shift when transmitted through the diffraction grating.
The vertical axis indicates the distance from the phase grating, and (d ² / λ) is divided into 100, and (d ² / λ) × (1/100) to (d ² / λ) × (99/100). The interval was calculated at an interval of 1/100 × (d ² / λ).
The vertical axis represents the distance between the light / dark periodic image formed by the X-rays transmitted through the phase grating and the phase grating.
The white circle plot indicates the distance between the position where the intensity of the bright / dark periodic image is maximum and the phase grating when the diffraction grating is a single layer, for each phase shift amount of the phase grating.
In addition, the white triangle plot shows the distance between the position of the second intensity of the light-dark periodic image and the phase grating in the case of a single grating layer for each phase shift amount of the phase grating.
Similarly, the black circle plot indicates the distance between the position where the maximum intensity of the light / dark periodic image at the time of diffraction grating lamination and the phase grating is present, and the black triangle plot indicates the position at which the second intensity of the light / dark periodic image at the time of diffraction grating lamination is obtained. The distance from the phase grating is shown.

As shown in FIG. 3, the distance from the phase grating when the intensity of the X-ray transmitted through the phase grating is the maximum or the second intensity is one layer shorter than the single layer. When the phase grating is used, it is shortened.
From the figure, the range of 0.07 ≦ A ≦ 0.89 is effective.
However, even in the range of 0 <A <0.07 and 0.8 <A <1, the effect of the stacking can be found if the third strongest position is considered.

In manufacturing the phase grating, the individual diffraction gratings constituting the phase grating can be formed on the substrate surface, inside the substrate, or both.
As shown in FIG. 4, the striped structure portion 7 having the phase difference Aπ may be formed using a material different from the material forming the substrate 8, or a part of the substrate is processed as shown in FIG. It is good also as the diffraction grating 9 provided with the structure part.
Further, although the diffraction grating shown in FIG. 5 has a non-penetrating structure, it may be penetrated. If it penetrates, there is no absorption of X-rays by the substrate, so that the utilization efficiency of X-rays is improved.
In FIG. 5, at least a part of the gap between the stripe structure portions may be filled with a material different from the material forming the stripe structure portion.
For example, in FIG. 6, a material is selected such that the phase difference between the X-ray transmitted through the striped structure portion a10 and the X-ray transmitted through the striped structure portion b11 is Aπ.
Furthermore, in order to obtain a multilayered diffraction grating, two or more substrates on which diffraction gratings are formed may be laminated as shown in FIG. 7, or diffraction produced by processing the front and back of the substrate as shown in FIG. A lattice 12 may be used.
For example, the first diffraction grating is formed on one surface side of a single substrate, and the second diffraction grating is formed on the other surface side of the single substrate with a quarter pitch shifted in the periodic direction. You may make it do.
At the time of stacking, it is preferable to stack the processed substrates so that the diffraction gratings are in contact with each other, but they may be separated from each other. At this time, the substrates are laminated so as to be parallel to each other.

Further, an alignment mark may be formed on the substrate in advance for alignment.
As another alignment method, the diffraction grating can be magnified and observed by an X-ray microscope for alignment.
Further, alignment may be performed while observing a self-image obtained by the Talbot effect by irradiating spatially coherent X-rays.
The phase grating after alignment may be fixed, or the X-ray phase image may be observed as it is. When fixing the phase grating, mechanical fixing using an adhesive such as an epoxy resin, gold-gold bonding, a clamp, or the like can be used.

It is preferable to use a material that absorbs less X-rays during X-ray irradiation.
If the shape is a thin plate and the front and back are mirror surfaces, the contrast is good. For example, a semiconductor wafer such as Si, GaAs, Ge, or InP, a glass substrate, or the like can be used.
Although X-ray absorption is larger than that of Si, a resin substrate such as polycarbonate (PC), polyimide (PI), or polymethyl methacrylate (PMMA) can also be used.

In order to form the diffraction grating, a photolithography method, a dry etching method, various film forming methods such as sputtering, vapor deposition, CVD, electroless plating, and electrolytic plating, a nanoimprint method, and the like can be used.
That is, after a resist pattern is formed by a photolithography method, the substrate may be processed by dry etching or wet etching, or a diffraction grating may be provided on the substrate by a lift-off method.
Further, a substrate or a material formed on the substrate may be processed by a nanoimprint method.

By using the phase grating of the present embodiment, it can be used as a Talbot interferometer by combining with a spatially coherent X-ray source and detector.
At that time, the output may be detected using a detector after forming the moire fringes using the absorption grating.
In addition, an X-ray phase tomographic image of a patient can be obtained by incorporating the X-ray phase image imaging apparatus of the present invention into a gantry used in a conventional computed tomography system.
In the embodiment of the present invention, an imaging apparatus capable of capturing an X-ray phase contrast image by using the phase grating used in the X-ray phase imaging of the above-described embodiment for an X-ray phase contrast image imaging apparatus. Can be realized.
In addition, an X-ray computed tomography system including such an X-ray phase contrast image imaging apparatus can be realized.

Examples of the present invention will be described below.
[Example 1]
In the first embodiment, a description will be given of a configuration example in which linear diffraction gratings in which linear stripe structures parallel to each other are periodically arranged at regular intervals are stacked as a phase grating.
In this embodiment, first, a resist coating is applied to the surface of a 4-inch diameter double-side polished 200 μm thick silicon wafer, and then a resist pattern having a line width of 2 μm and a gap of 2 μm is formed in a 60 mm square area by photolithography.
Next, the following processing is performed by deep reactive ion etching (Deep-RIE).
That is, after forming a slit structure having a width of 2 μm, a gap of 2 μm, and a depth of 9 μm, the resist is removed (see FIG. 5).
In 17.7 keV X-rays, the phase difference between 9 μm thick Si and 9 μm thick air is 0.4π. The phase grating is irradiated with 17.7 keV X-rays from the vertical structure of the wafer.
At this time, the X-ray intensity in the bright and dark image with X-ray intensity becomes maximum at a position of 138 mm from the phase grating, and the X-ray intensity in the bright and dark image with X-ray intensity becomes second highest at a position of 91.2 mm.

Next, the same pattern is produced on the surface of two wafers.
Two processed silicon wafers are bonded so that the pattern comes into contact (see FIG. 7).
At the time of pasting, the slit structures are made parallel to each other so that the amount of deviation in the periodic direction of the slits is 1 μm.
As in the case of a single layer, X-rays of 17.7 keV are irradiated from the vertical structure of the wafer. At this time, the position where the X-ray intensity in the X-ray intensity bright and dark image is maximum is 164 mm from the phase grating, but the position where the X-ray intensity in the X-ray intensity bright and dark image is the second highest is 64 mm from the phase grating. It becomes.
Comparing the shorter of the positions where the X-ray intensity is the maximum or the second, whichever is shorter, when the phase grating is a single layer, the distance from the phase grating of the bright and dark image of the X-ray intensity was 91.2 mm. On the other hand, when laminated, it becomes 64.0 mm, which is shortened by about 30%.

[Example 2]
In the second embodiment, a description will be given of a configuration example in which linear diffraction gratings in which linear stripe structures parallel to each other as phase gratings are periodically arranged at regular intervals are formed on the front and back of the substrate.
In this embodiment, first, a slit structure having a width of 4 μm, a gap of 4 μm, and a depth of 8.2 μm is prepared in 60 mm square areas on both sides of a 1 mm thick acrylic plate.
At this time, the striped structures formed on the front and back sides of the substrate are formed parallel to each other and shifted by 2 μm in the periodic direction (see FIG. 8).
In X-rays of 17.7 keV, the phase difference between 8.2 μm thick acrylic and 8.2 μm thick air is 0.2π.
For comparison, a substrate in which a slit structure having a width of 4 μm, a gap of 4 μm, and a depth of 8.2 μm is formed only on one side of an acrylic plate is also produced.
In the case of a phase grating in which a striped structure is formed on only one surface of an acrylic plate, the X-ray intensity in a bright and dark image of X-ray intensity is maximized at a position of 539 mm from the phase grating.
Further, the X-ray intensity in the bright and dark image of the X-ray intensity becomes the second highest at the position of 357 mm.

On the other hand, a substrate having a striped structure formed on the front and back sides of the acrylic plate is irradiated with 17.7 keV X-rays from the vertical structure of the wafer as in the case of a single layer.
At this time, the position where the X-ray intensity in the bright-dark image with the X-ray intensity is maximum becomes 657 mm from the phase grating, but the position where the X-ray intensity in the bright-dark image with the X-ray intensity is the second highest is 257 mm.
Comparing the shorter one of the positions where the X-ray intensity is maximum or second, when the phase grating is a single layer, the distance from the phase grating of the bright and dark image of the X-ray intensity is 357 mm. When laminated, it becomes 257 mm, which is shortened by about 30%.

The figure explaining the structural example of the phase grating used for the X-ray phase imaging which shifted and laminated | stacked the two-layer linear diffraction grating in embodiment of this invention. The figure which shows the phase difference of the X-ray which permeate | transmitted the phase grating | lattice which consists of a two-layer diffraction grating in which the parallel linear striped structure part in embodiment of this invention was periodically arrange | positioned at fixed intervals. The figure explaining that the position where the intensity | strength of the transmitted X-ray becomes the maximum or the 2nd when a phase grating is laminated | stacked becomes closer to a phase grating rather than the time of a single layer phase grating. The figure explaining the structural example which formed the diffraction grating of phase difference A (pi) using the material different from the material which forms the board | substrate in embodiment of this invention. The figure explaining the structural example which processed the part of the board | substrate in embodiment of this invention, and formed the diffraction grating. The figure explaining the structural example which processed two types of materials in embodiment of this invention, and formed the diffraction grating. The figure explaining the structural example which laminated | stacked two board | substrates in which the diffraction grating in embodiment of this invention was formed. The figure explaining the structural example using the diffraction grating produced by processing the front and back of the board | substrate in embodiment of this invention. The schematic diagram for demonstrating the pitch in the phase grating used for X-ray phase imaging, the thickness (height) of a striped structure part, the width | variety of a striped structure part, and an opening width. The figure explaining the Talbot interferometer for obtaining the X-ray phase image which is a prior art example. The figure for demonstrating the patent document 1 which is a prior art example.

Explanation of symbols

1: X-ray 2: First layer diffraction grating 3: Second layer diffraction grating 4: Phase difference 2Aπ region 5: Phase difference Aπ region 6: X-ray transmission region without phase change 7: Position Striped structure portion 8 having phase difference Aπ: Substrate 9: Diffraction grating 10 fabricated by processing a part of substrate 10: Striped structure portion a
11: Striped structure part b
12: Diffraction grating manufactured by processing the front and back of the substrate 13: X-ray source 14: Subject 15: Phase grating 16: Absorption grating 17: Detector 18: Partial grating

Claims (7)

A phase grating for modulating the phase of X-rays ,
Striped structure of multiple is configured by arranged periodic manner, comprises a first diffraction grating and second diffraction grating,
The plurality of striped structures of the first and second diffraction gratings have a width in a direction perpendicular to a direction through which X-rays pass and a thickness in the same direction as the direction through which the X-rays pass.
The thickness of the striped structure is such that the phase is shifted by a necessary amount with respect to the transmitted X-rays so that the X-ray intensity distribution in a plane parallel to the phase grating has a predetermined intensity. Set,
The width and spacing of the plurality of striped structure portions of the first diffraction grating are equal to the width and spacing of the plurality of striped structure portions of the second diffraction grating,
In the periodic direction in which the plurality of striped structure portions of the first and second diffraction gratings are arranged ,
Each of the plurality of stripe-like structure of the second diffraction grating, to have a 1/4 pitch shifting are stacked in the structure for each of a plurality of stripe-like structure of the first diffraction grating place phase lattice shall be the feature. Shift amount of the phase, position phase grating according to claim 1, wherein a Aπ against X-rays transmitted through (where 0 <A <1). Wherein the plurality of widths of stripe structure section, position phase grating according to claim 1 or claim 2, characterized in that equal to the periodically arranged plurality of striped structure spacing between. Wherein the first diffraction grating is formed on one surface of the base plate,
Position phase grating according to any one of claims 1 to 3, characterized in that said second diffraction grating are made form the other surface side of the front Kimoto plate. Imaging apparatus of an X-ray phase contrast images, characterized in that it comprises a detector for detecting the position phase grating passes through the said phase grating X-ray according to any one of claims 1 to 4. An X-ray computed tomography system comprising the X-ray phase contrast image imaging apparatus according to claim 5 . A step of laminating a first diffraction grating and a second diffraction grating, each of which is configured by arranging a plurality of striped structure portions periodically;
The plurality of striped structure portions of the first and second diffraction gratings have a width in a direction perpendicular to a direction through which X-rays pass and a thickness in the same direction as the direction through which the X-rays pass.
The width and spacing of the plurality of striped structure portions of the first diffraction grating are equal to the width and spacing of the plurality of striped structure portions of the second diffraction grating,
The laminating step includes
In the periodic direction in which the plurality of striped structure portions of the first and second diffraction gratings are arranged,
The first diffraction grating and the first diffraction grating are arranged so that each of the plurality of striped structure portions of the second diffraction grating is shifted by ¼ pitch with respect to each of the plurality of stripe structure portions of the first diffraction grating. A method of manufacturing a phase grating, comprising stacking a second diffraction grating.

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