WO2013096974A1

WO2013096974A1 - Multilayer-coated micro grating array for x-ray phase sensitive and scattering sensitive imaging

Info

Publication number: WO2013096974A1
Application number: PCT/US2013/020561
Authority: WO
Inventors: Han Wen
Original assignee: THE UNITED STATES OF AMERICA, as represented by THE SECRETARY DEPT. OF HEALTH AND HUMAN SERVICES
Priority date: 2011-12-21
Filing date: 2013-01-07
Publication date: 2013-06-27

Abstract

Transmission X-ray gratings (100) include a periodically stepped surface having a plurality of steps (104-109). A multilayer coating (114-119) is situated on each step in one set of substantially parallel step surfaces. The multilayer coating can be a series of alternating bilayers having different complex refractive indices at X-ray wavelengths. In one example, an etched silicon substrate (102) having periodic steps in a <100> surface is provided with suitable multilayer coatings having a common height (H) selected to correspond to a step height. A cap layer is formed over the multilayer coatings, so that the resultant X-ray grating has opposing parallel surfaces (124,126).

Description

MULTILAYER-COATED MICRO GRATING ARRAY FOR X-RAY PHASE SENSITIVE AND SCATTERING SENSITIVE IMAGING

FIELD

The disclosure pertains to X-ray diffraction gratings.

BACKGROUND

Conventional X-ray imaging systems are generally based on spatial variations in X-ray attenuation in specimens corresponding to spatial variations in the imaginary component of specimen refractive index. In order to reveal additional specimen details, X-ray imaging techniques have been proposed that take advantage of variations in the real component of specimen refractive index at X-ray

wavelengths. These methods can be referred to as phase-contrast or phase-sensitive methods. Other techniques detect the scattering of x-rays by unresolved

microscopic structures, and can be referred to as scattering-sensitive methods.

Phase- sensitive and scattering-sensitive X-ray systems face some unique challenges due to the intended X-ray wavelength range. First, practical X-ray sources tend to provide diffuse, broadband radiation, so that phase-sensitive and scattering-sensitive X-ray optical systems must operate "achromatically" due to the broad X-ray wavelength range. Because x-ray imaging systems that can simultaneously capture a large area of the specimen are preferred as they can have high imaging speeds, optical elements for X-ray systems generally must be large enough to cover the size of the specimen. One approach for such phase and scattering- sensitive imaging is a grating interferometer in which input X-radiation is split into beams associated with diffraction orders that are recombined to produce interference fringes. Insertion of a specimen into the beams changes the interference fringe pattern due to phase differences between the beams associated with beam transmission through the specimen, and dispersion of the beams associated with scattering by the medium of the specimen. The resulting interference fringe pattern can be used to produce a phase-contrast and a scattering-contrast specimen image. Conventional X-ray gratings for use in such phase and scattering-contrast X- ray imaging systems are based on periodic vertical structures comprising a series of high aspect ratio trenches in a silicon or other material substrate. The trenches can be left empty or filled with a material. The X-ray grating is then defined by the periodic refractive index variation between the trench walls and the unfilled or filled trenches. Unfortunately, small grating periods and deep trenches are needed, making such gratings difficult to fabricate. Kim et al., "Observation of the Talbot effect using broadband hard x-ray beam," Optics Express 18(24), 24975-24982, 2010, showed that a slice of a stack of deposited layers of alternating materials can be used as a transmission grating with the x-ray beam parallel to the layers. In Kim's approach the grating period is determined by the deposited layer thickness and can therefore be very small. However, the vertical size of the grating is the overall thickness of the multilayer stack, and the vertical size cannot exceed 100 μιη due to the very long deposition time and the build up of defects in the layers. Such a vertical size is not sufficient to image large specimens. Disclosed herein are X-ray gratings and systems using such gratings that can avoid the difficulties associated with conventional X-ray gratings and Kim et al.'s multilayer gratings.

SUMMARY

X-ray transmission gratings comprise a substrate having a front surface and a back surface opposing the front surface, wherein the back surface includes a plurality of steps having first step surfaces and second step surfaces situated at respective common orientations with respect to the back surface. Multilayer coating stacks are situated on the commonly oriented first step surfaces of the plurality of steps. Typically, the multilayer coating stacks have a stack height that is

substantially equal to the step height. Typically, the multilayer stacks are all deposited in a single deposition process. A filler layer is situated on the multilayer coating stacks, the filler layer having an exterior surface that is substantially parallel to the front surface of the substrate. In some embodiments, the steps are periodic and the multilayer stacks have a common configuration of layers. In some specific examples, the multilayer stacks comprise respective pluralities of bilayers having the same or similar composition. In some representative embodiments, the substrate and the filler layer are silicon layers. In other examples, at least one of the substrate and the filler layers is a polymer layer. In other embodiments, the multilayer coating stacks comprise a plurality of bilayers, the bilayers being formed of a tungsten layer and a silicon layer, a molybdenum layer and a silicon layer, or a titanium layer and a silicon layer. In some alternatives, the substrate is a silicon substrate, and at least one surface of the substrate is a <100> crystal surface and at least one step surface is a <111> surface. In other examples, an angle between the first and second step surfaces is about 70.5 degrees. Typically, the steps have a step height of between about 0.1 μιη and 200 μιη and a period of between 0.1 nm and 200 μιη, and thicknesses of the layers in the multilayer stacks are between about 0.1 nm and 2 μιη.

Methods comprise situating a plurality of multilayer stacks on a stepped surface of a substrate, wherein the multilayer stacks are situated on substantially parallel step surfaces. The substrate further includes a front surface opposite the stepped surface. A filler layer is provided over the plurality of multilayer stacks so that the front surface of the substrate and an outer surface of the filler layer are substantially parallel. In some embodiments, the multilayer stacks have a height substantially equal to a step height and the stepped surface is periodic. In representative examples, an etch stop layer is provided on the stepped surface of the substrate, and the substrate is etched to the etch stop layer. In some examples, a polymer layer is provided adjacent the etch stop layer after etching the substrate. In some representative embodiments, the substrate is a silicon substrate and the etch stop layer is a silicon nitride layer. In other examples, the substrate is a polymer substrate.

Imaging methods comprise situating an X-ray transmission grating in an X- ray beam at an angle of incidence of at least 10 degrees to transmit portions of the X-ray beam through a specimen to a detector plane so as to produce X-ray interference fringes. An X-ray image of the specimen is obtained by detecting the X-ray interference fringes. In some examples, the X-ray beam is a conical beam and the X-ray transmission grating comprises a plurality of multilayer stacks situated so that the conical X-ray beam is incident substantially parallel to the layers of the multilayer stacks. In other representative examples, the multilayer stacks comprise pluralities of bilayers such that the multilayer stacks have a common height, and each of the multilayer stacks is situated on a substrate step. Typically, the multilayer stack height is substantially the same as the step height.

The foregoing and other features and advantages of the disclosed technology will become more apparent from the following detailed description, which proceeds with reference to the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a representative X-ray transmission grating on an etched silicon substrate.

FIG. 2 illustrates a representative phase sensitive imaging system that includes a transmission grating.

FIG. 3 is a block diagram illustrating a representative method of making an X-ray transmission grating on an etched silicon substrate.

FIGS. 4A-4B are block diagrams of alternative methods of making an X-ray transmission grating.

FIGS. 5A-5D illustrate sub-assemblies produced in fabrication of an X-ray grating according to one representative method.

FIG. 6 illustrates an X-ray grating configuration adapted for use with a conical X-ray beam.

FIG. 7 illustrates a representative X-ray transmission grating that includes a silicon nitride layer.

FIG. 8 illustrates a portion of an X-ray transmission grating.

DETAILED DESCRIPTION

As used in this application and in the claims, the singular forms "a," "an," and "the" include the plural forms unless the context clearly dictates otherwise. Additionally, the term "includes" means "comprises." Further, the term "coupled" does not exclude the presence of intermediate elements between the coupled items.

The systems, apparatus, and methods described herein should not be construed as limiting in any way. Instead, the present disclosure is directed toward all novel and non-obvious features and aspects of the various disclosed

embodiments, alone and in various combinations and sub-combinations with one another. The disclosed systems, methods, and apparatus are not limited to any specific aspect or feature or combinations thereof, nor do the disclosed systems, methods, and apparatus require that any one or more specific advantages be present or problems be solved. Any theories of operation are to facilitate explanation, but the disclosed systems, methods, and apparatus are not limited to such theories of operation.

Although the operations of some of the disclosed methods are described in a particular, sequential order for convenient presentation, it should be understood that this manner of description encompasses rearrangement, unless a particular ordering is required by specific language set forth below. For example, operations described sequentially may in some cases be rearranged or performed concurrently. Moreover, for the sake of simplicity, the attached figures may not show the various ways in which the disclosed systems, methods, and apparatus can be used in conjunction with other systems, methods, and apparatus. Additionally, the description sometimes uses terms like "produce" and "provide" to describe the disclosed methods. These terms are high-level abstractions of the actual operations that are performed. The actual operations that correspond to these terms will vary depending on the particular implementation and are readily discernible by one of ordinary skill in the art.

For convenience in the following description, substrates typically include a front side and a back side, opposite the front side, wherein the back side defines a periodic or aperiodic array or series of one or more steps, grooves, or other features that can be used to provide surfaces for the deposition of layers. Layers or coatings applied to surfaces of multilayer stacks that are or were in contact with a substrate back side are referred to as front layers. Layers or coatings applied to surfaces of multilayer stacks that are not to contact a back surface of substrate (and generally do not directly contact periodic surface features in a substrate back side) are referred to as back layers or coatings. The terms "front" and "back" do not otherwise designate any particular orientation.

As used herein, substantially parallel surfaces or propagation directions are surfaces or directions that differ in angular orientation by less than about 0.1, 1, 2, or 5 degrees.

Representative Transmission Gratings

A representative transmission X-ray grating 100 is illustrated in FIG. 1. A stepped substrate 102 such as an anisotropically etched silicon substrate includes a plurality of steps 104-109 that are provided with respective multilayer coatings 114- 119. For purposes of illustration, an uncoated step 110 is also shown in order to illustrate a grating tilt angle φ. In the etched silicon substrate 102, the steps 104-110 correspond to sides of isosceles triangles having a base of length B. The multilayer coatings 114-119 are preferably configured to have a height H that is substantially the same as the associated step height. The multilayer coatings 114-119 generally comprise a number of alternating bilayers of relatively less dense and more dense materials. In the disclosed example, the etched silicon substrate 102 has a step height of about 8.16 μιη, and the multilayer coatings 114-119 include 20 Si/W bilayers with each layer having a thickness of about 200 nm. A silicon filler layer 122 is provided over the etched silicon substrate 102 and the multilayer coatings 114-119. This layer can be formed by depositing a silicon layer followed by polishing. The X-ray grating 100 then has a uniform thickness with parallel exterior surfaces 124, 126. The combination of constant multilayer coating height matching the step height, and the silicon filler layer 122 eliminates or reduces grating substrate envelope modulation in interfering diffraction orders.

Transmission gratings such as that of FIG. 1 can exhibit diffraction with little or no envelope modulation due to the substrate if the bilayers are configured to have a height that is substantially the same as the step height H of the substrate steps and the filler layer 126 is provided. However, gratings with substrate modulation can be used as the substrate modulation is fixed and can be compensated in image analysis.

Representative Phase Sensitive Imaging Systems A representative phase-sensitive imaging system 200 is illustrated in FIG. 2.

An X-ray beam 202 is directed along a propagation direction 204 to a diffraction grating 206 such as described above. The input X-ray beam 202 is illustrated as a plane wave and the grating 206 is tilted so that the direction of propagation 204 of the input beam 202 can be in the plane of the grating multilayers. Diffracted X-ray beams 210, 211 propagate in directions 218, 219, respectively, to sample 214.

Portions of the diffracted beams 210, 211 interact with the sample 214 and are incident to an X-ray detector or imaging screen 226. The diffracted portions of the beams 210, 211 can interfere at the screen 226.

As shown in FIG. 2, the diffracted beams 210, 211 propagate at an angle Θ with respect to each other, wherein Θ = 2 arcsin(A P) ~ 2 JP, wherein λ is an X-ray wavelength and P is a grating pitch. The diffracted beams 210, 211 acquire respective phases φ_\, <ρ , so that X-ray intensity I(x) can be expressed as:

I(x) = I₀ |exp0^'2/rx / P + <p_l) + exp(-i2/rx / P + <p₂)f ,

= I₀ / 2 + I₀ cos(4/rx / P + Αφ).

wherein Io is a scale factor, and a phase difference Αφ = φ_\ - ψ2. Thus, an interference pattern of period P/2 is formed on the screen 226, but fringe position is dependent on a phase difference between the paths of the diffracted beams. If a distance between the sample and the screen is L, the phase difference can be expressed as:

wherein n is a sample refractive index. The phase shift is associated with a gradient of the refractive index in the x-direction, and detection sensitivity (i.e., phase difference) is proportional to l/P.

Other imaging systems can include additional gratings or use different X-ray sources. For example, an X-ray beam having a cone shape can be used instead of a plane wave beam. A diffraction grating can be provided to form a suitable X-ray beam that is then directed to a grating such as the grating 206. In such a

configuration, the X-ray grating associated with the source can be referred to as a source grating, while the grating 206 can be referred to as a beam splitter grating as it produces multiple beams that are directed to a specimen. Such a beam splitter grating can also be configured to converge two input beams so as to overlap and form fringes after transmission through a specimen. In addition, fringes produced by beams propagating through a specimen can be at spatial frequencies to which some detectors lack substantial response. In such cases, an additional image grating can be provided at or near a detector plane to modulate fringes so as to appear at lower spatial frequencies. Such fringes can be considered as Moire patterns. When an image grating is present, one of the gratings can also be moved in a direction perpendicular to the direction of the fringes, and the resulting oscillation of the x-ray intensity that is sensed by the detector is used to measure the fringes.

Representative Fabrication Methods

With reference to FIG. 3, a representative method 300 includes selecting a suitable substrate at 302. Substrates that exhibit anisotropic etching suitable for etching steps are generally preferred. A convenient substrate is a substantially flat silicon wafer having <100> opposing surfaces. At 304, a mask containing a periodic structure is applied to one surface. In one example, the mask is a nitride mask, and consists of a plurality of strips with a 10 μιη period aligned with a silicon wafer <111> direction. At 306, the masked substrate is etched to define grating steps. A silicon wafer masked as described can be etched with a KOH solution to form steps having exposed silicon <111> surfaces. A grating angle can be set by the anisotropic etching of the substrate. For a silicon wafer, a grating angle is 54.7 degrees. At 307, the mask is removed, and at 308 a plurality of bilayers is deposited on one set of parallel steps surfaces (referred to as step floors) in a single deposition run. The bilayers can be formed by sputtering or by electron beam evaporation, or other methods. Typically, the substrate is tilted with respect to a deposition source so that the step surfaces are orthogonal to the multilayer deposition direction. In one example, bilayers can be formed by magnetron sputtering with the etched substrate placed at an angle of about 35 degrees with respect to sputtering targets. At 310, a filler layer is deposited over the bilayers and at 312, the filler layer is polished to substantially equalize X-ray path lengths. The filler layer can be a silicon layer or layer of other material.

The example method of FIG. 3 is based on etching and coating a silicon substrate or other substrate in which steps can be conveniently formed. In other examples, an etched silicon substrate (or other substrate) can be used to form X-ray transmission gratings by an imprinting process. Referring to FIG. 4A, at 402 an etched silicon substrate is provided having suitable periodic etched steps. At 404, a series of multilayer coatings are deposited on the etched silicon substrate. The multilayer coatings can include a plurality of bilayers or other coatings formed by sputtering, evaporation, chemical vapor deposition, atomic layer deposition, or other processes. At 406, a curable polymer layer is applied to the etched substrate by spin coating or other process. The polymer layer is cured, typically by exposure to ultraviolet radiation, to form a solid polymer layer at 407.

After curing, the polymer layer is removed from the etched silicon substrate but with the multilayer coatings attached at 408. The etched substrate can be discarded or reused. The combined polymer layer/multilayer coating assembly is coated by spin coating or other process at 410 with a front polymer layer, and the front polymer layer is cured at 412. As a result, a transmission grating is formed with multilayer coatings embedded between the front and back polymer layers. In this way, an etched silicon substrate is used in forming an X-ray grating, but is not as a part of the X-ray grating.

In the above example, an ultraviolet polymer is used as a support and to liftoff the multilayer coatings. In other examples, a layer of thermoplastic polymer can be spin coated or otherwise formed on the multilayer coatings and allowed to cool to form a solid layer. If desired, pressure can be applied to the solid layer. The polymer can then be removed from the substrate along with the multilayer coatings.

Typically, the multilayer coatings are multiple bilayers and each step is provided with substantially the same coatings so that the coatings can be provided to all steps in a common coating process. However, one or more steps can be provided with different coatings, if desired. The methods of FIGS. 4-5 can use an etched silicon substrate as a part of a finished grating or as part of an intermediate assembly. In still other examples, a stepped silicon substrate can be used as a mold in forming a stepped polymer substrate. For example, a polymer layer can be applied to a stepped silicon substrate and pressed into the substrate to form a polymer substrate that can serve as a component of an X-ray grating. Alternatively, the stepped polymer can be used as a mold to form complementarily molded stepped substrates. Using such polymer substrates, multilayer coatings can be applied directly to polymer step surfaces.

The method of FIG. 4A is illustrated with reference to sub-assemblies in FIGS. 5A-5D. As shown in FIG. 5A, a stepped substrate 502 is provided having a plurality of steps of step height, step base, step angle as may be deemed appropriate for a particular application. The substrate 502 is oriented so as to receive coatings along a direction 510. FIG. 5B shows the substrate 502 with a plurality of multilayer stacks 514-520 situated on respective steps. A front polymer layer 504 covers the multilayer stacks. In FIG. 5C, the substrate 502 is removed so that the multilayer stacks 514-520 remain secured to the front polymer layer 504. In FIG. 5C, a back polymer layer 506 is applied so that the multilayer stacks 514-520 are situated between the front and back polymer layers 504, 506 in a spatial arrangement defined by the substrate 502.

Fabrication methods in which one or more layers are removed and a substrate used as a template can have reduced yields. In other methods, an etched silicon substrate can be substantially removed by etching and replaced with a less dense polymer layer. Referring to FIG. 4B, a method 420 include providing a stepped silicon substrate at 422 and forming a nitride layer on the stepped surface at 423. The nitride serves as an etch stop layer. At 424, multilayer stacks are formed on the steps, and polymer layer is applied to the multilayer stacks and cured at 426, 427. At 428, the stepped silicon substrate is etched to the nitride layer. The nitride layer can be left intact or removed in a separate etching process, and a back polymer layer is applied at 430 and cured at 432. If desired, the back polymer layer/nitride layer/multilayer stack/front polymer layer assembly can be secured to one or more rigid or other substrates at the front or back polymer layers at 434. For example, the back polymer layer can be secured to a planar or non-planar surface of a glass substrate. Such a rigid substrate can be situated at exterior surfaces of either the front or back polymer layers.

Additional Grating Embodiments

In some applications, X-ray transmission gratings are situated in cone- shaped X-ray beams, and multilayer-based gratings are configured to accommodate the beam cone angle. Referring to FIG. 6, a cone shaped X-ray beam 602 includes propagation directions 604, 606, 608 that are directed toward a grating 607. For superior operation, multilayers of the disclosed X-ray gratings are generally situated so that X-ray beam propagation is substantially in the plane of the layers. Thus, as shown in FIG. 6, the multilayers 610, 612 are tilted with respect to the center propagation axis 606 of the cone beam 602. The multilayer stacks 610, 611, 612 are fixed to a substrate 614 which can include curved exterior surfaces 616, 617 that can be smooth curves, a series of planar surfaces, or other surfaces. Such a curved grating can be formed by securing a back polymer layer/multilayer stacks/front polymer layer assembly to a non-planar surface of a rigid substrate.

A representative grating 702 made by etching to remove a silicon substrate is shown in FIG. 7. The grating 702 includes multilayer stacks 714-720 that are situated on a silicon nitride layer 706 that forms a surface of a periodic arrangement of steps. The silicon nitride layer 706 and the multilayer stacks 714-720 are situated between a front polymer layer 722 and a back polymer layer 724.

Typically, transmission gratings are formed with multilayer stacks that consist of repeated bilayers. The bilayers can be selected to produce phase modulation, amplitude modulation, or a combination thereof. Generally, a relatively less dense material and a more dense material are selected for the bilayers.

Representative examples include Si/W, Mo/Si, Ti/Si, and Si/Au bilayers. Any particular bilayers may produce phase modulation or amplitude modulation depending on X-ray wavelengths. Multilayer stacks can include layer combinations other than bilayers, depending on the modulation to be impressed on an X-ray beam. Layer thickness is associated with the modulation to be applied, and is generally controlled to within about 10% or better. Silicon is a convenient substrate due to its wide availability and low cost, but other single crystal substrates in which steps can be formed can be used.

FIG. 8 illustrates representative bilayer stacks 812, 813 situated on a stepped surface 802. The stack 812 does not extend to a step top, but a gap 823 remains. It is generally preferable that the gap 823 be less than 0.05, 0.1, 0.2, or 0.5 times a bilayer thickness, and preferably less than 0.1 times a bilayer thickness. The stacks 812, 813 are generally selected to have equal numbers of bilayers, but different numbers can be used. However, it is generally preferable to keep any gap small as discussed above, so that the steps are substantially filled.

In view of the many possible embodiments to which the principles of the disclosed technology may be applied, it should be recognized that the illustrated embodiments are only preferred examples and should not be taken as limiting.

Rather, the scope of the invention is defined by the following claims. We therefore claim as our invention all that comes within the scope and spirit of these claims.

Claims

We claim:

1. A method, comprising:

situating a plurality of multilayer stacks on stepped surface of a substrate, wherein the multilayer stacks are situated on substantially parallel step surfaces, the substrate further including a front surface opposite the stepped surface; and

providing a filler layer over the plurality of multilayer stacks so that the front surface of the substrate and an outer surface of the filler layer are substantially parallel.

2. The method of claim 1, wherein the multilayer stacks have a height substantially equal to a step height.

3. The method of claim 2, wherein the steps of the stepped surface are periodic.

4. The method of claim 3, further comprising:

applying a back polymer layer to the stepped surface; and

curing the back polymer layer.

5. The method of claim 4, further comprising removing the back polymer layer and the multilayer stacks to form a polymer layer having a stepped surface with multilayer stacks on step surfaces.

6. The method of claim 5, applying a front polymer layer to the stepped surface of the back polymer layer.

7. The method of claim 3, further comprising:

providing an etch stop layer on the stepped surface of the substrate; and etching the substrate to the etch stop layer.

8. The method of claim 7, further comprising:

removing the etch stop layer by an etching process to expose the underlying front surface of the multilayer stacks.

9. The method of claim 7, further comprising providing a polymer layer adjacent the etch stop layer after etching the substrate, or when the etch stop layer is removed, the polymer layer is provided on the exposed front surface of the multilayer stacks.

10. The method of claim 9, wherein the substrate is a silicon substrate and the etch stop layer is a silicon nitride layer.

11. The method of claim 1, wherein the substrate is a polymer substrate.

12. An imaging method, comprising:

situating an X-ray transmission grating in an X-ray beam at an angle of incidence of at least 10 degrees to transmit portions of the X-ray beam through a specimen to a detector plane so as to produce X-ray interference fringes; and

obtaining an X-ray image based on the X-ray interference fringes.

13. The imaging method of claim 12, wherein the X-ray beam is a conical beam and the X-ray transmission grating comprises plurality of multilayer stacks situated so that the conical X-ray beam propagates substantially parallel to layers of the multilayer stacks.

14. The method of claim 11, wherein the multilayer stacks comprise pluralities of bilayers such that the multilayer stacks have a common height, and each of the multilayer stacks situated on a substrate step.

15. The method of claim 11, wherein the X-ray transmission grating comprises a stepped polymer surface that retains the multilayer stacks.

16. The method of claim 15, wherein the multilayer stacks of the X-ray transmission grating are situated between front and back polymer layers.

17. The method of claim 16, wherein at least one of the front and back polymer layers is stepped.

18. An X-ray transmission grating, comprising:

a substrate comprising a front surface and a back surface opposing the front surface, wherein the back surface includes a plurality of steps having first step surfaces and second step surfaces situated at respective common orientations with respect to the back surface;

multilayer coating stacks situated on the commonly oriented first step surfaces of the plurality of steps, wherein the multilayer coating stacks have a stack height that is substantially equal to the step height; and

a filler layer situated on the multilayer coating stacks, the filler layer having an exterior surface that is substantially parallel to the front surface of the substrate.

19. The X-ray transmission grating of claim 18, wherein the steps are periodic.

20. The X-ray transmission grating of claim 19, wherein the multilayer stacks have a common configuration of layers.

21. The X-ray transmission grating of claim 19, wherein the multilayer stacks comprise a plurality of bilayers.

22. The X-ray transmission grating of claim 18, wherein the substrate and the filler layer are silicon layers.

23. The X-ray transmission grating of claim 18, wherein at least one of the substrate layer and the filler layer is a polymer layer.

24. The X-ray transmission grating of claim 23, wherein the substrate layer and the filler layer are polymer layers.

25. The X-ray transmission grating of claim 18, wherein the multilayer coating stacks comprise a plurality of bilayers, the bilayers having one of a tungsten layer and a silicon layer, a molybdenum layer and a silicon layer, or a titanium layer and a silicon layer.

26. The X-ray transmission grating of claim 18, wherein the substrate is a silicon substrate, and at least one surface of the substrate is a <100> crystal surface and at least one step surface is a <111> surface.

27. The X-ray transmission grating of claim 18, wherein an angle between the first and second step surfaces is about 70.5 degrees.

28. The X-ray transmission grating of claim 18, wherein the steps have a step height of between about 0.1 μιη and 200 μιη and a period of between 0.1 nm and 200 μιη, and thicknesses of the layers in the multilayer stacks are between about 0.1 nm and 2 μιη.

29. The X-ray transmission grating of claim 18, wherein at least one of the front surface or the back surface is secured to a rigid non-planar surface of a support substrate.