U.S. patent application number 09/366028 was filed with the patent office on 2002-06-27 for multilayer optics with adjustable working wavelength.
Invention is credited to JIANG, LICAI, VERMAN, BORIS.
Application Number | 20020080916 09/366028 |
Document ID | / |
Family ID | 23441383 |
Filed Date | 2002-06-27 |
United States Patent
Application |
20020080916 |
Kind Code |
A1 |
JIANG, LICAI ; et
al. |
June 27, 2002 |
MULTILAYER OPTICS WITH ADJUSTABLE WORKING WAVELENGTH
Abstract
An electromagnetic reflector having a multilayer structure where
the electromagnetic reflector is configured to reflect multiple
electromagnetic frequencies.
Inventors: |
JIANG, LICAI; (ROCHESTER
HILLS, MI) ; VERMAN, BORIS; (TROY, MI) |
Correspondence
Address: |
HARNESS DICKEY & PIERCE PLC
PO BOX 828
BLOOMFIELD HILLS
MI
48303
|
Family ID: |
23441383 |
Appl. No.: |
09/366028 |
Filed: |
August 2, 1999 |
Current U.S.
Class: |
378/84 ;
378/145 |
Current CPC
Class: |
G21K 2201/061 20130101;
G02B 5/0883 20130101; G02B 5/0891 20130101; G21K 1/062 20130101;
B82Y 10/00 20130101; G21K 2201/067 20130101 |
Class at
Publication: |
378/84 ;
378/145 |
International
Class: |
G21K 001/00 |
Claims
I claim:
1. An electromagnetic reflector comprising: a multilayer structure
having a d-spacing, wherein said multilayer structure's curvature
may be varied by a movement apparatus to reflect multiple
electromagnetic frequencies.
2. The electromagnetic reflector of claim 1, wherein said
multilayer is deposited on a substrate.
3. The electromagnetic reflector of claim 1, wherein said d-spacing
is laterally graded.
4. The electromagnetic reflector of claim 1, wherein said
electromagnetic frequencies are x-ray frequencies.
5. The electromagnetic reflector of claim 1, wherein said movement
apparatus is a bender which alters the curvature of said multilayer
structure.
6. The electromagnetic reflector of claim 5, wherein said bender is
a four point bender.
7. An x-ray reflector comprising: a substrate; a multilayer
structure coupled to said substrate, wherein said multilayer
structure is of fixed curvature; and said multilayer structure
having at least two distinct groups of d-spacing, wherein the x-ray
reflector may reflect a plurality of x-ray frequencies.
8. The x-ray reflector of claim 7, wherein the thicker of said
groups of d-spacing is mounted on the top of said multilayer
structure.
9. The x-ray reflector of claim 7, wherein the mutlilayer is
laterally graded.
10. The x-ray reflector of claim 7, wherein the multilayer is
deposited on said substrate.
11. An electromagnetic optic comprising: a multilayer surface, said
multilayer surface having a variable curvature, whereby said
multilayer surface will reflect different wavelengths of
electromagnetic energy based on said variable curvature.
12. The electromagnetic optic of claim 11, wherein said multilayer
is laterally graded.
13. The electromagnetic optic of claim 11, wherein said
electromagnetic energy is x-rays.
14. The electromagnetic optic of claim 11 further including a
bender to alter the curvature of said multilayer surface.
15. A variable curvature x-ray reflector comprising: a substrate; a
multilayer surface coupled to said substrate, wherein said
multilayer is laterally graded; and wherein as said curvature of
the x-ray reflector is varied the frequency of reflected
electromagnetic radiation is also varied.
16. The variable curvature x-ray reflector of claim 15, wherein the
variable curvature x-ray reflector is shaped as a parabolic curve
and the p factor is varied to change the curvature of the variable
curvature x-ray reflector.
17. The variable curvature x-ray reflector of claim 15, wherein the
variable curvature x-ray reflector is shaped as an elliptical curve
and the minor radius is varied to change the curvature of the
variable curvature x-ray reflector.
18. A method of reflecting multiple electromagnetic frequencies
with a multilayer reflector comprising: generating electromagnetic
energy; directing said electromagnetic energy at the multilayer
reflector; and adjusting the curvature of the multilayer reflector
to reflect said electromagnetic energy in accordance with Bragg's
law.
19. An x-ray reflector comprising a plurality of stripe-like
multilayer sections arranged side by side, wherein each said
multilayer section has a d-spacing configured to reflect a
different x-ray frequency.
20. The x-ray reflector of claim 19, wherein said multilayer
sections are configured with an elliptical surface.
21. The x-ray reflector of claim 19, wherein said multilayer
sections are configured with a parabolic surface.
Description
BACKGROUND OF THE INVENTION
[0001] The present invention relates to an electromagnetic optic
element. More specifically the present invention relates to
reflective multilayer x-ray optics having adjustable working
wavelengths.
[0002] X-ray optics are used in many applications such as x-ray
diffraction analysis and spectroscopy that require the directing,
focusing, collimation, or monochromatizing of x-ray energy from an
x-ray source. The family of x-ray optics or reflectors used in such
applications presently include: total reflection mirrors having a
reflective surface coated with gold, copper, nickel, platinum, and
other similar elements; crystal diffraction elements such as
graphite; and multilayer structures.
[0003] The reflective surfaces in the present invention are
configured as multilayer or graded-d multilayer x-ray reflective
surfaces. Multilayer structures only reflect x-ray radiation when
Bragg's equation is satisfied:
n.lambda.=2dsin(.theta.)
[0004] where
1 n = the order of reflection .lambda. = wavelength of the incident
radiation d = layer-set spacing of a Bragg structure or the lattice
spacing of a crystal .theta. = angle of incidence
[0005] Multilayer or graded-d multilayer reflectors/mirrors are
optics which utilize their inherent multilayer structure to reflect
narrow band or monochromatic x-ray radiation. The multilayer
structure of the present invention comprises light element layers
of relatively low electron density alternating with heavy element
layers of relatively high electron density, both of which define
the d-spacing of the multilayer. The bandwidth of the reflected
x-ray radiation can be customized by manipulating the optical and
multilayer parameters of the reflector. The d spacing may be
changed depthwise to control the bandpass of the multilayer mirror.
The d-spacing of a multilayer mirror can also be tailored through
lateral grading in such a way that the Bragg condition is satisfied
at every point on a curved multilayer reflector.
[0006] Curved multilayer reflectors, including parabolic,
elliptical, and other aspherically shaped reflectors must satisfy
Bragg's law to reflect a certain specific x-ray wavelength (also
referred to as energy or frequency). Bragg's law must be satisfied
at every point on a curvature for a defined contour of such a
reflecting mirror. Different reflecting surfaces require different
d-spacing to reflect a specific x-ray wavelength. This means the
d-spacing should be matched with the curvature of a reflector to
satisfy Bragg's law such that the desired x-ray wavelength will be
reflected. Since Bragg's law must be satisfied, the incident angle
and d-spacing are normally fixed and thus the reflected or working
wavelength is fixed.
SUMMARY OF THE INVENTION
[0007] The present invention is a multilayer x-ray reflector/mirror
which may be used to reflect multiple x-ray wavelengths.
[0008] In a first embodiment, the multilayer structure has a
laterally graded d-spacing. The working (reflected) wavelength of
the multilayer reflector may be changed by simply varying its
curvature and thus the angle of incidence for an x-ray beam to
satisfy Bragg's law.
[0009] In a second embodiment, an electromagnetic reflector has a
fixed curvature and a multilayer structure that has been configured
to include a plurality of distinct d-spacings. The multilayer
structure has also been laterally graded such that the
electromagnetic reflector may reflect multiple x-ray wavelengths
according to Bragg's law. Thus, the lateral grading of the
d-spacings have been configured in conjunction with the curvature
of the multilayer coating to reflect a plurality of x-ray
wavelengths.
[0010] In a third embodiment of the present invention an
electromagnetic reflector is formed with stripe-like multilayer
coating sections. Each of the coating sections has a fixed
curvature and graded d-spacing tailored to reflect a specific
wavelength. To change the working wavelength of the reflector, the
mirror or x-ray source need to be moved relative to each other so
that the appropriate coating section is aligned with the x-ray
source.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] The various advantages of the present invention will become
apparent to those skilled in the art after reading the following
specification and by reference to the drawings, in which:
[0012] FIG. 1 is a cross-sectional diagrammatic view of a
multilayer Bragg reflector;
[0013] FIG. 2 is a cross-sectional diagrammatic view of a
multilayer reflector with a plurality of distinct d-spacings to
reflect multiple x-ray wavelengths;
[0014] FIG. 3 is a cross-sectional view of a parabolically shaped
reflector;
[0015] FIG. 4 is a cross-sectional view of an elliptically shaped
reflector;
[0016] FIG. 5 is a magnified cross-sectional view taken within
circle 5 of FIG. 3;
[0017] FIG. 6 is a magnified cross-sectional view taken within
circle 6 of FIG. 3;
[0018] FIG. 7 is a magnified cross-sectional view taken within
circle 7 of FIG. 4;
[0019] FIG. 8 is a magnified cross-sectional view taken within
circle 8 of FIG. 4;
[0020] FIG. 9 is a diagrammatic view of the first embodiment of the
reflector of the present invention illustrating its variable
curvature and ability to reflect different x-ray wavelengths;
[0021] FIG. 10 is a diagrammatic view of a bender used in the
present invention;
[0022] FIG. 11 is a cross sectional view of the second embodiment
of the reflector of the present invention having a fixed curvature
that is configured to include a plurality of distinct d-spacings
and laterally graded such that it may reflect multiple x-ray
wavelengths; and
[0023] FIG. 12 is a top view of the third embodiment of the
reflector of the present invention with stripe-like sections having
different d-spacings such that the reflector can reflect a
plurality of x-ray frequencies.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0024] FIG. 1 is a cross-sectional diagrammatic view of a
multilayer reflector 10. The multilayer reflector 10 is deposited
on a substrate 12 and comprises a plurality of layer sets with a
thickness d. Each layer set 14 is made up of two separate layers of
different materials; one with a relatively high electron density
and one with a relatively low electron density. In operation, x-ray
radiation 13 is incident on the multilayer reflector 10 and narrow
band or generally monochromatic radiation 16 is reflected according
to Bragg's law.
[0025] FIG. 2 is a cross sectional diagram of a multilayer
structure 18 having a plurality of distinct d-spacings d1 and d2
varying in the depth direction and defined as depth grading. The
multilayer structure 18 because of the distinct d-spacings d1 and
d2 may reflect multiple x-ray wavelengths (i.e. different groups of
d-spacing to satisfy a discrete range of reflected wavelengths). In
operation, polychromatic x-ray radiation 20 is incident on the
surface of the multilayer structure 18 and low energy x-rays 22 are
reflected by the relatively thicker d-spacings d2 and high energy
x-rays 24 are reflected by the relatively thinner d-spacings
d1.
[0026] FIGS. 3 and 4 are cross-sectional diagrams of fixed
curvature multilayer optics 26 and 28 which generally reflect only
one x-ray wavelength. FIG. 3 illustrates the parabolically shaped
multilayer optic 26 which collimates x-ray beams generated by an
idealized point x-ray source 30 and FIG. 4 illustrates the
elliptically shaped multilayer optic 28 which focuses x-ray beams
generated by an x-ray source 32 to a focal point 34. The curvature
and d-spacing of optics 26 and 28 have been permanently configured
to satisfy Bragg's law for a specific wavelength at every point on
the surface of the optics 26 and 28.
[0027] FIGS. 5, 6, 7, and 8 are cross-sectional magnified views of
the multilayer surfaces taken within circles 5, 6, 7, and 8 of
FIGS. 3 and 4. From these figures the variation in incident angle
and the lateral grading of the d-spacing in order to satisfy
Bragg's law for a specific frequency can be seen. In FIGS. 5 and 6
the parabolic optic 26 includes incident angle .theta..sub.1 and
d-spacing d3 at one area of its surface and incident angle
.theta..sub.2 and d-spacing d4 at another area. While these
parameters are different, the result is that these areas reflect
generally the same x-ray wavelength following Bragg's law.
Similarly, in FIGS. 7 and 8 the elliptical optic 28 includes
incident angle .theta..sub.3 and d-spacing d5 at one area of its
surface and incident angle .theta..sub.4 and d-spacing d6 at
another area which reflect the same x-ray wavelength. The
shortcomings with these type of fixed curvature reflectors is that
they may only be used to reflect a single x-ray wavelength or
narrow band.
[0028] As discussed previously, multilayer reflectors require
different d-spacing variations to reflect different x-ray
wavelengths at the same incident angle and the d-spacing should
match the surface curvature (angle of incidence) to reflect x-rays
according to Bragg's law. The present invention provides
electromagnetic reflectors which may be used to reflect a plurality
of x-ray wavelengths having substantially no overlap.
[0029] A first embodiment of the present invention shown by FIG. 8
comprises a multilayer reflector with variable curvature and a
laterally graded d-spacing. If a multilayer is a flat reflector
with uniform d-spacing, the flat reflector can be rotated to
reflect x-rays of different wavelengths, as the incidence angle
will vary. If a multilayer has a curved surface the d-spacing must
be laterally graded to satisfy Bragg's law at every point. Thus,
the d-spacing or incidence angle may be changed to vary the x-ray
wavelength reflected from a multilayer reflector. The following
discussion and equations will demonstrate that for certain x-ray
wavelengths the laterally graded d-spacing of a multilayer
reflector may remain constant while only the curvature is varied
and the curvature of a multilayer reflector may remain constant and
have multiple graded d-spacings such that multiple x-ray
wavelengths may be reflected by the multilayer reflector.
[0030] For parabolic, elliptical, and other aspherically shaped
multilayer optics, either the d-spacing variation of the multilayer
coating or the curvature of the optics can be manipulated such that
the multilayer optics reflect x-rays with different wavelengths.
Following Bragg's law the d-spacing is given by: 1 d = 2 sin ( 1
)
[0031] Where .theta. is the incident angle. It can be shown that
the sin .theta. can be written, at a very accurate approximation,
as a product of a factor "C"(an arbitrary constant) and common form
which is independent from the x-ray energy. The same d-spacing can
be used for different wavelengths by changing the factor C such
that .lambda./C is a constant. Accordingly, sin .theta., which is
determined by the configuration of the reflection surface, can be
maintained the same if d-spacing is proportionally changed with the
wavelength such that: 2 sin = 2 d ( 1 b )
[0032] is maintained constant for different wavelengths.
[0033] For a parabolic mirror the curvature of the reflecting
surface can be written as:
y={square root}{square root over (2px)} (2)
[0034] where p is the parabolic parameter. The accurate incident
angle can be given by the following formula: 3 = tan - 1 ( 2 px x -
p 2 ) - tan - 1 ( p 2 x
[0035] p generally is a number on the order of 0.1 and x is
generally in the range of several tens of millimeters to more than
100 millimeters. Due to the fact that .theta. is small where tan
.theta..apprxeq..theta., the incident angle can be written as: 4 =
p 1 2 x ( 3 )
[0036] Using small angle approximation, d-spacing is determined by:
5 d = p x 2 ( 4 )
[0037] From the equations shown above it can be shown that
d-spacing can be maintained for different reflected wavelengths by
altering the curvature or parabolic parameter (.rho.) of a
parabolic shaped multilayer reflector.
[0038] For an elliptical mirror, the reflection surface is
described by the equation: 6 x 2 a 2 + y 2 b 2 = 1 ( 5 )
[0039] Where x and y are points in a Cartesian coordinate system
and a is the major radius of the ellipse and b is the minor radius
of the ellipse. The incident angle is given by the equation: 7 =
tan - 1 ( b / a a 2 - x 2 x + c ) - tan - 1 ( - 2 bx a a 2 - x
2
[0040] where c is defined by the equation:
c={square root}{square root over (a.sup.2-b.sup.2)}
[0041] For an x-ray elliptical mirror, the minor radius is much
smaller than the major radius. Using small angle approximation, the
above equation can be written as: 8 q a 2 - x 2 x + a 1 - q 2 - - 2
qx a 2 - x 2
[0042] where q=b/a. Therefore the d-spacing is given by the
equation: 9 d = q 1 2 ( a 2 - x 2 x + a + 2 x a 2 - x 2 ) ( 6 )
[0043] From the above formula, it can be shown that the d-spacing
and focal position can be maintained by just changing the minor
radius b.
[0044] Furthermore, we determine how d-spacing is defined as well
as the wavelength dependency on d-spacing for a multilayer
reflector. The d-spacing used in this application is defined by
using first order Bragg's law (n=1), since multilayers generally
operate under first order reflection. The "real d-spacing", or the
"geometric d-spacing is different from the "first order Bragg
d-spacing" due to the effects of refraction in the multilayer
structure. In most applications a multilayer optic is used as a
first order Bragg reflector. This is the reason that "d-spacing" is
commonly defined and measured by the first order Bragg's law. Such
defined d-spacing is the same for different wavelengths as shown in
the following discussion.
[0045] The "real d-spacing" d.sub.r is given by the following
equation: 10 d r = d ( 1 - sin 2 ) ( 7 )
[0046] where .delta. is the optical index decrement. Therefore,
higher order measurement gives a d-spacing closer to the "real
d-spacing". However, the optical index is proportional to the
square of the wavelength and so is sin.sup.2.theta.. Therefore, the
above equation becomes:
d.sup.r=d(1-Ad.sup.2) (8)
[0047] where A is a constant not dependent on energy. This means
that the "first order d-spacing" is the same for different
wavelengths and the d-spacing measured by different wavelengths is
the same.
[0048] Referring to FIG. 9 and the first embodiment of the present
invention, a variable curvature multilayer reflector 36, is shown
in two positions 38 and 40 having two different curvatures defined
by the ellipses 33 and 35 and reflecting different x-ray
wavelengths 39 and 41 to a focal point 31. A similar scheme may be
configured for parabolic collimating mirrors which conform to two
different parabolas. The reflector 36 has more curvature at
position 38 then at position 40. The increased curvature will allow
the reflector to reflect larger x-ray wavelengths at position 38
then at position 40. The reflector at position 40 is modified with
less curvature then at position 38 and will reflect shorter x-ray
wavelengths. The curvature of the reflector 36 is exaggerated in
FIG. 9 to help illustrate the curvature at the alternate positions
38 and 40.
[0049] For a variable curvature parabolic mirror from Formula
4:
.lambda./{square root}{square root over (p)}=C
[0050] for all the wavelengths. Therefore the parabolic parameter
must change in the following way: 11 p = 2 C 2 ( 9 )
[0051] For an elliptical mirror, according to formula 6, the minor
radius b must change as: 12 b = a C ( 10 )
[0052] Thus, the manipulation of the parabolic parameter p of the
parabolic reflector and the minor radius b of the elliptical
reflector may be adjusted to vary the wavelength of the reflected
x-rays.
[0053] A four point bender 42 is shown in FIG. 10 having precision
actuators 44a and 44b which will vary the curvature of the
reflector 36. Posts 43 are fixed while members 45 are actuated to
alter the curvature of the reflector 36. The bender 42 will vary
the parabolic parameter p of a parabolically shaped multilayer
reflector and the minor radius b of an elliptically shaped
multilayer reflector as detailed above.
[0054] In a second embodiment of the present invention shown in
FIG. 11, a multilayer reflector 46 of fixed curvature, with a
plurality of distinct d-spacings d7 and d8, is configured to
reflect multiple x-ray wavelengths. Each d-spacing d7 and d8 will
satisfy Bragg's law for a specific x-ray wavelength. The relatively
larger d-spacing d8 will reflect longer wavelengths and the
relatively shorter d-spacing d7 will reflect shorter wavelengths.
The reflected wavelengths will have substantially no overlap. Since
the absorption for lower energy (longer wavelength) x-rays is
stronger, the reflection layer d8 for the lower energy x-rays
should be the top layers on the reflector 46. As can be seen in the
drawing, the d-spacings d7 and d8 are laterally graded in
cooperation with the curvature of the reflector 46 to satisfy
Bragg's law for a plurality of specific x-ray wavelengths. In
alternate embodiments of the present invention additional groups of
d-spacings may be used limited only by the dimensions and structure
of the reflector 46.
[0055] In a third embodiment of the present invention seen in FIG.
12 (an overhead or top view) a multilayer reflector 48 having
stripe like sections 50 with different d-spacings is shown. Each
stripe 50 has a d-spacing configured to reflect specific x-ray
wavelengths. An x-ray source 52 needs only to be translated
relative to the stripe like sections 50 of the reflector 48 to
change the wavelength of the x-rays reflected from the reflector
48. The preferred method of translation is to fix the position of
the x-ray source 52 while translating the reflector 48.
[0056] It is to be understood that the invention is not limited to
the exact construction illustrated and described above, but that
various changes and modifications may be made without departing
from the spirit and scope of the invention as defined in the
following claims.
* * * * *