Note: Descriptions are shown in the official language in which they were submitted.
~3'~85
INSTRUMENT AND METHOD FOR FOCUSING
X-RAYS, GAMMA RAYS AND NEUTRONS
This invention relates to diffraction by the use of
periodic structures such as crystals, gratings and the like
and more particularly to an instrument for diffraction in
which the spacing associa~ed with the crystalline planar or
grati.ng elements in the periodic structure is progressively
increased or decreasecl along a face or directi.on of the
structure to progress:ively change the Bragg diffraction
angle, and to a method of providing a controlled and pro-
gressive change in the Bragg angle along a face or direction
of the structure associated with diffraction spacing to
increase the usable diffraction area or acceptance angle
of the structure for monochromatic radiation and thereby
improve the extent that beams of photons and particles may
be focused or otherwise controlled. ~
In the drawings, illustrations of the prior art and
various embodiments of the invention have ~een provided to
aid in the und~rstanding and disclosure of th~ invention.
Reference will he made to certain of these figures before
detailed description of the invention is provided. The
figures are as follows:
Fig. la is a schematic representation of the
transmission type of crystal diffraction of the prior art
with a flat crystal and a point or line source.
Fig. lb is a schematic representation of the reflection
type of crystal diffraction of the prior art with a flat
crystal and a point or line source.
Fig. 2a is a schematic representation of the
transmission type of crystal diffraction of the prior art
where the crystal is bent and the beam is provided by a
broad source.
Fig. 2b is a schematic representation of the reflection
type of crystal diffraction of the prior ar~ where tne
crystal is bent and the beam is provided by a point source.
Fig. 3 is a schematic representation of one embodiment
of the invention utilizing the transmission type of crystal
diffraction with a flat crystal for focusing a beam from a
point or line source.
Fig. 4 is a second embodiment of the invention showing
a flat crystal of a differing concentration along its len~th
used in the transmission type of crystal diffraction.
Fig. 5 is a third embodiment of the invention showing a
spatial arrangement of three crystals with differing planar
, ~a,1~ ~
~`:
spacing used for the transmission type of crystal
diffraction.
Fig. 6 is a schematic representation of a fourth
embodiment of the invention showing a transmission type of
crystal diffraction where the crystal is bent and the beam
is provided by a point source.
Fig. 7 is a fifth embodiment of the invention showing a
refl~ction type of crystal diffraction where the crystal is
bent and the beam is provided by a point source.
Fig. 8 is a sixth embodiment of the invention showing a
transmission type of crystal diffraction where the crystal
is bent and the incident beam consists of parallel rays.
Fig. 9 is a seventh embodiment of the invention showing
a reflection type of crystal diffraction where the crystal
is bent and the incident beam consists of parallel rays.
Fig. 10 is an eighth embodiment of the invention
showing a transmission type of crystal diffraction where the
two bent crystals are used to focus the beam from a point
source to form a point image.
Fig. 11 is a pictorial representation of an instr~lment
utiliæing the invention and providing means for creating a
temperature difEerential across the crystal.
Fig. 12a is a schematic representation of the
transmission type and reflection type of diffraction (first
type) by gratings with varied spacings and which utilizes
the invention for the focusing of a point or line source to
a line image.
Fig. 12b is a schematic representation of an alternate
or second kind of geometry for the reflection type of
~,',~,;
~,
4 ~ ~t~
diffraction by gratings with varied spacings which utilizes
the invention for the focusing of a point or line source to
a line image.
Fig. 13a is a schematic representation of a
transmission type and reflection type (of the first type) of
diffraction showing the focusing characteristics of a
circular grating as an embodiment of this invention for the
case of a point source focused to a point image.
Fig 13b is a schematic representation of a trans-
mission type and reflection type of diffraction showing thefocusing characteristics of a circular grating for a
parallel beam source focused to a point image.
Fig. 14 is a schematic representation of a grating
curved in a ring-like structure for focusing and diverging
rays of a point source to a point image.
Fig. 15 is a schematic representation of a grating
curved to form a hollow conical section for focusing
parallel rays to a point image.
The diffraction of photons such as x-rays and gamma
rays by crystals is an old and well established discipline.
Crystal diffraction may generally be divided into two
classes, the "transmission" type and ~he "surface diffrac-
tion or reflection" type. In the transmission type as
illustrated in the schematic diagram of Fig. la, the
crystal planes used in the diffraction process are perpen-
dicular to the face or incident surface of ~he crystal and
the beam of photons pass through crystal. In the "surface
diffraction or reflection" type as illustrated in the
schematic diagram of Fig. lb, the crystal diffraction planes
, . ,
are parallel to the face or incident surface of
the crystal and the beam of photons are diffracted near
this surface so that they merge from the same face of
crystal that they entered. The transmission type
diffraction is used mainly for high energy photons with
their corresponding small Bragg angles whi]e the surface
type diffraction is more useful with lower energy photons
with their larger Bragg angles and higher absorption
coefficients.
Early diffraction instruments such as the spectrometer
used flat crystals and had efficiencies as low as 10 9
diffracted photons per source photon. The low efficiency
occurred because only a very thin slice of the crystal
satisfied the Bragg condition for the diffraction based on
the Bragg equation
n~ = 2d sin ~
where "n" is in the order of diffraction, "~" is the wave-
length of the photons, "d" is the crystalline plane spacing,
and "~" is the Bragg angle or incident angle. If the beam
of photons entered the crystal at an angle other than the
Bragg angle, reflection at that portion of the beam was
essentially eliminated. For purposes of illustration, the
usable narrow slice of a crystal may be only about 0.001 cm
for a high quality ~rystal with a rocking curve of about 2
seconds and with a source at a distance of about 100 cm.
Some of the important features of crystal diffraction
instruments relate to the extent that the beam of photons
6 ~
~i.e., x-rays and gamma rays) or particles (i.e., neutrons)
may be diffracted with a reasonable efficiency and focused
or otherwise controlled to provide an image o~ desired
intensity. Since the usable area or acceptance angle of
flat crystals is extremely limited, it has become necessary
to bend crystals to improve the area or acceptance angle
over which the Bragg condition was satisfied to improve the
efficiency and intensity levels of the diffracted beam. The
schematic diagrams of Figs. 2a and 2b provide illustrations
of bent crystals used for the transmission and reflection
type of crystal diffraction. While the use of bent crystals
improved efficiencies, intensities, and focusing operations
of the crystal diffraction instruments over those for
instruments using flat crystals, it was not always possible
to easily bend crystals to the desired extent and some
crystals such as those of bismuth and tin would tend to
break before being bent beyond a limited extent.
Further, the crystal diffraction instruments with bent
crystals had disadvantages. As illustrated in the schematic
diagram of Fig. 2a with the transmission type, it was
necessary to use a broad source to provide a concentration
of monochromatic radiation at a line image. With the
reflection type, as illustrated in the schematic diagram of
Fig. 2b, it was possible to form a focused line image from a
point source although the distances of the image and source
usually were equidistant irom a center line.
Focusing is of considerable importance to instruments
using crystal diffraction since accurate detection and
.~
measurement of diffracted beams often are dependent on the
intensity of the difracted beam and the extent that the
beam is focused within a small area. As illustrated in
Figs. la and lb for beams which are not effectively ~ocused,
the target or image area must be increased for effective
detection or measurement.
Focusing of parallel rays is also if importance. In
the telescope in the Einstein satellite which has been in
orbit around the earth, total reflecting mirrors are used to
focus parallel beams of x-rays and gamma rays from deep
space. Limitations in the performance of the reflecting
mirror system limited the usable photon energies for this
satellite telescope to about 5 KeV and below with more
satisfactory performance being at about 2-3 KeV. Increase
in the usable photon energies to values above about 5 KeV
would be desirable. Replacement of the mirror system with
crystal diffraction systems in the present state of the
art would not solve these problems since they do not
effectively focus parallel rays, even those of low photon
energies. Therefore, new crystal diffraction systems with
improved performance in focusing or converging parallel rays
at higher photon energies would be desirable for satellite
telescopes and other instruments.
In a similar manner, diffraction gratings have become
important for the focusing and imaging of soft x-rays,
ultraviolet, visible and infrared radiation. The basic
difference in these methods for fGcusing is that diffraction
occurs in the grating by a two dimensional phenomena while
it is three dimensional in the crystalline structure.
, ~
8 3~
Diffraction gratings are conventionally made by photographic
~echniques to produce a series of parallel lines in the film
and by etching or machining of conductive metals to produce
a similar pattern in the metal surfaces.
Since gratings have conventionally been made with the
diffraction spacing being essentially constant, the
effectiveness of these gratings has been limited for much
the same reasons that were discussed above for the crystal
diffraction case. The constant diffraction element spacing
results in a constant diffraction angle for the diffracted
beam. This makes it impossible to convert a parallel beam
into a convergent beam and/or to use the diffraction process
as a method for focusing radiation from any type of source
except in the very special case of the reflection type
diffraction grating used in the zero order (~ 2) where
no spectral discrimination occurs.
One of the objects of this invention is to provide a
means of increasing the area or acceptance angle in periodic
structures used for crystal diffraction and in grating
diffraction. Another object is to increase the efficiency
of the dlffraction process. An additional object is to
improve the intensity of the diffraction process. A further
o~)ject is to improve focusing in instruments utilizing
crystal diffraction or diffraction by gratings. ~et another
object is to provide means for Eocusing of parallel beams.
It is also an object to increase the energy levels to values
above 5 KeV for focused beams which may be diffracted by
diffraction instruments. These and other objects will
become apparent from the following description.
9 ~ ~ 8 ~
In this invention, the performance of a crystal or
of a grating for diffraction is improved by providing a
progressive change in the atomic planar spacing along the
face of the structure. With respect to the use of a cry.stal
and to the progressive change in spacing, the value of "d"
in the Bragg equation is changed resulting in a progressive
change in the Bragg angle along the crystalline face.
By the change in Bragg angle, a grea~er area or acceptance
angle of the crystal may be utilized resulting in improved
efficiency, intensity and focusing of a beam of photons or
particles. In addition, parallel beams may be focused or
otherwise converged or diverged in a controlled manner.
Another advantage is that crystals composed of materials of
higher atomic number may be utilized for diffracting
beams of energy levels above 5 KeV to values of 100 KeV and
above. Accordingly, the invention is directed to a crystal
diffraction instrument in which the means for diffracting a
beam of photons or particles includes a periodic structure
with a face having a length and periodic diffraction
surfaces spaced along that length with the spacing changing
progressively along the length. The progressive change in
spacing provides a progressive change in the Bragg angle and
thereby increases the usable area for the photon beam. The
change in Bragg angle for crystal diffraction and ~hus the
increase in efficiency of the instrument such as the
spectrometer can be obtained from the equation
~d/d = cot ~ ~
lo ~3~
where ~d is the change in the planar spacing and a~ is the
change in the Bragg angle over the usable face of the
crystal. For a value of ~d/d equal to 2.7 x 10 3 and the
Bragg angle a equal to 20, then ~he change in the Bragg
angle (~) under these representative conditions is equal to
about 10 3 radians or 200 seconds of arc. This may be
compared to about two seconds of arc for the rocking curve
or acceptance angle of a good crystal of the prior art
resulting in an improvement of about 100. It is eviden~
from the geometries of Fig. 3 that the acceptance angle for
a crystalline structure with a change in planar spacing is
essentially equal to the change in the Bragg angle.
It is further evident that the usable area is determined by
the distance from the source of a diverging beam but is
essentially proportional to the acceptance angle.
For the bent crystals utilizing the invention, there is
an interdependence between the radius of curvature (Rc) and
change in spacing (~d) for the transmission and reflection
types of crystal diffraction as indicated by the following
equations:
(transmission type)
R = 2RlR2/Cs ~ (R2 ~ Rl)
~d cos2 ~ (R2 ~~ Rl)
~ Q
(reflection type)
R = 2RlR2/Sin ~ (R2 ~ Rl)
~d -cos ~ (R2 ~ R
~-- 2 K2Rl
:
~ 32 ~ ~
where "Rl" e~uals the distance from the image to the
crystalline structure, "R2" equals the distance from the
source to the crystals, and "~" is the distance along the
surface of the crystal.
With respect to the use of gratings, the basic concept
is to vary the distance between and the width of the
scattering lines, slits, or grooves in the diffraction
grating in such a way so that the diffraction angle for
monochromatic radiation changes with the position on the
surface of the diffraction gratings so that the desired
focusing and/or imaging occurs.
The basic difference between diffraction by crystalline
structure or gratings is that the diffraction grating
represents essentially a two-dimensional diffracting medium
while the diffraction crystal is a ~hree-dimensional
diffracting medium. Further, in the diffraction grating,
the spacing between periodic spaced diffracting elements can
be made almost any value down to a prac~ical limit of a few
microns and is substantially under the control of the
~0 manufacturer while in the crystal diffractor case, the
spacings are controlled by the electronic forces between
atoms and are therefore much more restricted in what these
spacings can be and how fast they can change wi-th position
in the crystal. This new freedom in the control of the
spacing permits the manufacture of diffrac~ion systems with
much shorter focal lengths than in the diffraction crystal
case and that are usable over much longer ranges of
wavelengths.
12 ~ 3~
The general development of the mathematics is much
the same as previously explained for the crystalline
structures, where the Bragg diffraction angle ~ was gi~en
by the relation n~ - 2d sin a where ~ was bo~h the incident
and exit angle relative to the crystalline planes for both
types of diffraction as shown in Figs. la and lb. The
diffraction grating is based on a) the relationship
n~ = d(sin~l + sin~2) for the transmission case and the
reflection case of the first kind (both illustrated in
Fig. 12a) and b) the relationship and n~ = d(sin~l - sin~2)
for the reflection case of the second kind (as illustrated
in Fig. 12b). For the transmission case when ~ 2 then
essentially all the mathematics that apply to the crystal
diffraction examples in general apply to the diffraction
gratings so essentially all the solutions that have been
described previously apply. The case of ~1 + ~2 in the
reflection case is wavelength independent so the diffraction
grating acts like a plane mirror for "zero order
diffraction". ~owever, one of the advantages with
diffraction gratings is that ~1 does not have to equal ~2
and the respective distances to the source and to the image
need not be equal. Further with the limita~ion that -the
basic equation is satisfied, a family of solutions and
thereby images is possible. With beams of energy of mixed
frequencies, the gratings may be used as selective filters
in addition to diffracting with the multiple images being
associated with individual frequencies or wavelengths.
Since diffraction gratings in such structure as film may be
easil~ formed into curves and other shapes, new
13 ~
configurations for the focusing and imaging systems are also
possible (as illustrated in Figs. 14 and 15).
For focusing a monochromatic point source of light to a
line image as illustrated in Fig. 12a, the mathematics may
be set forth as follows:
n~ = d (sin~l + sin~2)
n~
d = ( i ~
sin~ ____ sin~ = x_ = x
1 Rl (X2 + D12~ 2 2 R2 (x2 + Dl)~
d n~ j(x2 + D2) 2 (x2 + D12)
L(X2 + D12) 2 + (X2 + D2)~2~
where "n" is the order of diffraction, "~" is the wave-
length, "d" is the spacing between the diffraction elements,
"~l" is the Bragg angle for the original beam, ~2" is the
Bragg angle for the diffracted beam9 I'Dl" is the distance
from the source to the grating, and "D2" is the distance
from the grating to an image. If ~l = a2~ the d = n~/2sin~
~nd the change in d as a function of o is given by
~- = cot ~Q~.
In the more general case where ~ 2
d = n~/~sin~l + sin 02)
ad , _ ~cOs~lQ~ coso2a~
in~l + sin~2
Qd = ~ ~ ]
~33~8
In addition to the diffraction structure as described
herein, the invention is directed to a method of conductin~
diffraction with respect to a beam which comprises the steps
of (1) providing a periodic structure with a face having a
length with a diffraction spacing between diffraction
sur aces along that length increasing progressively to
thereby provide an increased area satisfying the Bragg
condition for the beam, (2) directing the beam to the
periodic structure and (3~ receiving the diffracted beam.
By the invention, the acceptance area or angle of a periodic
structure which satisfies the Bragg condition may be
increased. In addition, increased efficiencies and
intensities may be obtained from these structures used for
diffraction. Further, improved focusing and the focusing of
parallel beams may also be obtained.
As described previously, the invention is directed to a
diffraction instrument in which the means for diffracting a
beam of photons or particles includes a periodic structure
wlth diffraction planes or elements being spaced in a
periodic pattern along a length of the face, with the
spacing changing progressively along the length to provide a
change in Bragg angle along that length. The invention
further relates to the diffraction means with the progress-
ively changed spacing and to a method of providing the
diffraction means. Advantageously, the periodic structures
include crystalline structures and diffraction gratings.
With respect to crystal diffraction, the invention
includes an instrument for crystal diffraction and a method
~ ~ ~ 3~ ~
of conducting crystal diffraction under conditions T,7hich
satisfy the Bragg condition based on the Bragg equation as
described above. With respect to diffraction by gratings,
the invention includes an instrument for diffraction by
the use of gratings and to a method of constructing a
grating with improved performance.
As is known with respect to crystal diffraction, the
Bragg condition also includes the relationship that the
incident angle is equal to the angle of reflection ln the
crystalline structure. In an instrument for diffracting a
beam of energy using means for diffracting the beam, the
improvement comprises a crystalline structure with a face
having a length and diffraction plane spacing along the
length with the spacing changing progressively along the
length in a direction parallel to the face to provide a
Bragg angle of decreasing values with respect to a
particular monochromatic radiation frequency (wavelength).
Ins~ruments of this ~ype include spectrometers,
medical devices used to focus or increase the intensity
o~ a beam for treatment purposes, satellite telescopes
used for ~ocusing parallel beams of photons such as x-rays
and gamma rays from deep space, and devices useful for
research purposes where beams of photons or particles are
directed against samples to determine particular character-
lstics of the samples. Usually these instruments include
means for receiving the diffracted beam on a target area
for providing an image and in many instances include an
aperture or other means for admitting the beam from the
- 16 ~ 3~ ~ ~
source to the diffracting means. In a spectrometer, the
means for receiving the beam include the exit or detector
slit while the entrance aper~ure may represent the means
admitting the beam. One or more colllmators may also be
used to separate the diffracted beam from the undiffracted
beam as is customary in this art. In addition, sections of
the inventive instrument may be movable to adjust to dif-
ferent portions of the admitted beam. For a satellite
telescope, means are provided for admitting a parallel
beam of photons from deep space and for focusing the
diffracted beam.
In the inventive method for the crystalline structure,
the steps include (1) providing a crystalline structure
with planar spacing along a length of a face of the structure
where the spacing progressively changes in value, (2) dir-
ecting a beam of elemental photons and/or particles to the
ace of the crystalline structure to provide a diffracted
beam, and (3) receiving the diffracted beam. The first
step ma~J be carried out by providing a temperature differ-
~0 ential or gradient along the length of the crystallinestructure to progressively change by a positive or negative
value, the planar spacing by utilizing the thermal coefficient
of expansion; or contraction; by providing a spatial arrange-
ment of two or more different crystalline structures to for~
a length with different planar spacing; by providing a
change in composition along a length of a cyrstalline structure
to provide a progressive change in planar spacing, or by
combinations of these techniques. Advantageously,
~ 3~ ~ ~
the crystalline structure with changed planar spacing is
provided by the use of a temperature gradient or a change
in crystalline composition and preferably by a temperatu-re
gradient of at least about 50C/cm in length.
Suitable crystalline structures include crystals with
an elevated melting point of at least about 200C, and
~referably above about 500C, and other characteristics
of atomic number and magnetic properties dependent on the
particular beam of interest. For lower energy beams, crystals
of lower atomic number are desired with the reverse being
the guideline for higher energy beams. For beams of neutrons,
crystals with some magnetic properties are desired. In
general, suitable crystals include those of quartz, calcite,
silicon, germanium, gold, tin, nickel, graphite, beryllium,
copper, zinc, sapphire, diamond, and the like. Combinations
of separate crystals of silicon and nickel, nickel and
germanium, germanium and tin, silicon and germanium, silicon
and tin, and the like, may be used. For crystalline structures
~ith changing compositions, combinations of crystals of
nickel with about 20 at.% of germanium, silicon or tin or
of caclmium with about 30 at.V/O of silver rnay be used. Char-
acteristics of these crystals with respect to composition
and planar spacing are in such references as "A Handbook
of Lattice Spacings and Structures of Metals and Alloys"
by W. B. Pearsons, Pergamon Press, London (1953 and 1967),
Vol. I, pp. 236, 288 and 290, Vol. II, pp. 512 and 980.
Preferably, the crystal is of high quality and preferably
quartz. The crystalline structure may be flat or bent
depending on the se].ection of the crystal and the need for
- 18 ~ ~ 1~ 3~ ~ ~
bending. Representative dimensions of a crystalline
structure are 1/2 to 10 cm in length, 1/2 to 10 cm wide and
1/10 to 5/10 cm in thickness with planar spacing being
about 1 to 10 ~, advantageously about 1 to 5 A, and pre-
ferably about 1 to 2 A, for use with the higher energy
(the latter values being for photons).
The change and preferably the increase in planar
spacing suitably is about 1/10 to 5% and preferably about
1/2 to 2% along the length of the crystalline face. With
the spacing being provided by a temperature differential,
a temperature differential of at least about 200C up to
the crystalline melting point (or Curie point for a beam
of neutrons) and advantageously abou-t 200 to 500C is
desired. A temperature gradient of at least about 50C/cm
up to a value of about 200C/cm (with the maximum tempera-
ture being below the crystalline melting point or Curie
point) is desired.
Schematic diagrams have been used in Figs. 1 to 10 to
illustrate characteristics of crystal diffraction of the
prior art and those provided by crystalline structures
based on the invention. The planar spacing and beams are
also enlarged to illustrate the characteristics o~ the
diffraction process.
Figs. 1 and 2 illustrate crystal diffraction based on
the prior art. In Figs. la and 2a, the transmission type
of crystal diffraction is illustrated while in Figs. lb and
2b, the reflection type is illustrated. For simplicity,
the reflectlon type is shown with the beam being reflected
- - 19 ~3~
from the face of th~ s~ructure although the diffraction
uses one or more layers of planar spacing. Figs. la and lb
illustrate the use of flat crystals while Figs. 2a and 2b
illustrate the use of bent crystals. As illustrated in
Fig. la, a beam from a point or line source lO is transmitted
through collimator 12 for selection of a beam 14 of narrow
width further identified by acceptance angle ~, and to
flat crystal 15 with face 16 having a length 17. The
planar spacing 18 of crystal 15 is essentially the same
along length 17 and therefore only a limited area 20 or
acceptance angle is capable of diffracting the monchromatic
portion of the beam under conditions w~Lich satisfy the Bragg
condition. The angle ~ in Fig. la represents the Bragg angle.
The diffracted beam 21 is directed to form a line image 22.
As illustrated, beam 21 diverges s].ightly so that line image
22 is not a focused image, and the distance Dl and D2 are
equal from the center line D3.
In Fig. lb, the planar spacing 30 of crystal 28 extends
parallel to face 32 along length 34. ~s illustrated, beam
35 is directed from point or line source 36, through colli-
mator 37 to face 32, and is diffracted to form diffracted
beam 38 which then forms line image 39. Beam 38 diverges
slightly so that line image 39 is not focused. Distances
Dl and D2 are shown as equal distance from center line D3.
~ bent crystal used for -the transmission type of
crystal diffraction is illustrated in Fig. 2a with a beam 40
being directed from the broad source 42 to face 45 of
crystal ~4. The diffracted beam 46 is directed through
~3i~
collimator 47 to form line image 48. As illustrated, che
radius 49 of the arc 50 at which crystal 44 is bent is
approximately twice the value for the radius 51 of the
focal circle.
In Fig. 2b, the reflection type of crystal diffraction
with a bent crystal is illustrated. Beam 54 from point
source 56 is directed to face 58 of crystal 57 and
diffracted by planar spacing 59 to form diffracted beam 6Q
forming line image 61. As illustrated, distances Dl and D2
are equal distance from center line D3 and the radius 62 of
arc 63 for the bent crystal is approximately twice the
radius 65 of the focal circle.
One embodiment of the invention is illustrated in
Fig. 3. Flat crystal 70 is used for the transmission type
of crystal diffraction and has planar spacing 72 increasing
in value along a length 73 of face 74 from a cold end 75 to
a hot end 76, with the atomic planes separating the spacing
72 extending across the thickness of the crystal. Since hot
end 76 would provide an increase in planar spacing 72; the
~ hot end 76 is located to provide a smaller Bragg angle 77
than angle 78 at the cold end 75. As illustrated, beam 79
is directed to face 74, and is diffracted to form diffracted
beam 80 which converges to form a focused line image 81.
In the second embodi~ent of the invention as illustrated
in Fig. 4, a crystalline structure 84 of a material such as
nickel is illustrated with an added ingredient such as tin
being present in a varied concentration along the length of
the crystalline structure to vary the planar spacing. The
concentration of tin is varied from a value of about zero
- 21 -
percent at end 85 to a value of about 10 at.% at end 8~
resulting in the planar spaci.ng 87 varying ~rom a value
for "d" of about 3.5172 A (at a temperature of about 16C~
at end 85 to about 3.6000 A (at a temperature of about 16C~
at end 86. In the crystal diffraction process for the
embodiment of Fig. 4, beam 88 from point or line source 89
is directed to a crystalline structure 84 and diffracted
by planes 87 to form a diffracted beam 90 which converges
to form a focused line image 91. As illustrated, distances
Dl and D2 are equidistant from the center line D3.
A spatial arrangement of three different crystals 94,
and 96, is illustrated as a third embodiment of the
invention in Fig. 5. As illustrated, each of the crystals
has opposite cold and hot ends so that the planar spacing
varles along the length of the crystal. In addition, the
composition o~ the dlfferent crystals varies so that the
planar spacing at the cold end is different for each crystal.
For purposes of illustration, crystal 94 may be relatively
pure nickel with a planar spacing of about 3.5172 A at the
~0 cold end with a temperature of about 16C, with crys~al 95
be~ng nlckel containing abou-t 3 at.% Sn having a planar
sp~cing o~ about 3.5~29 A at the cold end with a temperature
of about 16C, and crystal 96 being nickel containing about
6 at ./0 Sn having a planar spacing of about 3.5687 A at the
cold end with a temperature of about 16C. The combination
of faces 97, 98, and 99 form an overall length 100 over which
the planar spacing is varied -to provide an increase in spacing
along length 100. A temperature gradien-t (~t/cm) for crystals
9~, 95 and 96 (each of one cm in length) is in the respective
. . - 22 ~3 >~r
order of about 176C (192C - 16C), 177C (193C - 16C),
and 178C (194C - 16C). Crystals 94, 95 and 96 are
separated a slight distance (about 2 cm) by barriers pro-
viding insulation ~etween the adjacent ends. The acceptance
angle is approximately 540 arc seconds (for a 50 Ke~
monochromatic beam using the 100 planes of nickel and a
fifth order diffraction). In the diffraction process,
beam 102 from point or line source 103 is directed to the
combination 102 of crystals 94, 95 and 96 and diffracted
to form a diffracted beam lOS which converges to form. a
focused line image 106. Distances Dl and D2 are equidistant
from center line D3.
In the fourth embodiment of the invention showing a
transmission type of crystal diffraction as illustrated
in Fig. 6, a crystalline structure 110 of a material such
as quartz is bent so that face 111 is in convex shape along
length 112. A temperature gradient is applied over length
112 to provide a variation in the planar spacing along
length 112. This will provide a change in the Bragg angle
based on the preceding equations for the radius of curvature
(~c) and the desired ~d/d based on the further relationship
that ~d/d ~ ~t where "~" equals the coefficient of thermal
expansion and "~t" equals the temperature differential. Beam
113 from point or line source 114 is directed to face 111
over which the planar spacing 115 is varied and becomes
diffracted to form a diffracted beam 116. Line image 117
is formed by the converging beam 116. In Fig. 8, distances
Dl and D2 are at unequal distances from center line D3.
23
Fig. 7 illustrates the reflection type crystal
diffraction with crystalline structure 120 which is in a
concave shape being bent .so that the incident angle or Bragg
angle varies along length 123 of face 122 with the atomic
planes separating the spacing extending in a direction
parallel to face 122. As illustrated, a temperature gradient
is applied over the length 123 to provide the variation in
planar spacing that matches the variation in Bragg angle. In
the diffraction process, beam 124 from point or line source
125 is directed to face 122 and becomes diffracted to form
diffracted beam 126. The convergence of beam 126 forms line
image 127. As illustrated, distances Dl and D2 are unequal
with respect to center line D3.
In Figs, 8 and 9, crystalline structures 130 and 150 are
used as means to diffract and focus parallel beams 132 and
152, respectively, as in an instrument of the type used for a
satellite telescope. In Fig. 10, the temperature gradient is
applied across length 134 of face 133 of crystalline structure
130 to provide a variation in planar spacing. Beam 132 is
directed to face 133 and is diffracted to form diffracted beam
135 which converges to form focused line image 136. In a
similar manner, although utilizing the reflection type of
crystal diffraction, beam 152 is directed to face 153 of
crystalline structure 150 and is diffracted to form diffracted
beam lS5 which converges to form focused line image 156. As
illustrated, a temperature gradient is applied across length
15~ of face 153 to provide a variation in planar spacing.
In Fig. 10, a plurality of crystalline structures are
utilized to form a focused point image from a point source.
1.~'~ ''
24 ~ ~ ~ ~ 3~ ~ ~
As illustrated, crystalline structure 160 has a temperature
differential applied along the leng~h 163 of ace 162 to
provide a variation in planar spacing. As illustrated,
face 162 has a concave shape exposed to point source 164.
Beam 165 is directed to face 162 and forms a diffracted
beam 166 which converges to form line image 167 Crystalline
structure 168 is placed in the path of diffracted beam 166
and forms a second diffracted beam 169 which converges to
form point image 170. Crystalline structure 168 also has
a temperature differential applied along length 172 of
face 171 to provide a variation in planar spacing.
In the pictorial representation of instrument 180
as illustrated in Fig. 11, a flat crystal 182 i.s held
between brackets 184 and 185 and used to diffract a beam
1~6 of energy of appro~imately 50 KeV from source 187.
The diffracted beam 188 is transmitted to detector slit
189. The temperature gradient o~ about 300C is applied
by the use of electrical heating in brac~et 184 as illus-
trated by wires 190 and 191, and by cooling in bracket 185
2~ as illustrated in tubes 192 and 193. Shield 194 provides
~rotection for the detector 189 agalnst the rad:iation from
the source. Source 187 and detector slip 189 may be movable
~o adjust to different photon energies, dif~erent temperature
difEerentials, and di~ferent Bragg angles. An enclosure
195 is also provided so that the difEraction process is
carried out in a vacuum.
A.s described above, the invention provides a valuable
lnstru~lent for crystal diE~raction by providing a crystalline
- 25 - ;~ 3~5
structure with varied planar spacing along the face receiS~ing
the beam for diffraction. The planar spacing may be varied
by use of a temperature gradient, b~J the use of different
crystalline structures aligned along a length with each
structure of a different composition, by the use of a
crystalline structure with a varied composition along its
face, and by combinations of these techniques. Crystalline
structures with different compositions and with different
planar spacing are shown in "A Handbook of Lattice Spacings
and Structures of Metals and Alloys" by W. B. Pearson,
Pergamon Press, London (1958 and 1967), Vol. I, pp. 286,
288 and 290, Vol. II, pp. 512 and 980. A crystalline
structure with a change in composition along its face may
formed by zone refining where the composition at one end is
enriched wi.th a second component ~hich is then distributed
along the length of the crystalline structure during the
zone refining process.
As illustrated in F'ig. 12a, a diffraction grating 200
is positioned perpendicular to a line 204 connecting the
point source 202 to the line image 203 and provides focusing
o the point source. Grating 200 includes surface 206 with
Eace 207 havin~ di~fraction spacing 208 extending along the
length 210 of face 207 with the spacing increasing in the
direction of line 204. The Bragg angles ~1 and ~2 are
identified by numbers 212 and 214. In the transmission mode,
the image 203 is on the opposite side of grating 200 while
in the reflection mode, the image 216 is on the same side.
As i.llustra-ted, it is not necessary that distance Dl equals
- 26 -
distance D2. The diffraction elements may be represented
by the open spaces 209 between the dark line segments
211 in the transmission mode or by the dark line segmen~s
211 in the reflection mode.
In Fig. 12b, grating 220 is positioned parallel to
line 224 connecting point source 222 and line image 223
and provides focusing of a monochromatic portion of the
point source. The Bragg angles ~1 and ~2 are represented
by numbers 226 and 22~. As illustrated, it is not necessary
that Xl equal X2. In the reflection mode, the diffraction
elements are represented by the dark line segments 221
separated by spacing 225.
In Fig. 13a, the diffraction grating 230 includes the
difEraction elements arranged in circles 232 with a common
axis 234 with the separations 235 between circles 232
representing the spacing between the elements in the trans-
mission mode. As illustrated, grating 230 may be used to
ocus the rays 237 of a point source 236 along two dimensions
form point image 238 from the transmission rnode and
~0 point lmage 239 in the re:Election mode.
In Fig. 1,3b, dlEfraction grating 240, similar to
~rat:Lng 230 in Fig. 13a, is used to focus parallel beam
242 to Eorm point image 244 in the transmission mode and
point image 246 in the reflection mode.
As illustrated in Fig. 14, diffraction grating 250 is
in a ring-like shape 252 formed by bending a flat s~ructure.
DifEraction elements 254 extend in circles 256 with a
common axis 258 with ring 252 to focus point source 260
to ~orrn point image 262.
- 27 ~ 3~
In Fig. 15, grating 270 is in the form of a hollo~,~
conical section 272 having a ~apered surface 274 to focus
parallel beam 276 to form point image 278 in the normal
reflection mode and point image 280 in t'ne backward
scattering reflection mode.
Diffraction gratings of the invention having spaced
diffraction elements with the separations increasing or
decreasing along a length, provide a useful means for
diffracting beams of energy, Since these gratings may be
easily manufactured and shaped in a variety of forms, the
resultant gratings provide a relatively low cost source
of lens and other diffraction system for focusing or other-
wlse directing beams of energy. Further, they provide a
means of sPlecting a monochromatic portion of a beam with
mixed waveleng~hs and diffracting the monochromatic portion
to form an image apart from other images.
