Patent Number: 062691457
Section: summary

BACKGROUND--FIELD OF INVENTION This invention relates to an apparatus that uses a plurality of thin lenses for the focusing, collection, collimation and general manipulation of x-rays for medical, industrial and scientific applications. BACKGROUND--DESCRIPTION OF PRIOR ART In the prior art the collection and focusing of x-rays has long been difficult to accomplish because x-ray reflection and refraction is limited to very small angles. Most x-ray optics use small-grazing-angle reflective surfaces that are limited to soft to moderate x-ray energies. Until recently, x-ray refractive lenses that are similar to ordinary visible-light refractive lenses, which collect, bend and focus visible photons, have not been considered to be feasible. Refraction of x-rays is difficult because the refractive index of all materials is slightly less than 1, (i.e. (n-1)&lt;0 and .vertline.n-1.vertline.&lt;&lt;1) with the possible exception for photon energies near the photo-absorption shell edges of the lens substrate material, where n can be larger than 1. Recently, renewed interest has been given to refractive x-ray lenses due to an important, but simple, idea as theorized by Toshihisa Tomie (U.S. Pat. No., 5,594,773) and demonstrated by A. Snigirev, V. Kohn, I. Snigireva and B. Lengeler, ("A compound refractive lens for focusing high-energy X-rays, Nature 384, 49 (1996)). It has long been known for optics in the visible spectrum that a series of N closely spaced lenses, each having a focal length of f.sub.1, has an overall focal length of f.sub.1 /N (e.g. F. L. Pedrotti and L. Pedrotti, "Introduction to Optics," Prentice Hall, Chapt. 3. p.60, 1987). Recently, Tomie and Snigirev et al. have shown that this can also be done in the x-ray region of the spectrum using a series of holes drilled in a common substrate that effectively mimics a linear series of lenses. This "compound refractive x-ray lens" (CRL) is manufactured using N number of unit lenses, each constituted by a series of hollow cylinders or holes that are embedded inside a material capable of transmitting x-rays. Two closely spaced holes form what appears to be a concave-concave (bi-concave) lens at their closest juncture. N holes result in N unit lenses. For x rays, the index of refraction of the material is less than 1; thus, unlike optical refraction optics, which will cause visible rays to diverge, the bi-concave lens performs in opposite fashion and focuses x-ray photon energies instead. This embodiment of the prior art of Tomie and Snigirev et al. is shown in FIG. 1A and FIG. 1B. A unit x-ray lens, shown in a top view in FIG. 1A, is made of a hollow cylinder 2 of radius R.sub.h has a focal distance, f.sub.1, represented by: ##EQU1## where R.sub.h is the radius of the hole and the complex refractive index of material is expressed by EQU n=1-.delta.-i.beta. (2) As shown in FIG. 1A, a single hollow cylinder 2 represents two plano-concave lenses, 4. Closely spacing a series of these holes as shown in FIG. 1B results in a focal length of: ##EQU2## A series of hollow cylinders 2 approximates a series of bi-concave cylindrical lenses 6. Comparing eqn. (1) and (3), the focal length, f, for the series of lenses is reduced by 1/N from that of a single lens. Thus, a single lens made of a hole in A1 with radius R=100 .mu.m, will have a focal length of 10 meters at 30 keV, whereas, a compound refractive lens composed of 100 holes will give a 0.1 meter focal length. This is a dramatic reduction in focal length, making such a refractive lens useful. As stated previously, utilizing multiple lenses to reduce the focal length in other parts of the electromagnetic spectrum has been well know for years and is in a standard textbook for optics (Pedrotti and Pedrotti). The Tomie patent teaches particular fabrication techniques utilizing a single material substrate with holes or spheres for all the lens elements. In the prior art of Tomie, obtaining good focusing characteristics for a series of N lenses required that the machining of the holes be "conducted at a high precision capable of keeping the geometric error within a small fraction of the value obtained by dividing the wavelength of the x rays to be focused by .delta. of the lens material (=.lambda./.delta.)." Tomie suggests that arranging larger numbers of lenses in a cascading series of N individual unit lenses (not a single substrate for all lenses) stacked as shown in FIG. 2 would work to reduce the focal distance f by f/N: however, "In this configuration . . . many unit X-ray lenses have to be arranged after fabricating the individual unit X-ray lenses. The thickness of each unit x-ray lens has to be very thin to avoid strong absorption of X-rays, making each unit X-ray lens very fragile and difficult to handle. Moreover, aligning the optical axis of all units along the X-ray lens axis with high precision would be extremely difficult. Hence, arranging many X-ray lenses in the configuration shown in FIG. 1" (in the present patent: also FIG. 2) "is practically impossible." (our underline, Tomie, U.S. Pat. No. 5,594,773, coll. 4, lines 19-28). Note in FIG. 2, the thin lenses are in contact, which presents difficulties in both support and alignment. Indeed, there is no alignment or support structure shown. To solve this problem, Tomie utilizes a single common substrate with accurately machined holes or embedded spheres which act as quasi-lenses. He teaches that thin unit lenses that do not have such a common substrate cannot be utilized for CRLs since they would be difficult to stack and align (Their thinness and fragility prevent them from being stacked and aligned). The required thicknesses of between 1 to 100 microns make them difficult to stack without damage and difficult to align. In the prior art, accuracy of the lenses' dimensions, alignment and spacing is achieved by utilizing a single substrate material with holes drilled by conventional means such as computer-driven machine drilling or laser drilling. Such drilling methods make it difficult to achieve lens thicknesses (e.g. spacing between holes, .DELTA., as shown in FIG. 1B) of less than 25 microns, i.e. such spacing limits the minimum thickness of each individual lens component to 25 microns. Conventional machine drilling methods for hole spacing less than this will result in the drill breaking through the wall between holes. Conventional laser drilling techniques will result in tapered walls. Wall thicknesses of 25 microns or larger result in large absorption of x rays in a compound refractive lens of even a few single elements for x-ray energies below 4 keV. As stated by P. Elleaume, the Tomie lens design's "drawbacks are their limitation to high photon energies above 4 keV due to absorption, their strong chromatic aberrations and low aperture." (P. Elleaume, "Two-Plane Focusing of 30 keV Undulator Radiation with a Refractive Lens." pp. 33-35 in Research & Development, ESRF). Tomie also pointed out that rather than cylindrical or spherical shapes, a material having a concave shape of a paraboloid of revolution is theoretically ideal as an x-ray lens. As stated in the above quote from Elleaume, it is well known that cylindrical and spherical surfaces will give strong chromatic and spherical aberrations. An ideal surface would be parabolic in shape. Such a shape is impossible to obtain using conventional machine drill techniques. In the prior art, only machine drill techniques have been utilized to achieve the Tomie design. (P. Elleaume, and Snigirev et al. papers cited above). He also points out in his invention that the extent to which the focal length can be shortened by reducing the radius of the cylinder or sphere has limits due to fabrication techniques, and absorption in the lens material. Hence, "the focal length f remains quite long even after maximum practical reduction." Another problem with the simple Tomie configuration, as stated by P. Elleaume in the above quote, is that that the aperture of the lens array is limited. Snigirev has shown that the holes only approximate a lens. This is due to absorption at the edges of the lens and the fact that the lens shape is not parabolic. These effects make the compound refractive lens act like an iris as well as a lens. To first approximation, the radius of the aperture of the lens is the radius of the hole, R.sub.h. However, absorption suppresses the contribution of the outer part of the lens; thus the absorption aperture radius r.sub.a is given by: ##EQU3## where .mu. is the linear absorption coefficient of the lens material. If absorption is neglected, only the central part of the cylindrical hole approximates the required parabolic shape of an ideal lens. The parabolic aperture radius r.sub.p given by Snigirev to be: ##EQU4## where r.sub.i is the image distance and .lambda. is the x-ray wavelength. Rays outside this aperture do not focus at the same point as those inside. The second equation is approximately true if r.sub.o &gt;&gt;f. This is usually an accurate approximation for synchrotron sources where the distance to the source, r.sub.o, is quite large. The effective aperture radius r.sub.e is the minimum of the absorption aperture radius, r.sub.a, and the parabolic aperture radius, r.sub.p, and the hole aperture radius r.sub.h =R.sub.h ; that is: EQU r.sub.e =MIN(r.sub.a,r.sub.p,r.sub.h). (6) In the prior art of Snigirev, in which cylindrical lenses have been fabricated and tested, the aperture is limited to less than 200 .mu.m. (Snigirev et al. above). In the prior art very low Z materials were suggested to be best for hole lenses. Be metal was suggested by Yang (B. X. Yang "Fresnel and refractive lenses for X-rays", Nuclear Instruments and Methods in Physical Research A328 pp. 578-587 (1993)) to be the best material for making lenses. Yang's paper states that the best material possesses a large .delta./.beta., where .beta. and .delta. are the factors in the complex dielectric constant as given by eqn. 2. This is roughly a measure of how much the material can bend x-rays over the amount of absorption. Since Be gives the largest .delta./.beta., it was deemed the best lens material. Unfortunately, Be is extremely difficult to utilize since it is expensive and difficult to machine, being extremely toxic if airborne during the machining process. Machining for individual Fresnel refractive lenses would also be expensive since each lens of the linear array must be individually micromachined and not easily mass-produced. For very large photon energies (e.g. E&gt;30 keV), the use of low density low Z materials such as Be for the manufacture of lenses becomes difficult because of the large number of lenses required for each compound refractive lens. The number of individual lenses required for such designs increases to the point where the CRL would become too long and its aspect ratio (total CRL length to aperture diameter) becomes very large. Designs for Be lenses in the 30 keV to 100 keV range show that the number of lenses would be greater than 1000 for focal lengths of less than 1 meter. Another problem with the use of the Tomie/Snigirev CRL is that the focal length f varies dramatically with changes in x-ray photon energy (The focal length f varies as the square of the x-ray photon energy). Since the focal length f varies as equation (3) and .delta.=v.sup.2.sub.m /2v.sup.2 where v is the photon energy in keV, the focal length f varies roughly as f=Rv.sup.2 /Nv.sup.2.sub.m, where v.sub.m is plasma frequency of the lens material. Thus, the focal length f varies as the square of the photon energy. This is not ideal for many applications where one would like the focal length to be constant for a large range of x-ray photon energies. Thus there is need for a system of compound refractive lenses that is achromatic, which is not supplied by the prior art. In the prior art of B. X. Yang "Fresnel and refractive lenses for X-rays", Nuclear Instruments and Methods in Physical Research A328 pp. 578-587 (1993), it was proposed that single Fresnel lenses in both cylindrical and spherical form were superior focusing elements for hard x-rays. Both their design and fabrication were discussed for both x-ray Fresnel zone plates and refractive Fresnel lenses. Yang suggests that only single lenses were to be used. Thus issues such as multiple lens alignment to achieve focusing, as in the art of Tomie, were not addressed. In the prior art, it has been suggested that other shapes such as Fresnel, parabolic and spherical can be used (e.g. Robert K. Smithers, Ali M. Khounsary, and Shenglan Xu, "Potential of a Beryllium X-ray Lens, SPIE vol. 3151, p. 150, 1997). However, all have suggested that a common substrate or spit substrate (two-halves) be used. Machining difficult surfaces such as Fresnel lens in a periodic array into one substrate would be difficult. Tomie in his above cited patent has shown how to fabricate spheres in a split medium (two-halves) to from a CRL lens of many unit lenses capable of focusing in two dimensions. In the prior art of Tomie and Snigirev, complex optical systems such as telescopes or microscopes are difficult to construct because of the unwieldy geometry of the hole and sphere designs. In addition, these lenses have other drawbacks that limit their use in complex systems. These drawbacks are small aperture size, large x-ray absorption and spherical aberration. Furthermore, optical systems of more than one element must minimize x-ray absorption in the individual elements. In the prior art, it is difficult to achieve two-dimensional (2-D) focusing because of the difficulty of machining spheres into a single substrate. One solutions was utilized by A. Snigirev, B. Filseth, P. Elleaume, Th. Klocke, V. Kohn, B. Lengeler, I. Snigireva, A. Souvorov, J. Tummler ("Refractive lenses for high energy X-ray focusing" SPIE vol. 3151, p. 164, 1997) in which they used two CRLs whose cylindrical axes where crossed. As in optics two crossed cylindrical lenses will focus in two dimensions. This gives added absorption since two CRLs must be used. Advanced structures such as Fresnel lens surfaces can not be easily machined. Objects and Advantages The preferred embodiment of the present invention provides for an array of individual thin lenses without a common substrate but with a common optical axis. The present invention provides for a means of supporting and aligning of very thin unit lenses with accuracy adequate for x-ray collecting, focusing and imaging. The present invention teaches that small random displacements of the individual lenses off a common axis will not invariably lead to the lens array failure to collect and focus x-rays. The present invention shows that the prior teachings of Tomie are incorrect concerning the difficulty of achieving collection and focusing from a linear series of individually separate refractive lenses which are slightly displaced from one another. The embodiments of the present invention provide for the adequate support of the individual unit lenses using several techniques of lens support, thus permitting the use of very thin lenses and reducing x-ray absorption. In the present invention a small random displacement off the average axis of a linear series of lens elements which form a compound refractive lens is shown not to dramatically affect the focal spot size, focal length of the lens, and the lens aperture size. We take up these issues in the Description section. In the present invention, separate ultra-thin lenses are possible since the lenses need not be exactly in contact. This allows the unit lenses to be individually supported by structures that are thicker than the thin lenses, such as a rigid-ring structure. The unit lenses are then separated by a gap that is equal to that of the thickness of the support structure. The addition of the gap does not affect the collection and focusing of the x-rays as long as we can assume the thin lens formula assumption is still correct (f&gt;&gt;l), where l is the length of the CRL including the gaps between the unit lenses and f is the focal length of the CRL. The lens will still work if the CRL is thick (f.apprxeq.l), but the simple formula for the focal length must be modified. The rigid support structure is also used to aid in the alignment. A support and alignment structure is shown in FIGS. 3A and 3B. FIG. 3A shows an exploded view of one embodiment in which thin Fresnel lens 42 are supported by support disks 20 and aligned by means of alignment rods 40 (e.g. dowel pins) with a support base 50. As will be discussed and shown in FIGS. 13 and 14, the support structure is used to align the unit lenses either by pins or by a ring. The thin unit lenses must be aligned relative to the support structure alignment means, which in the case of the rings could be the outside diameter of the ring; i.e. this means that the unit lens should be concentric with the ring structure. When unit lenses are aligned using pins or screws, holes are placed in the support structure to align the lenses with the pins or screws or both. This is shown in FIG. 14. Unit lenses manufactured using compression molding techniques, where both the lens and the support structure are of the same material, are extremely uniform in their overall dimensionality and lend themselves to easy alignment using the techniques of FIGS. 13 and 14. The present invention permits unit lenses to be individually constructed using mass production techniques (e.g. compression and injection molding). Fabrication of individual lenses before assembly into compound structures is advantageous in that it permits unusual lens shapes such as parabolic or Fresnel surfaces to be utilized. These lenses will have the benefit of larger apertures over those of unit lenses composed of holes or spheres. As we will show, unit lenses of parabolic and Fresnel shapes can be used because small random displacements off the average axis will not appreciably affect the ability of a linear series of unit refractive Fresnel lenses of common average axis to collect and focus x-rays. In one embodiment, low-density plastics, such as polyethylene, are used as the lens substrate material. Lenses made of plastics are not as refractive or as transparent as Be; however, they are easier to safely mass produce into Fresnel and parabolic shapes. Current methods of fabricating optical (visible and infrared frequency range) Fresnel lenses are used in some embodiments of the present invention to manufacture unit x-ray Fresnel lenses for compound refractive lenses. There are mass production techniques of injection and compression molding that permit the inexpensive fabrication of Fresnel lenses. These techniques were developed for optical (visible and IR radiation) Fresnel lenses, and, as will be demonstrated, can be used for x-ray compound refractive lenses without undue requirements for accuracy of the lenses' surface features and their alignment relative to one another. The fabrication of individual lenses permits the construction of lenses that produce diverging x-rays (convex-convex lenses, plano-convex lenses). This permits the construction of lens systems that are similar to optical systems of lenses. For example, devices such as x-ray microscopes and telescopes can be manufactured using converging and diverging lenses. The manufacturing techniques of present invention permit the fabrication of much thinner lenses than those of the prior art of Snigeriv and Tomie. The ability to make individual lenses before stacking them permits a variety of fabrication techniques that result in thinner lenses. We have fabricated and tested CRLs composed of unit lenses whose maximum thickness was 19 .mu.m and whose minimum thickness was 5 .mu.m. Thinner thicknesses are possible. Thinner lenses permit reduced x-ray absorption and, thus, permit the use of systems of compound refractive lens systems to achieve a variety of devices that now exist only in the visible spectrum. Since .delta. is decreasing with increasing photon energy, designs for lenses that focus harder x-rays requires larger numbers of lenses. Thinner lenses permit the focusing of harder x-rays, since the number of lenses can be increased without undue absorption. Thinner lenses permit the use of more than one compound refractive lens for the construction of achromatic lens systems, x-ray microscopes and telescopes. In the present invention CRLs are designed for the hard x-ray region (10 keV to 100 keV) using high-density materials. CRLs are fabricated out of high Z materials so that the number of individual lenses that compose the CRL can be kept to a small enough number. Thus, the lens does not become too long or the aspect ratio too large such that the lens is difficult to align in the x-ray beam (or too expensive to manufacture). In the new art, lenses are designed to operate just below the K- or L-edge photon energy of the material from which the lenses is fabricated. The photon-energy region below the K- or L-shell absorption edge is more transparent to x-rays with energies just above the absorption edges, thus making the material a bandpass structure for the x-rays below the edge. Designing the lenses to operate at photon energies below the edge results in CRLs that are more transparent to the x-rays and have higher gains than those designed elsewhere. Such designs also help in utilizing higher Z-materials for the lenses, resulting in the benefits of a lower number of individual lenses for the CRL, and minimizing the overall length of the CRL and its aspect ratio. In summary, since the compound refractive lens can tolerate a small random displacement of the individual lens elements off the average axis, the individual lens elements can be manufactured in the new art as independent units rather than fabricated out of one substrate material. The individual units can then be supported by simple alignment means, permitting the lenses to be thinner than those of the prior art. This reduces the total x-ray absorption for the compound refractive lens, which in turn permits the utilization of more individual lens elements and, hence, reduces the focal length of the compound refractive lens (since f.infin.1/N, see eqn. (3)). The advantages of the present invention are: A reduced criterion for unit lens axis alignment. This permits the use of easily fabricated alignment and support structures for the unit lenses. Individual lens elements to be fabricated as separate units before final assembly in a compound refractive lens. The fabrication of unit lenses which are thinner (than those manufactured using the single substrate compound lens with holes or spheres), thereby reducing absorption of the x-rays in the lens materials and increasing the frequency range of use. The fabrication of both concave and convex lenses (convergent and divergent lenses). The fabrication of more optimal lens surface shapes such as parabolic and Fresnel surfaces. Manufacturing and fabrication techniques developed for lenses in optical (visible) region of the spectrum can be used. Manufacturing of unit lenses can be performed by existing machine shop techniques, injection-molding techniques, compression-molding techniques and lithographic techniques. The use of a greater variety of materials including plastics and higher Z-materials. The fabrication of compound refractive lens systems that include, for example, achromatic x-ray lens systems, x-ray telescopes and x-ray microscopes. The fabrication of lenses that can operate in the very hard x-ray region of the spectrum with lengths and aspect ratios that are not too large for lens alignment nor deleterious to the cost of fabrication.