Radiant energy – Electrically neutral molecular or atomic beam devices and...
Reexamination Certificate
2001-09-27
2004-07-20
Meier, Stephen D. (Department: 2853)
Radiant energy
Electrically neutral molecular or atomic beam devices and...
C250S505100
Reexamination Certificate
active
06765197
ABSTRACT:
BACKGROUND—FIELD OF INVENTION
This invention relates to an apparatus that uses a plurality of one-dimensional, axisymmetric or two-dimensional lenses for the focusing, collection, imaging, and general manipulation of neutrons for medical, industrial and scientific applications.
Background—Compound Refractive Lenses for X-rays
In the literature the collection and focusing of x-rays and neutrons has been accomplished using multiple refractive lenses composed of cylindrical, spherical and parabolic lenses. 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
1
, has an overall focal length of f
1
/N (e.g. F. L. Pedrotti and L. Pedrotti, “Introduction to Optics,” Prentice Hall, Chapt. 3. p.60, 1987).
Also in the literature Toshihisa Tomie (U.S. Pat. No., 5,594,773) and A. Snigirev, V. Kohn, I. Snigireva and B. Lengeler, (“A compound refractive lens for focusing high-energy X-rays, Nature 384, 49 (1996)) 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 a concave-concave (bi-concave) lens at their closest juncture. N holes result in N unit lenses. For x rays as well as for neutrons, the index of refraction of the material is less than 1; thus, unlike visible light refraction optics, which will cause visible rays to diverge, the bi-concave lens performs in opposite fashion and focuses x-rays and neutrons instead.
Individual Unit Lenses for X-rays
M. A. Piestrup, J. T. Cremer, R. H. Pantell and H. R. Beguiristain (U.S. Pat. No. 6,269,145) have used an array of individual thin lenses without a common substrate but with a common optical axis to form a refractive x-ray lens. These individual unit lenses can be parabolic, spherical, cylindrical or Fresnel. The patent shows 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. It 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. Small random displacement off the average axis of a linear series of lens elements which form a compound refractive lens are shown by Piestrup et al. (U.S. Pat. No. 6,269,145) not to dramatically affect the focal spot size, focal length of the lens, and the lens aperture size. Separate 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>>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≈l), but the simple formula for the focal length must be modified.
In the literature a closely-spaced series of N bi-concave lenses each of focal length f
1
results in a focal length f of:
f
=
f
1
N
=
R
2
N
δ
.
(
1
)
The unit lens focal length f
1
is given by:
f
1
=
R
2
δ
,
(
2
)
where the complex refractive index of the unit lens material is expressed by:
n
=
1
-
δ
+
i
(
λ
4
π
)
μ
,
(
3
)
R is the radius of curvature of the lens, &lgr; is the neutron wavelength and &mgr; is the linear attenuation coefficient of in the lens material. For cylindrical lenses R=R
h
, the radius of the cylinder, for spherical lenses R=R
s
, the radius of the sphere; for the case of parabolic unit lenses R=R
p
, the radius of curvature at the vertex of the paraboloid.
The aperture of the lens array is limited. This is due to increased absorption at the edges of the lens as the lens shape may be approximated by a paraboloid of revolution that increases thickness in relation to the square of the distance from the lens axis. These effects make the compound refractive lens act like an iris as well as a lens. For a radius R =R
h
, R
s
, or R
p
, the absorption aperture radius r
a
is given by Tomie and Snigirev et al. to be:
r
a
=
(
2
R
μ
N
)
1
2
=
(
4
δ
f
μ
)
1
2
.
(
4
)
If the lenses refract with spherical surfaces, only the central region of the lens approximates the required paraboloid of revolution shape of an ideal lens. The parabolic aperture radius r
p
where there is a &pgr; phase change from the phase of an ideal paraboloid of revolution given by:
r
p
=
2
(
(
Nf
δ
)
2
λ
r
i
)
1
4
≈
2
(
(
N
δ
)
2
f
3
λ
)
1
4
(
5
)
where r
i
is the image distance and &lgr; is the X-ray wavelength. Rays outside this aperture do not focus at the same point as those inside. The approximation in (5) is true for a source placed at a distance much bigger than f. For imaging the effective aperture radius r
e
is the minimum of the absorption aperture radius, r
a
, and the parabolic aperture radius, r
p
, and the mechanical aperture radius r
h
=R
h
; that is:
r
e
=MIN
(
r
a
, r
p
, r
h
). (6)
As shown by Piestrup et al, the compound refractive lens made of spherical, parabolic and cylindrical unit lenses can tolerate a small random displacement of the individual lens elements off the average axis. This is shown in
FIG. 1
wherein unit bi-concave lenses
9
are aligned as carefully as possible, but, due to unavoidable error, each has a displacement of t
i
off the mean optical axis
8
of all the unit lenses. In order to keep an adequate aperture, the root mean square, &sgr;
t
, of the average displacement of the unit lenses off the average optical axis of the unit lenses should be less than the effective aperture radius of the individual lenses or:
&sgr;
t
<r
e
(7)
As shown by Piestrup et al. (U.S. Pat. No. 6,269,145), the aperture is reduced somewhat when there is random variation of the unit lenses off the average optical axis of the lenses.
Piestrup et al (U.S. Pat. No. 6,269,145) also showed that if a refractive Fresnel lens is utilized for x-rays, absorption can be minimized and a large aperture can be achieved. Indeed, the aperture radius of the lens can be the mechanical aperture radius, r
m
. However, because there must be phase addition of the x-rays between each Fresnel zone, the standard deviation of each unit Fresnel lens must not be larger than the width of the smallest zone that is s
m
−s
m−1
. Piestrup et al. (U.S. Pat. No. 6,269,145) shows that the requirement is &sgr;
t
≦(s
m
−s
m−1
)/4. This is a more stringent requirement than the ordinary spherical, parabolic or cylindrical lenses. To cover most applications for x-rays where the Fresnel lens would still practically work with minor loss, Piestrup et al. (U.S. Pat. No. 6,269,145) required that &sgr;
t
≦(s
m
−s
m−1
.
Background—Compound Refractive Lenses for Neutrons
R. Gähler, J. Kalus, and W. Mampe (
Phys. Rev. D
25, 2887, 1982) use a neutron compound lens system (two unit lenses) to measure the electric charge of neutrons. This same setup is used as a practical example of lenses in neutron optics by Varley F. Sears, (
Neutron Optics,
Ch. 3, p 73-74, Oxford University Press, 1989). This reference clearly states that the compound refractive lens focal length f
Beguiristain Hector R.
Pantell Richard H.
Piestrup Melvin A.
Adelphi Technology Inc.
Dudding Alfred E
Meier Stephen D.
Smith Joseph H.
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