Ellipticized lens providing balanced astigmatism
First Claim
1. An ellipticized singlet azimuth versus elevation optimized and aperture extremized nonspherical lens with surfaces S and S'"'"' specified by the partial differential equations ##EQU9## the symmetry conditions ##EQU10## and the boundary conditions
on the ellipse
space="preserve" listing-type="equation">Γ
;
(x.sup.2 /b.sub.o.sup.2 cos.sup.2 ψ
.sub.o)+(y.sup.2 /b.sub.o.sup.2)=1whereS and S'"'"' are the lens surfaces having functional representations of the forms z=z(x,y) and z'"'"'=z'"'"'(x'"'"',y'"'"') wherein x'"'"' and y'"'"' are themselves functions x'"'"'=x'"'"'(x,y) and y'"'"'=y'"'"'(x,y) of the independent variables x and y, ∂
z/∂
x and ∂
z/∂
y are the partial derivatives of z with respect to the independent variables x and y respectively, ##EQU11## are the Jacobian of z'"'"' and y'"'"' with respect to the independent variables x and y, the Jacobian of x'"'"' and y'"'"' with respect to the independent variables x and y and the Jacobian of x'"'"' and z'"'"' with respect to the independent variables x and y respectively, F(A), G(A), F'"'"'(A) and G'"'"'(A) are the functions of the arguments A=(x,y,z,x'"'"',y'"'"',z'"'"') defined as ##EQU12## and where p and p'"'"' denote the path length elements defined by the expressions
space="preserve" listing-type="equation">p.sup.2 =x.sup.2 +(y-y.sub.o).sup.2 +(z-z.sub.o).sup.2,p'"'"'.sup.2 =(x'"'"'-x).sup.2 +(y'"'"'-y).sup.2 +(z'"'"'-z).sup.2,and no, yo, zo and ψ
o are respectively, the index of refraction of the lens material, the y and z coordinates of the finite focal point F and the off-axis angle to the infinite focal point F.sub.∞
, Γ
is the ellipse bounding the lens formed by S and S'"'"' and is defined by the equation shown in which x and y are the independent variables and bo is the maximum radius of the lens formed by S and S'"'"' and the semi-major axis of the ellipse Γ
.
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Abstract
An ellipticized singlet azimuth versus elevation optimized and aperture eemized nonspherical lens antenna of very low or even minimal F-number providing balanced astigmatism for wide angle acoustic, microwave or optical applications is described. The lens has an elliptical periphery and surfaces defined by a system of nonlinear partial differential equations, the surfaces acting together to produce two perfect primary off-axis foci F and F'"'"' at a finite distance in back of the lens and two perfect conjugate off-axis foci F.sub.∞ and F'"'"'.sub.∞ in front of the lens at infinity; i.e., the lens simultaneously focuses energy from the primary foci F and F'"'"' into two off-axis parallel ray plane wave beams directed towards infinity at equal but opposite angles with respect to the lens axis. The lens may be built of various materials depending on its intended application in acoustics, microwaves or optics.
25 Citations
14 Claims
- 1. An ellipticized singlet azimuth versus elevation optimized and aperture extremized nonspherical lens with surfaces S and S'"'"' specified by the partial differential equations ##EQU9## the symmetry conditions ##EQU10## and the boundary conditions
- space="preserve" listing-type="equation">z(x,y)=z'"'"'(x,y)=0,
on the ellipse
space="preserve" listing-type="equation">Γ
;
(x.sup.2 /b.sub.o.sup.2 cos.sup.2 ψ
.sub.o)+(y.sup.2 /b.sub.o.sup.2)=1where S and S'"'"' are the lens surfaces having functional representations of the forms z=z(x,y) and z'"'"'=z'"'"'(x'"'"',y'"'"') wherein x'"'"' and y'"'"' are themselves functions x'"'"'=x'"'"'(x,y) and y'"'"'=y'"'"'(x,y) of the independent variables x and y, ∂
z/∂
x and ∂
z/∂
y are the partial derivatives of z with respect to the independent variables x and y respectively, ##EQU11## are the Jacobian of z'"'"' and y'"'"' with respect to the independent variables x and y, the Jacobian of x'"'"' and y'"'"' with respect to the independent variables x and y and the Jacobian of x'"'"' and z'"'"' with respect to the independent variables x and y respectively, F(A), G(A), F'"'"'(A) and G'"'"'(A) are the functions of the arguments A=(x,y,z,x'"'"',y'"'"',z'"'"') defined as ##EQU12## and where p and p'"'"' denote the path length elements defined by the expressions
space="preserve" listing-type="equation">p.sup.2 =x.sup.2 +(y-y.sub.o).sup.2 +(z-z.sub.o).sup.2,p'"'"'.sup.2 =(x'"'"'-x).sup.2 +(y'"'"'-y).sup.2 +(z'"'"'-z).sup.2,and no, yo, zo and ψ
o are respectively, the index of refraction of the lens material, the y and z coordinates of the finite focal point F and the off-axis angle to the infinite focal point F.sub.∞
, Γ
is the ellipse bounding the lens formed by S and S'"'"' and is defined by the equation shown in which x and y are the independent variables and bo is the maximum radius of the lens formed by S and S'"'"' and the semi-major axis of the ellipse Γ
.- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
Specification
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- Resources
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Current Assigneethe united states of america as represented by the secretary of the navy
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Original Assigneethe united states of america as represented by the secretary of the navy
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InventorsSternberg, Robert L.
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Primary Examiner(s)Lieberman, Eli
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Application NumberUS05/949,711Time in Patent Office714 DaysField of Search343/753, 343/754, 343/755, 343/909, 343/911 RUS Class Current343/911.00RCPC Class CodesG02B 3/04 with continuous faces that ...G10K 11/30 using refraction, e.g. acou...H01Q 15/08 formed of solid dielectric ...
