WO1992010769A1

WO1992010769A1 - Gradient index lenses with at least one aspherical surface

Info

Publication number: WO1992010769A1
Application number: PCT/US1991/009051
Authority: WO
Inventors: David P. Hamblen
Original assignee: Eastman Kodak Company
Priority date: 1990-12-14
Filing date: 1991-12-06
Publication date: 1992-06-25

Abstract

The present invention is directed to a lens with an optical element (20) formed of a radiant energy transmitting material with a graded index of refraction having a predetermined profile which extends radially from a longitudinal axis (23) of the lens (20). A first surface (24) and an opposing second surface (26) of the optical element (20) extend radially outwards from the longitudinal axis (23) of the lens (20), and one of the first and second surfaces (24, 26) is aspherical. This optical element (20) can be combined coaxially with a second optical element to form a doublet lens. The second optical element is formed of a radiant energy transmitting material with or without a graded index, and when the graded index is included the second element has a gradient profile which is an inverse of the gradient profile of the first optical element (20). The second element has a first predetermined shaped surface arranged for rays of radiant energy from a remote source to be incident thereon, and an opposing second predetermined shaped surface. Each of the first and second surfaces extend radially outwards from a longitudinal axis of the lens.

Description

GRADIENT INDEX LENSES WITH AT

LEAST ONE ASPHERICAL SURFACE

Field of the invention

The present invention relates to gradient index lenses and, more particularly, to singlet and doublet gradient index lenses.

Background of the invention

Optical elements or lenses are being used in varied devices which, more recently, include video disks, compact disks, and optomagnetic recording apparatus or the like. Objective lenses for, for example, a compact disk (CD) system have stringent requirements since they must be made with tolerances close to the diffraction limit and large numerical apertures. In other words, the lenses must focus a laser beam onto an optical disk with a spot size of less than one micrometer in diameter. Until

recently, the above-mentioned CD objective lenses were homogeneous triplets whose small diameter and precision centering/mounting requirements provided a major cost to a total imaging system of the CD system. However, singlet lenses were recently designed to replace the costly homogeneous triplets. The singlet and doublet lenses designed for CD use are generally thick lenses with a short focal length.

U. S. Patent No. 4,643,535 (H. Ichikawa et al.), which issued on February 17, 1989, describes an optical singlet information/reproduction element which focuses and projects a substantially collimated light beam onto an optical information recording medium. The optical element has a transparent columnar body having a convex spherical surface as an input (light incident) surface, and a flat surface as an output (light emergent) surface. The columnar body is formed of a material having a refractive index distribution which decreases from a central axis towards an outer periphery of the optical element.

U. S. Patent.No. 4,457,590 (D. T. Moore), which issued on July 3, 1984, describes spherical gradient index lens designs wherein third-order and higher-order spherical aberrations are allegedly adjusted substantially to zero without the need for sixth-order refractive index profile control. The lenses of the design family are spherical singlet lenses having first and second refracting surfaces with separate spherical curvatures, and a graded radial refractive index profile according to a particular power series expansion formula.

U. S. Patent No. 4,647,159 (T. Baba), which issued on March 3, 1987, describes a gradient index singlet lens having a planar end on a light beam incident side and a convex surface on a light beam emergent side (plano-convex). The Baba patent suggests that "correction of spherical aberration is accomplished by the coefficients _N2, N₃,... of gradient index but a similar effect may also be obtained by introducing a non-spherical surface into the second surface." The use of a non-spherical surface, however, is not further explained as to the conditions required within the lens (e.g., if a gradient index is used or not).

U. S. Patent No. 4,639,094 (Y. Kawasaki), issued on January 27, 1987, describes a doublet gradient index lens system comprising a first and a second gradient index lens. The first and second lenses have flat end surfaces and are disposed in series along a longitudinal axis of the lens system, and each of the lenses have flat input and output surfaces. The first and second lenses are either cemented together or disposed with a predetermined air space therebetween. Additionally, each lens has a gradient index which is different from the gradient index of the other lens.

Centering of the gradient with the spherical lens axis is at times a problem and limits Optical Path Difference (OPD) of rays of a radiant energy and introduces some coma. Use of a spin (centrifugal) molding method as disclosed in U. S. Patent No.

4,022,855 (D. P. Hamblen), which issued on May 10, 1977, centers the radial gradient with the optical axis of the spherical lens. Single-element and double element lenses, with at least one spherical surface and a graded index still have some inherent aberrations. It is, therefore, desired to see how close one can approach a diffraction limited singlet or doublet lens.

Summary of the Invention

The present invention is directed to gradient index lenses with at least one aspherical surface. More particularly, the invention is

directed to a lens comprising an optical element formed of a radiant energy transmitting material and having a first surface and an opposing second

surface. Each of the first and second opposing surfaces extend radially outwards from a longitudinal axis of the lens, and one of the first and second surfaces is aspherical. The radiant energy

transmitting material has a graded index of

refraction having a predetermined profile which extends radially from the longitudinal axis of the lens.

It is an aspect of the present invention that the above-defined optical element can be a singlet lens or an element in a multiple-element lens. More particularly, for a dual element lens, the lens comprises a first optical element and a second optical element, each formed of a radiant energy transmitting material. The first optical element comprises a first predetermined shaped surface arranged for rays of radiant energy from a remote source to be incident thereon, and an opposing second predetermined shaped surface. Each of the first and second surfaces of the first optical element extend radially outwards from a longitudinal axis of the lens. The radiant energy transmitting material of the second optical element has a graded index of refraction with a predetermined profile which extends radially from the longitudinal axis of the lens. The second optical element comprises a first predetermined shaped surface disposed adjacent the second surface of the first optical element, and an opposing second aspherical surface, each of the first and second surfaces of the second optical element extending radially outwards from the

longitudinal axis of the lens.

The invention will be better understood from the following more detailed description and the accompanying drawings and claims.

Brief Description of the Drawings

FIG. 1 is a side sectional view of a front asphere-plano gradient index singlet lens in

accordance with the present invention which is placed in front of a compact disk;

FIG. 2 is a plot of an exemplary graded refractive index profile for the lens of FIG. 1;

FIG. 3 is a plot of ray intercept

performance for the lens of FIG. 1 having the graded index profile of FIG. 2; FIG. 4 is a plot of astigmatism performance for the lens of FIG. 1 with the graded index profile of FIG. 2;

FIG. 5 is a plot of modulation transfer function performance for the lens of FIG. 1 with the graded index profile of FIG. 2;

FIG. 6 is a plot of distortion performance for the lens of FIG. 1 with the graded index profile of FIG. 2;

FIG. 7 is a side sectional view of a asphere-asphere gradient index singlet lens in accordance with the present invention;

FIG. 8 is a plot of an exemplary graded refractive index profile for the lens of FIG. 7;

FIG. 9 is a plot of ray intercept

performance for the lens of FIG. 7 having the graded index profile of FIG. 8;

FIG. 10 is a plot of astigmatism performance for the lens of FIG. 7 with the graded index profile of FIG. 8;

FIG. 11 is a plot of modulation transfer function performance for the lens of FIG. 7 with the graded index profile of FIG. 8;

FIG. 12 is a plot of distortion performance for the lens of FIG. 7 with the graded index profile of FIG. 8;

FIG. 13 is a side sectional view of a asphere-asphere gradient index doublet lens in accordance with the present invention;

FIG. 14 is a plot of an exemplary graded refractive index profile for a first element of the doublet lens of FIG. 13;

FIG. 15 is a plot of an exemplary graded refractive index profile for a second element of the doublet lens of FIG. 13; FIG. 16 is a plot of ray intercept

performance for the doublet lens of FIG. 13 having the graded index profiles of FIGS. 14 and 15;

FIG. 17 is a plot of astigmatism performance for the doublet lens of FIG. 13 with the graded index profiles of FIGS. 14 and 15;

FIG. 18 is a plot of modulation transfer function performance for the doublet lens of FIG. 13 with the graded index profiles of FIGS. 14 and 15;

FIG. 19 is a plot of distortion performance for the doublet lens of FIG. 13 with the graded index profiles of FIGS. 14 and 15;

FIG. 20 is a side sectional view of a asphere/asphere, homogeneous/gradient index, doublet lens in accordance with the present invention;

FIG. 21 is a plot of an exemplary graded refractive index profile for a second element of the doublet lens of FIG. 20;

FIG. 22 is a plot of ray intercept performance for the lens of FIG. 20 having the graded index profile of FIG. 21;

FIG. 23 is a plot of astigmatism performance for the lens of FIG. 20 with the graded index profile of FIG. 21;

FIG. 24 is a plot of modulation transfer function performance for the lens of FIG. 20 with the graded index profile of FIG. 20;

FIG. 25 is a plot of distortion performance for the lens of FIG. 20 with the graded index profile of FIG. 21;

FIG. 26 is a side sectional view of a front plano-asphere doublet lens in accordance with the present invention with the asphere element having a gradient index; FIG. 27 is a side sectional view of a front plano-asphere doublet lens in accordance with the present invention where both elements have a gradient index;

FIG. 28 is a side sectional view of the front piano-asphere gradient index doublet lens of FIG. 27 in accordance with the present invention where the two elements are spaced-apart;

FIG. 29 is a side sectional view of a asphere-asphere gradient index doublet lens in accordance with the present invention where the first element is concave-concave and is spaced-apart from the second concave-convex element; and

FIG. 30 is a view in perspective of an exemplary plane-anamorphic gradient index singlet lens in accordance with the present invention;

The drawings are not necessarily to scale, and corresponding elements in the various figures have the same reference designations.

Detailed Description

It has been found that in optical elements (lenses) the use of a graded index with a spherical surface makes the spherical surface appear aspherical with respect to ray bending. In accordance with the present invention, advantages are achieved in lenses by combining aspherical surfaces with a graded refractive index (GRIN). More particularly, better correction of inherent aberrations of single-element lenses (singlets), or two-element lenses (doublets), is gained over prior art GRIN lenses which use a spherical surface. This is especially true when an aspheric surface is combined with a

parabolically-shaped index gradient profile in the lenses in accordance with the present invention.

These gradient/aspherical lens designs reduce the usually required large index of refraction difference (δN) for a short focal length lens over the

refractive index difference necessary for most prior art gradient/spherical lenses. With a reduced δN value, fabrication of a lens presents fewer

requirements on depositing large refractive index gradients in the various optical element designs.

Referring now to FIG. 1, there is shown a sectional view of an asphere/plano GRIN singlet lens 20 in accordance with the present invention which is positioned in front of a section of a Compact Disk (CD) 22. CD 22 could be any other suitable optical device. The lens 20 has a predetermined radius R₂ and is formed of a light transmitting material (e.g., glass, plastic) with a predetermined gradient index (δN) profile in a radial direction from a

longitudinal axis 23 of the lens 20. The lens 20 comprises a front (first) aspheric surface 24, and a cylindrical section extending back from the aspheric surface 24 which ends in a rear (second) planar light emergent surface 26. The front and rear surfaces 24 and 26, respectively, extend radially out from the axis 23. Rays 25 of a radiant energy (light) from a remote laser (not shown) are shown incident on surface 24 and pass through lens 20 and emerge from surface 26 and then are incident on CD 22. The compact disk comprises a front surface 28 on which rays 25 of light which have been refracted and focused by the lens 20 are incident, and a rear surface 29 onto which the rays 25 from lens 20 are focused.

It is known that the refractive index distribution of a gradient index medium, wherein the gradient index is radial (i.e., varies with distance from an optical axis through the medium), can be defined by a power series expansion in radius "r" in accordance with the equation N(r) = N₀ + N₁r² + N₂r⁴... .(1)

An exemplary lens 20 formed in accordance with the

present invention has the parameters shown in Table I wherein the dimensions are in millimeters unless

otherwise indicated; Sur = the surface (denoted by

its designation) in FIG. 1; R = the radius of the

surface; Th = is the thickness; and K = the conic

constant.

TABLE I

Sur R Th K N₀ N₁ N₂

24 2.743003 3.500 -1.283329 1.580 0.000485 -0.001885

26 Infinity 1.800 Air

28 Infinity 1.200(Plastic cover)1.570

29 Infinity Optical Disk

For a Lens 20 having an aperture = 4.5 mm.

δN = -0.04586

Effective Focal Length (EFL) = 4.46 mm

Numerical Aperture (NA) = 0.50

f number = f/0.89

Strehl Ratio = 0.975

Airy Radius = 0.718 micrometer

Working Distance (WD) = 1.8 mm between surfaces 26 & 28 Referring now to FIG. 2, there is shown a plot of a graded refractive index profile for the singlet lens 20 of FIG. 1. It is to be noted that the gradient profile is unusual in that it is flat for approximately half-way from the optical axis 23 out towards a periphery 30 of the lens 20. After the flat profile area, the gradient profile then assumes a parabolic contour for the

remaining distance to the periphery 30. The aspherical surface 24 helps correct spherical aberration, as is well known, allowing the gradient to handle off-axis

aberrations, i.e., coma, astigmatism, and distortion.

Therefore, the lens 20 in accordance with the present invention corrects for the various aberrations and is a new state-of-the-art lens design. Referring now to FIGS. 3, 4, 5, and 6, there are shown various aberration performance diagrams (plots) for the exemplary lens 20 having the

parameters indicated in Table I and the graded index shown in FIG. 2. These plots are self-explanatory to those skilled in the art, and are provided to show the ability of the lens 20 to provide a high degree of aberration correction. FIG. 3 shows an x-y plot of the Ray Intercept performance for the exemplary lens 20. This plot is interpreted as having minimal spherical aberrations and coma. The y-axis (from +0.005mm to -0.005mm) represents the height where the ray 25 is incident on an image plane (the surface 29). FIG. 4 shows a plot of normalized Astigmatism for the exemplary lens 20 where "S" represents the plot for the Sagittal rays and "T" represents the plot for the Tangential rays. The y-axis is shown for values of 0 to +1, representing pupil height in an image plane (e.g., surface 29). FIG. 5 shows a plot of the Modulation Transfer Function for the exemplary lens 20. In FIG. 5, the upper curve 34 (indicated by dotted measurement points) is the diffraction limit which is the best results

obtainable, while the lower curve 36 is the results obtained with the exemplary lens 20. FIG. 6 is a plot of normalized distortion for the exemplary lens 20 and shows that there is essentially no resulting distortion. It is to be understood that a piano (flat) rear surface 26 of lens 20 is preferred since the lens 20 must be actively focused. That is, the working distance 1.80 mm shown in Table I is

maintained between the lens 20 and the CD 22 to continuously adjust the optical focus during a

read/write operation on CD 22. Referring now to FIG. 7, there is shown a sectional view of an asphere/asphere (double asphere) GRIN singlet lens 40 in accordance with the present invention. The lens 40 has a predetermined radius R₂ and is formed of a light transmitting material (e.g., glass, plastic) with a predetermined gradient index (δN) profile in a radial direction from a longitudinal axis 42 of the lens 40. The lens 40 comprises a front (first) aspheric surface 44 on which rays 45 of a radiant energy (light) from a remote source (not shown) are incident, and a

cylindrical section extending back from the aspheric surface 44 which ends in a rear (second) aspheric light emergent surface 46. The front and rear surfaces 44 and 46, respectively, extend radially out from the axis 42. The rays 45 of light, after having been refracted and focused by the lens 40, are incident on a plane 48 which can be the surface of, for example, a compact disk or any other optical element .

Referring now to FIG. 8, there is shown an exemplary curve 50 of the gradient index of

refraction N along the radius R₂ on the y-axis versus increasing radii equal to Rι/R₂ on the

x-axis for the lens 40 of FIG. 7. The exemplary curve 50 for lens 40 is produced in the same manner used for producing the curve 32 of FIG. 2 for the lens 20 of FIG. 1, and R₁ and R₂ represent

similar radii measurements. The curve 50 has a profile indicating a refractive index which decreases parabolically to an outside periphery 52 of the lens 40. It is to be understood, however, that the curve 50 can have any suitable profile. An exemplary lens 40 formed in accordance with the present invention has the parameters shown in Table II wherein the dimensions are in millimeters unless otherwise indicated, and the "Sur", "R", "Th" and "K" headings correspond to the headings of Table I.

TABLE II

Sur R Th K N₀ N₁ N₂ 4430.584615 5.50 -9.620335 .1.560 -0.001043 -3.66355E-06 46 -30.584615 0.1529 6.444224

For a Lens 40 where: aperture=8.90 mm aud diameter=9.88 mm.

δN = -0.02769

EFL = 29.64 mm

NA = 0.15

f number = f/3.0

Strehl Ratio = 0.988

Airy Radius = 1.11 micrometers

Referring now to FIGS. 9, 10, 11, and 12, there are shown various aberration performance

diagrams (plots) for the exemplary lens 40 having the parameters indicated in Table II and the graded index shown in FIG. 8. These plots are self-explanatory to those skilled in the art, and are provided to show

the ability of the lens 40 to provide a high degree of aberration correction. FIG. 9 shows a plot of the Ray Intercept performance for the exemplary lens 40.

FIG. 10 shows a plot of normalized Astigmatism for

the exemplary lens 40 where "S" represents the plot for the Sagittal rays and "T" represents the plot for the Tangential rays. FIG. 11 shows a plot of the

Modulation Transfer Function for the exemplary lens

40. In FIG. 11, the upper curve (indicated by dotted measurement points) is the diffraction limit which is the best results obtainable, while the lower curve (indicated by the x measurement points) is the results obtained with the exemplary lens 40. FIG. 12 is a plot of normalized distortion for the exemplary lens 40 and shows that no distortion resulted. The curves of FIGS. 9, 10, 11 and 12 are to be

interpreted and represent values similar to that shown in FIGS. 3, 4, 5 and 6, respectively.

Referring now to FIG. 13, there is shown a sectional view of an asphere/asphere (double asphere) GRIN doublet lens 60 in accordance with the present invention. The lens 60 comprises a first

asphere/plano element 62 and a second plano/asphere element 64. The first and second elements 62 and 64, respectively, of the lens 60 have a predetermined radius R₂, and are formed of a light transmitting material (e.g., glass, plastic) with a separate gradient index (δN) profile in a radial direction from a longitudinal axis 66 of the lens 60 which is opposite from the gradient index profile of the other element. These opposing gradient profiles are better seen in FIGS. 14 and 15 which are discussed

hereinafter. The first element 62 comprises a front (first) aspheric surface 68, and a cylindrical section extending back from the aspheric surface 68 which ends in a rear (second) planar surface 69. The front and rear surfaces 68 and 69, respectively, extend radially out from the axis 66. The second element 64 comprises a front (first) planar surface 72 which is coupled (cemented) to the correspondingly shaped surface 69 of the first element 62, and a cylindrical section extending back from the planar surface 72 which ends in a rear (second) aspheric surface 74. Rays 70 of a radiant energy (light) from a remote source (not shown) are shown incident on surface 28 and pass through first and second elements 62 and 64, respectively, and emerge from surface 72. The rays 70 of light, after being refracted and focused by the lens 60, are incident on a plane 76 which can be the surface of, for example, a compact disk or any other suitable optical device.

Referring now to FIGS. 14 and 15, there is shown in FIG. 14 an exemplary curve 78 of the

gradient index of refraction N along the radius R₂, on the y-axis versus increasing radii equal to

Rli/R2 on the x-axis for tlιe first element 62 of the lens 60 of FIG. 13. FIG. 15 shows an exemplary curve 79 of the gradient index of refraction N along the radius R₂ on the y-axis versus increasing radii equal to R₁/R₂ on the x-axis for the second

element 64 of the lens 60 of FIG. 13. The exemplary curves 78 and 79 for lens 60 are produced in the manner used for producing the curve 32 of FIG. 2 for the lens 20 of FIG. 1, and R₁ and R₂ represent similar radii measurements. The curve 78 has a gradient profile indicating a refractive index which increases parabolically to an outside periphery 77 of the lens 60. The curve 79 has a gradient profile indicating a refractive index which decreases

parabolically to the outside periphery 77 of the lens 60 and has an opposing profile from that of curve 78. It is to be understood, however, that the curves 78 and 79 can have any suitable opposing profile.

An exemplary lens 60 formed in accordance with the present invention has the parameters shown in Table III wherein the dimensions are in

millimeters unless otherwise indicated, and the

"Sur", "R", "Th" and "K" headings correspond to the headings of Table I. TABLE Ill

Sur R Th K N₀ N₁

68 9.827199 2.4568 1.51680(BK7) 0.0026

69 Infinity 0

72 Infinity 2.4568 1.5600 -0.0026

74 -9.827119 2.4568 -2.00 Air

For a Lens 60 where the aperture = 4.9136 mm.

δN of element 62 = 0.01569

δN of element 64 = 0.01569

EFL = 10.00mm

NA = 0.245

f number = f/2.0

Referring now to FIGS. 16, 17, 18, and 19, there are shown various aberration performance diagrams (plots) for the exemplary lens 60 having the parameters indicated in Table III and the graded index profiles shown in FIGS. 14 and 15. These plots are self-explanatory to those skilled in the art, and are provided to show the ability of the lens 60 to provide a high degree of aberration correction. FIG. 16 shows a plot of the Ray Intercept performance for the exemplary lens 60. FIG. 17 shows a plot of normalized Astigmatism for the exemplary lens 60 where "S" represents the plot for the Sagittal rays and "T" represents the plot for the Tangential rays. FIG. 18 shows a plot of the Modulation Transfer

Function for the exemplary lens 60. In FIG. 18, the upper curve (indicated by dotted measurement points) is the diffraction limit which is the best results obtainable, while the lower curve (indicated by the x measurement points) is the results obtained with the exemplary lens 40. FIG. 19 is a plot of normalized distortion for the exemplary lens 60. The curves of FIGS. 16, 17, 18 and 19 are to be interpreted and represent values similar to that shown in FIGS. 3, 4, 5 and 6, respectively. Referring now to FIG. 20, there is shown a sectional view of an asphere/asphere (double asphere) GRIN doublet lens 90 in accordance with the present invention which is similar to the double asphere lens 60 of FIG. 13 and is disposed in front of an optical element 110. The lens 90 comprises a first

asphere/plano element 92 and a second plano/asphere element 94. The first and second elements 92 and 94, respectively, of the lens 90 have a predetermined radius R₂, and are formed of a light transmitting material (e.g., glass, plastic). The first element is formed of a homogeneous material with a

predetermined index of refraction while the second element 94 comprises a material with predetermined gradient index (δN) profile in a radial direction from a longitudinal axis 96 of the lens 90. The first element 92 comprises a front (first) aspheric surface 98, and a cylindrical section extending back from the aspheric surface 98 which ends in a rear (second) planar surface 99. The front and rear surfaces 98 and 99, respectively, extend radially out from the axis 96. The second element 94 comprises a front (first) planar surface 102 which is coupled (cemented) to the correspondingly shaped surface 99 of the first element 92, and a cylindrical section extending back from the planar surface 102 which ends in a rear (second) aspheric surface 104. Rays 100 of a radiant energy (light) from a remote source (not shown) are incident on the surface 98 of the first element and after passing through the first and second elements 92 and 94, respectively, emerges from surface 104 of the second element 94. The optical element 110 comprises a front surface 112 on which rays 100 of light are incident after having been refracted and focused by the lens 90, and a rear surface 114 onto which the rays 100 from lens 90 are focused. The optical element 110 can be, for

example, a compact disk.

Referring now to FIG. 21, there is shown an exemplary curve 116 of the gradient index of

refraction N along the radius R₂ on the y-axis

versus increasing radii equal to R₁/R₂ on the

x-axis for the second element 94 of the lens 90 of

FIG. 20. The exemplary curve 116 for lens 90 is

produced in the manner used for producing the curve

32 of FIG. 2 for the lens 20 of FIG. 1, and R₁ and

R₂ represent corresponding radii measurements. The curve 116 has a gradient profile indicating a

refractive index which decreases parabolically first in one direction and then the other to the outside

periphery 117 of the lens 90. It is to be

understood, however, that the curve 116 can have any suitable opposing profile.

An exemplary lens 90 formed in accordance with the present invention has the parameters shown in Table IV wherein the dimensions are in millimeters unless otherwise indicated, and the "Sur", "R", "Th" and "K" headings correspond to the headings of Table

I.

TABLE IV

Sur R Th K N₀ N₁ N₂

98 5.20 2.00 1.516(BK7)

99 Infinity 0

102 Infinity 4.00 1.5600 -0.010017 0.00844

104 -6.233408 0.050 -0, .012240 Air

112 Infinity 1.800 (Aperture = 4.00 mm)

114 Infinity 1.200 1.57 (Optical Disk)

For a Lens 60 where the diameter = 5.00 mm.

δN = -0.029646

EFL = 4.885

NA = 0.512

f number = f/0.977

Strehl = 0.963 Referring now to FIGS. 22, 23, 24, and 25, there are shown various aberration performance diagrams (plots) for the exemplary lens 90 having the parameters indicated above and the graded index profile shown in FIG. 21. These plots are

self-explanatory to those skilled in the art, and are provided to show the ability of the lens 90 to provide a high degree of aberration correction. FIG. 22 shows a plot of the Ray Intercept performance for the exemplary lens 90. FIG. 23 shows a plot of normalized Astigmatism for the exemplary lens 90 where "S" represents the plot for the Sagittal rays and "T" represents the plot for the Tangential rays. FIG. 24 shows a plot of the Modulation Transfer

Function for the exemplary lens 90. In FIG. 24, the upper curve (indicated by dotted measurement points) is the diffraction limit which is the best results obtainable, while the lower curve (indicated by the × measurement points) is the results obtained with the exemplary lens 90. FIG. 25 is a plot of normalized distortion for the exemplary lens 90. The curves of FIGS. 22, 23, 24 and 25 are to be interpreted and represent values similar to that shown in FIGS. 3, 4, 5 and 6, respectively.

Referring now to FIG. 26, there is shown a front plano/asphere GRIN doublet lens 120 in

accordance with the present invention positioned in front of an optical element 140. The lens 120 comprises a first plano/plano element 122 and a second plano/asphere element 124. The first and second elements 122 and 124, respectively, of the lens 90 have a predetermined radius R₂, and are formed of a light transmitting material (e.g., glass, plastic). The first element 122 is formed of a homogeneous material with a predetermined index of refraction while the second element 124 comprises a material with predetermined gradient index (δN) profile in a radial direction from a longitudinal axis 126 of the lens 120. The first element 122 comprises a front (first) planar surface 128, and a cylindrical section extending back from the planar surface 128 which ends in a rear (second) planar surface 129. The front and rear surfaces 128 and 129, respectively, extend radially out from the axis 126. Rays 130 of a radiant energy (light) from a source (not shown) are shown incident on the surface 128 and after passing through the first element 122 emerge from the rear surface 129.

The second element 124 comprises a front (first) planar surface 132 which is coupled

(cemented) to the correspondingly shaped surface 129 of the first element 122, and a rear (second)

aspheric surface 134. The second element 124 has a gradient index profile with a gradient index which is large adjacent longitudinal axis 126 and decreases radially outward to the periphery 136 of the lens 120. The optical element 140 comprises a front surface 142 on which rays 130 of radiant energy are incident after having been refracted and focused by the lens 120, and a rear surface 144 onto which the rays 130 from lens 120 are focused. The optical element 140 can be, for example, a compact disk.

Referring now to FIG. 27, there is shown a sectional view of a plano/asphere GRIN doublet lens 150 in accordance with the present invention disposed in front of an optical element 170. The lens 150 comprises a first plano/plano element 152 and a second plano/asphere element 154. The first and second elements 152 and 154, respectively, of the lens 150 have a predetermined radius R₂, and are formed of a light transmitting material (e.g., glass, plastic) with a separate gradient index (δN)

profile in a radial direction from a longitudinal axis 156 of the lens 150 which is opposite from the gradient index profile of the other element. These opposing gradient profiles are similar to the

profiles seen in FIGS. 14 and 15. The first element 152 comprises a front (first) planar surface 158 on which rays 160 of a radiant energy (light) from a remote source (not shown) are incident, and a

cylindrical section extending back from the planar surface 158 which ends in a rear (second) planar surface 159. The front and rear surfaces 158 and 159, respectively, extend radially outward from the axis 156. The second element 154 comprises a front (first) planar surface 162 which is coupled

(cemented) to the correspondingly shaped surface 159 of the first element 152, and a cylindrical section extending back from the planar surface 162 which ends in a rear (second) aspheric surface 164. The rays

160 of light which have been refracted and focused by the lens 150 are incident on a front surface 172 of the optical element 170 and are focused on a rear surface 174 of the optical element 170.

Referring now to FIG. 28, there is shown a sectional view of a plano/asphere GRIN doublet lens 180 in accordance with the present invention disposed in front of an optical element 200. Lens 180 is similar to the lens 150 of FIG. 27. The lens 180 comprises a first plano/plano element 182 and a second plano/asphere element 184. The first and second elements 182 and 184, respectively, of the lens 180 have a predetermined radius R₂, and are formed of a light transmitting material (e.g., glass, plastic) with a separate gradient index (δN) profile in a radial direction from a longitudinal axis 186 of the lens 180 which is opposite from the gradient index profile of the other element. These opposing gradient profiles for elements 182 and 184 are indicated by the arrows in FIG. 28 as being similar to the profiles seen in FIGS. 14 and 15, respectively. The first element 182 comprises a front (first) planar surface 188 on which rays 190 of a radiant energy (light) from a remote source (not shown) are incident, and a cylindrical section extending back from the planar surface 188 which ends in a rear (second) planar surface 189. The front and rear surfaces 188 and 189, respectively, extend radially out from the axis 186. The second element 184 comprises a front (first) planar surface 192 which is spaced-apart from the planar surface 189 of the first element 182, and a cylindrical section extending back from the planar surface 192 which ends in a rear (second) aspheric surface 194. The rays 190 of light, after having been refracted and focused by the lens 180, are incident on a front surface 202 of the optical element 200. These rays 190 are focused on a rear surface 204 of the optical element 200.

Referring now to FIG. 29, there is shown a sectional view of an asphere/asphere GRIN doublet lens 210 in accordance with the present invention. The lens 210 comprises a first asphere/asphere element 212, and a second asphere/asphere element 214. The first and second elements 212 and 214, respectively, of the lens 210 have a predetermined radius R₂, and are formed of a light transmitting material (e.g., glass, plastic) with a separate gradient index (δN) profile in a radial direction from a longitudinal axis 216 of the lens 210 which is opposite from the gradient index profile of the other element. These opposing gradient profiles for elements 212 and 214 are indicated by the arrows in FIG. 29 as being similar to the profiles seen in FIGS. 15 and 14, respectively. The first element 212 comprises a front (first) concave surface 218 on which rays 220 of a radiant energy (light) from a remote source (not shown) are incident, and a

cylindrical section extending back from the surface 218 which ends in a rear (second) concave surface 219. The front and rear surfaces 218 and 219, respectively, extend radially out from the axis 216, and at least one of the surfaces 218 and 219 is aspheric. The second element 214 comprises a front (first) concave surface 222 which is spaced-apart from the concave surface 219 of the first element 212, and a cylindrical section extending back from the concave surface 222 which ends in a rear (second) convex aspheric surface 224. It is to be understood that concave surface 222 can be spherical or

aspherical. The rays 220 of light which have been refracted and focused by the lens 210 are incident on a focal plane 226.

Referring now to FIG. 30, there is shown a singlet lens 230 in accordance with the present invention comprising a front surface 232 which can be planar, spherical or aspherical, and a cylindrical section which ends in a rear surface 234 which is anamorphic. The anamorphic surface 234 is formed with different zones having different curvatures to provide any desired optical aberration correction. The lens 230 is formed of a light transmitting material (e.g., glass, plastic) with a gradient index (δN) profile in a radial direction from a

longitudinal axis 236 of the lens 230. Lens 230 illustrates that the refractive surface 234 does not have to be either spherical or aspherical and can be a surface with zones of different curvatures

therein. The lens 23,0, however, still uses a graded index to bend rays (not shown) of a radiant energy in a desired manner.

The singlet lenses of FIGS. 1, 8 and 30, and the elements of the doublet lenses of FIGS. 13, 20, 26, 27, 28 and 29 are each formed by any suitable process as, for example, a spin (centrifugal) molding method described in U. S. Patent No. 4,022,855 (D. P. Hamblen) which issued on May 10, 1977. A reusable mold, for example, of silicone rubber, is made defining a cavity having the outer configuration of the optical element to be produced. The mold is then placed in a rotatable mold carrier and rotated about its center axis, which corresponds to an optical axis of the singlet lens or the element of the doublet lens. While the mold and the carrier are being spun, two copolymerizable materials having different indices of refraction are injected into the mold in a predetermined sequence to interdiffuse therein. For a homogeneous element, only one material with the proper index of refraction is injected into the mold. The speed of the mold and the carrier rotation is reduced, and the interdiffusing materials form a polymerization mixture which has an index of

refraction that varies radially outwards from the axis of rotation. More particularly, where the materials are predetermined photopolymers,

ultraviolet radiation and post baking, if necessary, produce a solid optical element requiring no further optical finishing. It is to be understood that the specif ic embodiments described herein are intended to be illustrative of the spirit and scope of the

invention. Modifications can be readily made by those skilled in the art consistent with the

principles of the invention. More particularly, the invention provides for a singlet or doublet lens which includes an element with a graded index and at least one aspheric or anamorphic surface. Therefore, any configuration other than those shown in FIGS. 1, 7, 13, 20 and 26-30 which meets the above described inventive criteria is consistent with the principles of the present invention.

Claims

What is Claimed is:

1. A lens comprising:

an optical element comprising:

a first surface and an opposing second surface which each extend radially outwards from a longitudinal axis of the lens where one of the first and second surfaces is aspherical; and

a radiant energy transmitting material having a graded index of refraction having a

predetermined profile which extends radially from the longitudinal axis of the lens.

2. The lens of claim 1 wherein:

the lens is a singlet lens;

the first surface is aspherical for receiving rays of radiant energy from a remote source; and

the second surface is planar.

3. The lens of claim 2 wherein the predetermined profile of the graded index of

refraction has a maximum index of refraction

extending radially outward from the longitudinal axis of the lens for a predetermined distance before decreasing parabolically to a periphery of the lens.

4. The lens of claim 1 wherein the lens is a singlet lens, and each of the first and second surfaces are curved.

5. The lens of claim 1 wherein the lens is a singlet lens and the aspherical surface is

anamorphic.

6. The lens of claim 1 further comprising a second optical element formed of a radiant energy transmitting material and comprising a first surface and an opposing second surface which each extend radially outwards from the longitudinal axis of the lens.

7. The lens of claim 6 wherein the radiant energy transmitting material of the second element has a homogeneous index of refraction, and the first and second elements are disposed in any sequence along the longitudinal axis of the lens.

8. The lens of claim 7 wherein the second element is disposed coaxially in front of the first element in order to receive rays of radiant energy from a remote source.

9. The lens of claim 8 wherein: the first and second surfaces of the first optical element are aspherical and planar,

respectively; and

the first and second surfaces of the second optical element are planar and curved, respectively, and the second surface of the first optical element and the first surface of the second optical element are coupled together.

10. The lens of claim 8 wherein: the first and second surfaces of the second optical element are planar; and

the first and second surfaces of the first optical element are planar and aspherical,

respectively, and the first surface of the first optical element and the second surface of the second optical element are coupled together.

11. The lens of claim 6 wherein: the radiant energy transmitting material of the second element comprises a graded index of refraction with a predetermined profile; and

the radiant energy transmitting material of one of the first and second elements has a graded index of refraction where the predetermined profile decreases radially outward from the longitudinal axis of that optical element, and the radiant energy transmitting material of the other one of the first and second elements has a graded index of refraction where the predetermined profile increases radially outward from the longitudinal axis of the lens.

12. The lens of claim 11 wherein:

the first and second surfaces of the first optical element are aspherical and planar,

respectively; and

13. The lens of claim 11 wherein: the first and second surfaces of the first optical element are aspherical and planar,

respectively; and

the first and second surfaces of the second optical element are planar, and the second element is disposed in front of the first element in order to receive rays of radiant energy from a remote source.

14. The lens of claim 13 wherein the second surface of the first optical element and the first surface of the second optical element are coupled together.

15. The lens of claim 13 wherein the second surface of the first optical element and the first surface of the second optical element are disposed adjacent and coaxially to each other with a

predetermined space therebetween.

16. The lens of claim 11 wherein: the first and second surfaces of the first optical element are curved and aspherical,

respectively; and

the first and second surfaces of the second optical element are curved, and the first surface of the first optical element and the second surface of the second optical element are disposed coaxially to each other with a space therebetween.

17. The lens of claim 16 wherein:

the first and second surfaces of the first optical element are concave and convex, respectively ; and

the first and second surfaces of the second element are concave.

18. A lens comprising:

a radiant energy transmitting material having a graded index of refraction with a

predetermined profile that extends radially from a longitudinal axis of the lens;

a first aspherical surface extending radially outwards from the longitudinal axis of the lens which is arranged for rays of radiant energy from a remote source to be incident thereon; and

a second surface which is either

substantially planar or having a very large radius of curvature extending radially outwards from a

longitudinal axis of the lens opposite the first aspherical surface for permitting the rays of radiant energy being refracted within the lens to emerge therefrom.

19. The lens of claim 18 wherein the predetermined profile of the graded index of

refraction has a maximum index of refraction

20. A lens comprising:

predetermined profile that extends radially from a longitudinal axis of the lens; and

a first surface and an opposing second surface which each are convex and extend radially outwards from the longitudinal axis of the lens , and one of the first and second surfaces is aspherical and the other surface is curved.

21. The lens of claim 20 wherein both the first and second surfaces are aspheric.

22. The lens of claim 20 wherein the predetermined profile, of the graded index of

refraction has a maximum index of refraction

23. A lens comprising:

a first optical element formed of a radiant energy transmitting material, and comprising a first predetermined shaped surface arranged for rays of radiant energy from a remote source to be incident thereon, and an opposing second predetermined shaped surface, each of the first and second surfaces extending radially outwards from a longitudinal axis of the lens; and

a second optical element formed of a radiant energy transmitting material having a graded index of refraction with a predetermined profile which extends radially from the longitudinal axis of the lens, the second optical element comprising a first

predetermined shaped surface disposed adjacent and coaxial with the second surface of the first optical element, and an opposing second aspherical surface, each of the first and second surfaces of the second optical element extending radially outwards from the longitudinal axis of the lens.

24. The lens of claim 23 wherein the radiant energy transmitting material of the first optical element is homogeneous.

25. The lens of claim 23 wherein the radiant energy transmitting material of the first optical element comprises a graded index of

refraction with a predetermined profile which extends radially from the longitudinal axis of the lens, and one of the first and second elements has a graded index of refraction where the predetermined profile decreases radially outward from the longitudinal axis of that optical element, and the other one of the first and second elements has a graded index of refraction where the predetermined profile increases radially outward from the longitudinal axis of the lens.

26. The lens of claim 23 wherein the first predetermined shaped surface of the first optical element is convex, and the second predetermined shaped surface of the first optical element and the first predetermined shaped surface of the second optical element are planar.

27. The lens of claim 23 wherein the first and second predetermined shaped surfaces of the first optical element and the first predetermined shaped surface of the second optical element are planar.

28. The lens of claim 27 wherein the first planar surface of the second optical element is coupled to the second planar surface of the first optical element.

29. The lens of claim 27 wherein the first planar surface of the second optical element is spaced apart from the second planar surface of the first optical element.

30. The lens of claim 23 wherein the first and second predetermined shaped surfaces of the first optical element and the first predetermined shaped surface of the second optical element are concave.