# Patent

## Title
Lenses for curved sensor systems

## Abstract

The subject disclosure is directed towards lenses for curved surfaces, including multi-element lens assemblies. In one or more implementations, an object-side meniscus lens is coupled to an image/curved surface side subassembly including a biconvex lens. The subassembly may comprise a single biconvex lens or a biconvex lens coupled to a negative meniscus lens.

## Background
BACKGROUND
Contemporary lenses are designed/optimized to focus on a planar image surface. However, optical lens systems do not generally have their best focus on a planar imaging surface. For example, spherical lens systems tend to best focus on a roughly hemispherical surface, called the Petzval surface. Much of the complexity of lens design is in forcing the lens system to achieve best focus on a planar imaging surface, far away from the Petzval surface.
Developments in sensor technology have yielded somewhat low resolution curved sensors (with the resolution likely to increase in the future) that provide for improved quality of images. However, with such curved sensors, lenses optimized for planar image surfaces are inappropriate.
SUMMARY
This Summary is provided to introduce a selection of representative concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used in any way that would limit the scope of the claimed subject matter.
Briefly, one or more of various aspects of the subject matter described herein are directed towards multi-element lens assemblies. One example implementation comprises a refractive object-side element having a positive object-facing surface, and one or more lenses optically coupled to the object-side element and configured to focus light onto a curved surface. Another example implementation comprises an object-side subassembly having overall positive refraction, and an image-side subassembly optically coupled to the object-side subassembly. The image-side subassembly is configured to receive light from the object-side subassembly and focus the received light onto a curved surface.
Other advantages may become apparent from the following detailed description when taken in conjunction with the drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
The present invention is illustrated by way of example and not limited in the accompanying figures in which like reference numerals indicate similar elements and in which:
FIGS. 1-3 are representations of example two-element lens assemblies, each including an object-side positive meniscus lens and an image-side biconvex lens, according to one or more example implementations.
FIGS. 4-6 are representations of example three-element lens assemblies, each including an object-side meniscus lens and an image-side subassembly comprising a biconvex lens and negative meniscus lens, according to one or more example implementations.
FIGS. 7-13 are representations of example four-element lens assemblies, each including an object-side positive refractive lens and an image-side negative refractive lens, according to one or more example implementations.
FIG. 14 is block diagram exemplifying a multiple lens assembly incorporated into a camera having a curved sensing surface, according to one or more example implementations



DETAILED DESCRIPTION
Various aspects of the technology described herein are generally directed towards multiple lens (multi-lens) assemblies configured to focus on a curved surface, such as a hemispherical or substantially hemispherical surface, e.g., a curved sensor. Two, three and four element multi-lens assemblies are exemplified herein, however it is understood that multi-lens assemblies having more than four elements, up to any practical number, are feasible. Further, wherever two or more lenses as shown as physically coupled, it is feasible to have a single lens ground, molded or otherwise manufactured as a single element provided that the materials were the same.
It should be understood that any of the examples herein are non-limiting. For instance, any of the refractive optical elements shown herein may be made of any suitable material, e.g., glass or plastic, and such materials may be used alone or in any combination in any lens assembly. Further, one or more reflective elements may be present instead of or in addition to refractive optical elements. As such, the present invention is not limited to any particular embodiments, aspects, concepts, structures, functionalities or examples described herein. Rather, any of the embodiments, aspects, concepts, structures, functionalities or examples described herein are non-limiting, and the present invention may be used various ways that provide benefits and advantages in lens technology in general.
FIG. 1 shows an example two-element refractive optical element assembly 100 including a refractive optical element (e.g., a generally positive meniscus lens 102) having a positive refractive power from the object-to image direction via a convex-object side surface and concave opposite side. As generally represented in FIG. 1, the convex object-facing side of the lens 102 has a larger radius of curvature than the opposite image-facing concave side. Note that FIG. 1 is not intended to convey any actual sizes or dimensions.
The positive meniscus lens 102 is coupled to a generally biconvex lens 104 to focus light onto a curved surface 108. As can be seen in FIG. 1, the lens 104 is configured to receive light from the lens 102. The lens 104 has an object-facing side with a smaller radius of curvature than its image/curved surface-facing side.
The lenses 102 and 104 are shown as physically coupled, however it is understood that they may be separated by a suitable gap filled with any liquid or gas, including air. The lenses 102 and 104 may be made of plastic, glass, or one plastic, one glass, for example. The following show data of one example implementation corresponding to FIG. 1:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STAN-
Infinity
Infinity
0
0



DARD






STO
EVENASPH
2.149059
1.143113
1.477866
0.3033693


2
EVENASPH
0.5794461
1.250096
2.454417
−0.8047933


3
EVENASPH
−2.715948
2.577189
2.676481
−0.7515823


IMA
STAN-
−4.180481
4.085812
−0.4251225
IMA



DARD










Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
−0.098497123



Coefficient on r{circumflex over ( )}4
−0.040043231



Coefficient on r{circumflex over ( )}6
0.026768729



Coefficient on r{circumflex over ( )}8
−0.061589691



Coefficient on r{circumflex over ( )}10
0.041752082



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.45158306



Coefficient on r{circumflex over ( )}4
−0.014772696



Coefficient on r{circumflex over ( )}6
−0.28951155



Coefficient on r{circumflex over ( )}8
0.19693689



Coefficient on r{circumflex over ( )}10
−0.089640559



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.03789558



Coefficient on r{circumflex over ( )}4
−0.0063094918



Coefficient on r{circumflex over ( )}6
0.0026530481



Coefficient on r{circumflex over ( )}8
−0.0048491677



Coefficient on r{circumflex over ( )}10
0.0027909406



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 2 is similar to FIG. 1, and thus shows a two-element assembly 200 having a positive meniscus lens 222 is coupled to a generally biconvex lens 224 to focus light onto a curved surface 228. Differences between FIG. 1 and FIG. 2 include the thicknesses of the lenses 222 and 224, as well as the ratio of each assembly's elements' thicknesses.
The following show data of one example implementation corresponding to FIG. 2:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


STO
EVENASPH
6.432122
1.799185
1.79147
0


2
EVENASPH
4.164469
1.833238
2.654085
0.


3
EVENASPH
−5.779919
2.572927
3.290749
0


IMA
STANDARD
−4.979109
4.4   
−0.1449482
IMA










Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.016949412



Coefficient on r{circumflex over ( )}4
−0.0060254369



Coefficient on r{circumflex over ( )}6
0.002018416



Coefficient on r{circumflex over ( )}8
−0.003288917



Coefficient on r{circumflex over ( )}10
0.0013935683



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
0.10488576



Coefficient on r{circumflex over ( )}4
0.0080114777



Coefficient on r{circumflex over ( )}6
−0.013581529



Coefficient on r{circumflex over ( )}8
0.0040498405



Coefficient on r{circumflex over ( )}10
−0.00072005712



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.064406122



Coefficient on r{circumflex over ( )}4
−0.0011588418



Coefficient on r{circumflex over ( )}6
−0.00049122944



Coefficient on r{circumflex over ( )}8
0.00020124711



Coefficient on r{circumflex over ( )}10
2.7372079e−005



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 3 is similar to FIGS. 1 and 2, having a two-element assembly 300 with a positive (object-side) meniscus lens 332 is coupled to a generally biconvex lens 334 to focus light onto a curved surface 338. The following show data of one example implementation corresponding to FIG. 3:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STAN-
Infinity
Infinity
0
0



DARD






STO
EVENASPH
1.91288
1.110882
1.623566
−0.1702735


2
EVENASPH
0.4475397
1.378157
2.557306
−0.8949009


3
EVENASPH
−2.76981
2.49896 
2.797017
−0.7235262


IMA
STAN-
−4.156886
4    
−0.4313463
IMA



DARD














Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
−0.11783356



Coefficient on r{circumflex over ( )}4
−0.03550621



Coefficient on r{circumflex over ( )}6
0.02213866



Coefficient on r{circumflex over ( )}8
−0.043313454



Coefficient on r{circumflex over ( )}10
0.024704316



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.7091958



Coefficient on r{circumflex over ( )}4
0.0034960593



Coefficient on r{circumflex over ( )}6
−0.31902203



Coefficient on r{circumflex over ( )}8
0.1978099



Coefficient on r{circumflex over ( )}10
−0.078643857



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.035138687



Coefficient on r{circumflex over ( )}4
−0.0051648925



Coefficient on r{circumflex over ( )}6
0.0030843072



Coefficient on r{circumflex over ( )}8
−0.0044482251



Coefficient on r{circumflex over ( )}10
0.002190287



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









In the two-element design, in general there is a high negative conic constant, and hence large relative asphericity. Correction of coma and astigmatism may be done as with the three-element design as described below, and is generally based upon the surfaces remote from the stop and solving simultaneously for zero SII and SIII:

0=SII+ε2·S*I2+ε3·S*I3 

0=SIII+ε22·S*I2+ε32·S*I3 

where SII and SIII are the coma and astigmatism terms of the whole system before correction, respectively, ε2 and ε3 are the ratio of the principal and marginal ray heights at the second and third surfaces and SI2* and SI3* are the additional spherical aberration terms at the second and third surfaces.

Given the relative size of the Δn at those boundaries for optical materials used in the visible, it is apparent that the actual asphericity in terms of surface sag needs to be larger at surface two than at surface three.
FIG. 4 shows a three-element assembly 440 having an object-side positive, generally meniscus lens 442 optically coupled to a generally biconvex intermediate lens 444. In turn, the intermediate lens 444 is coupled (e.g., physically or at least optically) to a generally negative meniscus lens-shaped lens 446, which focuses light onto the curved surface 448.
Although as in FIGS. 1-3, no sizes or dimensions are intended to be conveyed in FIG. 4, although the relative radii of curvature of the individual elements and the gaps are such that the focal lengths are appropriate. The following show data of one example implementation corresponding to FIG. 4:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


STO
EVENASPH
6.644491
0.9350005
4.586162
2.190639


2
EVENASPH
8.539573
1.159836
4.023222
10.7804


3
EVENASPH
4.935623
1.153228
2.607965
−4.112604


4
EVENASPH
−3.927883
0.9223948
2.604223
−0.2457859


5
EVENASPH
−4.481268
2.140144
3.366548
−3.722884


IMA
STANDARD
−4.128595
4.4
0.113461
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
0.067316768



Coefficient on r{circumflex over ( )}4
0.0013146276



Coefficient on r{circumflex over ( )}6
0.00035928207



Coefficient on r{circumflex over ( )}8
−1.936854e−005



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
0.0017789485



Coefficient on r{circumflex over ( )}4
0.0013930933



Coefficient on r{circumflex over ( )}6
3.0658734e−005



Coefficient on r{circumflex over ( )}8
−9.2314671e−005



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.042529249



Coefficient on r{circumflex over ( )}4
0.00303047



Coefficient on r{circumflex over ( )}6
0.0044255189



Coefficient on r{circumflex over ( )}8
−0.00060161924



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.36101226



Coefficient on r{circumflex over ( )}4
−0.025921905



Coefficient on r{circumflex over ( )}6
−0.0023854566



Coefficient on r{circumflex over ( )}8
0.0022634492



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 5 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.07956166



Coefficient on r{circumflex over ( )}4
0.0021746083



Coefficient on r{circumflex over ( )}6
6.0171164e−006



Coefficient on r{circumflex over ( )}8
0.00059107681



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 5 shows an embodiment of another three-element assembly 550. The object-side lens 552 is close to plano-convex, but is still somewhat of a generally a positive meniscus lens. The biconvex lens 554 receives light from the object-side lens 552, and is shown as being physically coupled to a negative meniscus lens 556, which focuses the light onto the curved surface 558.
The following show data of one example implementation corresponding to FIG. 5:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


STO
EVENASPH
10.04376
2.500336
5.938842
−2.612775


2
EVENASPH
12.47944
0.7280293
3.826284
18.71383


3
EVENASPH
5.209887
1.091996
2.482273
−1.745061


4
EVENASPH
−2.867931
1.300414
2.532966
−1.174326


5
EVENASPH
−5.473922
1.711776
3.566488
4.812232


IMA
STANDARD
−4.024843
4.4
0.457535
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
0.062615788



Coefficient on r{circumflex over ( )}4
0.00059644135



Coefficient on r{circumflex over ( )}6
9.8295376e−006



Coefficient on r{circumflex over ( )}8
−9.0673164e−006



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.012678592



Coefficient on r{circumflex over ( )}4
−0.00047655241



Coefficient on r{circumflex over ( )}6
−0.00079881155



Coefficient on r{circumflex over ( )}8
5.0952505e−005



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.036716283



Coefficient on r{circumflex over ( )}4
0.00017478943



Coefficient on r{circumflex over ( )}6
0.001604258



Coefficient on r{circumflex over ( )}8
−0.00029375864



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.2496809



Coefficient on r{circumflex over ( )}4
−0.04802043



Coefficient on r{circumflex over ( )}6
−0.037620033



Coefficient on r{circumflex over ( )}8
0.023786848



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 5 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.071578632



Coefficient on r{circumflex over ( )}4
0.0054829717



Coefficient on r{circumflex over ( )}6
0.00016838389



Coefficient on r{circumflex over ( )}8
0.00044381629



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 6 shows an embodiment of another three-element assembly 660. The object-side lens 662 is a generally positive meniscus lens. A biconvex lens 664 receives light from the object-side lens 662, and is shown as being physically coupled to a negative meniscus lens 666, which focuses the light onto the curved surface 668.
The following show data of one example implementation corresponding to FIG. 6:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


STO
EVENASPH
2.982782
1.579595
4.635227
0


2
EVENASPH
8.397587
0.6721739
3.783354
0


3
EVENASPH
3.775295
1.038479
2.383311
0


4
EVENASPH
−1.307395
0.8361284
2.462342
0


5
EVENASPH
−2.109334
1.640701
3.354517
0


IMA
STANDARD
−3.623487
3.992889
0.2323074
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
0.026790834



Coefficient on r{circumflex over ( )}4
0.001466062



Coefficient on r{circumflex over ( )}6
0.00018799414



Coefficient on r{circumflex over ( )}8
1.1263726e−005



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0075103766



Coefficient on r{circumflex over ( )}4
0.0044773476



Coefficient on r{circumflex over ( )}6
−0.00096070056



Coefficient on r{circumflex over ( )}8
8.9569244e−005



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0082692559



Coefficient on r{circumflex over ( )}4
−0.0035430794



Coefficient on r{circumflex over ( )}6
−0.0047729108



Coefficient on r{circumflex over ( )}8
0.0037146523



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
0.012763776



Coefficient on r{circumflex over ( )}4
0.021906493



Coefficient on r{circumflex over ( )}6
0.0034661071



Coefficient on r{circumflex over ( )}8
0.010609723



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 5 EVENASPH










Coefficient on r{circumflex over ( )}2
0.046717901



Coefficient on r{circumflex over ( )}4
0.0094163635



Coefficient on r{circumflex over ( )}6
0.0016692686



Coefficient on r{circumflex over ( )}8
−8.2571674e−005



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIGS. 7-13 are examples of four element lens assemblies. As can be seen, each of these example lens assemblies has a lens closet to the curved sensor that is a negative meniscus lens, (although in the examples of FIG. 12 and FIG. 13 the lenses are close to plano-concave). For purposes of brevity, rather than describe the individual lenses in each of the exemplified four-element lens assemblies, the data for each is provided.
The following show data of one example implementation corresponding to FIG. 7:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


1
EVENASPH
224.3738
18.41708
95.81648
−11.33441


2
EVENASPH
273.4945
42.98881
81.69407
32.00641


3
EVENASPH
−231.447
13.22963
47.1052
−480.5678


STO
EVENASPH
81.19232
7.7093
11.33238
−73.30876


5
EVENASPH
−33.06094
4.035196
12.72217
17.45717


6
EVENASPH
−27.76914
20.93704
17.26029
4.856911


IMA
STANDARD
−29.79523
32
0.2489563
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
0.0009050068



Coefficient on r{circumflex over ( )}4
−1.2866628e−007



Coefficient on r{circumflex over ( )}6
−2.9977403e−011



Coefficient on r{circumflex over ( )}8
−6.285853e−016



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
0.0016432507



Coefficient on r{circumflex over ( )}4
−5.968454e−007



Coefficient on r{circumflex over ( )}6
−5.8903375e−011



Coefficient on r{circumflex over ( )}8
−2.4605836e−014



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0027362957



Coefficient on r{circumflex over ( )}4
1.7252281e−006



Coefficient on r{circumflex over ( )}6
−1.9753377e−009



Coefficient on r{circumflex over ( )}8
4.4952875e−013



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.0061035575



Coefficient on r{circumflex over ( )}4
−1.1573733e−005



Coefficient on r{circumflex over ( )}6
−3.8576759e−007



Coefficient on r{circumflex over ( )}8
3.8540073e−009



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 5 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.048220655



Coefficient on r{circumflex over ( )}4
−0.00017573318



Coefficient on r{circumflex over ( )}6
−8.9580864e−007



Coefficient on r{circumflex over ( )}8
−2.3634797e−009



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 6 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.022321611



Coefficient on r{circumflex over ( )}4
−2.5698424e−005



Coefficient on r{circumflex over ( )}6
−1.2705637e−008



Coefficient on r{circumflex over ( )}8
5.0233863e−010



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 8 example lens assembly details:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


1
EVENASPH
162.123
32.50005
119.0927
3.010826


2
EVENASPH
129.3732
34.26242
81.72527
4.196508


3
EVENASPH
32.65833
5.173827
23.27261
−2.239026


4
EVENASPH
51.06849
3.007101
19.19739
−5.892531


STO
EVENASPH
31.85256
5.302895
10.03037
24.96704


6
EVENASPH
−24.50952
4.964779
9.685754
20.14663


7
EVENASPH
−27.137
14.95837
15.27177
−6.28567


IMA
STANDARD
−24.65858
32
0.3400413
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
0.00026574669



Coefficient on r{circumflex over ( )}4
1.3090292e−007



Coefficient on r{circumflex over ( )}6
−8.067507e−011



Coefficient on r{circumflex over ( )}8
3.2095808e−015



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
0.00084216787



Coefficient on r{circumflex over ( )}4
6.1215846e−007



Coefficient on r{circumflex over ( )}6
−5.3812441e−010



Coefficient on r{circumflex over ( )}8
3.5072263e−014



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
0.0092935737



Coefficient on r{circumflex over ( )}4
−5.5951183e−006



Coefficient on r{circumflex over ( )}6
−7.2230948e−008



Coefficient on r{circumflex over ( )}8
−7.3651341e−010



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0024420196



Coefficient on r{circumflex over ( )}4
−2.2371721e−006



Coefficient on r{circumflex over ( )}6
−8.2333791e−008



Coefficient on r{circumflex over ( )}8
−4.4480187e−010



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.0097938162



Coefficient on r{circumflex over ( )}4
−2.3705972e−006



Coefficient on r{circumflex over ( )}6
4.256789e−007



Coefficient on r{circumflex over ( )}8
−1.4665789e−010



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 6 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.073096589



Coefficient on r{circumflex over ( )}4
5.7190799e−005



Coefficient on r{circumflex over ( )}6
4.6297098e−007



Coefficient on r{circumflex over ( )}8
−1.1106303e−009



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 7 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.014538394



Coefficient on r{circumflex over ( )}4
4.4184008e−005



Coefficient on r{circumflex over ( )}6
3.8845346e−007



Coefficient on r{circumflex over ( )}8
3.6819816e−009



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 9 example lens assembly details:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


1
EVENASPH
62.96768
44.60342
66.41456
0.3010589


2
EVENASPH
31.11318
0.7130898
27.68156
1.258264


3
EVENASPH
24.76477
14.99275
26.88566
1.960634


4
EVENASPH
115.5418
0.1125
19.6447
107.2977


STO
EVENASPH
38.72699
10.74507
17.99032
10.32326


6
EVENASPH
−17.98552
3.940343
18.76694
2.402588


7
EVENASPH
−26.68607
10.7144
22.89597
2.670887


IMA
STANDARD
−21.95436
21.99506
0.4361121
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0027228227



Coefficient on r{circumflex over ( )}4
2.7447576e−007



Coefficient on r{circumflex over ( )}6
−8.0962734e−011



Coefficient on r{circumflex over ( )}8
−1.1754249e−013



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.00080108496



Coefficient on r{circumflex over ( )}4
1.7707049e−005



Coefficient on r{circumflex over ( )}6
1.2244301e−008



Coefficient on r{circumflex over ( )}8
1.5406142e−010



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
0.010033911



Coefficient on r{circumflex over ( )}4
9.1856009e−006



Coefficient on r{circumflex over ( )}6
−7.4005883e−009



Coefficient on r{circumflex over ( )}8
−2.3732676e−011



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.014248381



Coefficient on r{circumflex over ( )}4
2.4639797e−005



Coefficient on r{circumflex over ( )}6
−3.0974358e−007



Coefficient on r{circumflex over ( )}8
2.1326118e−009



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.0031486196



Coefficient on r{circumflex over ( )}4
−6.719473e−006



Coefficient on r{circumflex over ( )}6
−4.2952055e−007



Coefficient on r{circumflex over ( )}8
2.3378143e−010



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 6 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.024585082



Coefficient on r{circumflex over ( )}4
−0.00015759285



Coefficient on r{circumflex over ( )}6
7.5876778e−007



Coefficient on r{circumflex over ( )}8
−1.7075289e−009



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 7 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.012329076



Coefficient on r{circumflex over ( )}4
−1.0162983e−005



Coefficient on r{circumflex over ( )}6
1.9008622e−007



Coefficient on r{circumflex over ( )}8
−5.7975021e−010



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 10 example lens assembly details:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


1
EVENASPH
15.48462
6.4366753
18.01328
0.7350255


2
EVENASPH
8.848879
0.55726
11.00158
1.003955


3
EVENASPH
9.032038
6.399996
10.93563
1.201861


4
EVENASPH
52.28122
0.6596292
8.418669
−102.507


STO
EVENASPH
11.75226
4.029279
5.893034
7.760635


6
EVENASPH
−5.062495
1.4752
6.311816
0.8644125


7
EVENASPH
−9.769045
3.78492
7.504619
0.3084521


IMA
STANDARD
−8.85309
8.334322
0.4148249
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0071907745



Coefficient on r{circumflex over ( )}4
3.5659214e−005



Coefficient on r{circumflex over ( )}6
−6.2172173e−008



Coefficient on r{circumflex over ( )}8
−4.0974779e−009



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0088366866



Coefficient on r{circumflex over ( )}4
0.00040564053



Coefficient on r{circumflex over ( )}6
9.3202089e−007



Coefficient on r{circumflex over ( )}8
−1.0213473e−007



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
0.017895107



Coefficient on r{circumflex over ( )}4
0.00040857664



Coefficient on r{circumflex over ( )}6
−3.2173946e−006



Coefficient on r{circumflex over ( )}8
−3.0588291e−007



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.038343155



Coefficient on r{circumflex over ( )}4
0.00049343981



Coefficient on r{circumflex over ( )}6
−2.6827802e−005



Coefficient on r{circumflex over ( )}8
7.0872313e−007



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.0057852056



Coefficient on r{circumflex over ( )}4
0.00020538583



Coefficient on r{circumflex over ( )}6
−3.5523241e−005



Coefficient on r{circumflex over ( )}8
−1.8504176e−007



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 6 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.070725522



Coefficient on r{circumflex over ( )}4
−0.001121991



Coefficient on r{circumflex over ( )}6
5.9885948e−005



Coefficient on r{circumflex over ( )}8
8.3858477e−006



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 7 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.019022298



Coefficient on r{circumflex over ( )}4
0.00011123481



Coefficient on r{circumflex over ( )}6
2.6657465e−005



Coefficient on r{circumflex over ( )}8
−2.3693164e−007



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 11 example lens assembly details:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


1
EVENASPH
34.46149
21.6879
36.8607
0


2
EVENASPH
22.25803
3.200012
18.05265
0


3
EVENASPH
−43.37931
15.34823
17.64078
0


4
EVENASPH
−15.71166
3.197076
12.67488
0


STO
EVENASPH
33.63017
7.563545
6.623186
0


6
EVENASPH
−9.632602
6.408138
9.044731
0


7
EVENASPH
−25.75564
9.774625
12.14408
0


IMA
STANDARD
−24.33541
16.11549
0
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0023330882



Coefficient on r{circumflex over ( )}4
−2.0063176e−006 



Coefficient on r{circumflex over ( )}6
1.712178e−009



Coefficient on r{circumflex over ( )}8
−4.8168342e−012 



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
0.0039164919



Coefficient on r{circumflex over ( )}4
8.2553246e−006



Coefficient on r{circumflex over ( )}6
2.4164262e−007



Coefficient on r{circumflex over ( )}8
3.8123788e−010



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
0.012882344



Coefficient on r{circumflex over ( )}4
−5.6454175e−005 



Coefficient on r{circumflex over ( )}6
3.7235058e−007



Coefficient on r{circumflex over ( )}8
−2.5203063e−009 



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0052614684



Coefficient on r{circumflex over ( )}4
0.0001875086



Coefficient on r{circumflex over ( )}6
−2.2633249e−006 



Coefficient on r{circumflex over ( )}8
1.5881566e−008



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.0034148683



Coefficient on r{circumflex over ( )}4
0.00026669857



Coefficient on r{circumflex over ( )}6
−4.7164879e−006 



Coefficient on r{circumflex over ( )}8
8.4829314e−008



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 6 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.016533876



Coefficient on r{circumflex over ( )}4
−0.00028941833



Coefficient on r{circumflex over ( )}6
−1.0187295e−005 



Coefficient on r{circumflex over ( )}8
9.2891838e−007



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 7 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.0062723283



Coefficient on r{circumflex over ( )}4
4.010936e−005



Coefficient on r{circumflex over ( )}6
6.2071785e−007



Coefficient on r{circumflex over ( )}8
1.0114067e−008



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 12 example lens assembly details:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


1
EVENASPH
7.057435
2.988707
5.674679
1.814324


2
EVENASPH
3.258223
0.08128771
3.426519
−0.5657294


3
EVENASPH
2.901909
0.9694701
3.392434
0.05291388


4
EVENASPH
−31.11675
0
3.368211
0


STO
EVENASPH
2.944861
1.764741
2.528473
−0.3409325


6
EVENASPH
−1.574102
0.3459662
2.519126
−1.902648


7
EVENASPH
−5.186811
1.116115
2.59444
−28.09088


IMA
STANDARD
−3.470872
3.036393
0.2865449
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.032551323



Coefficient on r{circumflex over ( )}4
−0.0048517168



Coefficient on r{circumflex over ( )}6
−0.00019793491



Coefficient on r{circumflex over ( )}8
1.3280715e−005



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
0.028308733



Coefficient on r{circumflex over ( )}4
−0.002587907



Coefficient on r{circumflex over ( )}6
0.0076772372



Coefficient on r{circumflex over ( )}8
−0.0013908962



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
0.052136909



Coefficient on r{circumflex over ( )}4
−0.0025480509



Coefficient on r{circumflex over ( )}6
0.0063986009



Coefficient on r{circumflex over ( )}8
−0.00051891927



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.055267632



Coefficient on r{circumflex over ( )}4
0.0010476998



Coefficient on r{circumflex over ( )}6
0.0031384482



Coefficient on r{circumflex over ( )}8
−0.00032573638



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.052303764



Coefficient on r{circumflex over ( )}4
0.0013254458



Coefficient on r{circumflex over ( )}6
0.011041063



Coefficient on r{circumflex over ( )}8
−0.0042722676



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 6 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.12060363



Coefficient on r{circumflex over ( )}4
0.032302384



Coefficient on r{circumflex over ( )}6
−0.032302727



Coefficient on r{circumflex over ( )}8
−0.0035113698



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 7 EVENASPH










Coefficient on r{circumflex over ( )}2
0.015231714



Coefficient on r{circumflex over ( )}4
0.012736379



Coefficient on r{circumflex over ( )}6
0.005512558



Coefficient on r{circumflex over ( )}8
0.0040815702



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 13 example lens assembly details:

















Surf
Type
Radius
Thickness
Diameter
Conic





OBJ
STANDARD
Infinity
Infinity
0
0


1
EVENASPH
5.859769
1.839874
3.996322
−0.0417652


2
EVENASPH
2.831865
0.2170869
2.506635
−0.5090163


3
EVENASPH
2.306807
0.5873021
2.334853
0.5058974


4
EVENASPH
80.21697
0.1369206
2.228267
4182.971


STO
EVENASPH
3.152057
1.341948
1.701928
−1.099714


6
EVENASPH
−1.410627
0.3361722
1.949082
−1.114667


7
EVENASPH
−4.960287
1.375117
2.223864
−21.00731


IMA
STANDARD
−3.508075
3.001053
0
IMA










Surface 1 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.02899649



Coefficient on r{circumflex over ( )}4
−0.010051793



Coefficient on r{circumflex over ( )}6
−0.00048326198



Coefficient on r{circumflex over ( )}8
9.7659737e−005



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 2 EVENASPH










Coefficient on r{circumflex over ( )}2
0.024143729



Coefficient on r{circumflex over ( )}4
−0.00055718234



Coefficient on r{circumflex over ( )}6
0.0058160331



Coefficient on r{circumflex over ( )}8
−0.0023649112



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 3 EVENASPH










Coefficient on r{circumflex over ( )}2
0.049071226



Coefficient on r{circumflex over ( )}4
0.0097786873



Coefficient on r{circumflex over ( )}6
0.0089052798



Coefficient on r{circumflex over ( )}8
0.0023761706



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 4 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.050967198



Coefficient on r{circumflex over ( )}4
0.0062549297



Coefficient on r{circumflex over ( )}6
0.013279928



Coefficient on r{circumflex over ( )}8
−0.0047169231



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface STO EVENASPH










Coefficient on r{circumflex over ( )}2
0.036069468



Coefficient on r{circumflex over ( )}4
−0.0019326477



Coefficient on r{circumflex over ( )}6
0.010929391



Coefficient on r{circumflex over ( )}8
−0.019845718



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 6 EVENASPH










Coefficient on r{circumflex over ( )}2
−0.04959238



Coefficient on r{circumflex over ( )}4
−0.03986785



Coefficient on r{circumflex over ( )}6
−0.040731282



Coefficient on r{circumflex over ( )}8
0.012511117



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0







Surface 7 EVENASPH










Coefficient on r{circumflex over ( )}2
0.022642757



Coefficient on r{circumflex over ( )}4
0.010081191



Coefficient on r{circumflex over ( )}6
0.013106754



Coefficient on r{circumflex over ( )}8
0.00031467056



Coefficient on r{circumflex over ( )}10
0



Coefficient on r{circumflex over ( )}12
0



Coefficient on r{circumflex over ( )}14
0



Coefficient on r{circumflex over ( )}16
0









FIG. 14 shows an example of a camera 1440 containing a lens assembly 1442 constructed in accordance with the technology described herein. As can be seen, lens subassemblies 14461-1446n focus light, which may be visible light and/or other light (such as infrared) onto a curved surface 1448.
Additional Example Details
In general, some of the exemplified designs are relatively wide-aperture and wide-field and may be constructed using high-order aspheres. Designs may be re-optimized for a lower aperture, and higher-order terms may be dropped. This brings the designs within reach of a description using first-order and third-order wavefront expansions—the domain in which Seidel aberration analysis is appropriate and hence enables the optical function of the various surfaces to be explained.
The lens elements are in general thick in comparison to their separation and therefore a thin-lens solution is not appropriate.












Seidel

Correction


aberration
Comment
needed







SI
Spherical aberration
Yes


SII
Coma
Yes


SIII
Astigmatism
Yes


SIV
Petzval sum (field
No



curvature if SIII = 0)



SV
Distortion
 No*


CI
Longitudinal chromatic aberration
Yes


CII
Transverse chromatic aberration
Yes









In these designs, field curvature is effectively left to float and the image sensor is placed at the Petzval surface. Note that distortion correction is desirable in principle, but the effect of correcting distortion is to flatten the image field and hence negate some of the benefits of the curved image field so it is left uncorrected.
Note that even without the aspheres, the system at moderate apertures is well-corrected for the first three primary monochromatic aberrations. The primary offender is astigmatism, and there are only a few wavelengths of this at f/4; by comparison a thin-lens of similar power at the stop would have about 21 wavelengths of astigmatism. Low starting aberrations tend to be helpful to the design.
In one aspect, the design is pseudo-symmetric, which makes coma and transverse color low by default. The design is also generally pseudo-centro-symmetric, which makes coma and astigmatism low at the external surfaces of the lens (the principal ray is roughly normal to the surface).
One or more implementations start with a positive curvature (as with most lenses), as well as having the first element overall positive to help minimize total track. One or more implementations use one aplanatic surface before the stop and/or in which the marginal ray is close to normal at this surface, and make the surface at the stop nearly concentric with the preceding surface. The curvature may be used to control astigmatism as desired.
The buried surface both corrects for longitudinal color and introduces overcorrected (negative) spherical aberration, which helps compensate for that at the external surfaces of the lens.
If an implementation allows aspheres, astigmatism maybe corrected by introducing an asphere into a surface remote from the stop. The effect of the asphere is to introduce a spherical aberration term that, dependent on the ratio of the principal ray height to the marginal ray height will correct some or all of the astigmatism. However, there is likely some coma. Because this was already low, this additional coma is corrected in another surface.
Correcting the residual spherical aberration can be done by an asphere at the stop. One basic approach finds a Gaussian solution that gives low lateral and longitudinal color, ignoring field curvature but using some of the resulting freedom to minimize total track, which is helpful if a solution has low coma and spherical aberration overall so that aspherics do not have to be excessive. Astigmatism may be corrected using a back surface (or the surface furthest from the stop). Coma may be corrected using a front surface (or the surface next furthest from the stop). Remaining spherical aberration may be corrected using the surface at the stop
CONCLUSION
While the invention is susceptible to various modifications and alternative constructions, certain illustrated embodiments thereof are shown in the drawings and have been described above in detail. It should be understood, however, that there is no intention to limit the invention to the specific forms disclosed, but on the contrary, the intention is to cover all modifications, alternative constructions, and equivalents falling within the spirit and scope of the invention.

## Claims

1. A system comprising:
a curved surface; and
a two element lens assembly, the two element lens assembly comprising:
a first aspherical refractive element with positive refractive power having a first object-facing surface and a first image-facing surface;
a second aspherical refractive element comprising a second object-facing surface and a second image-facing surface, the second object-facing surface coupled to the first image-facing surface of the first aspherical refractive element, the second aspherical refractive element configured to focus light onto the curved surface, the second aspherical refractive element comprising a biconvex lens; and
an aspherical buried surface defined by the interface of the second object-facing surface of the second aspherical refractive element and the first image-facing surface of the first aspherical refractive element, the aspherical buried surface configured to introduce negative spherical aberration.

2. The system of claim 1, wherein the first aspherical refractive element comprises a positive meniscus lens.

3. The system of claim 1, wherein the first object-facing surface has a radius of curvature that is greater than a radius of curvature of the first image-facing surface.

4. The system of claim 1, wherein the biconvex lens is physically coupled to the first aspherical refractive element.

5. The system of claim 1, wherein the second object-facing surface has a radius of curvature that is less than a radius of curvature of the second image-facing surface.

6. The system of claim 1, wherein the curved surface comprises a curved sensor.

7. The system of claim 1, wherein the curved surface comprises a hemispherical surface.

8. A lens assembly comprising:
an object-side subassembly having overall positive refraction; and
an image-side subassembly optically coupled to the object-side subassembly, the image-side subassembly configured to receive light from the object-side subassembly and focus the received light onto a curved surface, the image-side subassembly comprising:
a first aspherical refractive element having a first object-facing surface and a first image-facing surface;
a second aspherical refractive element comprising a second object-facing surface and a second image-facing surface, the second object-facing surface coupled to the first image-facing surface of the first aspherical refractive element; and
an aspherical buried surface defined by the interface of the second object-facing surface of the second aspherical refractive element and the first image-facing surface of the first aspherical refractive element, the aspherical buried surface configured to introduce negative spherical aberration.

9. The lens assembly of claim 8, wherein the object-side subassembly comprises a positive meniscus lens.

10. The lens assembly of claim 8, wherein the image-side subassembly comprises a biconvex lens and a negative meniscus lens.

11. The lens assembly of claim 10, wherein the object-side subassembly comprises at least two refractive optical elements.

12. The lens assembly of claim 8, having an object-side positive refractive lens, at least two intermediary lenses, and an image side negative refractive lens.

13. The lens assembly of claim 8, wherein the second aspherical refractive element comprises a single biconvex lens.

14. A camera comprising:
a curved surface; and
a lens assembly configured to focus light onto the curved surface, the lens assembly comprising:
a first lens assembly;
a second lens assembly optically coupled to the first lens assembly, the second lens assembly configured to receive light from the first lens assembly and focus the received light onto the curved surface, wherein the second lens assembly comprises a biconvex lens, the second lens assembly comprising an aspherical buried surface defined by the interface of a first and second lens, the aspherical buried surface configured to introduce negative spherical aberration.

15. The camera of claim 14, wherein the first lens assembly comprises an aspherical object-side positive refractive lens and the second lens assembly comprises an aspherical image side negative refractive lens.

16. The camera of claim 14, wherein the biconvex lens of the second lens assembly comprises an object-facing side having a radius of curvature that is less than a radius of curvature of a negative image-facing side.

17. The camera of claim 14, wherein the first lens assembly comprises a positive meniscus lens.

18. The camera of claim 14, wherein the second lens assembly is a two element lens assembly, comprising two optically coupled elements.

19. The camera of claim 14, wherein the biconvex lens of the second lens assembly receives light from the first lens assembly, the biconvex lens optically coupled to a negative meniscus lens focuses the light onto the curved surface.

20. The camera of claim 19, wherein the biconvex lens is physically coupled to the negative meniscus lens.