Abstract

In the final stage of lens design, it is usually a critical step to balance the optical performance of a lens system across the sampled fields, which is achieved by adjusting the weights to these fields. Because the current optical design software packages use fixed weights in the optimization process, the task of weight adjustment is left to the optical designer, who has to change the weights manually after each optimization trail. However, this process may take a very long time to finish, especially when many fields of the lens system are sampled, and the results are subjectively affected by the designer’s design experience. In this paper, we propose an automatic performance balancing method. An automatic outer loop is added in the optimization process. The weight for each sampled field and azimuth is calculated appropriately according to the actual performance of the current design and the system requirements, and it is applied to the corresponding field and azimuth automatically in the next optimization trial. The method is successfully implemented in CODE V, and design examples show that it is very effective.

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References

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  1. H. S. Jeong, H. S. Yoo, S. H. Lee, and H. R. Oh, “Low-profile optic design for mobile camera using dual freeform reflective lenses,” Proc. SPIE 6288, 628808 (2006).
    [CrossRef]
  2. O. Cakmakci, B. Moore, H. Foroosh, and J. P. Rolland, “Optimal local shape description for rotationally non-symmetric optical surface design and analysis,” Opt. Express 16(3), 1583–1589 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-3-1583 .
    [CrossRef] [PubMed]
  3. CODE V is a registered trademark of Optical Research Associates, http://www.opticalres.com .
  4. M. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83 (1991).
    [CrossRef]
  5. L. G. Seppala, “Optical interpretation of the merit function in Grey’s lens design program,” Appl. Opt. 13(3), 671–678 (1974), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-13-3-671 .
    [CrossRef] [PubMed]
  6. W. B. King, “Use of the modulation-transfer function (MTF) as an aberration-balancing merit function in automatic lens design,” J. Opt. Soc. Am. 59(9), 1155–1158 (1969), http://www.opticsinfobase.org/abstract.cfm?URI=josa-59-9-1155 .
    [CrossRef]
  7. D. Malacara, and Z. Malacara, Handbook of Optical Design, 2nd ed. (Marcel Dekker, 2003).
  8. H. Hua, Y. Ha, and J. P. Rolland, “Design of an ultralight and compact projection lens,” Appl. Opt. 42(1), 97–107 (2003), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-42-1-97 .
    [CrossRef] [PubMed]
  9. D. Cheng, Y. Wang, H. Hua, and M. M. Talha, “Design of an optical see-through head-mounted display with a low f-number and large field of view using a freeform prism,” Appl. Opt. 48(14), 2655–2668 (2009), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-14-2655 .
    [CrossRef] [PubMed]
  10. 10. S. Lerner, “Optical Design Using Novel Aspheric Surfaces,” Ph.D. Thesis, University of Arizona (2003).

2009 (1)

2008 (1)

2006 (1)

H. S. Jeong, H. S. Yoo, S. H. Lee, and H. R. Oh, “Low-profile optic design for mobile camera using dual freeform reflective lenses,” Proc. SPIE 6288, 628808 (2006).
[CrossRef]

2003 (1)

1991 (1)

M. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83 (1991).
[CrossRef]

1974 (1)

1969 (1)

Bruegge, T. J.

M. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83 (1991).
[CrossRef]

Cakmakci, O.

Cheng, D.

Foroosh, H.

Ha, Y.

Hua, H.

Jeong, H. S.

H. S. Jeong, H. S. Yoo, S. H. Lee, and H. R. Oh, “Low-profile optic design for mobile camera using dual freeform reflective lenses,” Proc. SPIE 6288, 628808 (2006).
[CrossRef]

King, W. B.

Kuper, T. G.

M. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83 (1991).
[CrossRef]

Lee, S. H.

H. S. Jeong, H. S. Yoo, S. H. Lee, and H. R. Oh, “Low-profile optic design for mobile camera using dual freeform reflective lenses,” Proc. SPIE 6288, 628808 (2006).
[CrossRef]

Moore, B.

Oh, H. R.

H. S. Jeong, H. S. Yoo, S. H. Lee, and H. R. Oh, “Low-profile optic design for mobile camera using dual freeform reflective lenses,” Proc. SPIE 6288, 628808 (2006).
[CrossRef]

Rimmer, M. P.

M. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83 (1991).
[CrossRef]

Rolland, J. P.

Seppala, L. G.

Talha, M. M.

Wang, Y.

Yoo, H. S.

H. S. Jeong, H. S. Yoo, S. H. Lee, and H. R. Oh, “Low-profile optic design for mobile camera using dual freeform reflective lenses,” Proc. SPIE 6288, 628808 (2006).
[CrossRef]

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Opt. Express (1)

Proc. SPIE (2)

M. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83 (1991).
[CrossRef]

H. S. Jeong, H. S. Yoo, S. H. Lee, and H. R. Oh, “Low-profile optic design for mobile camera using dual freeform reflective lenses,” Proc. SPIE 6288, 628808 (2006).
[CrossRef]

Other (3)

D. Malacara, and Z. Malacara, Handbook of Optical Design, 2nd ed. (Marcel Dekker, 2003).

10. S. Lerner, “Optical Design Using Novel Aspheric Surfaces,” Ph.D. Thesis, University of Arizona (2003).

CODE V is a registered trademark of Optical Research Associates, http://www.opticalres.com .

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Figures (18)

Fig. 1
Fig. 1

Flow chart of the optimization process for (a) manual and (b) automatic image performance balancing.

Fig. 2
Fig. 2

(a) Two dimension layout of the lens; (b) MTF curves of the initial design (manually balanced); (c) MTF curves after applying the automatic balancing method; (d) Mean, RMS and spread values of MTF.

Fig. 3
Fig. 3

Error function variation curves.

Fig. 4
Fig. 4

MTF curves at 33lps/mm in both azimuths.

Fig. 5
Fig. 5

Weight variation curves for each field in (a) sagittal; (b) tangential azimuth.

Fig. 6
Fig. 6

MTF curves of the design optimized by the automatic balancing method with specified targets.

Fig. 7
Fig. 7

Error function variation curves.

Fig. 8
Fig. 8

Two dimension layout of example 2.

Fig. 9
Fig. 9

(a)(c)(e) MTF curves after local optimization with same weights for all fields and azimuths; (b)(d)(f) MTF curves after automatic performance balancing.

Fig. 10
Fig. 10

Error function variation curve

Fig. 11
Fig. 11

MTF variation curves at 200lps/mm in both azimuths.

Fig. 12
Fig. 12

Weight variation curves for each field in (a) sagittal; (b) tangential azimuth.

Fig. 13
Fig. 13

Two dimension layout of example 3.

Fig. 15
Fig. 15

MTF variation curves at 33lps/mm in both azimuths.

Fig. 14
Fig. 14

Error function variation curve.

Fig. 16
Fig. 16

(a)(c)(e) MTF curves after local optimization with same weights for all fields and azimuths; (b)(d)(f) MTF curves after automatic performance balancing.

Fig. 17
Fig. 17

MTF variation curves for each field at 33lps/mm in (a) sagittal; (b) tangential azimuth.

Fig. 18
Fig. 18

Weight variation curves for each field in (a) sagittal; (b) tangential azimuth.

Equations (9)

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ω = Z n z F n f λ n w R n r [ W W ( Z , λ ) W A ( Z , R ) W X ( Z , F ) Δ x ] 2 + [ W W ( Z , λ ) W A ( Z , R ) W Y ( Z , F ) Δ y ] 2 ,
W A ( Z , R ) = 1 A 1 ( x p 2 + y p 2 ) α ,
W X i ( Z , F ) = { [ 1 + ( ζ ¯ ζ x ( Z , F ) ) ] × m h × W X i 1 ( Z , F )             ζ x > ζ ¯ [ 1 + ( ζ ¯ ζ x ( Z , F ) ) ] × m l × W X i 1 ( Z , F )             ζ x < ζ ¯ ,
W Y i ( Z , F ) = { [ 1 + ( ζ ¯ ζ y ( Z , F ) ) ] × m h × W Y i 1 ( Z , F )             ζ y > ζ ¯ [ 1 + ( ζ ¯ ζ y ( Z , F ) ) ] × m l × W Y i 1 ( Z , F )             ζ y < ζ ¯ ,
ζ ¯ = z n z f n f [ ζ x ( Z z , F f ) + ζ y ( Z z , F f ) ] 2 × n z × n f .
W X i ( Z , F ) = { [ 1 + ( ζ x t ( Z , F ) ζ x ( Z , F ) ) ] × m h × W X i 1 ( Z , F ) )           ζ x > ζ ¯ [ 1 + ( ζ x t ( Z , F ) ζ x ( Z , F ) ) ] × m l × W X i 1 ( Z , F ) )             ζ x < ζ ¯ ,
W Y i ( Z , F ) = { [ 1 + ( ζ y t ( Z , F ) ζ y ( Z , F ) ) ] × m h × W Y i 1 ( Z , F )             ζ y > ζ ¯ [ 1 + ( ζ y t ( Z , F ) ζ y ( Z , F ) ) ] × m l × W Y i 1 ( Z , F )             ζ y < ζ ¯ .
W X ( Z , F ) = W X ( Z , F ) max ( W X ( Z , F ) ) ,
W Y ( Z , F ) = W Y ( Z , F ) max ( W Y ( Z , F ) ) .

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