Abstract

Control of chromatic aberration through purely optical means is well known. We present a novel, to our knowledge, optical–digital method of controlling chromatic aberration. The optical–digital system, which incorporates a cubic phase-modulation (CPM) plate in the optical system and postprocessing of the detected image, effectively reduces a system’s sensitivity to misfocus in general or axial (longitudinal) chromatic aberration, in particular. A fully achromatic imaging system (one that is corrected for a continuous range of wavelengths) can be achieved by initial optimization of the optical system for all aberrations except chromatic aberration. The chromatic aberration is corrected by the inclusion of the CPM plate and postprocessing.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Tribastone, C. Gardner, W. G. Peck, “Precision plastic optics applications from design to assembly,” in Design, Fabrication, and Applications of Precision Plastic Optics, X. Ning, R. T. Hebert, eds., Proc. SPIE2600, 6–9 (1995).
    [CrossRef]
  2. P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997), pp. 194–196.
  3. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 89–92.
  4. D. Malacara, Z. Malacara, “Achromatic aberration correction with only one glass,” in Current Developments in Optical Design and Optical Engineering IV, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 81–87 (1994).
    [CrossRef]
  5. T. Stone, N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. 27, 2960–2971 (1988).
    [CrossRef] [PubMed]
  6. K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
    [CrossRef]
  7. K. Spaulding, G. M. Morris, “Achromatization of optical waveguide components using diffractive elements,” in Miniature and Micro-Optics: Fabrication and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. SPIE1751, 225–228 (1992).
    [CrossRef]
  8. E. R. Dowski, W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 6, pp. 120–125.
  10. P. M. Woodward, Probability and Information Theory with Applications to Radar (Permagon, New York, 1953).

1995 (1)

1988 (1)

Cathey, W. T.

Dowski, E. R.

Gardner, C.

C. Tribastone, C. Gardner, W. G. Peck, “Precision plastic optics applications from design to assembly,” in Design, Fabrication, and Applications of Precision Plastic Optics, X. Ning, R. T. Hebert, eds., Proc. SPIE2600, 6–9 (1995).
[CrossRef]

George, N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 6, pp. 120–125.

Iwaki, M.

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[CrossRef]

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 89–92.

Macdonald, J.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997), pp. 194–196.

Malacara, D.

D. Malacara, Z. Malacara, “Achromatic aberration correction with only one glass,” in Current Developments in Optical Design and Optical Engineering IV, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 81–87 (1994).
[CrossRef]

Malacara, Z.

D. Malacara, Z. Malacara, “Achromatic aberration correction with only one glass,” in Current Developments in Optical Design and Optical Engineering IV, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 81–87 (1994).
[CrossRef]

Maruyama, K.

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[CrossRef]

Morris, G. M.

K. Spaulding, G. M. Morris, “Achromatization of optical waveguide components using diffractive elements,” in Miniature and Micro-Optics: Fabrication and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. SPIE1751, 225–228 (1992).
[CrossRef]

Mouroulis, P.

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997), pp. 194–196.

Ogawa, R.

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[CrossRef]

Peck, W. G.

C. Tribastone, C. Gardner, W. G. Peck, “Precision plastic optics applications from design to assembly,” in Design, Fabrication, and Applications of Precision Plastic Optics, X. Ning, R. T. Hebert, eds., Proc. SPIE2600, 6–9 (1995).
[CrossRef]

Spaulding, K.

K. Spaulding, G. M. Morris, “Achromatization of optical waveguide components using diffractive elements,” in Miniature and Micro-Optics: Fabrication and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. SPIE1751, 225–228 (1992).
[CrossRef]

Stone, T.

Tribastone, C.

C. Tribastone, C. Gardner, W. G. Peck, “Precision plastic optics applications from design to assembly,” in Design, Fabrication, and Applications of Precision Plastic Optics, X. Ning, R. T. Hebert, eds., Proc. SPIE2600, 6–9 (1995).
[CrossRef]

Wakamiya, S.

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[CrossRef]

Woodward, P. M.

P. M. Woodward, Probability and Information Theory with Applications to Radar (Permagon, New York, 1953).

Appl. Opt. (2)

Other (8)

C. Tribastone, C. Gardner, W. G. Peck, “Precision plastic optics applications from design to assembly,” in Design, Fabrication, and Applications of Precision Plastic Optics, X. Ning, R. T. Hebert, eds., Proc. SPIE2600, 6–9 (1995).
[CrossRef]

P. Mouroulis, J. Macdonald, Geometrical Optics and Optical Design (Oxford U. Press, New York, 1997), pp. 194–196.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 89–92.

D. Malacara, Z. Malacara, “Achromatic aberration correction with only one glass,” in Current Developments in Optical Design and Optical Engineering IV, R. E. Fischer, W. J. Smith, eds., Proc. SPIE2263, 81–87 (1994).
[CrossRef]

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[CrossRef]

K. Spaulding, G. M. Morris, “Achromatization of optical waveguide components using diffractive elements,” in Miniature and Micro-Optics: Fabrication and System Applications II, C. Roychoudhuri, W. B. Veldkamp, eds., Proc. SPIE1751, 225–228 (1992).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap. 6, pp. 120–125.

P. M. Woodward, Probability and Information Theory with Applications to Radar (Permagon, New York, 1953).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Demonstration of axial chromatic aberration with a single lens. The distances f r , f g , and f b are the focal lengths for red, green, and blue light, respectively.

Fig. 2
Fig. 2

Experimentally acquired PSF’s from a chromatically aberrated system. (a) The composite PSF. (b) The red PSF. (c) The green PSF. (d) The blue PSF.

Fig. 3
Fig. 3

Traditional optical system consisting of two singlets; a clear rectangular aperture; a CCD at the image plane; and red, green, and blue color filters.

Fig. 4
Fig. 4

Ray-intercept curve for the system shown in Fig. 3. Here FY is the ray height at the exit pupil and DY is the height at which a ray crosses the image plane. The three graphs are for a point at (a) the full field, (b) 0.7 of the full field, and (c) an on-axis field.

Fig. 5
Fig. 5

CPM system consisting of two singlets; a clear rectangular aperture; a CPM plate; a CCD at the image plane; and red, green, and blue color filters.

Fig. 6
Fig. 6

Surface of the CPM plate with a phase function of Φ = α(x 3 + y 3), with α = 20π, |x| ≤ 1, and |y| ≤ 1.

Fig. 7
Fig. 7

Images of the entire U.S. Air Force resolution target with (a) the traditional and (b) the postprocessed CPM systems.

Fig. 8
Fig. 8

Portion of the U.S. Air Force resolution chart taken with (a) a traditional system and (b) the postprocessed CPM system. At the top are the three-color composite images and below are the individual color-constituent images.

Fig. 9
Fig. 9

Small portion of the U.S. Air Force resolution chart showing the effects of chromatic aberration on the pixel level. (a) The traditional system composite image and the constituent images. (b) The postprocessed CPM-system images.

Fig. 10
Fig. 10

Single thin-lens element with a focal length f. The distance l is the object distance, and the distance l′ is the image distance. The ray height is related to the ray angle u through the paraxial approximation y = lu = l′ u′.

Fig. 11
Fig. 11

Two lenses, (a) and (b), separated by a distance d that are designed to correct for axial chromatic aberration for two wavelengths by use of only one material. The lenses have focal lengths f a and f b , respectively, and collimated light of the two wavelengths focuses at a distance l′ behind lens (b).

Equations (36)

Equations on this page are rendered with MathJax. Learn more.

K 1 V 1 + K 2 V 2 = 0 , K 1 + K 2 = K ,
1 d i = 1 f - 1 d 0 .
1 f = n λ - 1 1 R 1 - 1 R 2 ,
d i λ = 1 f λ - 1 d 0 - 1 .
ψ λ = π L 2 4 λ 1 f λ - 1 d 0 - 1 d CCD = 2 π W 020 ,
P x ,   y = P x ,   y exp j ψ λ x 2 + y 2 ,
H f x ,   ψ λ = Λ f x 2 f 0 sinc 2 ψ λ f x f 0 - ψ λ f x f 0 2 ,
Λ x = 1 - | x | | x | 1 0 otherwise .
exp j Φ x ,   y ,     Φ x ,   y = α x 3 + y 3 ,
P x ,   y = P x ,   y exp j ψ λ x 2 + y 2 exp j Φ x ,   y .
H f x ,   ψ λ π 12 α f x L 2 1 / 2 exp j ϑ x i + 2 f x ψ λ x i ± π / 4 ,
ν x = -   h x u x - x d x = h x   *   u x ,
u x = 1 x 0 0 otherwise .
Hf = ν ,
f = H T H - 1 H T ν .
1 l - 1 l = n - 1 1 R 1 - 1 R 2 = n - 1 c = 1 f ,
- 1 l C + 1 l F + 1 l C - 1 l F = n F - n C c , l C - l F l 2 - l C - l F l 2 = n F - n C c   n d - 1 n d - 1 = 1 fV ,
L ch y 2 l 2 - L ch y 2 l 2 = - y 2 fV , L ch u 2 - L ch u 2 = - y 2 fV ,
L ch j u j 2 - L ch j u j 2 = - i = 1 j y i 2 f i V i .
K 1 V 1 + K 2 V 2 = 0 ,
y a 2 f a V a + y b 2 f b V b = 0 .
f b V b = - f a V a 1 - d / f a 2 .
1 F = 1 f a + 1 f b - d f a f b = 1 f a + 1 - d / f a f b .
f a = F 1 - V b V a 1 - d / f a , f b = F 1 - d / f a 1 - V a 1 - d / f a V b .
f a = Fd / f a d / f a - 1 ,     f b = - Fd d / f a - 1 / f a .
1 l = 1 f a - d + 1 f b .
1 l 1 - d / f a = 1 f a + 1 f b 1 - d / f a = 1 F ,
l = F 1 - d / f a = - F d / f a - 1 .
1 F C = n aC - 1 c a + n bC - 1 c b - d n aC - 1 c a × n bC - 1 c b , 1 F F = n aF - 1 c a + n bF - 1 c b - d n aF - 1 c a × n bF - 1 c b .
n C - 1 c a + c b - dc a c b n C - 1 = n F - 1 c a + c b - dc a c b n F - 1 .
n C - n F c a + c b - dc a c b n C + n F - 2 = 0 .
1 V 1 f a + 1 f b - dc b f a n d - 1 n d - 1 n C + n F - 2 = 0 .
1 V 1 f a + 1 f b - d f a f b n C + n F - 2 n d - 1 = 0 .
d = 1 f a + 1 f b   f a f b n d - 1 n C + n F - 2 .
d = f a + f b n C + n F - 2 n C + n F - 2 1 2 .
d = f a + f b 2 .

Metrics