Abstract

Situations exist in the area of optical information processing where one may choose between either a single large lens or many small lenslets side by side. The choice will be influenced by many parameters, among others by the space-bandwidth product SW. The SW is an upper limit for the number of data channels which can be handled in parallel. Hence, we investigate the scaling behavior of the space-bandwidth product. Professional lens designers sometimes have viewpoints different from those of designers of systems for digital optics. That fact may justify this investigation, performed by a nonlens designer.

© 1989 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Bartelt, F. Sauer, “Space-Variant Filtering with Holographic Multifacet Elements,” Opt. Commun. 53, 296–301 (1985).
    [CrossRef]
  2. N. Bareket, “Second Moment of the Diffraction Point Spread Function as an Image Quality criterion,” J. Opt. Soc. Am. 69, 1311–1312 (1979).
    [CrossRef]
  3. V. Gerbig, A. W. Lohmann, “Is lens design legal?”; submitted to Appl. Opt.
  4. J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

1988

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

1985

H. Bartelt, F. Sauer, “Space-Variant Filtering with Holographic Multifacet Elements,” Opt. Commun. 53, 296–301 (1985).
[CrossRef]

1979

Bareket, N.

Bartelt, H.

H. Bartelt, F. Sauer, “Space-Variant Filtering with Holographic Multifacet Elements,” Opt. Commun. 53, 296–301 (1985).
[CrossRef]

English, J. H.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

Gerbig, V.

V. Gerbig, A. W. Lohmann, “Is lens design legal?”; submitted to Appl. Opt.

Gossard, A. C.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

Jewell, J. L.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

Lee, Y. H.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

Lohmann, A. W.

V. Gerbig, A. W. Lohmann, “Is lens design legal?”; submitted to Appl. Opt.

McCall, S. L.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

Sauer, F.

H. Bartelt, F. Sauer, “Space-Variant Filtering with Holographic Multifacet Elements,” Opt. Commun. 53, 296–301 (1985).
[CrossRef]

Scherer, A.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

J. Opt. Soc. Am.

J. Phys.

J. L. Jewell, S. L. McCall, Y. H. Lee, A. Scherer, A. C. Gossard, J. H. English, J. Phys. 49, C2–39 (1988).

Opt. Commun.

H. Bartelt, F. Sauer, “Space-Variant Filtering with Holographic Multifacet Elements,” Opt. Commun. 53, 296–301 (1985).
[CrossRef]

Other

V. Gerbig, A. W. Lohmann, “Is lens design legal?”; submitted to Appl. Opt.

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 (3)

Fig. 1
Fig. 1

Lens systems for spatial filtering: (A) macro; (B) micro; (C) hybrid.

Fig. 2
Fig. 2

Scaling behavior. The lateral aberration ξ varies with scale change. Curvatures, angles, and diffraction blur remain constant.

Fig. 3
Fig. 3

Space–bandwidth product SW, for (from the top) no aberrations; with aberration (variable stop number); no diffraction; with aberration (fixed stop). M is the scaling factor, with M = 1 referring to a focal length of 1 mm.

Tables (1)

Tables Icon

Table I Tabular Representation of Eq. (9)

Equations (16)

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

I 1 M 2 K 2 W 1 2 ¯ ( K = 2 π / λ ) .
A p = ( δ x ) 2 + ( δ ξ ) 2 = λ 2 F 2 + ξ 2 ¯ .
A p ( M ) = λ 2 F 2 + M 2 ξ 1 2 ¯ .
A F ( M ) = Δ x Δ y = M 2 Δ x 1 Δ y 1 .
SW ( M ) = M 2 Δ x 1 Δ y 1 λ 2 F 2 + M 2 ξ 1 2 ¯ .
SW D = M 2 SW D 1 .
SW A = Δ x 1 Δ y 1 / ξ 1 2 ¯ = SW A 1 .
M C 2 = λ 2 F 2 / ξ 1 2 ¯ .
f ( mm ) = F 3 .
ξ ( x , M ) = M [ a ( x / M ) b ( x / M ) 3 ] .
| x | B / 2 .
F = ( f ) 1 / 3 = M 1 / 3 ; f 1 = 1 mm , B = M 2 / 3 .
( δ x ) 2 = λ 2 F 2 = λ 2 M 2 / 3 .
ξ 2 ¯ = b 2 / 2800 .
A p = λ 2 M 2 / 3 + b 2 / 2800 .
SW = M 2 Δ x 1 Δ y 1 λ 2 M 2 / 3 + b 2 / 2800 .

Metrics