Abstract

I derive the imaging condition for the complex amplitude of a monochromatic field by a sequence of lenslike elements.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Baues, Optoelectronics 1, 37 (1969).
  2. S. B. Collins, J. Opt. Soc. Am. 60, 1168 (1970).
    [CrossRef]
  3. G. N. Lawrence, S. W. Hwang, Appl. Opt. 31, 5201 (1992).
    [CrossRef] [PubMed]
  4. H. T. Yura, S. G. Hanson, J. Opt. Soc. Am. A 4, 1931 (1987).
    [CrossRef]
  5. The identification of the condition B = 0 with the imaging condition of a lenslike system is given inA. Yariv, J. Opt. Soc. Am. 66, 301 (1976)as well as in Ref. 6.
    [CrossRef]
  6. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 596.
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 96.
  8. M. Born, Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), p. 430.

1992 (1)

1987 (1)

1976 (1)

1970 (1)

1969 (1)

P. Baues, Optoelectronics 1, 37 (1969).

Baues, P.

P. Baues, Optoelectronics 1, 37 (1969).

Born, M.

M. Born, Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), p. 430.

Collins, S. B.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 96.

Hanson, S. G.

Hwang, S. W.

Lawrence, G. N.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 596.

Wolf,

M. Born, Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), p. 430.

Yariv, A.

Yura, H. T.

Appl. Opt. (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

Optoelectronics (1)

P. Baues, Optoelectronics 1, 37 (1969).

Other (3)

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 596.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 96.

M. Born, Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), p. 430.

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

Generalized lenslike system.

Fig. 2
Fig. 2

Imaging by a thin lens.

Fig. 3
Fig. 3

Function F(x,B) = (2πB)−1/2 cos(x2/2B) for B = 1, 0.5, 0.1.

Equations (16)

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

| A B C D | = | A n B n C n D n | | A 1 B 1 C 1 D 1 | .
f 1 ( x 1 , y 1 ) = i k 2 π B exp ( - i k L ) Σ 0 f 0 ( x 0 , y 0 ) exp { ( - i k 2 B ) [ D ( x 1 2 + y 1 2 ) - 2 x 1 x 0 - 2 y 1 y 0 + A ( x 0 2 + y 0 2 ) ] } d x 0 d y 0 .
f 1 ( x 1 , y 1 ) = i k 2 π B exp [ ( - i k 2 B ) ( D - 1 A ) ( x 1 2 + y 1 2 ) ] × Σ 0 f 0 ( x 0 , y 0 ) exp { ( - i k 2 B ) × [ A ( x 0 - x 1 A ) 2 + A ( y 0 - y 1 A ) 2 ] } d x 0 d y 0 .
Y ( x ) lim B 0 i 2 π B exp ( - i x 2 2 B ) = δ ( x ) ,
f 1 ( x 1 , y 1 ) B 0 = exp ( - i k L ) A f 0 ( x 1 A , y 1 A ) × exp [ - i k ( D A - 1 ) 2 A B ( x 1 2 + y 1 2 ) ] .
f 1 ( x 1 , y 1 ) B 0 = exp ( - i k L ) A f 0 ( x 1 A , y 1 A ) × exp [ - i k C 2 A ( x 1 2 + y 1 2 ) ] .
| A B C D | = | 1 d i 0 1 | | 1 0 - 1 f 1 | | 1 d 0 0 1 | = | 1 - d i f d 0 d i ( 1 d 0 + 1 d i - 1 f ) - 1 f 1 - d 0 f | .
1 f = 1 d 0 + 1 d i ,
f 1 ( x , y ) = - 1 M exp { - i [ k L + k ( x 2 + y 2 ) 2 M f ] } × f 0 ( - x M , - y M ) .
Y ( t ) lim B 0 ( i 2 π B ) 1 / 2 exp ( - i 2 t 2 2 B ) = δ ( t ) ,
- Y ( t ) d t = 1
t 1 t 2 Y ( t ) d t = 0
F ( x , B ) ( 1 2 π B ) 1 / 2 cos ( x 2 2 B ) .
C ( ω ) = 0 ω cos ( π 2 τ 2 ) d τ , S ( ω ) = 0 ω sin ( π 2 τ 2 ) d τ , C ( ) = S ( ) = 0.5 ,
t 1 t 2 Y ( t ) d t = 1 2 ( 1 + i ) lim B 0 { C ( t 2 π B ) - C ( t 1 π B ) - i [ S ( t 2 π B ) - S ( t 1 π B ) ] } = 1 2 ( 1 + i ) { C ( ) - C ( ) - i [ S ( ) - S ( ) ] } = 0
- Y ( t ) d t = ( 1 + i ) [ C ( ) - i S ( ) ] = 1 .

Metrics