Abstract

The analytical illuminance monitoring technique provides an exact expression within the geometrical optics limit for the illuminance over an image surface for light that has passed through a multiinterface optical system. The light source may be collimated rays, a point source, or an extended source. The geometrical energy distributions can be graphically displayed as a line or point spread function over selected image planes. The analytical illuminance technique gives a more accurate and efficient computer technique for evaluating the energy distribution over an image surface than the traditional scanning of the spot diagram mathematically with a narrow slit. The analytical illuminance monitoring technique also provides a closed form expression for the caustic surface of the optical system. It is shown by examining the caustic surface for a number of lens systems from the literature that the caustic is a valuable merit function for evaluating the aberrations and the size of the focal region.

© 1976 Optical Society of America

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References

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  1. D. L. Shealy, D. G. Burkhard, Opt. Acta 22, 485 (1975).
  2. D. L. Shealy, W. M. Rosenblum, Opt. Eng. 14, 237 (1975).
  3. O. N. Stavroudis, D. P. Feder, J. Opt. Soc. Am. 44, 163 (1954).
  4. E. R. G. Eckert, E. M. Sparrow, Int. J. Heat Mass Transfer 3, 42 (1961).
  5. S. H. Lin, E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).
  6. J. A. Plamondon, T. E. Horton, Int. J. Heat Mass Transfer 10, 655 (1967).
  7. J. B. Keller, H. B. Keller, J. Opt. Soc. Am. 40, 48 (1950).
  8. J. B. Keller, W. Streifer, J. Opt. Soc. Am. 61, 40 (1971).
  9. V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, New York, 1965), Chap. 8.
  10. M. Kline, I. W. Kay, Electromagnetic Theory and Geometrical Optics (Interscience, New York, 1965), pp. 184–190.
  11. G. A. Deschamps, Proc. IEEE 60, 1022 (1972).
  12. M. Herzberger, Modern Geometrical Optics (Wiley-Interscience, New York, 1958).
  13. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 127.
  14. O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972).
  15. S. C. Parker, “Properties and Applications of Generalized Ray Tracing,” Technical Report 71, Optical Sciences Center, University of Arizona, Tucson, Arizona (1971).
  16. H. Schench, J. Opt. Soc. Am. 47, 653 (1957).
  17. V. Z. Barkowski, Optik 18, 22 (1961).
  18. V. Z. Barkowski, Optik 19, 226 (1962).
  19. J. B. Scarborough, Appl. Opt. 3, 1445 (1964).
  20. D. L. Shealy, D. G. Burkhard, Appl. Opt. 12, 2955 (1973).
  21. H. M. A. El-Sum, J. Opt. Soc. Am. 62, 1375A (1972).
  22. D. L. Shealy, D. G. Burkhard, Opt. Acta 20, 287 (1973).
  23. W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964).
  24. O. N. Stavroudis, L. E. Sutton, “Spot Diagrams for the Prediction of Lens Performance from Design Data,” National Bureau of Standards Monograph 93 (1965).
  25. D. L. Shealy, J. Opt. Soc. Am. 66, 76 (1976).
  26. Private communication, D. G. Burkhard, Physics Department, University of Georgia, Athens, Georgia 30602.
  27. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

1976 (1)

1975 (2)

D. L. Shealy, D. G. Burkhard, Opt. Acta 22, 485 (1975).

D. L. Shealy, W. M. Rosenblum, Opt. Eng. 14, 237 (1975).

1973 (2)

D. L. Shealy, D. G. Burkhard, Opt. Acta 20, 287 (1973).

D. L. Shealy, D. G. Burkhard, Appl. Opt. 12, 2955 (1973).

1972 (2)

H. M. A. El-Sum, J. Opt. Soc. Am. 62, 1375A (1972).

G. A. Deschamps, Proc. IEEE 60, 1022 (1972).

1971 (1)

1967 (1)

J. A. Plamondon, T. E. Horton, Int. J. Heat Mass Transfer 10, 655 (1967).

1965 (2)

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).

O. N. Stavroudis, L. E. Sutton, “Spot Diagrams for the Prediction of Lens Performance from Design Data,” National Bureau of Standards Monograph 93 (1965).

1964 (1)

1962 (1)

V. Z. Barkowski, Optik 19, 226 (1962).

1961 (2)

E. R. G. Eckert, E. M. Sparrow, Int. J. Heat Mass Transfer 3, 42 (1961).

V. Z. Barkowski, Optik 18, 22 (1961).

1957 (1)

1954 (1)

1950 (1)

Barkowski, V. Z.

V. Z. Barkowski, Optik 19, 226 (1962).

V. Z. Barkowski, Optik 18, 22 (1961).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 127.

Brouwer, W.

W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964).

Burkhard, D. G.

D. L. Shealy, D. G. Burkhard, Opt. Acta 22, 485 (1975).

D. L. Shealy, D. G. Burkhard, Appl. Opt. 12, 2955 (1973).

D. L. Shealy, D. G. Burkhard, Opt. Acta 20, 287 (1973).

Private communication, D. G. Burkhard, Physics Department, University of Georgia, Athens, Georgia 30602.

Deschamps, G. A.

G. A. Deschamps, Proc. IEEE 60, 1022 (1972).

Eckert, E. R. G.

E. R. G. Eckert, E. M. Sparrow, Int. J. Heat Mass Transfer 3, 42 (1961).

El-Sum, H. M. A.

H. M. A. El-Sum, J. Opt. Soc. Am. 62, 1375A (1972).

Feder, D. P.

Fock, V. A.

V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, New York, 1965), Chap. 8.

Herzberger, M.

M. Herzberger, Modern Geometrical Optics (Wiley-Interscience, New York, 1958).

Horton, T. E.

J. A. Plamondon, T. E. Horton, Int. J. Heat Mass Transfer 10, 655 (1967).

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Kay, I. W.

M. Kline, I. W. Kay, Electromagnetic Theory and Geometrical Optics (Interscience, New York, 1965), pp. 184–190.

Keller, H. B.

Keller, J. B.

Kline, M.

M. Kline, I. W. Kay, Electromagnetic Theory and Geometrical Optics (Interscience, New York, 1965), pp. 184–190.

Lin, S. H.

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).

Parker, S. C.

S. C. Parker, “Properties and Applications of Generalized Ray Tracing,” Technical Report 71, Optical Sciences Center, University of Arizona, Tucson, Arizona (1971).

Plamondon, J. A.

J. A. Plamondon, T. E. Horton, Int. J. Heat Mass Transfer 10, 655 (1967).

Rosenblum, W. M.

D. L. Shealy, W. M. Rosenblum, Opt. Eng. 14, 237 (1975).

Scarborough, J. B.

Schench, H.

Shealy, D. L.

D. L. Shealy, J. Opt. Soc. Am. 66, 76 (1976).

D. L. Shealy, W. M. Rosenblum, Opt. Eng. 14, 237 (1975).

D. L. Shealy, D. G. Burkhard, Opt. Acta 22, 485 (1975).

D. L. Shealy, D. G. Burkhard, Opt. Acta 20, 287 (1973).

D. L. Shealy, D. G. Burkhard, Appl. Opt. 12, 2955 (1973).

Sparrow, E. M.

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).

E. R. G. Eckert, E. M. Sparrow, Int. J. Heat Mass Transfer 3, 42 (1961).

Stavroudis, O. N.

O. N. Stavroudis, L. E. Sutton, “Spot Diagrams for the Prediction of Lens Performance from Design Data,” National Bureau of Standards Monograph 93 (1965).

O. N. Stavroudis, D. P. Feder, J. Opt. Soc. Am. 44, 163 (1954).

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972).

Streifer, W.

Sutton, L. E.

O. N. Stavroudis, L. E. Sutton, “Spot Diagrams for the Prediction of Lens Performance from Design Data,” National Bureau of Standards Monograph 93 (1965).

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 127.

Appl. Opt. (2)

Int. J. Heat Mass Transfer (2)

E. R. G. Eckert, E. M. Sparrow, Int. J. Heat Mass Transfer 3, 42 (1961).

J. A. Plamondon, T. E. Horton, Int. J. Heat Mass Transfer 10, 655 (1967).

J. Heat Transfer (1)

S. H. Lin, E. M. Sparrow, J. Heat Transfer 87C, 299 (1965).

J. Opt. Soc. Am. (6)

National Bureau of Standards Monograph 93 (1)

O. N. Stavroudis, L. E. Sutton, “Spot Diagrams for the Prediction of Lens Performance from Design Data,” National Bureau of Standards Monograph 93 (1965).

Opt. Acta (2)

D. L. Shealy, D. G. Burkhard, Opt. Acta 22, 485 (1975).

D. L. Shealy, D. G. Burkhard, Opt. Acta 20, 287 (1973).

Opt. Eng. (1)

D. L. Shealy, W. M. Rosenblum, Opt. Eng. 14, 237 (1975).

Optik (2)

V. Z. Barkowski, Optik 18, 22 (1961).

V. Z. Barkowski, Optik 19, 226 (1962).

Proc. IEEE (1)

G. A. Deschamps, Proc. IEEE 60, 1022 (1972).

Other (9)

M. Herzberger, Modern Geometrical Optics (Wiley-Interscience, New York, 1958).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965), p. 127.

O. N. Stavroudis, The Optics of Rays, Wavefronts, and Caustics (Academic, New York, 1972).

S. C. Parker, “Properties and Applications of Generalized Ray Tracing,” Technical Report 71, Optical Sciences Center, University of Arizona, Tucson, Arizona (1971).

V. A. Fock, Electromagnetic Diffraction and Propagation Problems (Pergamon, New York, 1965), Chap. 8.

M. Kline, I. W. Kay, Electromagnetic Theory and Geometrical Optics (Interscience, New York, 1965), pp. 184–190.

W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964).

Private communication, D. G. Burkhard, Physics Department, University of Georgia, Athens, Georgia 30602.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

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Figures (15)

Fig. 1
Fig. 1

Meridional intersection of equiconvex lens, typical ray paths, and caustic surfaces.

Fig. 2
Fig. 2

Spherical aberration vs shape factor for singlet lens.

Fig. 3
Fig. 3

Tangential and sagittal coma and oblique spherical aberration as a function of the shape factor for singlet lens.

Fig. 4
Fig. 4

Same as Fig. 1 for shape factor equal 0.9.

Fig. 5
Fig. 5

Caustic of f/4.0 cemented doublet.

Fig. 6
Fig. 6

Caustic of Petzval lens.

Fig. 7
Fig. 7

Caustic of Cooke triplet.

Fig. 8
Fig. 8

Caustic of Tessar.

Fig. 9
Fig. 9

Caustic of aerial camera lens: 7.6 cm, f/1.5.

Fig. 10
Fig. 10

Caustic of aerial camera lens: 15-cm, f/2.0, 50° field.

Fig. 11
Fig. 11

Enlarged view of Fig. 10 for alpha = 0.

Fig. 12
Fig. 12

Enlarged view of Fig. 10 for alpha = 10°.

Fig. 13
Fig. 13

Caustic of aerial camera lens: 30-cm, f/4.5, 80° field.

Fig. 14
Fig. 14

Caustic of aerial camera lens: 91-cm, f/3.7.

Fig. 15
Fig. 15

Caustic of aerial camera lens: 91-cm, f/14.0.

Equations (20)

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E d S i - d S i + 1 = σ 0 i ρ 0 i cos ϕ ( i ) cos ϕ ( i + 1 ) L 0 ( i ) + r ( i , i + 1 ) L 1 ( i ) + r 2 ( i , i + 1 ) L 2 ( i ) ,
L 0 ( i ) = A ( i ) · [ x ( i ) / u i ] × [ x ( i ) / v i ] / g 1 / 2 ( i ) ;
L 1 ( i ) = A ( i ) · { [ x ( i ) / u i ] × [ A ( i ) / v i ] + [ A ( i ) / u i ] × [ x ( i ) / v i ] } / g 1 / 2 ( i ) ;
L 2 ( i ) = A ( i ) · [ A ( i ) / u i ] × [ A ( i ) / v i ] / g 1 / 2 ( i ) ;
g 1 / 2 ( i ) = [ x ( i ) / u i ] × [ x ( i ) / v i ] .
x ( i ) = x ( u i , v i ) I + y ( u i , v i ) J + z ( u i , v i ) K .
L 0 ( i ) + r i , c L 1 ( i ) + r i , c 2 L 2 ( i ) = 0 ,
x c ( i ) = x ( i ) + r i , c A ( i ) ,
c ( u , v ) = a ( u , v ) + κ s ( u , v ) ,
κ 2 ( s · s u × s v ) + κ ( s · a u × s v + s · s u × a v ) + s · a u × a v = 0.
L A = z s ( x T ) - z s ( 0 ) ,
Q = ( r 2 + r 1 ) / ( r 2 - r 1 ) ,
r 1 = 2 f ( n - 1 ) Q + 1 ,             r 2 = 2 f ( n - 1 ) Q - 1 ,
[ r i , c ( s ) ] / ( x ) = 0 ,             [ r i , c ( t ) ] / ( x ) = 0
L A s = z s ( x T ) - z s ( x 0 ) ,
Z t = x G I P ( x 0 ) - x t ( x 0 ) ,
Z s = x G I P ( x 0 ) - x s ( x 0 ) .
A = Z t - Z s .
C t = z t ( x B ) - z t ( x T ) ,
C s = z s ( x B ) - z s ( x T ) ,

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