Abstract

Results of our studies on the primary aberrations of a thin lens that has different object and image space media are presented. It is shown that the usual formalism for treatment of the primary aberrations of a thin lens in air can be extended to this case of unequal object and image space media by suitable redefinition of the shape factor and the conjugate variable. The inequality in refractive indices and dispersion characteristics of the object and image space media gives rise to interesting properties of the primary aberrations. The latter may be utilized in the treatment of the analysis and synthesis of unconventional optical components.

© 1998 Optical Society of America

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References

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  1. D. P. Feder, “Automatic optical design,” Appl. Opt. 2, 1209–1226 (1963).
    [CrossRef]
  2. M. Laikin, Lens Design (Marcel Dekker, New York, 1955).
  3. B. Brixner, “Lens design and local minima,” Appl. Opt. 20, 384–387 (1981).
    [CrossRef] [PubMed]
  4. D. Sturlesi, D. C. O’Shea, “A global view of optical design space,” Opt. Eng. (Bellingham) 30, 207–218 (1991).
    [CrossRef]
  5. M. Kidger, P. Leary, “The existence of local minima in lens design,” in 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE1354, 69–76 (1990).
    [CrossRef]
  6. T. G. Kuper, T. J. Harris, R. S. Hilbert, “Practical lens design using a global method,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 46–51.
  7. G. Hearn, “Design optimization using generalized simulated annealing,” in Current Developments in Optical Engineering II, Robert E. Fisher, Warren J. Smith, eds., Proc. SPIE818, 258–264 (1987).
  8. A. E. W. Jones, G. W. Forbes, “Application of adaptive simulated annealing to lens design,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 42–45.
  9. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).
  10. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).
  11. H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
    [CrossRef]
  12. L. N. Hazra, “Structural design of multicomponent lens systems,” Appl. Opt. 23, 4440–4444 (1984).
    [CrossRef] [PubMed]
  13. K. Yamaji, “Design of zoom lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1967), Vol. VI, pp. 105–170.
  14. I. C. Gardner, Application of the Algebraic Aberration Equations to Optical Design, Scientific Papers of the Bureau of Standards, Vol. 22, No. 550 (U.S. Department of Commerce, Washington, D.C., 1927).
  15. A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), Vol. 2.
  16. A. Walther, “Eikonal theory and computer algebra,” J. Opt. Soc. Am. A 13, 523–531 (1996).
    [CrossRef]
  17. M. Von Rohr, Geometrical Investigation of the Formation of Images in Optical Instruments (His Majesty’s Stationary Office, London, 1920).
  18. P. Turrière, Optique Industrielle (Delagrave, Paris, 1920).
  19. H. Coddington, A Treatise on the Reflexion and Refraction of Light (Marshall, London, 1929).
  20. H. D. Taylor, A System of Applied Optics (Macmillan, London, 1906).
  21. D. Argentieri, Ottica Industriale (U. Hoepli, Milan, 1954).
  22. H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, London, 1950).
  23. H. H. Emsley, Aberrations of Thin Lenses (Constable, London, 1956).
  24. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  25. H. Chrétien, Calcul des Combinaisons Optiques (Masson, Paris, 1980).
  26. G. G. Slyussarev, Aberrations and Optical Design Theory (Hilger, Bristol, 1984).
  27. C. G. Wynne, “Thin lens aberration theory,” Opt. Acta 8, 255–265 (1961).
    [CrossRef]
  28. W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, 1986), p. 227.
  29. See Ref. 22, p. 87.
  30. W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, 1986), p. 139. Note that the sign convention for paraxial angle u in this treatise is the opposite of the paraxial angle u used here.
  31. See Ref. 22, p. 123.
  32. R. V. Shack, “The use of normalization in the application of simple optical systems,” in Effective Systems Integration and Optical Design, G. W. Wilkerson, ed., Proc. SPIE54, 155–162 (1974).
    [CrossRef]

1996 (1)

1991 (1)

D. Sturlesi, D. C. O’Shea, “A global view of optical design space,” Opt. Eng. (Bellingham) 30, 207–218 (1991).
[CrossRef]

1984 (1)

1981 (1)

1970 (1)

H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

1963 (1)

1961 (1)

C. G. Wynne, “Thin lens aberration theory,” Opt. Acta 8, 255–265 (1961).
[CrossRef]

Argentieri, D.

D. Argentieri, Ottica Industriale (U. Hoepli, Milan, 1954).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Brixner, B.

Chrétien, H.

H. Chrétien, Calcul des Combinaisons Optiques (Masson, Paris, 1980).

Coddington, H.

H. Coddington, A Treatise on the Reflexion and Refraction of Light (Marshall, London, 1929).

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), Vol. 2.

Emsley, H. H.

H. H. Emsley, Aberrations of Thin Lenses (Constable, London, 1956).

Feder, D. P.

Forbes, G. W.

A. E. W. Jones, G. W. Forbes, “Application of adaptive simulated annealing to lens design,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 42–45.

Gardner, I. C.

I. C. Gardner, Application of the Algebraic Aberration Equations to Optical Design, Scientific Papers of the Bureau of Standards, Vol. 22, No. 550 (U.S. Department of Commerce, Washington, D.C., 1927).

Harris, T. J.

T. G. Kuper, T. J. Harris, R. S. Hilbert, “Practical lens design using a global method,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 46–51.

Hazra, L. N.

Hearn, G.

G. Hearn, “Design optimization using generalized simulated annealing,” in Current Developments in Optical Engineering II, Robert E. Fisher, Warren J. Smith, eds., Proc. SPIE818, 258–264 (1987).

Hilbert, R. S.

T. G. Kuper, T. J. Harris, R. S. Hilbert, “Practical lens design using a global method,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 46–51.

Hopkins, H. H.

H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, London, 1950).

Jones, A. E. W.

A. E. W. Jones, G. W. Forbes, “Application of adaptive simulated annealing to lens design,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 42–45.

Kidger, M.

M. Kidger, P. Leary, “The existence of local minima in lens design,” in 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE1354, 69–76 (1990).
[CrossRef]

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

Kuper, T. G.

T. G. Kuper, T. J. Harris, R. S. Hilbert, “Practical lens design using a global method,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 46–51.

Laikin, M.

M. Laikin, Lens Design (Marcel Dekker, New York, 1955).

Leary, P.

M. Kidger, P. Leary, “The existence of local minima in lens design,” in 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE1354, 69–76 (1990).
[CrossRef]

O’Shea, D. C.

D. Sturlesi, D. C. O’Shea, “A global view of optical design space,” Opt. Eng. (Bellingham) 30, 207–218 (1991).
[CrossRef]

Rao, V. V.

H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

Shack, R. V.

R. V. Shack, “The use of normalization in the application of simple optical systems,” in Effective Systems Integration and Optical Design, G. W. Wilkerson, ed., Proc. SPIE54, 155–162 (1974).
[CrossRef]

Slyussarev, G. G.

G. G. Slyussarev, Aberrations and Optical Design Theory (Hilger, Bristol, 1984).

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

Sturlesi, D.

D. Sturlesi, D. C. O’Shea, “A global view of optical design space,” Opt. Eng. (Bellingham) 30, 207–218 (1991).
[CrossRef]

Taylor, H. D.

H. D. Taylor, A System of Applied Optics (Macmillan, London, 1906).

Turrière, P.

P. Turrière, Optique Industrielle (Delagrave, Paris, 1920).

Von Rohr, M.

M. Von Rohr, Geometrical Investigation of the Formation of Images in Optical Instruments (His Majesty’s Stationary Office, London, 1920).

Walther, A.

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, 1986), p. 227.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, 1986), p. 139. Note that the sign convention for paraxial angle u in this treatise is the opposite of the paraxial angle u used here.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Wynne, C. G.

C. G. Wynne, “Thin lens aberration theory,” Opt. Acta 8, 255–265 (1961).
[CrossRef]

Yamaji, K.

K. Yamaji, “Design of zoom lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1967), Vol. VI, pp. 105–170.

Appl. Opt. (3)

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

Opt. Acta (2)

H. H. Hopkins, V. V. Rao, “The systematic design of two component objectives,” Opt. Acta 17, 497–514 (1970).
[CrossRef]

C. G. Wynne, “Thin lens aberration theory,” Opt. Acta 8, 255–265 (1961).
[CrossRef]

Opt. Eng. (Bellingham) (1)

D. Sturlesi, D. C. O’Shea, “A global view of optical design space,” Opt. Eng. (Bellingham) 30, 207–218 (1991).
[CrossRef]

Other (25)

M. Kidger, P. Leary, “The existence of local minima in lens design,” in 1990 International Lens Design Conference, G. N. Lawrence, ed., Proc. SPIE1354, 69–76 (1990).
[CrossRef]

T. G. Kuper, T. J. Harris, R. S. Hilbert, “Practical lens design using a global method,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 46–51.

G. Hearn, “Design optimization using generalized simulated annealing,” in Current Developments in Optical Engineering II, Robert E. Fisher, Warren J. Smith, eds., Proc. SPIE818, 258–264 (1987).

A. E. W. Jones, G. W. Forbes, “Application of adaptive simulated annealing to lens design,” in International Optical Design Conference, G. W. Forbes, ed., Vol. 22 of OSA Proceedings Series (Optical Society of America, Washington D.C.1994), pp. 42–45.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

M. Von Rohr, Geometrical Investigation of the Formation of Images in Optical Instruments (His Majesty’s Stationary Office, London, 1920).

P. Turrière, Optique Industrielle (Delagrave, Paris, 1920).

H. Coddington, A Treatise on the Reflexion and Refraction of Light (Marshall, London, 1929).

H. D. Taylor, A System of Applied Optics (Macmillan, London, 1906).

D. Argentieri, Ottica Industriale (U. Hoepli, Milan, 1954).

H. H. Hopkins, Wave Theory of Aberrations (Oxford U. Press, London, 1950).

H. H. Emsley, Aberrations of Thin Lenses (Constable, London, 1956).

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

H. Chrétien, Calcul des Combinaisons Optiques (Masson, Paris, 1980).

G. G. Slyussarev, Aberrations and Optical Design Theory (Hilger, Bristol, 1984).

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, 1986), p. 227.

See Ref. 22, p. 87.

W. T. Welford, Aberrations of Optical Systems (Hilger, Bristol, 1986), p. 139. Note that the sign convention for paraxial angle u in this treatise is the opposite of the paraxial angle u used here.

See Ref. 22, p. 123.

R. V. Shack, “The use of normalization in the application of simple optical systems,” in Effective Systems Integration and Optical Design, G. W. Wilkerson, ed., Proc. SPIE54, 155–162 (1974).
[CrossRef]

K. Yamaji, “Design of zoom lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1967), Vol. VI, pp. 105–170.

I. C. Gardner, Application of the Algebraic Aberration Equations to Optical Design, Scientific Papers of the Bureau of Standards, Vol. 22, No. 550 (U.S. Department of Commerce, Washington, D.C., 1927).

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), Vol. 2.

M. Laikin, Lens Design (Marcel Dekker, New York, 1955).

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Figures (9)

Fig. 1
Fig. 1

a) Paraxial ray paths through a single lens of refractive index μ. The object and image spaces have indices n1 and n2. b) Equivalent thin lens for the singlet assuming d0. Stop is on the lens.

Fig. 2
Fig. 2

Variation of ΣI with X. Y=0, μ=1.5, n=1. (a) n=1, (b) n=1.2, (c) n=1.4, (d) n=1.6, (e) n=1.8, (f) n=2.

Fig. 3
Fig. 3

Variation of ΣI with X. Y=-1, μ=1.6, n=1. (a) n=1, (b) n=1.2, (c) n=1.4, (e) n=1.8, (f) n=2.

Fig. 4
Fig. 4

Variation of ΣI with X. Y=2, μ=1.7, n=1. (a) n=1, (b) n=1.2, (c) n=1.4, (d) n=1.6, (e) n=1.8, (f) n=2.

Fig. 5
Fig. 5

Variation of ΣII with X. Y=0, μ=1.5, n=1. (a) n=1, (b) n=1.2, (c) n=1.4, (d) n=1.6, (e) n=1.8, (f) n=2.

Fig. 6
Fig. 6

Variation of ΣII with X. Y=-1, μ=1.6, n=1. (a) n=1, (b) n=1.2, (c) n=1.4, (e) n=1.8, (f) n=2.

Fig. 7
Fig. 7

Variation of ΣII with X. Y=2, μ=1.7, n=1. (a) n=1, (b) n=1.2, (c) n=1.4, (d) n=1.6, (e) n=1.8, (f) n=2.

Fig. 8
Fig. 8

Variation of ΣIII with Y. μ=1.5, n=1. (a) n=1, (b) n=1.2, (c) n=1.4, (d) n=1.6, (e) n=1.8, (f) n=2.

Fig. 9
Fig. 9

Variation of ΣIV with X. μ=1.5, n=1. (a) n=1, (b) n=1.2, (c) n=1.4, (d) n=1.6, (e) n=1.8, (f) n=2.

Equations (88)

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μu1-n1u1=h1(μ-n1)c1
u2=u1,
h2=h1-du2,
n2u2-μu2=h2(n2-μ)c2.
n2u2-n1u1=hK
K=(μ-n1)c1-(μ-n2)c2.
X=(μ-n1)c1+(μ-n2)c2K
c1=K(X+1)2(μ-n1),
c2=K(X-1)2(μ-n2).
Δc1=K2(μ-n1)ΔX,
Δc2=K2(μ-n2)ΔX,
Y=n2u2+n1u1n2u2-n1u1=n2u2+n1u1hK.
u2=hK2n2(Y+1),
u1=hK2n1(Y-1).
Y=1+M1-M.
A1=n1(hc1-u1)=12n1hKXμ-n1-Yn1+μn1(μ-n1).
A2=n2(hc2-u2)=12n2hKXμ-n2-Yn2-μn2(μ-n2).
A¯1=n2(hc¯2-u¯2)=-n1u¯1=Hh,
A¯2=n1(hc¯1-u¯1)=-n2u¯2=Hh,
H=n1(u1h¯-u¯1h)=-n1u¯1h=n2(u2h¯-u¯2h)=-n2u¯2h.
Δ1=u1μ-u1n1,
Δ2=u2n2-u2μ.
Δ1=12hK1n12+Xμ2-μ2-n12μ2n12Y,
Δ2=12hK1(n2)2-Xμ2+μ2-(n2)2μ2(n2)2Y.
SI=A12hΔ1+A22hΔ2.
SI=18h4K3(a1X3+a2Y3+a3X2Y+a4XY2+a5X2+a6Y2+a7XY+a8X+a9Y+a10),
a1=1μ2n2(μ-n)2-(n)2(μ-n)2,
a2=-1μ2μ2-n2n2-μ2-(n)2(n)2,
a3=-1μ2μ+3nμ-n-μ+3nμ-n,
a4=1μ22µ+3nn-2µ+3nn,
a5=1μμ+2n(μ-n)2+μ+2n(μ-n)2,
a6=1μ3µ+2nn2+3µ+2n(n)2,
a7=-4μμ+nn(μ-n)+μ+nn(μ-n),
a8=2µ+nn(μ-n)2-2µ+nn(μ-n)2,
a9=-3µ+nn2(μ-n)-3µ+n(n)2(μ-n),
a10=μ21n2(μ-n)2+1(n)2(μ-n)2.
a1=a2=a3=a4=a8=a9=0,
(SI)n=n=14h4K3μ+2nμ(μ-n)2X2+3µ+2nμn2Y2-4(μ+n)μn(μ-n)XY+μ2n2(μ-n)2.
(SI)n=n=1=14h4K3μ+2μ(μ-1)2X2+3µ+2μY2-4(μ+1)μ(μ-1)XY+μ2(μ-1)2=14h4K3μ+2μ(μ-1)2X-2(μ2-1)μ+2Y2+μ2(μ-1)2-μμ+2Y2.
ΣI=SIh4K3.
d2ΣIdX2=0.
X˜=-a33a1Y-a53a1.
asnμ, a3a10anda5a1-3,
(SI)nμ=18h4K3(a1+a2Y3+a3Y+a4Y2+a5+a6Y2+a7Y+a8+a9Y+a10),
a1=1μ2n2(μ-n)2.
ΣI(X, Y, n, n, μ)=ΣI(-X,-Y, n, n, μ).
SII=A¯1A1hΔ1+A¯2A2hΔ2.
SII=H(A1Δ1+A2D2).
SII=14h2K2H(p1X2+p2Y2+p3XY+p4X+p5Y+p6),
p1=1μ2nμ-n-nμ-n,
p2=1μ2μ2-n2n2-μ2-(n)2(n)2,
p3=-1μ2μ+2nn-μ+2nn,
p4=1μμ+nn(μ-n)+μ+nn(μ-n),
p5=-1μ2µ+nn2+2µ+n(n)2,
p6=μ1n2(μ-n)-1(n)2(μ-n).
p1=p2=p3=p6=0,
(SII)n=n=12h2K2Hμ+nμn(μ-n)X-2µ+nμn2Y.
(SII)n=n=1=12h2K2Hμ+1μ(μ-1)X-2µ+1μY.
ΣII=SIIh2K2H.
(SII)nμ=14h2K2H(p1+p2Y2+p3Y+p4+p5Y+p6),
p1=1μ2nμ-n.
ΣII(X, Y, n, n, μ)=-ΣII(-X,-Y, n, n, μ).
SIII=A¯12hΔ1+A¯22hΔ2.
SIII=12H2K1n2+1(n)2-1n2-1(n)2Y.
(SIII)n=n=H2Kn2.
(SIII)n=n=1=H2K.
ΣIII=SIIIH2K.
ΣIII(Y, n, n)=ΣIII(-Y, n, n).
SIV=H2(P1+P2),
P1=-c11μ-1n1,
P2=-c21n2-1μ.
SIV=H2K2µ1n+1n+1n-1nX.
(SIV)n=n=H2Kμn.
(SIV)n=n=1=H2Kμ.
ΣIV=SIVH2K.
ΣIV(X, n, n)=ΣIV(-X, n, n),
SV=A¯1A1(H2P1+A¯12hΔ1)+A¯2A2(H2P2+A¯22hΔ2),
SV=H3h21n2-1(n)2,
CL=A1hΔ1δnn+A2hΔ2δnn,
Δ1δnn=δμμ-δn1n1,
Δ2δnn=δn2n2-δμμ.
CL=12h2K1μ-n+1μ-nδμ-δnn(μ-n)+δnn(μ-n)μ+δμμnμ-n-nμ-n-δnμ-n-δnμ-nX+δnn-δnnY,
(CL)n=n=h2Knδμ-δnμn(μ-n).
(CL)n=n=1=h2Kδμμ-1=h2KV,
ΣL=CLh2K,
ΣL(X, Y, n, n, μ)=ΣL(-X,-Y, n, n, μ).
CT=A¯1hΔ1δnn+A¯2hΔ2δnn.
CT=Hδnn-δnn.

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