Abstract

The two caustic surfaces, which are in turn the loci of the image points, are formed in the image region by each element of the source of an optical system. Lens optimization is achieved herein by adjusting parameters so that the caustic surfaces formed by rays from selected points of the object coalesce and converge to the corresponding Gaussian image points. A merit function, specifying the sum of the distances between each caustic surface and the corresponding Gaussians image, is defined and minimized subject to the constraints that the system focal length and physical length are constant and that the third-order aberrations of the system are zero. An optimization procedure, based on minimizing the caustic merit function, is used to design a singlet, doublet, and triplet lens system.

© 1989 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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1981

1980

D. O. Burkhard, D. L. Shealy, “Simplified Formula for the Illuminance in an Optical System,” Appl. Opt. 20, 897 (1980).
[CrossRef]

R.-S. Chang, O. N. Stavroudis, “Generalized Ray Tracing, Caustic Surfaces, Generalized Bending, and the Construction of a Novel Merit Function for Optical Design,” J. Opt. Soc. Am. 70, 976 (1980).
[CrossRef]

P. N. Robb, “Lens Design Using Optical Aberration Coefficients,” Proc. Soc. Photo-Opt. Instrun. Eng. 237, 109 (1980).

F. Kondoh, “Lens Designing Utilizing Seidel’s Coefficients,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 120 (1980).

1976

D. L. Shealy, “Analytical Illuminance and Caustic Surface Calculations in Geometrical Optics,” Appl. Opt. 15, 2588 (1976).
[CrossRef] [PubMed]

D. L. Shealy, D. G. Burkhard, “Caustic Surface Merit Functions in Optical Design,” J. Opt. Soc. Am. 66, 1122 (1976).
[CrossRef]

1973

1963

1962

1956

L. Seidel, “On Dioptics on the Development of Third Order Coefficients,” Astron. Nachr. 43, 289 (1956).
[CrossRef]

1947

Brouwer, W.

W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964), p. 149.

Buchdahl, H. A.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. P., London, 1970), pp. 305–310.

Burkhard, D. G.

D. G. Burkhard, D. L. Shealy, “Simplified Formula for the Illuminance in an Optical System,” Appl. Opt. 20, 897 (1981).
[CrossRef] [PubMed]

D. L. Shealy, D. G. Burkhard, “Caustic Surface Merit Functions in Optical Design,” J. Opt. Soc. Am. 66, 1122 (1976).
[CrossRef]

Burkhard, D. O.

Chang, R.-S.

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), p. 436.

Cox, A.

A. Cox, A System of Optical Design (Focal Press, London, 1964), p. 430.

Feder, D. P.

Hardy, A. C.

A. C. Hardy, F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932), p. 89.

Herzberger, M.

Hopkins, R. E.

Jamieson, T. H.

T. H. Jamieson, Optimization Techniques in Lens Design (American Elsevier, New York, 1971), pp. 33–49.

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamental of Optics (McGraw-Hill, New York, 1957), p. 173.

Johnson, R. B.

Kassim, A. M.

A. M. Kassim, “Caustic Wave Aberration Theory for General Optical Systems,” Ph. D. Dissertation, U. Alabama at Birmingham (1985).

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1976), pp. 55–57.

Kondoh, F.

F. Kondoh, “Lens Designing Utilizing Seidel’s Coefficients,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 120 (1980).

Perrin, F. H.

A. C. Hardy, F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932), p. 89.

Robb, P. N.

P. N. Robb, “Lens Design Using Optical Aberration Coefficients,” Proc. Soc. Photo-Opt. Instrun. Eng. 237, 109 (1980).

Robinowitz, P.

P. Robinowitz, Numerical Method for Non-Linear Algebraic Equations (Gerdonrd Breach Science Publisher, New York, 1970), p. 115.

Sands, P. J.

Seidel, L.

L. Seidel, “On Dioptics on the Development of Third Order Coefficients,” Astron. Nachr. 43, 289 (1956).
[CrossRef]

Shealy, D. L.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 341–346.

Spencer, G.

Stavroudis, O. N.

Sutton, L. E.

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974), pp. 46–66.

White, H. E.

F. A. Jenkins, H. E. White, Fundamental of Optics (McGraw-Hill, New York, 1957), p. 173.

Appl. Opt.

Astron. Nachr.

L. Seidel, “On Dioptics on the Development of Third Order Coefficients,” Astron. Nachr. 43, 289 (1956).
[CrossRef]

J. Opt. Soc. Am.

Proc. Soc. Photo-Opt. Instrum. Eng.

F. Kondoh, “Lens Designing Utilizing Seidel’s Coefficients,” Proc. Soc. Photo-Opt. Instrum. Eng. 237, 120 (1980).

Proc. Soc. Photo-Opt. Instrun. Eng.

P. N. Robb, “Lens Design Using Optical Aberration Coefficients,” Proc. Soc. Photo-Opt. Instrun. Eng. 237, 109 (1980).

Other

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1976), pp. 55–57.

F. A. Jenkins, H. E. White, Fundamental of Optics (McGraw-Hill, New York, 1957), p. 173.

W. Brouwer, Matrix Methods in Optical Instrument Design (Benjamin, New York, 1964), p. 149.

A. C. Hardy, F. H. Perrin, The Principles of Optics (McGraw-Hill, New York, 1932), p. 89.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), pp. 341–346.

T. H. Jamieson, Optimization Techniques in Lens Design (American Elsevier, New York, 1971), pp. 33–49.

A. E. Conrady, Applied Optics and Optical Design (Dover, New York, 1957), p. 436.

A. Cox, A System of Optical Design (Focal Press, London, 1964), p. 430.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. P., London, 1970), pp. 305–310.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974), pp. 46–66.

P. Robinowitz, Numerical Method for Non-Linear Algebraic Equations (Gerdonrd Breach Science Publisher, New York, 1970), p. 115.

A. M. Kassim, “Caustic Wave Aberration Theory for General Optical Systems,” Ph. D. Dissertation, U. Alabama at Birmingham (1985).

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Figures (6)

Fig. 1
Fig. 1

Meridional intersection of the tangential and sagittal sheets of the caustic surfaces for a singlet lens.

Fig. 2
Fig. 2

(a) Average caustic merit function and (b) rms blur circle radius vs the shape factor of a singlet lens for on-axis light.

Fig. 3
Fig. 3

Average caustic merit function for on-axis light incident on a doublet lens vs (a) the left element focal length and (b) the left element shape factor.

Fig. 4
Fig. 4

Average caustic merit function vs lens spacing ratio for a series of lenses satisfying Eq. (10) based on the starting lens given in Table I.

Fig. 5
Fig. 5

Root-mean-square blur circle radius vs the field angle for the Hopkins and optimized triplet lens.

Fig. 6
Fig. 6

Root-mean-square blur circle radius vs the field angle for the triplet lenses given in Table III.

Tables (3)

Tables Icon

Table I Triplet Lens Parameters from Ref. 26 with Effective Focal Length of 10 cm and Aperture Radius of 1.5 cm (F/3.3)

Tables Icon

Table II Optimum Triplet Lens Parameters with Effective Focal Length of 10 cm and Aperture Radius of 1.5 cm (F/3.3), Starting System Given In Table 1

Tables Icon

Table III Triplet Lens Parameters for Initial System (1), System Optimized by Chang-Stavroudis11 (2), and System Optimized by use of the Caustic Merit Function (3)a

Equations (16)

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Φ 2 = x c - x F 2 + x c - x F 2 = ( x c - x F ) 2 + ( y c - y F ) 2 + ( Z c - Z F ) 2 + ( x c - x F ) 2 + ( y c - y F ) 2 + ( Z c - Z F ) 2 ,
Φ = 1 N ρ N ϕ i = 1 N ϕ j = 1 N ρ Φ ( i , j ) ,
R 1 = ( n - 1 ) ( Q + 1 ) { f ± [ f 2 + f t ( Q + 1 ) n ( Q - 1 ) ] 1 / 2 } ,
R 2 = R 1 ( Q + 1 ) ( Q - 1 ) ,
R 3 = ( n 2 - 1 ) { - 1 + ( n 2 - 1 ) t 2 n 2 R 2 } { 1 f 2 - ( n 2 - 1 ) R 2 } ,
1 f 2 = 1 f T - 1 f 1 .
S = i = 1 6 S i = i = 1 6 n i 2 h i θ i 2 { α i n i - α i n i } ,
B = i = 1 6 S i γ i ,
Z = i = 1 6 S i γ i 2 ,
P = i = 1 6 P i = i = 1 6 ( n i - n i - 1 ) n i n i - 1 R i ,
D = i = 1 6 ( S i γ i 2 + P i ) γ i ,
α i = 1 n i { ( n i - n i ) R i h i + n i α i } ,
h i + 1 = h i - α i d i ,
θ i = h i R i - α i .
γ i = 1 h i θ i n i + j = 1 6 d j n j h j h j + 1 .
F k ( R 1 , , R 6 , X , Y ) = 0 for k = 1 , 2 , , 6.

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