Abstract

It has been recently shown that the complex problem of thin lens structural design of a multicomponent lens system with a prespecified set of primary aberration residuals and Gaussian characteristics can be reduced to the problem of design of individual components with specified Gaussian parameters and central aberration targets. This paper reports a systematic approach to study the feasibility of using singlets for the individual components. The method provides an analytical procedure to select the optimum glass in a semiautomatic manner. It also attempts to ascertain the practical viability of a singlet solution by considering the possible effects of the structure of the singlet on higher-order aberrations. A set of graphs for rapid study of the feasibility of a singlet solution is also presented.

© 1986 Optical Society of America

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References

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  1. L. N. Hazra, “Structural Design of Multicomponent Lens Systems,” Appl. Opt. 23, 4440 (1984).
    [CrossRef] [PubMed]
  2. H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950).
  3. W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).
  4. M. I. Khan, J. Macdonald, “Cemented Doublets, a Method for Rapid Design,” Opt. Acta 29, 807 (1982).
    [CrossRef]
  5. Scientific Subroutine Package (SSP), Program No. 1130-CM-02X (IBM, New York, 1968).
  6. F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1974).

1984

1982

M. I. Khan, J. Macdonald, “Cemented Doublets, a Method for Rapid Design,” Opt. Acta 29, 807 (1982).
[CrossRef]

Hazra, L. N.

Hildebrand, F. B.

F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1974).

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950).

Khan, M. I.

M. I. Khan, J. Macdonald, “Cemented Doublets, a Method for Rapid Design,” Opt. Acta 29, 807 (1982).
[CrossRef]

Macdonald, J.

M. I. Khan, J. Macdonald, “Cemented Doublets, a Method for Rapid Design,” Opt. Acta 29, 807 (1982).
[CrossRef]

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).

Appl. Opt.

Opt. Acta

M. I. Khan, J. Macdonald, “Cemented Doublets, a Method for Rapid Design,” Opt. Acta 29, 807 (1982).
[CrossRef]

Other

Scientific Subroutine Package (SSP), Program No. 1130-CM-02X (IBM, New York, 1968).

F. B. Hildebrand, Introduction to Numerical Analysis (McGraw-Hill, New York, 1974).

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950).

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974).

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Figures (8)

Fig. 1
Fig. 1

Diameter Φ of a component chosen just large enough to permit the full aperture pencil from the edge of the object to pass through it.

Fig. 2
Fig. 2

Rectangular domain in the (μ, V) diagram represents the flexibility in glass selection introduced by floating of aberration targets for the singlet.

Fig. 3
Fig. 3

I vs ∑II curves and | c ¯ max| vs ∑II lines for different values of μ at Y = 0: ........, μ = 1.4; – · · – · · – · · – · · – · ·, μ = 1.5; – x – x – x – x, μ = 1.6; – – – – – –, μ = 1.7; – · – · – · – ·, μ = 1.8; —, μ = 1.9.

Fig. 4
Fig. 4

I vs ∑II curves and | c ¯ max|vs ∑II lines for different values of μ at Y = 1: ........, μ = 1.4; – · · – · · – · · – · ·, μ = 1.5; – x – x – x – x–, μ = 1.6; – – – – – – –, μ 1.7; – · – · – · – · – · – ·, μ = 1.8; —, μ = 1.9. For Y = −1 read the abscissa as −∑II.

Fig. 5
Fig. 5

I vs ∑II curves and | c ¯ max| vs ∑II lines for different values of μ at Y = 2: ........, μ = 1.4; – · · – · · – · · – · ·, μ = 1.5; – x – x – x – x –, μ = 1.6; – – – – – – –, μ = 1.7; – · – · – · – · – · – ·, μ = 1.8; —, μ = 1.9. For Y = −2 read the abscissa as −∑II.

Fig. 6
Fig. 6

I vs ∑II curves and | c ¯ max| vs ∑II lines for different values of μ at Y = 3: ........, μ = 1.4; – · – · – · – · – · –, μ = 1.5; – x – x – x – x –, μ = 1.6; – – – – – –, μ = 1.7; – · – · – · – · –, μ = 1.8; —, = 1.9. For Y = −3 read the abscissa as −∑II.

Fig. 7
Fig. 7

I vs ∑II curves and | c ¯ max| vs ∑II lines for different values of μ at Y = 4: ........, μ = 1.4; – · · – · · – · · – · · – · · – · ·, μ = 1.5; – x – x – x – x –, μ = 1.6; – – – – –, μ = 1.7; – · – · – · – · –, μ = 1.8; —, μ = 1.9. For Y = −4 read the abscissa as − ∑II.

Fig. 8
Fig. 8

I vs ∑II curves and | c ¯ max| vs ∑II lines for different values of μ at Y = 5: ........, μ = 1.4; – · · – · · – · · – · ·, μ = 1.5; – x – x – x – x –, μ = 1.6; – – – – – –, μ = 1.7; – · – · – · – · – · –, μ = 1.8; —, μ = 1.9. For Y = −5 read the abscissa as − ∑II.

Equations (18)

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Σ I = S I / h 4 K 3 , Σ I I = S I I c / h 2 K 2 H , Γ L = C L / h 2 K .
Σ I = 1 4 { μ + 2 μ ( μ - 1 ) 2 [ X - 2 ( μ 2 - 1 ) ( μ + 2 ) Y ] 2 + [ μ 2 ( μ - 1 ) 2 - μ μ + 2 Y 2 ] } , Σ I I = 1 2 { μ + 1 μ ( μ - 1 ) X - 2 μ + 1 μ Y } , Γ L = 1 V ,
X = c 1 + c 2 c 1 - c 2 ,
c 1 = 1 2 K ( X + 1 μ - 1 )             c 2 = 1 2 K ( X - 1 μ - 1 ) .
Y = u + u u - u = 1 + M 1 - M ,
D # = F / Φ = 1 / ( Φ K ) .
R = Φ c / 2 = c ¯ / 2 D # ,
R max = c ¯ max / 2 D # .
equivalent V - No . = V ˜ = 1 / Γ L .
Σ I = ( Σ I ) 0 + β [ Σ I I - ( Σ I I ) 0 ] 2 ,
( Σ I ) 0 = 1 4 [ ( μ μ - 1 ) 2 - μ μ + 2 Y 2 ] , β = μ ( μ + 2 ) ( μ + 1 ) 2 , ( Σ I I ) 0 = - 1 2 ( μ + 2 ) Y .
i = 0 5 A i μ 5 = 0 ,
A 0 = { - 8 Σ I } , A 1 = { 16 Σ I I 2 + 8 Σ I I Y - 4 Σ I } , A 2 = { 2 - 2 Y 2 - 16 Σ I I 2 - 12 Σ I I Y + 16 Σ I } , A 3 = { 5 + 3 Y 2 - 12 Σ I I 2 + 8 Σ I } , A 4 = { 4 + 8 Σ I I 2 + 4 Σ I I Y - 8 Σ I } , A 5 = { 1 - Y 2 + 4 Σ I I 2 - 4 Σ I } .
c 1 = K 2 ( X + 1 ) ( μ ˜ - 1 ) = K 2 [ μ ˜ ( μ ˜ + 1 ) { 2 Σ I I + ( 2 μ ˜ + 1 ) μ ˜ Y } + 1 ( μ ˜ - 1 ) ] , c 2 = K 2 ( X - 1 ) ( μ ˜ - 1 ) = K 2 [ μ ˜ ( μ ˜ + 1 ) { 2 Σ I I + ( 2 μ ˜ + 1 ) μ ˜ Y } - 1 ( μ ˜ - 1 ) ] .
c ¯ 1 = c 1 / K ,             c ¯ 2 = c 2 / K ,
c ¯ max = max { c ¯ 1 , c ¯ 2 } .
δ Σ I = δ S I h 4 K 3 ,             δ Σ I I = δ S I I c h 2 K 2 H .
x l = [ ( μ l - μ ˜ ) 2 + w ( V l - V ˜ ) 2 ] ½ ,

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