Abstract

In this paper, the sensitivity control for manufacturing errors is treated from three aspects. A wavefront-based sensitivity function is proposed, the effect of which is verified with the modulation transfer function (MTF)-based Monte Carlo simulation. Then, the direct optimization of the MTF-based Monte Carlo simulation result is proposed. Finally, the effect of the sensitivity control function to get better lens types is shown.

© 2010 Optical Society of America

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References

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  1. G. Catalan, “Design method of an astronomical telescope with reduced sensitivity to misalignment,” Appl. Opt. 33, 1907–1915 (1994).
    [CrossRef] [PubMed]
  2. J. R. Rogers, “Using global synthesis to find tolerance-insensitive design forms,” Proc. SPIE 6342, 63420M (2006).
    [CrossRef]
  3. J. P. McGuire, Jr., “Designing easily manufactured lenses using a global method,” Proc. SPIE 6342, 63420O (2006).
    [CrossRef]
  4. M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” Proc. SPIE 6342, 63420N (2007).
    [CrossRef]
  5. D. S. Grey, “Tolerance sensitivity and optimization,” Appl. Opt. 9, 523–526 (1970).
    [CrossRef] [PubMed]
  6. M. Rimmer, “Analysis of perturbed lens systems,” Appl. Opt. 9, 533–537 (1970).
    [CrossRef] [PubMed]
  7. M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Section 9.1.
  8. See, for example, Y. Shinohara, “Imaging lens,” U.S. patent 7,453,654 (18 November 2008).

2007 (1)

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” Proc. SPIE 6342, 63420N (2007).
[CrossRef]

2006 (2)

J. R. Rogers, “Using global synthesis to find tolerance-insensitive design forms,” Proc. SPIE 6342, 63420M (2006).
[CrossRef]

J. P. McGuire, Jr., “Designing easily manufactured lenses using a global method,” Proc. SPIE 6342, 63420O (2006).
[CrossRef]

1994 (1)

1970 (2)

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Section 9.1.

Catalan, G.

Grey, D. S.

Isshiki, M.

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” Proc. SPIE 6342, 63420N (2007).
[CrossRef]

Kaneko, S.

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” Proc. SPIE 6342, 63420N (2007).
[CrossRef]

McGuire, J. P.

J. P. McGuire, Jr., “Designing easily manufactured lenses using a global method,” Proc. SPIE 6342, 63420O (2006).
[CrossRef]

Rimmer, M.

Rogers, J. R.

J. R. Rogers, “Using global synthesis to find tolerance-insensitive design forms,” Proc. SPIE 6342, 63420M (2006).
[CrossRef]

Sinclair, D. C.

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” Proc. SPIE 6342, 63420N (2007).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Section 9.1.

Appl. Opt. (3)

Proc. SPIE (3)

J. R. Rogers, “Using global synthesis to find tolerance-insensitive design forms,” Proc. SPIE 6342, 63420M (2006).
[CrossRef]

J. P. McGuire, Jr., “Designing easily manufactured lenses using a global method,” Proc. SPIE 6342, 63420O (2006).
[CrossRef]

M. Isshiki, D. C. Sinclair, and S. Kaneko, “Lens design: global optimization of both performance and tolerance sensitivity,” Proc. SPIE 6342, 63420N (2007).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Section 9.1.

See, for example, Y. Shinohara, “Imaging lens,” U.S. patent 7,453,654 (18 November 2008).

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Figures (16)

Fig. 1
Fig. 1

Coordinate system and the reference sphere.

Fig. 2
Fig. 2

Section drawing of Example 1.

Fig. 3
Fig. 3

Through-focus MTF of Example 1.

Fig. 4
Fig. 4

Correlation between the decenter sensitivity function and the average MTF loss of the Monte Carlo simulation (on-axis).

Fig. 5
Fig. 5

Correlation between the decenter sensitivity function and the average MTF loss of the Monte Carlo simulation (0.7 full field tangential).

Fig. 6
Fig. 6

Correlation between the curvature error sensitivity function and the average MTF loss of the Monte Carlo simulation (on-axis).

Fig. 7
Fig. 7

Correlation between the curvature error sensitivity function and the average MTF loss of the Monte Carlo simulation (0.7 full field tangential).

Fig. 8
Fig. 8

Section drawing of Example 2.

Fig. 9
Fig. 9

Through-focus MTF of Example 2.

Fig. 10
Fig. 10

Correlation between the decenter sensitivity function and the average MTF loss of the Monte Carlo simulation (on-axis).

Fig. 11
Fig. 11

Correlation between the decenter sensitivity function and the average MTF loss of the Monte Carlo simulation (0.7 full field tangential).

Fig. 12
Fig. 12

Correlation between the exact calculation and the approximate calculation of the average MTF loss.

Fig. 13
Fig. 13

Average MTF loss of the Monte Carlo simulation (0.7 full field tangential) before and after the direct optimization.

Fig. 14
Fig. 14

Three solutions from the parallel plates of Example 3.

Fig. 15
Fig. 15

Correlation between the decenter sensitivity function and the average MTF loss of the Monte Carlo simulation.

Fig. 16
Fig. 16

Decenter sensitivity of each surface at the 0.7 full field.

Tables (3)

Tables Icon

Table 1 Specification of Example 1

Tables Icon

Table 2 Specification of Example 2

Tables Icon

Table 3 Specification of Example 3

Equations (19)

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i ( P ) 1 ( 2 π λ ) 2 ( Δ Φ P ) 2 .
Φ = Φ + H ρ 2 + K ρ sin θ + L ρ cos θ + M ,
z = z + 2 ( R a ) 2 H , x = x + ( R a ) K , y = y + ( R a ) L ,
Φ i + l i x Δ x + l i y Δ y + l i z Δ z Φ 0 = 0 ( i = 1 n ) ,
f + A d = 0 ,
f = ( Φ 1 Φ n ) , A = ( l 1 x l 1 y l 1 z 1 l n x l n y l n z 1 ) , d = ( Δ x Δ y Δ z Φ 0 ) .
d = ( A t A ) 1 A t f ,
Δ f = f A ( A t A ) 1 A t f ,
( Δ f ) t Δ f = f t ( I A ( A t A ) 1 A t ) f f t B f .
( Δ f ) t Δ f = ( f + δ f ) t B ( f + δ f ) = f t B f + δ f t B f + f t B δ f + δ f t B δ f .
( Δ f ) t Δ f = f t B f + δ f t B δ f .
δ f = i c i δ f i ,
δ f t B δ f = i c i 2 δ f i t B δ f i .
Δ z = Δ z 0 + j c j δ z j ,
Φ i = Φ i 0 + j c j δ Φ i j ,
Φ i + j c j ( δ Φ i j + l i z δ z j ) + l i x Δ x + l i y Δ y + l i z Δ z 0 Φ 0 = 0 ( i = 1 n ) .
Γ = N l · n N l · n ,
d = n z ( h h 0 ) 2 δ z 0 ,
d = n z ( g y ) δ y ,

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