Abstract

Mid-spatial-frequency (MSF) surface errors are left after processing aspheres or freeforms by small bits. MSF errors sometimes have significant effects on the image quality of optical systems. The efforts on the analysis and tolerancing of the MSF errors have been paid. This paper focuses on the desensitization to the MSF errors. The design target for the desensitization to the MSF errors is defined. A possibility of the desensitization is shown for optical systems in which freeforms are used with spheres.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. A. Yabe, “General method of sensitivity control for manufacturing errors,” Appl. Opt. 49(27), 5175–5182 (2010).
    [Crossref]
  2. A. Yabe, “Sensitivity control to surface irregularity,” Proc. SPIE 6342, ThB4 (2006).
    [Crossref]
  3. R. N. Youngworth, “Tolerancing Forbes aspheres: advantages of an orthogonal basis,” Proc. SPIE 7433, 74330H (2009).
    [Crossref]
  4. A. Yabe, “Desensitization of axially asymmetric optical systems,” Adv. Opt. Technol. 2(1), 63–73 (2013).
    [Crossref]
  5. G. W. Forbes, “Never-ending struggles with mid-spatial-frequencies,” Proc. SPIE 9525, 95251B (2015).
    [Crossref]
  6. R. N. Youngworth and B. D. Stone, “Simple estimates for the effect of mid-spatial-frequency surface errors on image quality,” Appl. Opt. 39(13), 2198–2209 (2000).
    [Crossref]
  7. J. M. Tamkin, T. D. Milster, and W. Dallas, “Theory of modulation transfer function artifacts due to mid-spatial-frequency errors and its application to optical tolerancing,” Appl. Opt. 49(25), 4825–4835 (2010).
    [Crossref]
  8. J. M. Tamkin and T. D. Milster, “Analysis and tolerancing of structured mid-spatial frequency errors in imaging systems,” Proc. SPIE 7652, 765218 (2010).
    [Crossref]
  9. D. M. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems,” Optical Fabrication and Testing 2008, OTuA1 (2008).
  10. E. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83–91 (1991).
    [Crossref]
  11. A. Yabe, “Global optimization of zoom lenses,” Proc. SPIE 3482, 122–125 (1998).
    [Crossref]
  12. A. Yabe, “Method to allocate freeform surfaces in axially asymmetric optical systems,” Proc. SPIE 8167, 816703 (2011).
    [Crossref]
  13. G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007).
    [Crossref]
  14. A. Yabe, “Representation of freeform surfaces suitable for optimization,” Appl. Opt. 51(15), 3054–3058 (2012).
    [Crossref]

2015 (1)

G. W. Forbes, “Never-ending struggles with mid-spatial-frequencies,” Proc. SPIE 9525, 95251B (2015).
[Crossref]

2013 (1)

A. Yabe, “Desensitization of axially asymmetric optical systems,” Adv. Opt. Technol. 2(1), 63–73 (2013).
[Crossref]

2012 (1)

2011 (1)

A. Yabe, “Method to allocate freeform surfaces in axially asymmetric optical systems,” Proc. SPIE 8167, 816703 (2011).
[Crossref]

2010 (3)

2009 (1)

R. N. Youngworth, “Tolerancing Forbes aspheres: advantages of an orthogonal basis,” Proc. SPIE 7433, 74330H (2009).
[Crossref]

2007 (1)

2006 (1)

A. Yabe, “Sensitivity control to surface irregularity,” Proc. SPIE 6342, ThB4 (2006).
[Crossref]

2000 (1)

1998 (1)

A. Yabe, “Global optimization of zoom lenses,” Proc. SPIE 3482, 122–125 (1998).
[Crossref]

1991 (1)

E. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83–91 (1991).
[Crossref]

Aikens, D. M.

D. M. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems,” Optical Fabrication and Testing 2008, OTuA1 (2008).

Bruegge, T. J.

E. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83–91 (1991).
[Crossref]

Dallas, W.

DeGroote, J. E.

D. M. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems,” Optical Fabrication and Testing 2008, OTuA1 (2008).

Forbes, G. W.

G. W. Forbes, “Never-ending struggles with mid-spatial-frequencies,” Proc. SPIE 9525, 95251B (2015).
[Crossref]

G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007).
[Crossref]

Kuper, T. G.

E. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83–91 (1991).
[Crossref]

Milster, T. D.

J. M. Tamkin and T. D. Milster, “Analysis and tolerancing of structured mid-spatial frequency errors in imaging systems,” Proc. SPIE 7652, 765218 (2010).
[Crossref]

J. M. Tamkin, T. D. Milster, and W. Dallas, “Theory of modulation transfer function artifacts due to mid-spatial-frequency errors and its application to optical tolerancing,” Appl. Opt. 49(25), 4825–4835 (2010).
[Crossref]

Rimmer, E. P.

E. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83–91 (1991).
[Crossref]

Stone, B. D.

Tamkin, J. M.

J. M. Tamkin, T. D. Milster, and W. Dallas, “Theory of modulation transfer function artifacts due to mid-spatial-frequency errors and its application to optical tolerancing,” Appl. Opt. 49(25), 4825–4835 (2010).
[Crossref]

J. M. Tamkin and T. D. Milster, “Analysis and tolerancing of structured mid-spatial frequency errors in imaging systems,” Proc. SPIE 7652, 765218 (2010).
[Crossref]

Yabe, A.

A. Yabe, “Desensitization of axially asymmetric optical systems,” Adv. Opt. Technol. 2(1), 63–73 (2013).
[Crossref]

A. Yabe, “Representation of freeform surfaces suitable for optimization,” Appl. Opt. 51(15), 3054–3058 (2012).
[Crossref]

A. Yabe, “Method to allocate freeform surfaces in axially asymmetric optical systems,” Proc. SPIE 8167, 816703 (2011).
[Crossref]

A. Yabe, “General method of sensitivity control for manufacturing errors,” Appl. Opt. 49(27), 5175–5182 (2010).
[Crossref]

A. Yabe, “Sensitivity control to surface irregularity,” Proc. SPIE 6342, ThB4 (2006).
[Crossref]

A. Yabe, “Global optimization of zoom lenses,” Proc. SPIE 3482, 122–125 (1998).
[Crossref]

Youngworth, R. N.

R. N. Youngworth, “Tolerancing Forbes aspheres: advantages of an orthogonal basis,” Proc. SPIE 7433, 74330H (2009).
[Crossref]

R. N. Youngworth and B. D. Stone, “Simple estimates for the effect of mid-spatial-frequency surface errors on image quality,” Appl. Opt. 39(13), 2198–2209 (2000).
[Crossref]

D. M. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems,” Optical Fabrication and Testing 2008, OTuA1 (2008).

Adv. Opt. Technol. (1)

A. Yabe, “Desensitization of axially asymmetric optical systems,” Adv. Opt. Technol. 2(1), 63–73 (2013).
[Crossref]

Appl. Opt. (4)

Opt. Express (1)

Proc. SPIE (7)

E. P. Rimmer, T. J. Bruegge, and T. G. Kuper, “MTF optimization in lens design,” Proc. SPIE 1354, 83–91 (1991).
[Crossref]

A. Yabe, “Global optimization of zoom lenses,” Proc. SPIE 3482, 122–125 (1998).
[Crossref]

A. Yabe, “Method to allocate freeform surfaces in axially asymmetric optical systems,” Proc. SPIE 8167, 816703 (2011).
[Crossref]

J. M. Tamkin and T. D. Milster, “Analysis and tolerancing of structured mid-spatial frequency errors in imaging systems,” Proc. SPIE 7652, 765218 (2010).
[Crossref]

A. Yabe, “Sensitivity control to surface irregularity,” Proc. SPIE 6342, ThB4 (2006).
[Crossref]

R. N. Youngworth, “Tolerancing Forbes aspheres: advantages of an orthogonal basis,” Proc. SPIE 7433, 74330H (2009).
[Crossref]

G. W. Forbes, “Never-ending struggles with mid-spatial-frequencies,” Proc. SPIE 9525, 95251B (2015).
[Crossref]

Other (1)

D. M. Aikens, J. E. DeGroote, and R. N. Youngworth, “Specification and Control of Mid-Spatial Frequency Wavefront Errors in Optical Systems,” Optical Fabrication and Testing 2008, OTuA1 (2008).

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Figures (6)

Fig. 1.
Fig. 1. Quantities to calculate the Gamma factor at the surface 1.
Fig. 2.
Fig. 2. Gamma factor as the function of the sine of incident angle.
Fig. 3.
Fig. 3. Designs without and with the sensitivity control.
Fig. 4.
Fig. 4. Field plot of the MTF.
Fig. 5.
Fig. 5. Sensitivity to MSF errors.
Fig. 6.
Fig. 6. Character of freeforms

Tables (1)

Tables Icon

Table 1. Specifications

Equations (8)

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W ( u ) = W 0 ( u ) + i Γ i ( u ) d i ( u ) ,
Γ = N l n N l n ,
d i ( u ) = s i ( u ) + f i ( u ) ,
W 1 ( u ) W 0 ( u ) + i Γ i ( u ) s i ( u ) .
W d 2 u = ( W 1 + i Γ i f i ) d 2 u = W 1 d 2 u ,
W 2 d 2 u = W 1 2 d 2 u + 2 W 1 i Γ i f i d 2 u + i , j Γ i Γ i f i f j d 2 u = W 1 2 d 2 u + i , j Γ i Γ i f i f j d 2 u .
W 2 d 2 u = W 1 2 d 2 u + i Γ i 2 f i 2 d 2 u .
W 2 d 2 u = W 1 2 d 2 u + i f i 2 ¯ Γ i 2 d 2 u .

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