Abstract

Often the tolerancing of an optical system is performed by treating the optical system as a black box in which the designer sets tolerances for perturbations and then runs a Monte Carlo analysis to determine the as-built performance. When the effects of the perturbations are not considered, the tolerances might result tighter than necessary, proper compensation might be missed, and manufacturing cost can be increased. By acquiring aberration sensitivity for each type of perturbation, an optical engineer can increase tolerances by ad hoc compensation. An aberration sensitivity evaluation can be performed quickly and can be incorporated into the initial lens design phase. A lens designer can find what surfaces or elements within the optical system will be problematic before any time-consuming Monte Carlo run is performed. In this paper we use aberration theory of plane symmetric systems to remove, to some useful extent, the black-box tolerancing approach and to provide some insights into tolerancing. The tolerance sensitivities that are analyzed are with respect to surface tilt, center thickness, index value, and radius. To analyze these perturbations, exact wavefront calculations are performed for the following aberrations: uniform astigmatism, uniform coma, linear astigmatism, distortion I, distortion II, spherical aberration, linear coma, quadratic astigmatism, and cubic distortion. We provide a discussion about how the aberration tolerancing analysis is useful.

© 2014 Optical Society of America

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References

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  1. D. S. Grey, “Tolerance sensitivity and optimization,” Appl. Opt. 9, 523–526 (1970).
    [CrossRef]
  2. M. P. Rimmer, “Analysis of perturbed lens systems,” Appl. Opt. 9, 533–537 (1970).
    [CrossRef]
  3. R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (Academic, 2010).
  4. R. R. Shannon, The Art and Science of Optical Design, 1st ed. (Cambridge University, 1997).
  5. W. J. Smith, “Fundamentals of establishing an optical tolerance budget,” Proc. SPIE 0531, 196–204 (1985).
  6. M. J. Kidger, Intermediate Optical Design, 1st ed. (SPIE, 2004).
  7. M. R. Descour and J. M. Sasian, “Power distribution and symmetry in lens systems,” Opt. Eng. 37, 1001–1004 (1998).
    [CrossRef]
  8. J. M. Sasian, “How to approach the design of a bilateral symmetric optical system,” Opt. Eng. 33, 2045–2061 (1994).
    [CrossRef]
  9. J. M. Sasian, “Imagery of the bilateral symmetrical optical system,” Ph.D. thesis (The University of Arizona, 1988).
  10. L. Wang and J. M. Sasian, “Merit figures for fast estimating tolerance sensitivity,” Proc. SPIE 7652, 76521P (2010).
    [CrossRef]
  11. J. M. Sasian, “Extrinsic aberrations in optical imaging systems,” Adv. Opt. Technol. 2, 75–80 (2013).
  12. Zemax, Product of Radiant Zemax (Redmond, Washington, 2013).
  13. J. L. Bentley, C. Glazowski, and J. M. Zavislan, “Apochromatic immersion objective for in-vivo imaging for low coherence confocal microscopy,” Proc. SPIE 6342, 63420G (2007).
    [CrossRef]
  14. Optimax Systems, “Manufacturing tolerance chart,” http://www.optimaxsi.com/innovation/optical-manufacturing-tolerance-chart/ .

2013 (1)

J. M. Sasian, “Extrinsic aberrations in optical imaging systems,” Adv. Opt. Technol. 2, 75–80 (2013).

2010 (1)

L. Wang and J. M. Sasian, “Merit figures for fast estimating tolerance sensitivity,” Proc. SPIE 7652, 76521P (2010).
[CrossRef]

2007 (1)

J. L. Bentley, C. Glazowski, and J. M. Zavislan, “Apochromatic immersion objective for in-vivo imaging for low coherence confocal microscopy,” Proc. SPIE 6342, 63420G (2007).
[CrossRef]

1998 (1)

M. R. Descour and J. M. Sasian, “Power distribution and symmetry in lens systems,” Opt. Eng. 37, 1001–1004 (1998).
[CrossRef]

1994 (1)

J. M. Sasian, “How to approach the design of a bilateral symmetric optical system,” Opt. Eng. 33, 2045–2061 (1994).
[CrossRef]

1985 (1)

W. J. Smith, “Fundamentals of establishing an optical tolerance budget,” Proc. SPIE 0531, 196–204 (1985).

1970 (2)

Bentley, J. L.

J. L. Bentley, C. Glazowski, and J. M. Zavislan, “Apochromatic immersion objective for in-vivo imaging for low coherence confocal microscopy,” Proc. SPIE 6342, 63420G (2007).
[CrossRef]

Descour, M. R.

M. R. Descour and J. M. Sasian, “Power distribution and symmetry in lens systems,” Opt. Eng. 37, 1001–1004 (1998).
[CrossRef]

Glazowski, C.

J. L. Bentley, C. Glazowski, and J. M. Zavislan, “Apochromatic immersion objective for in-vivo imaging for low coherence confocal microscopy,” Proc. SPIE 6342, 63420G (2007).
[CrossRef]

Grey, D. S.

Johnson, R. B.

R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

Kidger, M. J.

M. J. Kidger, Intermediate Optical Design, 1st ed. (SPIE, 2004).

Kingslake, R.

R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

Rimmer, M. P.

Sasian, J. M.

J. M. Sasian, “Extrinsic aberrations in optical imaging systems,” Adv. Opt. Technol. 2, 75–80 (2013).

L. Wang and J. M. Sasian, “Merit figures for fast estimating tolerance sensitivity,” Proc. SPIE 7652, 76521P (2010).
[CrossRef]

M. R. Descour and J. M. Sasian, “Power distribution and symmetry in lens systems,” Opt. Eng. 37, 1001–1004 (1998).
[CrossRef]

J. M. Sasian, “How to approach the design of a bilateral symmetric optical system,” Opt. Eng. 33, 2045–2061 (1994).
[CrossRef]

J. M. Sasian, “Imagery of the bilateral symmetrical optical system,” Ph.D. thesis (The University of Arizona, 1988).

Shannon, R. R.

R. R. Shannon, The Art and Science of Optical Design, 1st ed. (Cambridge University, 1997).

Smith, W. J.

W. J. Smith, “Fundamentals of establishing an optical tolerance budget,” Proc. SPIE 0531, 196–204 (1985).

Wang, L.

L. Wang and J. M. Sasian, “Merit figures for fast estimating tolerance sensitivity,” Proc. SPIE 7652, 76521P (2010).
[CrossRef]

Zavislan, J. M.

J. L. Bentley, C. Glazowski, and J. M. Zavislan, “Apochromatic immersion objective for in-vivo imaging for low coherence confocal microscopy,” Proc. SPIE 6342, 63420G (2007).
[CrossRef]

Zemax,

Zemax, Product of Radiant Zemax (Redmond, Washington, 2013).

Adv. Opt. Technol. (1)

J. M. Sasian, “Extrinsic aberrations in optical imaging systems,” Adv. Opt. Technol. 2, 75–80 (2013).

Appl. Opt. (2)

Opt. Eng. (2)

M. R. Descour and J. M. Sasian, “Power distribution and symmetry in lens systems,” Opt. Eng. 37, 1001–1004 (1998).
[CrossRef]

J. M. Sasian, “How to approach the design of a bilateral symmetric optical system,” Opt. Eng. 33, 2045–2061 (1994).
[CrossRef]

Proc. SPIE (3)

W. J. Smith, “Fundamentals of establishing an optical tolerance budget,” Proc. SPIE 0531, 196–204 (1985).

J. L. Bentley, C. Glazowski, and J. M. Zavislan, “Apochromatic immersion objective for in-vivo imaging for low coherence confocal microscopy,” Proc. SPIE 6342, 63420G (2007).
[CrossRef]

L. Wang and J. M. Sasian, “Merit figures for fast estimating tolerance sensitivity,” Proc. SPIE 7652, 76521P (2010).
[CrossRef]

Other (6)

Optimax Systems, “Manufacturing tolerance chart,” http://www.optimaxsi.com/innovation/optical-manufacturing-tolerance-chart/ .

Zemax, Product of Radiant Zemax (Redmond, Washington, 2013).

M. J. Kidger, Intermediate Optical Design, 1st ed. (SPIE, 2004).

J. M. Sasian, “Imagery of the bilateral symmetrical optical system,” Ph.D. thesis (The University of Arizona, 1988).

R. Kingslake and R. B. Johnson, Lens Design Fundamentals, 2nd ed. (Academic, 2010).

R. R. Shannon, The Art and Science of Optical Design, 1st ed. (Cambridge University, 1997).

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Figures (5)

Fig. 1.
Fig. 1.

Ten different design solutions to microscope objective lens in order of increasing element numbers (Fig. 5 in Bentley’s paper [13]).

Fig. 2.
Fig. 2.

Single plane symmetric comparison of microscope objective designs.

Fig. 3.
Fig. 3.

Rotationally symmetric comparison of microscope objective designs.

Fig. 4.
Fig. 4.

Distortion comparison of microscope objective designs.

Fig. 5.
Fig. 5.

RMS wavefront error comparison of microscope objective designs.

Tables (3)

Tables Icon

Table 1. Tilted Component Optical System Aberrations to Fourth Order

Tables Icon

Table 2. Tolerance Values Used to Evaluate Optical Systems

Tables Icon

Table 3. Sensitivities: Change of Aberration Value under Perturbation

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

OPD[HxρxHyρy],
Ray Height[HxxHyy],
Uniform Coma=OPD[0001]OPD[0001]2,
Uniform Astigmatism={OPD[0100]+OPD[0100]2}{OPD[0001]+OPD[0001]2},
+HΔρ={OPD[0011]+OPD[0011]2}{OPD[0110]+OPD[0110]2},
HΔρ={OPD[0011]+OPD[0011]2}{OPD[0110]+OPD[0110]2},
Linear Astigmatism=[(+HΔρ)(HΔρ)]2.
Smile=[Ray Height[1001]Ray Height[0001]Ray Height[1100]]*100,
Keystone={([Ray Height[0011]Ray Height[1100]]Ray Height[1100])*100}Smile,
Spherical Aberration=OPD[0001],
Linear Coma=OPD[0011]OPD[0011]2,
Quadratic Astigmatism={OPD[0011]+OPD[0011]2}{OPD[0110]+OPD[0110]2},
Cubic Distortion={y¯yrefyref}*100.

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