An analytic expression for the field dependence of Zernike polynomials in rotationally symmetric optical systems

doi:10.1364/OE.20.016436

Optics Express

Editor: C. Martijn de Sterke
Vol. 20, Iss. 15 — Jul. 16, 2012
pp: 16436–16449

An analytic expression for the field dependence of Zernike polynomials in rotationally symmetric optical systems

Robert W. Gray, Christina Dunn, Kevin P. Thompson, and Jannick P. Rolland »View Author Affiliations

Optics Express, Vol. 20, Issue 15, pp. 16436-16449 (2012)
http://dx.doi.org/10.1364/OE.20.016436

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Abstract
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References (16)
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Abstract

Zernike polynomials have emerged as the preferred method of characterizing as-fabricated optical surfaces with circular apertures. Over time, they have come to be used as a sparsely sampled in field representation of the state of alignment of assembled optical systems both during and at the conclusion of the alignment process using interferometry. We show that the field dependence of the Zernike polynomial coefficients, which has to-date been characterized essentially by aperture dependence, can be introduced by association to the field dependent wave aberration function of H.H. Hopkins.

OCIS Codes
(080.2740) Geometric optics : Geometric optical design
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(080.1005) Geometric optics : Aberration expansions

ToC Category:
Geometric Optics

History
Original Manuscript: April 25, 2012
Revised Manuscript: June 22, 2012
Manuscript Accepted: June 26, 2012
Published: July 5, 2012

Citation
Robert W. Gray, Christina Dunn, Kevin P. Thompson, and Jannick P. Rolland, "An analytic expression for the field dependence of Zernike polynomials in rotationally symmetric optical systems," Opt. Express 20, 16436-16449 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16436

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References

The Fringe Zernike polynomial was developed by John Loomis at the University of Arizona, Optical Sciences Center in the 1970s, and is described on page C-8 of the CODE V® Version 10.4 Reference Manual (Synopsys, Inc.) (2012)
ISO 10110–5:1996(E), “Optics and optical instruments – Preparation of drawings for optical elements and systems – Part 5: Surface form tolerances.
H. H. Hopkins, The Wave Theory of Aberrations (Oxford on Clarendon Press), p. 48 (1950).
M. P. Rimmer, C. M. King, and D. G. Fox, “Computer program for the analysis of interferometric test data,” Appl. Opt.11(12), 2790–2796 (1972). [CrossRef] [PubMed]
J. Sasián, “Theory of sixth-order wave aberrations,” Appl. Opt.49(16), D69–D95 (2010). [CrossRef] [PubMed]
K. P. Thompson, “Beyond optical Design: interaction between the lens designer and the real world,” The International Optics Design Conference, Proc. SPIE554, 426 (1985).
J. R. Rogers, personal communication, (2012).
B. A. McLeod, “Collimation of fast wide-field telescopes,” PASP108, 217–219 (1996). [CrossRef]
A. Rakich, “Calculation of third-order misalignment aberrations with the Optical Plate diagram,” SPIE-OSA 7652 (2010).
C. R. Burch, “On the optical see-saw diagram,” Mon. Not. R. Astron. Soc.103, 159–165 (1942).
L. Noethe and S. Guisard, “Final alignment of the VLT,” Proc. SPIE4003 (2000).
T. Matsuyama and T. Ujike, “Orthogonal aberration functions for microlithographic optics,” Opt. Rev.11(4), 199–207 (2004). [CrossRef]
R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope on its aberration field,” Proc. SPIE251, 146–155 (1980).
J. G. Baker, I. King, G. H. Conant, Jr., W. R. Angell, Jr., and E. Upton, “Technical report no. 2 – The utilization of automatic calculating machinery in the field of optical design,” May 31, 1952.
M. R. Rimmer, Optical Aberration Coefficients, Master Thesis, University of Rochester, 1963.
J. C. Mather, ed., Astronomical Telescopes and Instrumentation Glasgow, (SPIE), 5487, SPIE, Bellingham, WA (2004).

Appl. Opt.

Mon. Not. R. Astron. Soc.

C. R. Burch, “On the optical see-saw diagram,” Mon. Not. R. Astron. Soc.103, 159–165 (1942).

Opt. Rev.

T. Matsuyama and T. Ujike, “Orthogonal aberration functions for microlithographic optics,” Opt. Rev.11(4), 199–207 (2004). [CrossRef]

PASP

B. A. McLeod, “Collimation of fast wide-field telescopes,” PASP108, 217–219 (1996). [CrossRef]

Proc. SPIE

K. P. Thompson, “Beyond optical Design: interaction between the lens designer and the real world,” The International Optics Design Conference, Proc. SPIE554, 426 (1985).
R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope on its aberration field,” Proc. SPIE251, 146–155 (1980).
L. Noethe and S. Guisard, “Final alignment of the VLT,” Proc. SPIE4003 (2000).

Other

J. G. Baker, I. King, G. H. Conant, Jr., W. R. Angell, Jr., and E. Upton, “Technical report no. 2 – The utilization of automatic calculating machinery in the field of optical design,” May 31, 1952.
M. R. Rimmer, Optical Aberration Coefficients, Master Thesis, University of Rochester, 1963.
J. C. Mather, ed., Astronomical Telescopes and Instrumentation Glasgow, (SPIE), 5487, SPIE, Bellingham, WA (2004).
J. R. Rogers, personal communication, (2012).
A. Rakich, “Calculation of third-order misalignment aberrations with the Optical Plate diagram,” SPIE-OSA 7652 (2010).
The Fringe Zernike polynomial was developed by John Loomis at the University of Arizona, Optical Sciences Center in the 1970s, and is described on page C-8 of the CODE V® Version 10.4 Reference Manual (Synopsys, Inc.) (2012)
ISO 10110–5:1996(E), “Optics and optical instruments – Preparation of drawings for optical elements and systems – Part 5: Surface form tolerances.
H. H. Hopkins, The Wave Theory of Aberrations (Oxford on Clarendon Press), p. 48 (1950).

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