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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 10 — Apr. 1, 2013
  • pp: 2062–2074

Imaging characteristics of Zernike and annular polynomial aberrations

Virendra N. Mahajan and José Antonio Díaz  »View Author Affiliations


Applied Optics, Vol. 52, Issue 10, pp. 2062-2074 (2013)
http://dx.doi.org/10.1364/AO.52.002062


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Abstract

The general equations for the point-spread function (PSF) and optical transfer function (OTF) are given for any pupil shape, and they are applied to optical imaging systems with circular and annular pupils. The symmetry properties of the PSF, the real and imaginary parts of the OTF, and the modulation transfer function (MTF) of a system with a circular pupil aberrated by a Zernike circle polynomial aberration are derived. The interferograms and PSFs are illustrated for some typical polynomial aberrations with a sigma value of one wave, and 3D PSFs and MTFs are shown for 0.1 wave. The Strehl ratio is also calculated for polynomial aberrations with a sigma value of 0.1 wave, and shown to be well estimated from the sigma value. The numerical results are compared with the corresponding results in the literature. Because of the same angular dependence of the corresponding annular and circle polynomial aberrations, the symmetry properties of systems with annular pupils aberrated by an annular polynomial aberration are the same as those for a circular pupil aberrated by a corresponding circle polynomial aberration. They are also illustrated with numerical examples.

© 2013 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(110.0110) Imaging systems : Imaging systems
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.1010) Optical design and fabrication : Aberrations (global)

ToC Category:
Imaging Systems

History
Original Manuscript: December 19, 2012
Revised Manuscript: February 15, 2013
Manuscript Accepted: February 18, 2013
Published: March 26, 2013

Citation
Virendra N. Mahajan and José Antonio Díaz, "Imaging characteristics of Zernike and annular polynomial aberrations," Appl. Opt. 52, 2062-2074 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-10-2062


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References

  1. V. N. Mahajan, Optical Imaging and Aberrations, Part II: Wave Diffraction Optics, 2nd ed. (SPIE, 2011).
  2. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1999).
  3. V. N. Mahajan, “Symmetry properties of aberrated point-spread functions,” J. Opt. Soc. Am. A 11, 1993–2003 (1994). [CrossRef]
  4. C.-J. Kim and R. R. Shannon, “Catalog of Zernike polynomials,” in Applied Optics and Optical Engineering (Elsevier, 1987), Vol. X, pp. 193–221.
  5. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  6. V. N. Mahajan, “Zernike polynomials and wavefront fitting,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (Wiley, 2007), pp. 498–546.
  7. V. N. Mahajan, “Orthonormal polynomials in wavefront analysis,” in Handbook of Optics, V. N. Mahajan and E. V. Stryland, eds., 3rd ed. (McGraw-Hill, 2010), Vol. II, pp. 11.3–11.41.
  8. The isometric and contour plots of Zernike polynomial aberrations are also given (without mentioning the aberration value) in J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering (Elsevier, 1992), Vol. XI, pp. 1–53. These authors do not use polynomials in their orthonormal form, and they order them differently as well.
  9. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Company, 2004).
  10. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,” J. Opt. Soc. Am. 71, 75–85 (1981). [CrossRef]
  11. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils (Errata),” J. Opt. Soc. Am. 71, 1408 (1981). [CrossRef]
  12. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,” J. Opt. Soc. Am. 1, 685(1984). [CrossRef]
  13. V. N. Mahajan, “Zernike annular polynomials and optical aberrations of systems with annular pupils,” Appl. Opt. 33, 8125–8127 (1994). [CrossRef]

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