Limitations and applicability of the Maréchal approximation

Applied Optics

Volumn 48, Issue 10, 2009, Pages 1812-1818

  Ross, T Sean ^a  

^a AIR FORCE RESEARCH LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GAUSSIAN NOISE (ELECTRONIC);

RANDOM-PHASE; STREHL RATIO; WAVEFRONT DISTORTION;

PROBABILITY DENSITY FUNCTION;

EID: 65249164127     PISSN: 1559128X     EISSN: 15394522     Source Type: Journal    
DOI: 10.1364/AO.48.001812     Document Type: Article

References (19)

1. K. Strehl, "Über Luftschlieren und Zonenfehler," Z. Instru- mentenkd. 22, 213-217 (1902).
2. L.C.Roberts,Jr. M.D.Perrin,F.Marchis,A.Sivaramakrishnan, R.B. Makidon, J. C. Christen, B. A. Macintosh, L. A. Poyneer, M. A. van Dam, and M. Troy "Is that really your Strehl ratio?" Proc. SPIE 5490,504-515 (2004).
3. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1997), Chap. 9.1.3, Eq. (24), p. 464.
4. A. Maréchal, "Étude des effets combinés de la diffraction et des aberrations géometriques sur l'image d'un point lumineux," Rev. Opt. Theor. Instrum. 26,257-277 (1947)
5. G. Martial, "Strehl ratio and aberration balancing," J. Opt. Soc. Am. A 1, 164-170(1991); see comment surrounding Eq. (8).
6. V. N. Mahajan, "Strehl ratio for primary aberrations: some analytical results for circular and annular pupils," J. Opt. Soc. Am. 72, 1258-1266 (1982).
7. D. D. Lowenthal, "Maréchal intensity criteria modified for Gaussian beams," Appl. Opt. 13, 2126-2132 (1974).
8. V. N. Mahajan, "Strehl ratio of a Gaussian beam," J. Opt. Soc. Am. A 22, 1824-1833 (2005).
9. J. Ojeda-Castañeda, M. Martínez-Corral, P. Andrés, and A. Pons, "Strehl ratio versus defocus for noncentrally obscured pupils," Appl. Opt. 33, 7611-7616 (1994).
10. S. Szapiel, "Maréchal intensity criteria modified for circular apertures with nonuniform intensity transmission: Dini series approach," Opt. Lett. 2, 124-126 (1978).
11. W. B. King, "Dependence of the Strehl ratio on the magnitude of the variance of the wave aberration," J. Opt. Soc. Am. 58, 655-661 (1968).
12. R. Herloski, "Strehl ratio for untruncated aberrated Gaussian beams," J. Opt. Soc. Am. A 2, 1027-1029 (1985).
13. V. N. Mahajan, "Strehl ratio for primary aberrations in terms of their aberration variance," J. Opt. Soc. Am. 73, 860-861 (1983).
14. M. J. Yzuel J. Campos, and E Calvo, "Maréchal intensity criteria for apertures with polynomial non-uniform transmission. Evaluation of the diffraction focus and the Strehl ratio," J. Mod. Opt. 38, 349-362 (1991).
15. H. T. Yura, "Variance of the Strehl ratio of an adaptive optics system," J. Opt. Soc. Am. A 15, 2107-2110 (1998).
16. V. H. Shui and N. A. Thyson, "Dependence of Strehl ratio on turbulence model," Proc. SPIE 2222, 726-734 (1994).
17. http://en.wikipedia.org/wiki/Expected-value.
18. http://mathworld.wolfram.com/ExpectationValue.html.
19. A. N. Kolmogorov, "A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number," J. Fluid Mech. 13, 82-85 (1962).