## Diffraction Patterns Formed by an Off-Axis Paraboloid Surface

Applied Optics, Vol. 40, Issue 17, pp. 2909-2916 (2001)

http://dx.doi.org/10.1364/AO.40.002909

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### Abstract

We derive a general, closed-form expression for the diffraction patterns including the aberrations that are due to off-axis alignment and positioning, of a paraboloid mirror. The diffraction patterns obtained in the focal plane of an off-axis paraboloidal mirror suffer modifications by the aberrations that are inherent in these surfaces: astigmatism and coma. Different magnifications in two perpendicular spatial directions indicate astigmatism. The Airy function, which affects a single spatial coordinate, describes the coma aberration. We identified the coma by the increased number of intensity zeros within adjacent lobules.

© 2001 Optical Society of America

**OCIS Codes**

(050.1940) Diffraction and gratings : Diffraction

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(070.2590) Fourier optics and signal processing : ABCD transforms

(220.1010) Optical design and fabrication : Aberrations (global)

(220.1140) Optical design and fabrication : Alignment

(220.1250) Optical design and fabrication : Aspherics

**Citation**

Pedro Arguijo, Marija Strojnik Scholl, and Gonzalo Paez, "Diffraction Patterns Formed by an Off-Axis Paraboloid Surface," Appl. Opt. **40**, 2909-2916 (2001)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-40-17-2909

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### References

- A. E. Siegman, Lasers (University Science, Sausalito, Calif., 1986), pp. 901–906.
- E. A. Phillips, J. P. Reilly, and D. B. Northam, “Off-axis unstable laser resonator: operation,” Appl. Opt. 15, 2159–2166 (1976).
- G. W. Sutton, M. M. Weineir, and S. A. Mani, “Fraunhofer diffraction patterns from illuminated square output apertures with noncentred square obscurations,” Appl. Opt. 15, 2228–2232 (1976).
- M. S. Scholl, “Recursive exact ray trace equations through the foci of the tilted off-axis confocal prolate spheroids,” J. Mod. Opt. 43, 1583–1588 (1996).
- J. L. Flores, G. Paez, and M. Strojnik, “Design of a diluted-aperture by use of the practical cutoff frequency,” Appl. Opt. 38, 6010–6018 (1999).
- M. S. Scholl, “Design parameters for a two-mirror telescope for stray-light sensitive infrared applications,” Infrared Phys. Technol. 37, 251–257 (1996).
- M. S. Scholl and G. Paez, “Using the y, y-bar diagram to control stray light noise in IR systems,” Infrared Phys. Technol. 38, 25–30 (1997).
- J. Nelson, “University of California ten meter telescope project,” in Advanced Technology Optical Telescopes, G. Burbidge and L. Barr, eds., Proc. SPIE 332, 109–116 (1982).
- G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, and T. Mast, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
- J. Rodriguez and P. Alvares, “Gran telescopio Canarias: a 10-m telescope for the ORM,” in Optical Telescope of Today and Tomorrow: Following in the Direction of Tycho Brahe, A. Ardebeg, ed., Proc. SPIE 2871, 69–85 (1996).
- F. Bash, T. Sebring, F. Ray, and L. Ramsey, “The extremely large telescope: a twenty-five meter aperture for the twenty-first century,” in Optical Telescope of Today and Tomorrow: Following in the Direction of Tycho Brahe, A. Ardebeg, ed., Proc. SPIE 2871, 272–290 (1996).
- M. Ruda, “Alignment of off-axis aspheric surfaces,” in Optical Alignment, R. N. Shagam and W. C. Sweatt, eds., Proc. SPIE 251, 29–36 (1980).
- M. A. Lundgren and W. L. Wolfe, “Alignment of a three-mirror off-axis telescope by reverse optimization,” Opt. Eng. 30, 307–311 (1991).
- J. E. Harvey, “Fourier treatment of near-field scalar diffraction theory,” Am. J. Phys. 47, 974–980 (1979).
- V. N. Mahajan, “Aberrated point spread functions for rotationally symmetric aberrations,” Appl. Opt. 22, 3035–3041 (1983).
- R. Barakat and A. Houston, “Diffraction effects of coma,” J. Opt. Soc. Am. 54, 1084–1088 (1964).
- M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1993), pp. 477–479.
- R. Barakat and A. Houston, “The aberrations of non-rotationally symmetric systems and their diffraction effects,” Opt. Acta 13, 1–30 (1966).
- J. Lubliner and J. E. Nelson, “Stressed mirror polishing. 1. A technique for producing nonaxisymmetric mirrors,” Appl. Opt. 19, 2332–2340 (1980).
- O. Cardona-Nunez, A. Cornejo-Rodriguez, J. R. Diaz-Uribe, A. Cordero-Davila, and J. Pedraza-Contreras, “Conic that best fits an off-axis conic section,” Appl. Opt. 25, 3585–3588 (1986).
- G. Moretto and J. R. Kuhn, “Off-axis systems for 4-m class telescopes,” Appl. Opt. 37, 3539–3546 (1998).
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 60.
- D. Mendlovic and H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation. I,” J. Opt. Soc. Am. A 10, 1875–7881 (1993).
- P. Pellat-Finet, “Fresnel diffraction and the fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994).
- M. Abromowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970), p. 477.
- G. N. Watson, A Treatise on the Theory of Bessel Functions (Cambridge U. Press, Cambridge, UK, 1966), pp. 188–190.
- A. W. Lohmann, J. Ojeda-Castañeda, and J. G. Ibarra, “Airy function and Laguerre polynomials: optical display and processing,” Opt. Commun. 109, 361–367 (1994).

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