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A New Approach to Telescope Fourier Optics

DOI: 10.4236/oalib.1105856, PP. 1-14

Subject Areas: Numerical Mathematics, Applied Physics

Keywords: Fourier Optics, Fourier Transforms, Convolution, Bessel Functions, Filon Quadrature

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In this paper we take a new approach to solving the Ray-leigh-Sommerfeld-Smythe equation for a telescope’s optical impulse re-sponse to a monochromatic point source spherical wave radiating outward from the origin in the object plane. Two cases are covered: 1) the point source at the origin in the telescope’s near-field object plane; 2) the point source at the origin in the far-field object plane as is the case with satellite infrared sensors when the distance between the telescope and the point source is very much greater than the telescope’s circular aperture diameter. With only the assumption of a thin circular aperture we 1) derive a general solution that erases the distinction among the three classically defined zones of the optical axis: Near, Fresnel, and Fraunhofer; 2) reduce the computational complexity down from two-dimensional to one-dimensional Fourier transform integrals and; 3) identify Filon quadrature as the numerical method of choice for accurately and efficiently approximating the values of these integrals and; 4) provide a computational example.

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Danchick, R. (2019). A New Approach to Telescope Fourier Optics. Open Access Library Journal, 6, e5856. doi:


[1]  George, N. (2012) Fourier Optics. Monograph, Hajim School of Engineering and Applied Sciences, University of Rochester, Rochester, 8.
[2]  Dubois, A. (2013) Fourier Optics. Monograph, Institut d’Optique, ParisTech, 14.
[3]  Abromowitz, M.A. and Stegun, I. (1972) Mathematical Handbook for Scientists and Engineers. Dover Publications Inc., New York, 890-891.


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