Procedures for speeding up the exact evaluation of diffraction integrals by semiperiodic-zone division of the integration domain

Josep Ferre-Borrull; Salvador Bosch

doi:10.1117/12.559408

14 October 2004 Procedures for speeding up the exact evaluation of diffraction integrals by semiperiodic-zone division of the integration domain

Josep Ferre-Borrull, Salvador Bosch

Author Affiliations +

Proceedings Volume 5523, Current Developments in Lens Design and Optical Engineering V; (2004) https://doi.org/10.1117/12.559408
Event: Optical Science and Technology, the SPIE 49th Annual Meeting, 2004, Denver, Colorado, United States

Abstract

We develop a method for the calculation of the integrals arising in the diffraction theory of aberrations. This method is developed from in a previous one based in the division of the diffracting aperture in semiperiodic zones, which enabled the exact calculation of the Point-Spread Function of an optical system. By a careful analysis of the integration process and of the properties of the semiperiodic zones, we develop a set of formulae that give an approximate value of the result of the diffraction integrals. This permits to avoid the numerical calculation of the integrals, which is a computationally intensive procedure and enables a substantial reduction of the computation times. The method has been tested on aberration-free optical systems and real optical systems and has shown a good accuracy, although some minor problems require further investigation.

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Josep Ferre-Borrull and Salvador Bosch "Procedures for speeding up the exact evaluation of diffraction integrals by semiperiodic-zone division of the integration domain", Proc. SPIE 5523, Current Developments in Lens Design and Optical Engineering V, (14 October 2004); https://doi.org/10.1117/12.559408

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