Analytical formula for calculating the focal shift in apodized systems
- 1 August 1998
- journal article
- research article
- Published by Taylor & Francis in Journal of Modern Optics
- Vol. 45 (8) , 1671-1679
- https://doi.org/10.1080/09500349808230661
Abstract
We report a quite simple analytical formula for the evaluation of the focal shift in apodized systems, with or without rotational invariance. Specifically it is shown that the magnitude of the focal shift is determined by the product of the Fresnel number of the focusing geometry and the standard deviation of a mapped version of the azimuthal average of the pupil transmittance. To illustrate our approach, several examples are examined.Keywords
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