Zernike representation and Strehl ratio of optical systems with variable numerical aperture |
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Authors: | AJEM Janssen P Dirksen JJM Braat |
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Affiliation: | 1. Philips Research Europe , Eindhoven, The Netherlands;2. Faculty of Applied Sciences, Optics Research Group , Delft University of Technology , Delft, The Netherlands |
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Abstract: | We consider optical systems with variable numerical aperture (NA) on the level of the Zernike coefficients of the correspondingly scalable pupil function. We thus present formulas for the Zernike coefficients and their first two derivatives as a function of the scaling factor ε ≤ 1, and we apply this to the Strehl ratio and its derivatives of NA-reduced optical systems. The formulas for the Zernike coefficients of NA-reduced optical systems are also useful for the forward calculation of point-spread functions and aberration retrieval within the Extended Nijboer–Zernike (ENZ) formalism for optical systems with reduced NA or systems that have a central obstruction. Thus, we retrieve a Gaussian, comatic pupil function on an annular set from the intensity point-spread function in the focal region under high-NA conditions. |
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Keywords: | NA reduction Zernike coefficients Strehl ratio central obstruction aberration retrieval ENZ theory |
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