Abstract
The use of pupil-plane filters in microscopes has been proposed as a method of producing superresolution. Here it is shown that pupil-plane filters cannot increase the support of the transfer function for a large class of optical systems, implying that resolution cannot be improved solely by adding pupil-plane filters to an instrument. However, pupil filters can improve signal-to-noise performance and modify transfer-function zero crossing positions, as demonstrated through a confocal fluorescence example.
Highlights
Point spread function (PSF) engineering using pupil-filters is currently an active area of research [1,2,3,4,5,6,7]
Other benefits are possible from pupil filters — a confocal fluorescence example is used to demonstrate benefits in terms of signal-to-noise ratio and imaging with a finite-sized confocal pinhole
For a considerable class of optical instruments the use of pupil-plane filters cannot increase the support of the system’s transfer function, which implies that they offer no fundamental increase in achievable resolution despite suggestive spatial domain results
Summary
Point spread function (PSF) engineering using pupil-filters is currently an active area of research [1,2,3,4,5,6,7]. This paper is written to call attention to the fact that the use of pupil filters alone in PSF engineering cannot increase the fundamental achievable resolution for a large class of linear, shift-invariant, far-field optical instruments. A full three-dimensional, vectorial, frequency-domain analysis is used to show the addition of pupil-plane filters will not improve the resolution, as no additional frequency-domain components of the object are passed by the instrument. Other benefits are possible from pupil filters — a confocal fluorescence example is used to demonstrate benefits in terms of signal-to-noise ratio and imaging with a finite-sized confocal pinhole
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