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Three‐dimensional transfer function of optical microscopes in reflection mode
Author(s) -
Lehmann Peter,
Pahl Tobias
Publication year - 2021
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/jmi.13040
Subject(s) - optical transfer function , optics , point spread function , fourier transform , diffraction , transfer function , pupil function , microscope , contrast transfer function , reflection (computer programming) , spatial frequency , fourier optics , physics , frequency domain , mathematics , mathematical analysis , computer science , spherical aberration , quantum mechanics , engineering , programming language , electrical engineering , lens (geology)
Three‐dimensional (3D) transfer functions build the basis for a comprehensive characterization of optical imaging systems in the spatial frequency domain. Utilizing the projection‐slice theorem, the 2D modulation transfer function of an incoherent imaging system can be derived from a 3D transfer function by integration with respect to the axial spatial frequency. For a diffraction limited microscope with homogeneous incoherent pupil illumination, the modulation transfer function equals the 2D autocorrelation function of a circular disc. However, until now to the best of our knowledge no 3D transfer function has been published, which exactly leads to the 2D modulation transfer function of a diffraction limited microscope in reflection mode. In this article, we derive a formula, which after integration with respect to the axial spatial frequency coordinate perfectly fits to the diffraction limited 2D modulation transfer function. The inverse three‐dimensional Fourier transform of the 3D transfer function results in a complex‐valued 3D point spread function, from which the depth of field, the lateral resolution and, in addition, the corresponding 3D point spread function of both, a conventional and an interference microscope, can be obtained.