Equivalence of the Huygens–Fresnel and Debye approach for the calculation of high aperture point-spread functions in the presence of refractive index mismatch
Egner
A.
author
Hell
S.W.
author
1999
As discussed in recent work (Sheppard, C. J. R. & Török, P., J. Microsc., 185, 366–384; Török et al., J. Microsc., 188, 158–172), two approaches have been used extensively for vectorial computations of high aperture confocal point-spread functions when focusing through a dielectric interface. Whereas the equation by Hell, Reiner, Cremer & Stelzer (J. Microsc., 169, 391–405) is based on the Huygens–Fresnel principle, the more recent approach by Török, Varga & Booker (J. Opt. Soc. Am. A, 12, 325–332; J. Opt. Soc. Am. A, 12, 2136–2144) is based on the Debye approximation. While the earlier theory considers a large but finite focal length the second theory is derived for an infinitely high Fresnel number. In a high aperture microscope, a high Fresnel number is equivalent to assuming that the focal length be infinitely large with respect to the wavelength. So far, the two theories are regarded as different, with the one by Török et al. being rigorous. In this paper, we demonstrate that, if the same conditions are applied, the equation by Török et al. can be analytically derived from that by Hell et al. Producing the same results, the benefit brought about by the equation by Török et al. is improved flexibility and computational speed for cases with azimuthal symmetry.
aberration
confocal
fluorescence
microscopy
multiphoton
point spread function
refractive index mismatch
resolution
to read
2020/12/11/13:15:12
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text
http://onlinelibrary.wiley.com/doi/abs/10.1046/j.1365-2818.1999.00462.x
http://onlinelibrary.wiley.com/doi/abs/10.1046/j.1365-2818.1999.00462.x
Egner+Hell1999
Journal of Microscopy
1999
continuing
periodical
academic journal
193
3
244
249
1365-2818