Monte Carlo evaluation of focus shift and PSF distortion in the presence of refractive index mismatch in scattering media

Abstract

The shift of the focus and the distortion of point spread function (PSF) in a biological tissue are studied using a Monte Carlo simulation. In many biological applications of confocal and multiphoton fluorescence microscopy, the optically-thick sample is usually mounted in a medium with an index of refraction, which is different from that of the immersion medium – a situation that is normally termed as the refractive index mismatch.
In addition, the observation of internal organs and sites is hampered by the presence of intervening tissues that degrade the signal-to-noise ratio of the generated fluorescence image. In addition to the presence of scatterers and absorbers, the intervening medium also has a complicated refractive index variation. The disparity between the refractive indices aberrates the PSF of the imaging system. The aberration caused by refractive index mismatch in the cases when the index of the ambient medium (n₀) is (a) greater and (b) smaller than that of the objective medium (n_i) is shown, where F₀ denotes the geometrical focus in the absence of the mismatch. These aberrations are expected to cause a reduction and shift of the location of the peak intensity of the PSF along the optical axis. Moreover, the unwanted PSF broadening results to a considerable decrease in the axial and lateral resolution. In fluorescence microscopy, the presence of scattering and mismatch in the refractive index is expected to degrade the signal-to-noise ratio (SNR) of the generated fluorescence image.
In order to reconstruct high-resolution images of biological tissues, it is necessary to know how the PSF is altered by the simultaneous presence of refractive index mismatches and scatterers. The resulting PSF, which can be called effective PSF, can be used to enhance the low SNR fluorescence images via deconvolution. In the presence of index mismatch alone, the effective PSF can be extracted using analytical method based on the Huygens-Fresnel principle. In the presence of scattering, however, its functional form cannot be obtained analytically and numerical techniques such as the Monte Carlo method are employed.