An FFT - based Method for Attenuation

A problem in three-dimensional imaging by a confocal scanning laser microscope (CSLM) in the (epi))uorescence mode is the darkening of the deeper layers due to absorption and scattering of both the excitation and the uorescence light. In this paper we propose a new method to correct for these eeects. Our approach, valid for weak attenuation, consists in multiplying the measured uorescent intensity by a correction factor involving a convolution integral of the measured signal, which can be computed eeciently by the Fast Fourier Transform. We give analytical and numerical estimates as to the degree of attenuation under which our method is valid, and apply the method to various test images. We also show a restoration of a real CSLM image. Finally the method is compared with a recent iterative method with regard to numerical accuracy and computational eeciency.