ENHANCED 3-DIMENSIONAL RECONSTRUCTION FROM CONFOCAL SCANNING MICROSCOPE IMAGES .2. DEPTH DISCRIMINATION VERSUS SIGNAL-TO-NOISE RATIO IN PARTIALLY CONFOCAL IMAGES

The enhanced depth discrimination of a confocal scanning optical micro scope is produced by a pinhole aperture placed in front of the detecto r to reject out-of-focus light. Strictly confocal behavior is impracti cal because an infinitesimally small aperture would collect very littl e light and would result in images with a poor signal-to-noise ratio ( SNR), while a finite-sized partially confocal aperture provides a bett er SNR but reduced depth discrimination. Reconstruction algorithms, su ch as the expectation-maximization algorithm for maximum likelihood, c an be applied to partially confocal images in order to achieve better resolution, but because they are sensitive to noise in the data, there is a practical trade-off involved. With a small aperture, fewer itera tions of the reconstruction algorithm are necessary to achieve the des ired resolution, but the low a priori SNR will result in a noisy recon struction, at least when no regularization is used. With a larger aper ture the a priori SNR is larger but the resolution is lower, and more iterations of the algorithm are necessary to reach the desired resolut ion; at some point the a posteriori SNR is lower than the a priori val ue. We present a theoretical analysis of the SNR-to-resolution trade-o ff partially confocal imaging, and we present two studies that use the expectation-maximization algorithm as a postprocessor; these studies show that a for a given task there is an optimum aperture size, depart ures from which result in a lower a posteriori SNR.