Masking, photobleaching, and spreading effects in Hadamard transform imaging and spectroscopy systems

In analyzing the behavior of a Hadamard transform imaging spectroscopic sys tem in an optical sectioning microscope, a previously undescribed masking e ffect was observed. During the process of characterizing this artifact, it was noted that while many masking errors have been reported previously in t he literature, no attempt has been made to classify them or to systematical ly treat their effects in a variety of imaging and spectroscopy arrangement s. Previous reports have documented echo artifacts in one-dimensional Hadam ard mask systems based on sequences of length 2" - 1, for which the echoes are well defined. Other valid cyclic S-sequences, such as those of prime le ngth Im + 3 not equal 2" - 1, do not exhibit such behavior. Masking errors may be present with these sequences, but they do not appear as echoes. Reco vered intensities are observed having both positive and negative magnitude distributed throughout the transform axis. These masking defects appear sup erficially to be "noise", making associated errors more difficult to diagno se. Masking effects in two-dimensional systems have not been previously rep orted. in these, the relationship between the original image and resulting "echoes" can be quite complicated. This paper treats a variety of masking e ffects theoretically and presents simulations based on that treatment. Mask errors are divided into first- and second-order effects depending on wheth er the encoding passes through a mask once or twice. Symmetric, asymmetric, and static masking errors in one-dimensional Hadamard transform systems ar e treated in both first- and second-order arrangements. Where prior data ex ist, an attempt has been made to collect and categorize known mask-related artifacts and where appropriate provide additional documentation. Mask erro rs may be spatially varying or spatially invariant over the mask or within a given pixel. In systems which are spatially variant, proper sampling of t he image or spectrum hy the elements composing the mask is a prerequisite f or successful correction of the data. Corrections applied to data from mask s with spatially variant errors may cause artifacts to appear and, in some instances, complete correction may be impossible. The effects of photobleac hing and mask spreading due to processes such as diffraction or aberrations in both one- and two-dimensional-mask systems are investigated. Photobleac hing is relatively easy to correct when an exponential decay model is appli cable. In second-order systems, mask spreading gives rise to echoes or dist ortion even in perfectly implemented masks. Mask spreading can, in many cas es, be corrected by analyzing the observed "echoes" and building a correcti on matrix or by using knowledge of the point, line, or other spreading func tion of the system. Finally, in masks of length 2(n)- 1, a few simple rules greatly assist in diagnosing masking effects.