The optical transfer function (OTF) and the noise power or Wiener spectrum
are defined for detectors consisting of a lattice of discrete elements with
the assumptions of linear response, Gaussian statistics, and stationarity
under the discrete group of translations which leave the lattice fixed. For
the idealized classification task of determining the presence or absence o
f a signal under signal known exactly/background known exactly (SKE/BKE) co
nditions, the Wiener spectrum, the OTF, along with an analog of the gray-sc
ale transfer characteristic, determine the signal-to-noise ratio (SNR), whi
ch quantifies the ability of an ideal observer to perform this task. While
this result is similar to the established result for continuous detectors,
such as screen-film systems, the theory of discrete lattices of detectors m
ust take into account the fact that the lattice only supports a bounded but
(in the limit of a detector of arbitrarily great extent) continuous range
of frequencies. Incident signals with higher spatial frequencies appear in
the data at lower aliased frequencies, and there are pairs of signals which
are not distinguishable by the detector (the SNR vanishes for the task of
distinguishing such signals). Further, the SNR will in general change if th
e signal is spatially displaced by a fraction of the lattice spacing, altho
ugh this change will be small for objects larger than a single pixel. Some
of the trade-offs involved in detectors of this sort, particularly in deali
ng with signal frequencies above those supported by the lattice, are studie
d in a simple model. (C) 2000 American Association of Physicists in Medicin
e. [S0094-2405(00)00908-1].