QC 351 A7 no. 22 / The statistical approach must be used to describe the image when
object brightness, optical pupil characteristics, and image detection are
all subject to random fluctuations. Use of the statistical characteristic
W (the Fourier transform of probability density) is found to clarify the
phenomenon and to result in a linear theory. There is a characteristic
function W, corresponding to the joint statistics of the log modulus and
the phase, for: the object spectrum, optical transfer function, detection
transfer function and image spectrum. These four W-functions are the statistical analogy to the four Fourier spectra themselves, if the object
radiation is either perfectly coherent or perfectly incoherent. Thus, in
analogy to the ordinary Fourier theory of image formation, there is (1) a
statistical transfer theorem linking object and image fluctuations, (2) a
statistical transfer function for the optics, which may be computed from
the optical pupil statistics, (3) sampling theorems, and other analogous
results. The W-functions are found to determine all moments of each spectral distribution, and to imply that the moments themselves obey a transfer
theorem. Also, the optical characteristic W-function seems to be useful as
a quality criterion of optical system stability. In the deterministic
limit, the statistical theory goes over into the ordinary Fourier theory of
image formation. Random detection noise is a natural parameter of the theory,
so that application to practical problems seems eminently possible.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/621615 |
| Date | 21 February 1968 |
| Creators | Frieden, B. Roy |
| Publisher | Optical Sciences Center, University of Arizona (Tucson, Arizona) |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | Technical Report |
| Rights | Copyright © Arizona Board of Regents |
| Relation | Optical Sciences Technical Report 22 |
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