V.D.1 Processing Overview

IRAS Explanatory Supplement
V. Data Reduction
D. Point Source Confirmation
D.1 Processing Overview

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The arrangement of the detectors in the focal plane of the telescope and the survey strategy permitted reobservation of inertially fixed point sources after time intervals of several seconds, several hours, and several weeks. The confirmation process consisted of examining those multiple observations and identifying which plausibly belonged to the same object. Once this identification was made for a given source, refinement of the parameters describing that source was performed by combining the observations into a single improved description.

When comparing two sightings, positional agreement was always a part of the decision whether to accept them as the same object. Over the seconds and hours intervals, photometric agreement was required as well. Because the cross-scan position was tested only by requiring that a real object be sighted by a compatible pair (or triplet) of detectors, the decision problem at the seconds-confirmation level involved only in-scan position agreement, and the tests could be based on Gaussian error models.

At the hours and weeks level, the position error had to be modeled as a non-Gaussian random variable because of the uniform uncertainty due to the cross-scan extents of the detector slots.

The hours-and weeks-confirmation decision was based on the correlation of the probability density functions which describe the two-dimensional position information. The parameter which was required to be above a certain threshold to confirm two sightings was the cross-covariance of these density functions, evaluated at the separation of the nominal positions. The formalism is discussed and derived by Fowler and Rolfe (1982). There were several virtues in this approach, among which the most important was its freedom from the Gaussian approximation. The position error due to the detector slots was uniformly distributed, making any Gaussian algorithm unacceptable. Another aspect of the decision algorithm was that the fraction of true cases accepted increased as the size of the position uncertainties decreased. Because the threshold could not easily be set to accept a specific fraction of all cases, it was set during simulation tests by opening up the the threshold until just before the acceptance of false events became significant.
Figure V.D.1 a) As described in the text, the position and associated uncertainty of each source is represented by a probability distribution function consisting of Gaussian and uniform components. Shown here (left) are the distribution functions for two sightings of a single source. b) The position of the source resulting from the merging of the two sightings shown in V.D.1.a is described by the new probability distribution function shown here (right).
larger largest

Figure V.D.1a depicts two position probability density functions in a typical case. Each density function has a broad, flat ridge which shows the uniform contribution of the net intersection of the seconds-confirmed detector slots' cross-scan domains. The orthogonal direction is that of the scanning motion, and the corresponding position errors were found to be well modeled as Gaussian. In the figure, the agreement between the two position estimates is about as good as it could be. The large difference shown between the scan directions occurred only at the weeks-confirmation level. At hours-confirmation, the major axes of the density functions were approximately parallel. Refinement of position leads to a new probability density function which is more centrally concentrated as shown ia Fig. V.D.1b for the current example.

The confirmation decisions are summarized in Table V.D.1 which gives, for each step in the confirmation process, the type of position test (Gaussian or two-dimensional), the threshold used the flux agreement required and the net effect of these criteria on real sources.

Although the confirmation decision and parameter refinement lay at the core of the point source confirmation processing, many peripheral issues also had to handled. These aspects are discussed at a level of detail which attempts to be concise while not leaving an inordinate number of questions unanswered.
Confirmation Summary
Table V.D.1
Flux Ratio
Seconds 4.4 Sigma Compat. Det. -2 1 Real per 50,000 Rejected
Band Merge 4.2 Sigma Compat. Det. - - 1 Real Match per 40,000 Rejected
Hours - - 1x10-4sr-1 2 1 Real Match per 20,000 Rejected
Months - - 1x10-4sr-1 - 1 Real Match per 20,000 Rejected

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