IRAS Explanatory Supplement
V. Data Reduction
D. Point Source Confirmation
D.5 Overview of Hours-Confirmation
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- Hours-Confirmation Decision
- Position Agreement
- Photometric Agreement
- Hours-Confirmation Confusion Processing
- Hours-Confirmation Position and Photometric Refinement
- Hours-Confirmation Statistical Processing
- Special Considerations Regarding Hours-Confirmation
The "drop-dead" approach was used again to select a source for processing. When the oldest source became 36 hours older than the most recently acquired source, then the oldest source became eligible for hours-confirmation processing. A maximum of four scans were allowed to participate in one hours-confirmation of one source. Match candidates were selected by taking all subsequent unconfirmed observations within a coarse window centered on the drop-dead source. This window was 27.5' across in ecliptic longitude and 10.3' high in latitude. When the drop-dead source was within 30' of an ecliptic pole, all unconfirmed sources within 30' of that pole were included in the candidate set.
Both seconds-confirmed/band-merged and non-seconds-confirmed (NSC) sources were included in the processing. but drop-dead sources were taken only from the seconds-confirmed set until all eligible ones had been processed after which all eligible NSC sources were used in time order as drop-deads.
D.5.a Hours-Confirmation Decision
The candidates were required to come from orbits other than that of the drop-dead source, or else they were discarded from the processing of the drop-dead. They were also required to have detected fluxes (i.e., not band-filled fluxes) in at least one band in common with the drop-dead. Those remaining were then tested pairwise with the drop-dead for position agreement, and any which were not acceptable on this basis were discarded. Those that passed were grouped into sets belonging to individual orbits and checked for confusion. If no two remaining candidates were from the same orbit, then processing proceeded to flux tests and combined flux/position tests. If two or more candidates from the same orbit had detected fluxes in at least one common band, then confusion was diagnosed and status bits were set which would identify this condition to all downstream processing (Section V.D.8). If more than one candidate remained from a given orbit, but no common bands were found then the situation was not labeled as confusion, but only one candidate was retained; this was the one which passed the combined flux/position test with the highest score.
If no candidates were found to be acceptable, the drop-dead source was rejected. Otherwise parameter refinement was performed for the flux and position information. Tracking of known sources was performed and various statistical computations were carried out. Candidates which were not confirmed with the drop-dead source remained for subsequent use, but confirmed candidates were not available for further hours-confirmation.
D.5.b Position Agreement
Each pairing of the drop-dead source with a candidate was tested for position agreement with the method mentioned at the beginning of this section. The position of the candidate was transformed to the local in-scan/cross-scan coordinates of the drop-dead and the two-dimensional cross-covariance of the two position probability density functions was evaluated for the separation observed. If the result was below the threshold (Table V.D.1), the candidate was not considered further for confirmation with the drop-dead. Otherwise the result was stored for use later, and the candidate remained viable.
The threshold was set during simulation tests, and it was verified as acceptable during the processing of early survey data. As in the known source correlation processing, it was easier to arrive at a threshold experimentally than to attempt to accept a specific fraction of ail true cases. This follows from the fact that the algorithm's acceptance fraction of true cases increases as the position uncertainties decrease.
D.5.c Photometric Agreement
Each candidate which survived the position test was examined for photometric agreement with the drop-dead in all bands in which both sources had detected fluxes. A 2 test was used which was based on the logarithmic discrepancies of the fluxes and the corresponding variances. The number of degrees of freedom was the number of common bands. The parameter tested was the complement of the cumulative probability; this was required to be above 1 × 10-4, or else the candidate was discarded. No more than one true case out of every ten thousand should be rejected by this test. If the requirement was met, then a combined flux/position test was performed which required the product of the flux test score and the position test score to be above ten. Again the candidate was discarded or retained based on the outcome of this test, which also served as the tie breaker when more than one candidate from the same orbit passed all the tests.
D.5.d Hours-Confirmation Confusion Processing
When more than one candidate was confirmed with the drop-dead source, a series of pairings of each candidate with each other was performed and the requirements placed on each pairing were to have at least one band with detected fluxes in common, to pass the position test, the flux test, and the combined flux/position test. When one of these requirements was not met, the candidate with the higher combined flux/position test score with respect to the drop-dead source was retained and the other was discarded.
D.5.e Hours-Confirmation Position and Photometric Refinement
Position refinement was performed for the drop-dead source and all confirmed candidates by applying the technique discussed by Fowler and Rolfe (1982) in pairwise fashion to the drop-dead source and the first candidate, then to the result of this process and the next candidate, and so on until all source observations involved had been processed. The method essentially computes the renormalized product of all of the position probability density functions and calculates the parameters which describe this product in terms an approximation to the original form of the density function. In this way, the near-optimal treatment of the non-Gaussian errors was maintained.
Pairwise photometric refinement was performed in a manner analogous to the position refinement. Bands in which the paired observations had equal flux status were refined otherwise the flux with the higher status was retained alone. Fluxes obtained by detection with the point-source template were taken as having the highest status; seconds-confirmed and non-seconds-confirmed both qualified. These were refined with Gaussian estimation applied to the logarithms of the fluxes, and so seconds-confirmed fluxes were usually weighted more heavily because of their smaller uncertainties. Low signal-to-noise ratio fluxes were refined by simple weighted averaging of the fluxes, with the signal-to-noise ratio values used as the weights. Upper limits based on noise were refined by retaining the lower value. All detector numbers involved were stored in arrays (see Section V.D.1) and kept with the confirmed source with the following exceptions. Detectors supplying noise fills which were not used were discarded. When four source observations were confirmed, only the first, second and last set of detector number arrays were kept; this was done for purposes of space conservation, and a flag was set to indicate this condition.
D.5.f Hours-Confirmation Statistical Processing
Confirmed source positions were written to an output file for downstream tracking of confirmation frequency as a function of sky position, and histogram data were maintained to display confirmation frequency as a function of signal-to-noise ratio. A histogram counter corresponding to the highest signal to-noise ratio in, any rejected source was also maintained.
Flux discrepancies in each band were processed to obtain the mean and the standard deviation as functions of signal-to-noise ratio; this was done in a format similar to that of seconds-confirmation, and was used in the photometric uncertainty analysis to feed back a posteriori dispersions for use as subsequent a priori errors. 2 tests on the fidelity of the photometric error modeling showed that this process was working as expected. Only confirmed sources devoid of confusion, outer-slot confinement, and other questionable symptoms were used to generate the photometric dispersion data. The standard deviations were similar to those of seconds-confirmation but slightly larger, indicating more power in the photometric error spectrum at orbital frequencies.
Position discrepancies were examined for in-scan mean error, variance, and statistical significance, and the cross-scan discrepancies were studied as functions of latitude. The solar motion caused the scan overlap from one orbit to the next to be a function of latitude, and the overlap was designed to minimize the total cross-scan error of single-band sources. This anticipated effect was confirmed, and this strengthened confidence in the fidelity of the error modeling. Slightly larger discrepancies were found very near the ecliptic, and these were probably due to the confirmation of asteroids which moved slightly between observations but not enough to preclude confirmation. This effect was not included in the pre-launch estimation of position errors at hours-confirmation. The primary effect, larger cross-scan errors for single-band sources at latitudes between 40 degrees and 50 degrees from the ecliptic, was clearly present.
Histograms of the threshold parameters were generated to show their distributions. The main concern was for the cutoffs to lie in regions where variations in value did not cause significant variations in the number of confirmations and rejections. This would be possible if the noise processes were not saturating the decision process, and if the cutoffs were placed well above the values produced by most correct matches and well below the values produced by most false matches. This appeared to be the case.
Confirmation and rejection of numbered asteroids were tracked and printed in the summary. The fraction of these which survived hours-confirmation was about half, as predicted before launch.
Some complications to the hours-confirmation processing were omitted from the discussion above in order to limit its intricacy. These provisos will be described briefly in this section.
As mentioned in the discussion of seconds-confirmation, sometimes a source was observed only on detectors which lay at the cross-scan boundary of the survey array. It was not possible on a single pass to determine whether the source actually missed the detector slots, so that both its flux and position information would be incorrect. The position uncertainties were expanded as described above, as this could be done in a way which virtually guaranteed bracketing the true position; there could be no such guarantee for the flux. As a result, the flux test was not performed when at least one of the sightings involved only outer-slot detectors in all bands containing detected fluxes. Flux refinement was also bypassed in these cases unless both sightings being processed were exclusively on outer slots; when this happened, the refined flux kept the status of being outer-slot only. If a subsequent pairing involved a sighting with detections inside the survey array cross-scan boundaries, its fluxes were retained without any averaging, and the outer-slot status was removed.
When any source was processed which was detected but not seconds-confirmed in the 25 µm band next to the gap left by the demise of detectors 17 and 20, special checking was performed. If detections in other bands were present, the detector geometry was examined to determine whether actual image center passage between the cross-scan limits of the 25 µm band detector could be verified; if so, no further special action was taken. Otherwise the flux in the 25 µm band-was treated as an outer-slot flux, since the image center may actually have missed the slot involved in the detection. This disqualified the source's 25 µm flux from testing, inclusion in the photometric dispersion analysis, and contributing to refinement unless no better data were available.
Particle radiation posed a significant threat to the photometric accuracy, and sources observed in all four bands were more likely to be affected by it. The error caused by this source of noise produced a broad non-Gaussian component to the photometric dispersion which highlighted the fact that it did not conform to the assumptions underlying the 2 tests used for flux agreement. A rule was implemented, therefore, which was applied when the sources tested had at least three bands in common and failed the flux test. In such a case, the single most discrepant band was removed from consideration, and the 2 test with one fewer degree of freedom was used. This exemption could be invoked only once per source pair.
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