IRAS Explanatory Supplement
VII. Analysis of Processing
C. Positional Accuracy
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C.1 Positional Accuracy of Catalog Sources
Stars from the Star Catalog of the Smithsonian
Astrophysical Observatory (1966, henceforth the SAO Catalog) and UGC
galaxies with accurately determined positions
(Dressel
and Condon 1976, henceforth the Dressel and Condon Catalog) were used
to investigate the accuracy of the positions quoted in the IRAS point source
catalog.
Small areas of half-width 20" in-scan by 75" cross-scan around sources brighter at 12 µm than at 25 µm and located more than 20 degrees from the Galactic plane, were searched for SAO stars. Stars with spectral class O, B, and A, and those with no spectral classification were specifically excluded. Inadvertently, slim of spectral types MA, MB, NA and NB were also excluded. This reduced the size of the sample of stars used but, as a subsequent examination revealed had no effect on the statistics reported below.
| Number of HCONs | Number of WSDB Sources | Number of Sources after clean-up | Number of Catalog sources |
|---|---|---|---|
| 1 | 317,764 | 304,334 | 0 |
| 2 | 129,336 | 122,705 | 76,724 |
| 3 | 150,545 | 151,039 | 132,974 |
| 4 | 27,233 | 28,028 | 24,902 |
| 5 | 6,906 | 7,289 | 6,479 |
| 6 | 2,731 | 2,958 | 2,617 |
| 7 | 1,565 | 1,730 | 1,586 |
| 8 | 406 | 456 | 433 |
| 9-23 | 100 | 124 | 124 |
| Total weeks- confirmed (  2 HCONs) | 318,822 | 314,329 | 245,839 |
| Combination | Number | Type S | Type G | Type C | Type O |
|---|---|---|---|---|---|
| 1000 | 67,332 | 57,315 | 10,017 | ||
| 1100 | 67,015 | 61,776 | 5,239 | ||
| 1110 | 13,233 | *9,387 | *4,114 | 1,454 | |
| 1111 | 6,343 | *2,287 | *4,583 | 290 | |
| 0100 | 3,936 | 3,936 | |||
| 0110 | 3,642 | 3,470 | 172 | ||
| 0111 | 3,873 | 3,860 | 13 | ||
| 0010 | 19,264 | 18,494 | 770 | ||
| 0011 | 22,702 | 22,197 | 505 | ||
| 0001 | 33,146 | 33,146 | |||
| 1101 | 2,025 | 1,478 | 547 | ||
| 1010 | 1,100 | *647 | *1,062 | 33 | |
| 1011 | 520 | *297 | *515 | 3 | |
| 1001 | 1,207 | 905 | 302 | ||
| 0101 | 501 | 501 | |||
Total | 245,839 | 134,092* | 58,295* | 33,146 | 23,782 |
| *3,476 sources are both Type S and G categories. | |||||
Areas of the same size around sources detected at 60 µm , which were brighter at 60 µm than at 25 µm , and located more than 30° from the Galactic plane, were searched for a galaxy in the Dressel and Condon catalog. If there was more than one cataloged star or galaxy within the search box of the IRAS source, the source was not used. Matches with position differences greater than seven times the a priori uncertainty on either axis were also discarded. No galaxies and fewer than 0. 1% of the stars were rejected for this reason.
The analysis was done separately for bright sources (flux densities greater than 1.2 and 1.9 Jy at 12 and 60 µm respectively) and faint sources (flux densities lower than the above limits). The number of such sources in each sample are given in Table VII.C.1.
| Number N | Mean difference (") | In-Scan Population  (") |  2/N | Mean difference (") | Cross-Scan Population (") | 2/N |
|
|---|---|---|---|---|---|---|---|
| SAO Stars | |||||||
| Bright | 4757 | 0.0 | 1.9 | 0.42 | 0.1 | 8.4 | 0.55 |
| Faint | 10558 | 0.0 | 2.8 | 0.50 | 0.2 | 15.6 | 0.87 |
| Galaxies | |||||||
| Bright | 340 | -1.2 | 5.3 (3.5*) | 1.04 | 1.0 | 12.8 (12.2*) | 1.30 |
| Faint | 814 | -1.2 | 5.7 (4.1*) | 0.91 | 0.4 | 15.2 (14.7*) | 1.00 |
| * 4" uncertainty removed. | |||||||
C.1a Accuracy of the Absolute Positions
 |
|
Figure VII.C.1 Position differences and uncertainties for the
IRAS stellar sources associated with SAO stars in the in-scan
direction. See text. larger largest |
The absolute positional differences between the 12 µm sources
and the associated stars are shown in Figs. VII.C.1
and VII.C.2 for the in-scan and cross-scan
directions. The same information is given for 60 µm
sources and the associated galaxies in figs. VII.C.3
and VII.C.4. In the
top panel of each figure a histogram of the number of bright sources is
plotted as a function of the absolute position difference. The bottom panel
repeats this plot for the fainter sources. In each case an equal-area Gaussian
distribution with the mean and standard deviation of the sample is plotted
for comparison. from these figures it is apparent that the in-scan errors
are reasonably well represented by Gaussian distributions. The cross-scan
errors are less Gaussian, showing a more concentrated center and more extended
tails.
 |
|
Figure VII.C.2 Position differences and uncertainties for the
IRAS stellar sources in the cross-scan direction. See text. larger largest |
 |
|
Figure VII.C.3 Position differences and uncertainties for the galaxies associated
with Dressel and Condon galaxies in the in-scan direction. See text. larger largest |
 |
|
Figure VII.C.4 Position differences and uncertainties for the galaxies
associated with Dressel and Condon galaxies in the cross-scan direction. See
text. larger largest |
The mean and population standard deviation of the positional differences for all sources in the samples described above are given in Table VII.C.1. Because the SAO positions are more accurate than the IRAS positions, the fisted discrepancies should be representative of the IRAS position errors for sources detected at the short wavelengths. Since the rms position errors in the Dressel and Condon catalog are 4" in each direction, i.e., approximately the same as the IRAS in-scan errors, it is necessary to correct the statistics for this additional uncertainty. The estimates obtained by subtracting the 4" errors in quadrature from the calculated standard deviations in both directions are given in parentheses in the table. No account has been made for any offset of the IRAS source from the optical nucleus of the galaxy. Any such effect would cause an overestimate of the IRAS position errors.
The mean positions of the IRAS stars do not deviate significantly from the SAO positions. This is not surprising since the in-flight calibration of the IRAS focal plane geometry used SAO stars detected at 12 µm to determine the geometric position of the infrared focal plane with respect to the visible star sensors (Section V.D.3). There is also no significant deviation of the cross-scan position of the IRAS galaxy sample based on the galaxy positions. Table VII.C.1 does, however, show a small, but statistically significant discrepancy for the in-scan positions of the galaxies. This small error is consistent with the differences in the positions of the seconds-confirmed sightings in individual wavelength bands of sources seen at multiple wavelengths. While there is no significant discrepancy between the 12 µm and 25 µm positions, there is an 0.8" discrepancy between the in-scan positions of sources as measured at 12 µm and 60 µm , and a 2.4" discrepancy between the in-scan positions of sources as measured at 12 µm and 100 µm. A 0.2% error in the image scale of the telescope could account for this effect. Because the band-merging process used positional information from all detected bands for a source, multiband sources would suffer least from this error sources detected only at 100 ¯o;m could suffer from the full 2.4" error.
The standard deviations of the position errors, given in Table VII.C.1, show that the absolute position errors are quite small. The in-scan position errors depend as expected, on source brightness and wavelength. The cross-scan positions of the brighter sources are significantly better than those of the faint sources, in large part because these sources were detected at multiple wavelengths. The difference between the errors in the bright stars and the errors in the galaxies is consistent with the expected diffraction effects and detector sampling rates.
C.1.b The Quoted Position Uncertainties
The quality of the IRAS position uncertainties is shown in Fig. VII.C.5 for the in-scan and cross-scan directions. Separately plotted for each of the bright and faint source samples are the mean absolute position differences of those sources as a function of the quoted standard deviation. For comparison, the value of this same quantity for a Gaussian distribution of position errors would be
 | for stars and |
 | for galaxies. |
(VII.C.1)
These relations are shown as a solid line in each figure. The difference
in form for the galaxies is due to the 4" uncertainty,
DC, in the
Dressel and Condon catalog. from the figures it is evident that the IRAS
position uncertainties are accurate estimates of the position errors only
for small values and a considerable overestimate for large values.
The overall quality of the quoted error estimates is measured by the
2 parameter, defined as
(VII.C.2)
for stars and 
for galaxies.
 |
|
Figure VII.C.5 Observed position differences vs. the quoted uncertainties.
The top panel for stars and the bottom are for galaxies. See text. larger largest |
Values of 2 per degree of
freedom are given in Table VII.C.1 for the
various samples. As can be seen from the table, the position uncertainties
are overestimated for the stellar sources in both the in-scan and cross-scan
directions, while the uncertainties are reasonably estimated for the galaxy
population, as a whole.
It should be noted that the uncertainties for a limited set of catalog objects include an ad hoc additive component. A preliminary analysis of the IRAS position uncertainties indicated that there was a systematic underestimate of the IRAS in-scan position uncertainties for sources that were both faint and had the minimum possible (1") uniform cross-scan uncertainty. This was probably because non-Gaussian position errors were approximated by a Gaussian distribution when multiple hours-confirmed source positions were combined and the scan paths were close to the 4.6' angular difference where the Gaussian approximation was introduced (Section V.D.5). This approximation was in error only for faint sources. Based on this preliminary analysis an additional 3" was added in quadrature to the in-scan uncertainty for those IRAS catalog sources that had both a 1" uniform cross-scan uncertainty and no individual measured HCON flux density greater than 1.2, 1.4, 1.9 and 6.6 Jy at 12, 25, 60 and 100 µm . Approximately 40% of the sources in the IRAS catalog met these criteria
C.2 Accuracy of Scan-by-Scan Pointing Reconstruction
As a check on the quality of the pointing reconstruction for each scan, the positions of seconds-confirmed band-merged sources were compared with the positions of a preselected set of standard stars (Sections V.B and V.D.4). This set was composed primarily of K stars selected from the SAO Catalog excluding stars within 2.5° of the Galactic plane or within 3' of another detectable star.
It should be borne in mind that the observed position errors are not due entirely to reconstruction errors. Detection timing errors form a significant component in the in-scan direction, so that the IRAS positions of the brighter stars are determined more precisely than those of the faint stars because of the greater accuracy of the timing of the detection of high signal-to-noise objects. In the cross-scan direction the uniform component of the position uncertainty due to the rectangular aspect of the detectors often dominated the errors of position reconstruction. To minimize this effect in assessing the performance of the pointing reconstruction processor only triple (edge) detections were used. In these cases the image of a source traversed the focal plane in the narrow region of overlap between three detectors in a single band.
The differences between the IRAS and SAO positions after seconds-confirmation are summarized in Table VII.C.2. The data are reported for three different periods during the mission. The first and longest period had the best pointing reconstruction and lasted from the beginning of the survey (SOP 29) through the end of the second hours-confimring coverage (SOP 425). The second period began with the start of the third coverage (SOP 426) when the survey strategy required large cross-scan slews. These resulted in larger thermal misalignments and limit-cycle bursts (see Section V.B) and the quality of the pointing reconstruction suffered in both the in-scan and cross-scan directions A third period started at SOP 466 when on-board atittude control was switched from the noisy z-axis gyro ZA to the quieter ZB gro at SOP 466. The quality of the in-scan positions regained its earlier value, while the cross-scan accuracy, although improved, never returned to values seen earlier in the mission.