IV.F. ISSA Reject Set Background Analysis

ISSA Explanatory Supplement
IV. ANALYSIS RESULTS
F. ISSA Reject Set Background Analysis

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The ISSA Reject images, covering the part of the sky within 20° of the ecliptic plane, are of reduced quality compared to the rest of the ISSA data. The zodiacal dust bands and residuals from the removal of the broad zodiacal emission make significant contributions to the ISSA surface brightness at low ecliptic latitudes, especially at 12 and 25 µm, and can interfere with photometry. This section presents some measures of the magnitude of the problems that might be encountered while using the ISSA Reject data for photometric measurements and gives some suggestions for background estimation techniques to minimize photometric problems. The user is advised to read this section carefully prior to using the ISSA Reject images.

The magnitude of photometric error which might be encountered during the use of the ISSA Reject Set was estimated by processing the reject images with special first and second derivative filters that simulate the procedure of background subtraction in aperture photometry measurements with the ISSA images. In these procedures the background to be subtracted from the object plus background measurement is typically derived from one or more measurements of the sky near the object of interest. If the background is not perfectly flat and featureless this method does not give a perfect background subtraction. If a single background measurement is used, the residual background will be proportional to the first derivative of the background. Similarly, if two symmetrically placed background measurements are made, the residual will be proportional to the second derivative of the background.

The special feature of the derivative filters used for this error estimation is that the derivative was combined with a boxcar average to pixel sizes of 0.5° and 2.0°. The 0.5° and 2.0° pixel sizes are appropriate for background measurements taken about 0.5° and 2.0° away, respectively. These two separations were chosen to cover approximately the range of separations that might be used in actual practice. The derivatives were taken in two directions, perpendicular to and parallel to the ecliptic plane, since residual zodiacal emission in the reject fields is seen to produce bands roughly parallel to the ecliptic plane. The kernels for the two derivative filters were

\def{antom{-}}

\left(\matrix{ 0 &  0 & 0 \cr
	       0 & -1 & 0 \cr
	       0 &  1 & 0 \cr}\right)

for the perpendicular derivative and

\left(\matrix{ 0 &  0 & 0 \cr
	       0 & -1 & 1 \cr
	       0 &  0 & 0 \cr}\right)

for the parallel derivative. The second derivative was obtained by application of the filter twice. These derivative filters were applied to ISSA data that had been reprojected into ecliptic coordinates with a nongeometric projection in which longitude runs linearly with pixel number in one direction and latitude runs linearly with pixel number in the other direction. This projection has the effect of underestimating the derivative by the cosine of latitude, a 10% error at 30°.

Tables IV.F.1 through IV.F.4 summarize the results of the uncertainty analysis. The derivatives have been converted to units of residual signal as discussed above for the two methods of background subtraction. The SNR is the ratio of the flux expected from minimum visible cirrus structures to the residual signal. Values for parts of the nonreject ISSA data (>20° and -20° >) are given for comparison. The tabulated values are averages of the absolute value of the background residual over 6°× 6° squares in the projection described above. Compact bright sources generate derivatives of very large absolute value. The use of background references containing such sources should naturally be avoided in actual measurements of the ISSA data, so the averages over the 6°× 6° squares excluded the extreme upper 1% and lower 1% of the samples, or the upper and lower sample in the case of the averages over the 2° pixels. The tables also include the ratio of the flux expected from the minimum visible cirrus structure to the mean absolute residual. The minimum visible cirrus surface brightness is estimated to be 0.1 MJy sr^-1 at 12 and 25 µm, which gives predicted fluxes of 7.6 Jy and 122 Jy for the 0.5° and 2.0° beams, respectively. Several useful hints about background subtraction techniques can be read from Tables IV.F.1 through IV.F.4. First, as expected, residual background errors can be up to ten times worse in the ISSA reject region than at higher ecliptic latitudes in the nonrejected region. Also as expected, two symmetrically placed reference regions provide a better estimate of the background than a single reference. The generally smaller difference between the parallel and perpendicular components of the derivative at high latitudes indicates that the orientation of the placement of the reference apertures is not critical at high ecliptic latitudes. Conversely, the larger difference between components at low latitude, especially at 25 µm, indicate that better background estimates can be expected from references placed at the same latitude as the object of interest. Clearly the optimum placement of reference areas can best be determined from examination of the actual area being measured, both at low and high ecliptic latitude. The banding of the residual zodiacal features parallel to the ecliptic plane will generally favor parallel placement of reference areas at low latitudes.

**Table IV.F.1 Parallel Error Analysis**
Pixel Size = 0.5°
12 µm
ecl lat	ecl lon	Derivative
		First		Second
		Jy^*	SNR⁺	Jy^*	SNR⁺
0	135	3.0	2.5	1.5	5.1
0	0	2.3	3.3	1.7	4.5
-27	135	3.4	2.2	1.8	4.2
-27	0	1.7	4.5	1.3	5.8
27	135	1.8	4.2	1.1	6.9
27	0	2.6	2.9	1.8	4.2

25 µm
ecl lat	ecl lon	Derivative
		First		Second
		Jy^*	SNR⁺	Jy^*	SNR⁺
0	135	3.8	2.0	2.1	3.6
0	0	3.3	2.3	1.8	4.2
-27	135	3.5	2.2	1.9	4.0
-27	0	2.4	3.2	1.5	5.1
27	135	1.8	4.2	1.0	7.6
27	0	2.7	2.8	1.6	4.8

^*Mean absolute residual for 0.5° pixel over a 6° square area as described in text.
⁺SNR is the ratio of the flux expected from the minimum visible cirrus structures to the mean absolute residual, see text §IV.F.

**Table IV.F.2 Parallel Error Analysis**
Pixel Size = 2.0°
12 µm
ecl lat	ecl lon	Derivative
		First		Second
		Jy^*	SNR⁺	Jy^*	SNR⁺
0	135	166	0.7	83	1.5
0	0	56	2.2	49	2.5
-27	135	163	0.7	90	1.4
-27	0	32	3.8	22	5.5
27	135	61	2.0	34	3.6
27	0	73	1.7	83	1.5

25 µm
ecl lat	ecl lon	Derivative
		First		Second
		Jy^*	SNR⁺	Jy^*	SNR⁺
0	135	151	0.8	100	1.2
0	0	144	0.8	97	1.3
-27	135	195	0.6	168	0.7
-27	0	93	1.3	61	2.0
27	135	76	1.6	68	1.8
27	0	137	0.9	80	1.5

^*Mean absolute residual for 2.0° pixel over a 6° square area as described in text.
⁺SNR is the ratio of the flux expected from the minimum visible cirrus structures to the mean absolute residual, see text §IV.F.

**Table IV.F.3 Perpendicular Error Analysis**
Pixel Size = 0.5°
12 µm
ecl lat	ecl lon	Derivative
		First		Second
		Jy^*	SNR⁺	Jy^*	SNR⁺
0	135	6.1	1.2	1.7	4.5
0	0	6.1	1.2	2.0	3.8
-27	135	1.9	4.0	1.2	6.3
-27	0	1.2	6.3	0.9	8.4
27	135	1.1	6.9	0.7	11.
27	0	2.5	3.0	1.5	5.1

25 µm
ecl lat	ecl lon	Derivative
		First		Second
		Jy^*	SNR⁺	Jy^*	SNR⁺
0	135	17.5	0.4	5.0	1.5
0	0	16.8	0.5	5.7	1.3
-27	135	2.3	3.3	1.1	6.9
-27	0	1.7	4.5	1.1	6.9
27	135	1.5	5.1	0.5	15.
27	0	2.9	2.6	1.6	4.8

**Table IV.F.4 Perpendicular Error Analysis**
Pixel Size = 2.0°
12 µm
ecl lat	ecl lon	Derivative
		First		Second
		Jy^*	SNR⁺	Jy^*	SNR⁺
0	135	297	0.4	188	0.6
0	0	341	0.4	210	0.6
-27	135	88	1.4	34	3.6
-27	0	32	3.8	14	8.7
27	135	36	3.4	16	7.6
27	0	71	1.7	46	2.7

25 µm
ecl lat	ecl lon	Derivative
		First		Second
		Jy^*	SNR⁺	Jy^*	SNR⁺
0	135	1050	0.1	682	0.2
0	0	1100	0.1	707	0.2
-27	135	134	0.9	58	2.1
-27	0	80	1.5	22	5.5
27	135	58	2.1	21	5.8
27	0	85	1.4	54	2.3

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ISSA Explanatory Supplement IV. ANALYSIS RESULTS F. ISSA Reject Set Background Analysis

ISSA Explanatory Supplement
IV. ANALYSIS RESULTS
F. ISSA Reject Set Background Analysis