ISSA Explanatory Supplement

IV. ANALYSIS RESULTS

F. ISSA Reject Set Background Analysis

IV. ANALYSIS RESULTS

F. ISSA Reject Set Background Analysis

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.

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 |

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.

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 |

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.

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 |

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 |

^{*}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.

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 |

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 |

^{*}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.