# Explanatory Supplement to the 9P/Tempel 1 IRAS Survey Images

# Delivered to University of Maryland

December 29, 2000

Russ Walker

Vanguard Research, Inc.

5321 Scotts Valley Drive, Suite 204

Scotts Valley, CA 95066

Revised August 9, 2005

# by PDS-SBN, University of Maryland

to reflect modifications requested during the PDS Peer Review

## Survey Scan Radiance and Noise Maps - Background

The bulk of the IRAS observation time was spent in the survey mode that
systematically mapped the sky with a series of overlapping and
confirming scans. This redundancy can be used to produce a survey with
fainter limiting magnitude, such as the IRAS Faint Source Survey, or to
improve the spatial resolution in the scanned fields. Const­ruction of
images from survey data is complicated by the fact that the confirming
scans cross each other at varying angles. Construction of comet images
also requires compensation for the motion of the comet and the changing
spacecraft parallax during the relatively large time interval (\>103
minutes) between the confirming scans necessary to build the image. All
the images in the delivered set were constructed from survey scans. They
are thus "time-averaged" images of the comet emission history. Table 3
at the end of this document lists the Survey Scans used in each
"time-averaged" image.

The method for the production of comet images uses a computer algorithm
based on the Maximum Correlation Method (MCM) for Image Construction
(Aumann, Fowler, and Melnyk, 1990), and closely parallels the \"HiRes
Processing\" performed at IPAC (Melnyk and Rice, 1991). The major
departure from the IPAC scheme occurs in the Comet Image Preprocessor
(CIPP) where the coordinates of each detector footprint (data sample)
are transformed to a moving Sun-referenced coordinate system with the
comet at the origin.

The Comet Image Preprocessor (CIPP) - The CIPP program reads the scan
data and performs three main functions; 1) transform the coordinates of
the data samples to a coordinate system that moves with the comet; 2)
remove data artifacts, such as baseline, tails, and radiation hits
(glitches) that tend to be magnified by the image construction
processing; and 3) associate each data sample with the specific pixels
in the map covered by the detector response function and their weights
in the observed response. This latter information is stored in an array
and is \"looked up\" by the processor (described below) at each
iteration of the image construction.

The Comet Image Processor (CIP) - Once the CIPP has \"cleaned up\" the
scan, the CIP program applies the MCM algorithm to construct
high-resolution images of the comet from the survey scans. The spatial
response functions of the IRAS detectors that were used are modified
versions of those given by Moshir, 1986. They have been \"de-tailed\"
and their response extended to 1% of the peak by approximating the point
spread function of the IRAS telescope mirror with a two-dimensional
Gaussian blur that contains 85% of the flux from a point source within a
circle of diameter 25\", 25\", 60\", and 100\" for the 12, 25, 60, and
100 micron bands (Beichman, et al, 1988).

CIP begins with a map of uniform low level radiance, and builds an image
by scanning an analytical version of the IRAS focal plane over the map,
simulating the IRAS data-taking process. The analytical data samples are
compared to the real scan data samples (cleaned by the CIPP) and pixel
correction factors determined. Details of this process are given by
Aumann, et al, 1990 and Melnyk and Rice, 1991. Building the map is an
iterative process, wherein each iteration begins with the most recent
estimate of map radiance. Statistics relating to pixel noise and
convergence are generated at each iteration. A typical image will
converge after 15 to 40 iterations. For each iteration, two image
products were produced from the Tempel 1 survey scans:

A. Radiance Map - The radiance map is the surface brightness image
produced by the CIP. Two radiance maps were produced for archive; 1) the
map resulting from the first iteration (equivalent to the IPAC FRESCO
image, see Melnyk, 1990), and 2) the high-resolution map produced at the
final iteration.

B. Photometric Noise Map - This is an image of the internal photometric
uncertainty (standard deviation) of the radiance in a pixel as a result
of averaging overlapping detector samples. The photometric noise map may
be used to estimate the error in aperture photometry of the comet,
photometric profiles, and flux ratios.

## Radiance and Noise Maps - File Designations and Content

The delivered data set includes radiance and noise images, processing
logs, aperture photometry files, the scan list, and a file of the
osculating orbital elements used for Tempel 1. IRAS scans are identified
by a satellite operations plan (SOP) number. The images are identified
by a "mean" SOP number, since several scans are used to make an image.
The IRAS observations were made in four spectral bands centered
nominally at 12μm, 25μm, 60μm, and 100μm. Radiance images and noise maps
are supplied for the first iteration (01) and the final iteration (nn)
determined by the convergence of the flux in all the pixels in the
scanned path. Thus, the following file names were adopted:

Radiance and Noise Maps in /data/survey/images/:

Radiance Maps (40) -- sSOP_Band_Iteration#\_radiance.fit

Noise Maps (40) -- sSOP_Band_Iteration#\_noise.fit

The numbers in parenthesis above are the number of files that PDS-SBN
received. Values for Band are 12μm, 25μm, 60μm, and 100μm. Iteration
values are 01 for the first iteration or the number of the final
iteration (15 through 40).

For convenience, Russell Walker included the spectral response files of
the IRAS detector bands that he used to process the Survey Scans. The
12μm and 100μm files that he used included refinements to the spectral
response files available at IPAC. The spectral response files are named
/calib/bandN_WWWum.tab, where N is the IRAS band number, 1, 2, 3, or 4,
that is equivalent to WWW, the nominal wavelength (at band center):
12μm, 25μm, 60μm, and 100μm.

The Radiance and Noise Maps are in FITS image format. They have
extensive headers that provide all the data that you need to use the
images. The following is an example from a 100μm image that converged
after 16 iterations.

SIMPLE = T / Written by IDL: 27-Dec-2000 17:25:50.00

BITPIX = -32 / IEEE single precision floating point

NAXIS = 2

NAXIS1 = 150 / Fastest varying axis

NAXIS2 = 075 / Slowest varying axis

BSCALE = 1.00000 /

BUNIT = \'Watts/cm2/sr\' /

BZERO = 0.000000 /

OBJECT = \'9P/TEMPEL 1\' / Target

DATAMAX = 3.15750E-10 / Watts/cm2/sr (in-band radiance)

DATAMIN = 0.00000E+00 / Watts/cm2/sr (in-band radiance)

CRVAL1 = 96.94210 / Solar elon of target via orbital elements

CRPIX1 = 77 / X-axis origin, pixel at comet max

CDELT1 = 24 / X-axis pixel width (arcsec)

CTYPE1 = \'ELONGATION\' / Angle between IRAS line of sight and Sun

CRVAL2 = 359.40880 / Solar incl of target via orbital elements

CRPIX2 = 37 / Y-axis origin, pixel at comet max

CDELT2 = 24 / Y-axis pixel width (arcsec)

CTYPE2 = \'INCLINATION\' / Angle between ecl plane, E-S plane and obs
dir

COMMENT COMET Tempel 1 1983 XI

COMMENT FLUX MAP

COMMENT Iteration 016

COMMENT Converged Pixels 09741

COMMENT Jan 2003, PDS Small Bodies Node modified the header:

COMMENT 1) Corrected several keywords and values to standards.

COMMENT 2) Added keyword comments for clarification.

COMMENT 3) Removed peak flux comment line per R.Walker.

COMMENT 4) Added observation-specific keywords at end of header.

COMMENT 5) Image size is 1.0 degree by 0.5 degree.

COMMENT 6) Pixel size is 24 arcsec by 24 arcsec.

FILENAME= \'s339_100um_16_radiance.fit\' / OUTPUT FILE NAME

COMETMAX= 1.15603E-11 / Watts/cm2/sr (in-band radiance)

WAVE = 100 / Wavelength (microns)

MEAN_JD = 2445529.789 / Mean Julian date of combined observations

MEANDT = \'1983-07-14\' / Mean UTC date of combined obs

MEANTM = \'06:56:09.600\' / Mean UTC time of combined obs

MEAN_RA = 205.57081 / deg

MEAN_DEC= -11.23130 / deg

SOP = 339 / Scan Orbit

NOBS = 7 / Number of observations

RHO = 1.492 / Sun-Comet distance (AU)

DELTA = 0.976 / Earth-Comet distance (AU)

PHASE = 42.566 / Phase angle (S-T-O) (deg)

TOBS = 336 / Summed time of observations (sec)

UTCSTART= 2445529.6202 / UTC at start of obs (Julian date)

UTCSTOP = 2445530.0499 / UTC at end of obs (Julian date))

STARTDT = \'1983-07-14\' / UTC date at start of obs

STARTTM = \'02:53:05.360\' / UTC time at start of obs

STOPDT = \'1983-07-14\' / UTC date at end of obs

STOPTM = \'13:11:47.180\' / UTC time at end of obs

SCSTART = 79843985.36 / IRAS time at start of obs

SCSTOP = 79881107.18 / IRAS time at end of obs

END

The image is 150 x 75 pixels (NAXIS1 x NAXIS2).

The coordinate system is solar elongation and inclination, a natural
coordinate system for IRAS. Elongation θ is the angle between the line
of sight and the Sun. Inclination I~0~ is the angle between the ecliptic
plane and the plane containing the Earth, Sun, and observation direction
(that is, the azimuth angle about the Earth-Sun axis). The value of I~0~
is zero when IRAS looks at the ecliptic plane in the direction opposite
to the motion of the Earth around the Sun. The value increases clockwise
around the Earth-Sun axis when facing the Sun, and opposite from the
direction of the motion of the satellite in its polar orbit about the
Earth. These angles are related to geocentric ecliptic coordinates by

cos(θ) = cos(β)cos(λ-λ~o~)

sin(I~0~) = sin(β)/sin(θ)

where β is ecliptic latitude, λ is ecliptic longitude, and λ~o~ is the
longitude of the Sun.

Figure 1 illustrates the IRAS native coordinate system of solar
elongation θ and observation inclination I~0~. Inclination I~0~ is
related to the IRAS clock angle φ~0~ by

I~0~ = 90 degrees - φ~0~

where the clock angle φ~0~ is measured in the plane perpendicular to the
Sun line and clockwise as viewed from the Sun.

![](media/image1.jpeg){width="5.555555555555555in"
height="4.888888888888889in"}

> Figure 1. A solar elongation and clock angle system defines the
> geometry of a scan. The solar elongation angle θ is the angle between
> the satellite-to-Sun line and the boresight. The IRAS clock angle φ~0~
> is measured in the plane perpendicular to the Sun line and clockwise
> as viewed from the Sun. Sometimes the inclination of the IRAS
> observation, I~0~ = 90 degrees - φ~0~, is used. I~0~ is the angle
> between the ecliptic plane and the plane containing the Earth, Sun,
> and observation direction (that is, the azimuth angle about the
> Earth-Sun axis). This graphic was copied from the IRAS Explanatory
> Supplement, available online at the IPAC website,
> <http://irsa.ipac.caltech.edu/IRASdocs/exp.sup/ch3/B.html>.

The images were constructed by referencing the radiance samples to the
orbital position of the comet at the time of the sample. Thus the comet
(by virtue of its orbital elements) is always at pixels 75 and 37. This
is the map center reference and has mean elongation and inclination as
given in the header. However, as in the header above the maximum
radiance of the comet (COMETMAX) did not occur at 75,37 but at 77,37.
The pixel size is 24 x 24 arcsec. Also note that in this image the
maximum radiance (DATAMAX) does not occur at the comet (COMETMAX). This
is a map of the radiance and includes background radiance, thus DATAMIN
= 0 and the comet radiance is biased up by the background radiance.

Since the images are constructed from many survey scans at different
times, the mean coordinates (RA, DEC, Elongation, Inclination) were
listed for the comet at the mean Julian Date (MEAN JD). Scans that
occurred at nearly the same heliocentric and geocentric distances were
selected. The sSOP_Band.log files and the survey_scans_used.tab contain
much helpful data on this, and are self-explanatory. You will encounter
the time variable UTCS. This is IRAS time. It may be converted to Julian
date by

JD = 2445335.5d0+(UTCS - 63072000.0d0) / 86400.0d0

The UTCS start and stop times for each image were converted to UTC
Julian dates and Gregorian dates and included in the FITS headers.

Although the images are binned into 24" pixels, the actual resolution
within the image is dependent on (among other things) the number of
iterations. All iterations were ran until the variations of the flux
within each pixel (that was actually scanned) had converged to within
the photometric noise of that pixel. There was no direct measure of the
spatial resolution achieved, however, Rice (1993) measured the mean
dimensions of 13 bright IRAS stellar point sources as a function of the
number of iterations. The Rice (1993) results in the following table:

+-------------+-------------+-------------+-------------+-------------+
| Table 0.    |             |             |             |             |
| FWHM        |             |             |             |             |
| Cross-scan  |             |             |             |             |
| x In-scan   |             |             |             |             |
| (arcsec)    |             |             |             |             |
+-------------+-------------+-------------+-------------+-------------+
| MCM         | 12μm        | 25μm        | 60μm        | 100μm       |
| Iteration   |             |             |             |             |
+-------------+-------------+-------------+-------------+-------------+
| 01          | 256 x 64    | 270 x 67    | 301 x 121   | 403 x 282   |
+-------------+-------------+-------------+-------------+-------------+
| 05          | 79 x 34     | 72 x 36     | 123 x 63    | 182 x 134   |
+-------------+-------------+-------------+-------------+-------------+
| 10          | 51 x 28     | 48 x 28     | 86 x 50     | 131 x 103   |
+-------------+-------------+-------------+-------------+-------------+
| 20          | 37 x 23     | 35 x 23     | 62 x 41     | 98 x 80     |
+-------------+-------------+-------------+-------------+-------------+
|             |             |             |             |             |
+-------------+-------------+-------------+-------------+-------------+
| Notes: 1.   |             |             |             |             |
| Un          |             |             |             |             |
| certainties |             |             |             |             |
| in the mean |             |             |             |             |
| dimensions  |             |             |             |             |
| are less    |             |             |             |             |
| than 8%     |             |             |             |             |
|             |             |             |             |             |
| 2\. The     |             |             |             |             |
| geometric   |             |             |             |             |
| detector    |             |             |             |             |
| beam is ∼   |             |             |             |             |
| 300"        |             |             |             |             |
| cross-scan  |             |             |             |             |
| and ∼ 45",  |             |             |             |             |
| 45", 90",   |             |             |             |             |
| and         |             |             |             |             |
|             |             |             |             |             |
| 180" at 12, |             |             |             |             |
| 25, 60, and |             |             |             |             |
| 100μm       |             |             |             |             |
| r           |             |             |             |             |
| espectively |             |             |             |             |
| along the   |             |             |             |             |
| in-scan     |             |             |             |             |
| direction.  |             |             |             |             |
|             |             |             |             |             |
| 3\. Little  |             |             |             |             |
| or no       |             |             |             |             |
| improvement |             |             |             |             |
| of          |             |             |             |             |
| resolution  |             |             |             |             |
| was noted   |             |             |             |             |
| after 20    |             |             |             |             |
| iterations. |             |             |             |             |
+-------------+-------------+-------------+-------------+-------------+

## 

## Aperture Photometry

The data set that Russell Walker delivered included aperture photometry
files. However, the original photometry files will be replaced by
photometry data being derived by and published for the Deep Impact
Mission. Neither of these photometry data is included in this archive;
the new photometry data will be archived in the future. This Aperture
Photometry section remains in the document as a record of Russell
Walker's photometry work.

## Aperture Photometry - File Designations and Content

IRAS Survey Scans are identified by a satellite operations plan (SOP)
number. The images and photometry tables are identified by a "mean" SOP
number, since several scans are used to make an image. The IRAS
observations were made in four spectral bands centered nominally at
12μm, 25μm, 60μm, and 100μm. Photometry files are supplied for the final
iteration (nn) determined by the convergence of the flux in all the
pixels in the scanned path. Thus, the following file names were adopted
for the Survey Scan photometry tables:

Radiance Photometry Files (20) -- sSOP_Band_Iteration#\_radiance.tab

Noise Photometry Files (20) -- sSOP_Band_Iteration#\_noise.tab

The numbers in parenthesis above are the number of files that PDS-SBN
received. Values for Band are 12μm, 25μm, 60μm, and 100μm. Iteration
value is for the iteration final iteration (15 through 40).

## Aperture Photometry - Methodology

The radiance (and noise) photometry files are the result of summing the
radiance (and variance) from all the pixels that are within a selected
distance from the pixel of maximum comet radiance. There are three
columns in the files. The first is the distance (radius) that includes
the pixels summed. Zero is the central pixel, etc. The second column is
the summed radiance (or noise) in units of Watts cm^-2^. The third
column is the number of pixels actually included in the sum. Most of the
coma flux should be contained within a few pixels radius. There is
0.846125 x 10^-8^ steradian per 15" square pixel or 2.166080 x 10^-8^
steradian per 24" square pixel.

The original photometry files delivered to PDS-SBN during December 2000
for the Survey Scan Images used the image median to estimate the
background and subtract that from the image prior to photometry. This is
usually a reasonable thing to do for stars, etc. However, for the comet,
the dust tail may be a significant source of background (or foreground)
for estimates of the coma flux (see Figure 2a). In the case of a point
source in a uniform background one expects the aperture photometry curve
to rise to an asymptotic value if the background has been properly
subtracted (Figure 2b). R. Walker modified his photometry program to
iterate the background radiance until the profile tends toward
asymptotic at radii greater than 30 pixels from the maximum comet
radiance. He chose to call this "coma aperture photometry" and the value
of the asymptote an estimate of the total coma flux. The difference
between of the original and revised methods for estimating the
background is illustrated in Figures 1a and 1b. The revised fluxes for
the survey scan data, generated by the "coma aperture photometry"
process, and are presented in Table 1.

Photometry for the survey scan images was redone by R. Walker using the
new software and radiance survey "coma" photometry files were delivered
to PDS-SBN in February 2001 (data/survey/phot/).

![](media/image2.png){width="5.050694444444445in"
height="3.7270833333333333in"}

Figure 2a. Aperture photometry of the 12 μm survey radiance image #339
with median background subtraction as delivered on December 29, 2000.

![](media/image3.png){width="5.050694444444445in"
height="3.7215277777777778in"}

Figure 2b. Aperture photometry of the 12 μm survey radiance image #339
with iterative background subtraction (coma photometry).

+-----+-----+-------+-------+------+----------+----------------------+
| Ta  |     |       |       |      |          |                      |
| ble |     |       |       |      |          |                      |
|  1. |     |       |       |      |          |                      |
| R   |     |       |       |      |          |                      |
| esu |     |       |       |      |          |                      |
| lts |     |       |       |      |          |                      |
| of  |     |       |       |      |          |                      |
| "Co |     |       |       |      |          |                      |
| ma" |     |       |       |      |          |                      |
| Ap  |     |       |       |      |          |                      |
| ert |     |       |       |      |          |                      |
| ure |     |       |       |      |          |                      |
| P   |     |       |       |      |          |                      |
| hot |     |       |       |      |          |                      |
| ome |     |       |       |      |          |                      |
| try |     |       |       |      |          |                      |
| on  |     |       |       |      |          |                      |
| the |     |       |       |      |          |                      |
| Sur |     |       |       |      |          |                      |
| vey |     |       |       |      |          |                      |
| Obs |     |       |       |      |          |                      |
| erv |     |       |       |      |          |                      |
| ati |     |       |       |      |          |                      |
| ons |     |       |       |      |          |                      |
+-----+-----+-------+-------+------+----------+----------------------+
| SOP | OBS | RHO   | DELTA | BAND | FLUX     | REMARKS              |
|     |     |       |       |      |          |                      |
|     |     | (AU)  | (AU)  | (μm) | (w       |                      |
|     |     |       |       |      | cm^-2^)  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
| 339 |     | 1.491 | 0.976 | 12   | 4.99 x   |                      |
|     |     |       |       |      | 10^-16^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 25   | 3.97 x   |                      |
|     |     |       |       |      | 10^-16^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 60   | 7.03 x   |                      |
|     |     |       |       |      | 10^-17^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 100  | 7.16 x   | Noise/Background     |
|     |     |       |       |      | 10^-18^  | Structure            |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       |      |          |                      |
+-----+-----+-------+-------+------+----------+----------------------+
| 368 |     | 1.503 | 1.064 | 12   | 4.14 x   |                      |
|     |     |       |       |      | 10^-16^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 25   | 3.55 x   |                      |
|     |     |       |       |      | 10^-16^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 60   | 6.63 x   |                      |
|     |     |       |       |      | 10^-17^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 100  | 8.79 x   | Noise/Background     |
|     |     |       |       |      | 10^-18^  | Structure            |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       |      |          |                      |
+-----+-----+-------+-------+------+----------+----------------------+
| 389 |     | 1.521 | 1.138 | 12   | 3.65 x   |                      |
|     |     |       |       |      | 10^-16^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 25   | 2.86 x   |                      |
|     |     |       |       |      | 10^-16^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 60   | 6.05 x   |                      |
|     |     |       |       |      | 10^-17^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 100  | 6.90 x   | Noise/Background     |
|     |     |       |       |      | 10^-18^  | Structure            |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       |      |          |                      |
+-----+-----+-------+-------+------+----------+----------------------+
| 421 |     | 1.561 | 1.265 | 12   | 2.96 x   |                      |
|     |     |       |       |      | 10^-16^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 25   | 2.69 x   |                      |
|     |     |       |       |      | 10^-16^  |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 60   | (6 x     | Background Structure |
|     |     |       |       |      | 10^-17^) |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 100  | ?        | Noise/Background     |
|     |     |       |       |      |          | Structure            |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       |      |          |                      |
+-----+-----+-------+-------+------+----------+----------------------+
| 493 |     | 1.695 | 1.624 | 12   | (1.8 x   | Crowded Field        |
|     |     |       |       |      | 10^-16^) |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 25   | (1.3 x   | "                    |
|     |     |       |       |      | 10^-16^) |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 60   | \>5.3 x  | "                    |
|     |     |       |       |      | 10       |                      |
|     |     |       |       |      | ^--17^   |                      |
+-----+-----+-------+-------+------+----------+----------------------+
|     |     |       |       | 100  | ?        | Noise/Background     |
|     |     |       |       |      |          | Structure            |
+-----+-----+-------+-------+------+----------+----------------------+

## Comments on Colors and Flux Measures

One can convert the in-band radiance (w cm^-2^ sr^-1^) to flux density
units (Jy sr^-1^) by dividing the in-band radiance by (13.48, 5.16,
2.58, and 1.00) x 10^-18^ for the 12, 25, 60, and 100μm bands
respectively. This must then be corrected for the spectrum of the
source, for example: for a blackbody at 250K the flux densities must be
divided by 0.87, 1.11, 1.19, and 1.07 for the 12, 25, 60, and 100μm
bands respectively. It is recommended that model spectral radiances be
integrated over the IRAS spectral response and compared to the observed
in-band radiances rather than converting the observations to flux
densities.

Colors (flux ratios) are a more complicated problem. Even after running
the MCM high-resolution process the spectral bands have different
resolutions. Ratios made from the 12μm and 25μm bands will have meaning
since these two bands have virtually the same resolution at all
iteration steps. However, if one wants to compare radiance ratios, say,
R(12μm)/R(60μm), R(25μm)/R(60μm), etc. he will not obtain the desired
result due to the different beam sizes involved. There are two
sophisticated ways to approach this problem: 1) *Cross-band simulation*
wherein a new set of images is made by scanning the high-res images with
a simulation of the IRAS focal plane, running MCM on these new images to
produce images that have the same resolution and can then be ratioed.
2*) Prior-knowledge* technique wherein say the 60μm high-res image is
used as the starting point for constructing a 100μm image and vice
versa. This technique results in an image of higher resolution than the
cross-band technique. Both of these methods are described by Fowler and
Aumann (1994).

A simple approach would use the beam-size information in the above table
to estimate the two-dimensional gaussian beam profile necessary to
convolve with the higher resolution image to produce an image at the
resolution of the lower resolution image. These can then be ratioed for
comparison to calculated spectral ratios. For example: one wishes to
ratio a 20 iteration 12μm image with a 10 iteration 60μm image; the FWHM
of the gaussian kernel would be 1) cross-scan: sqrt(86^2^ - 37^2^) =
77.6 and 2) in-scan: sqrt(50^2^ -- 23^2^) = 44.4. The 12μm map is then
convolved with the 77.6 x 44.4 kernel and the two maps ratioed. Values
for other numbers of iterations and band combinations can be
interpolated in the table. The assumption that the output PSF of MCM is
gaussian is not really a bad one.

In addition, the noise images are good measures of the relative noise
from one part of an image to another. They are poor estimates of the
absolute noise level. The photometric noise map indicates the internal
photometric error of the detector samples resulting from the averaging
of overlapping samples. It does not include absolute errors such as
calibration errors. This applies to both the survey and additional
observations (AO) data. Beichman, et al (1988) estimates that the
absolute errors in the IRAS absolute calibration are 2%, 5%, 5%, and 10%
at 12μm, 25μm, 60 μm, and 100μm respectively due to uncertainty in the
models used. These numbers should be RSSd with 3% uncertainty in the
standard stars used and 4% uncertainty for spectral bandpass errors. I
have removed some systematic errors by re-calibrating IRAS in accordance
with Cohen, et al (1992). Thus an estimate of the uncertainties of the
radiance data can be had by combining the above absolute errors with the
noise map values in the root sum squared sense.

## Some Interesting Plots

Figure 3 is a plot of the "coma" fluxes from survey scans in Table 1 and
additional observations (AO) in Table 2. "Coma" fluxes from the tables
are divided by the pre-perihelion "coma" flux (s287 o13). Curvature in
these plots is an indication of spectral variations at differing
heliocentric distances. The heliocentric distances are labeled on the
plot. One expects the spectrum to change due to variations in grain
temperature, size distribution, and possibly composition.

  -------------- ------ -------- -------- ------- -------------- ------------------
  Table 2.                                                       
  Results of                                                     
  "Coma"                                                         
  Aperture                                                       
  Photometry on                                                  
  the AO                                                         
  Observations                                                   

  SOP            OBS    RHO      DELTA    BAND    FLUX (w        REMARKS
                                                  cm^-2^)        

  287            13     1.507    0.853    12      5.89 x 10^-16^ 

                                          25      4.07 x 10^-16^ 

                                          60      6.78 x 10^-17^ 

                                          100     8.98 x 10^-18^ 

                                                                 

  407            12     1.541    1.204    12      3.63 x 10^-16^ 

                                          25      2.60 x 10^-16^ 

                                          60      4.02 x 10^-17^ 

                                          100     4.88 x 10^-18^ Noise/Structure

                                                                 

  407            43     1.541    1.206    12      3.56 x 10^-16^ 

                                          25      2.67 x 10^-16^ 

                                          60      4.53 x 10^-17^ 

                                          100     4.91 x 10^-18^ Noise/Structure

                                                                 

  509            40     1.735    1.725    12      ?              Source Confusion

                                          25      ?              "

                                          60      ?              "

                                          100     ?              "

                                                                 

  510            22     1.737    1.730    12      ?              Source Confusion

                                          25      ?              "

                                          60      ?              "

                                          100     ?              "
  -------------- ------ -------- -------- ------- -------------- ------------------

![](media/image4.png){width="6.0in" height="4.8in"}

Figure 3. Tempel 1 spectrum relative to its pre-perihelion spectrum at
1.507 AU.

Figure 4 is a plot of the relative "activity" of Tempel 1 as a function
of heliocentric distance. The "activity" is defined as ∆^2^ x Flux (∆),
where ∆ is the geocentric distance of the comet. This quantity is a
measure of the dust production rate, or perhaps more properly, the
resident time of dust within the beam. These data are normalized to the
"activity" of the pre-perihelion observation. The heliocentric distances
are labeled.

![](media/image5.png){width="6.0in" height="4.8in"}

Figure 4. Activity of Tempel 1.

> Table 3. Survey Scans Used
>
> Scans used to create the survey images:
>
> MEAN SOP OBS UTCS JD RA DEC RHO DELTA PHASE ELONGATION UTCS(start)
> UTCS(end)
>
> SOP (sec) (days) (hour) (deg) (AU) (AU) (deg) (deg) (sec) (sec)
>
> 339 338 27 79844009.36 2445529.62 13.699 -11.152 1.492 .975 42.562
> 96.497 79843985.36 79844033.36
>
> 339 3 79850184.32 2445529.69 13.701 -11.181 1.492 .975 42.564 96.974
> 79850160.32 79850208.32
>
> 339 9 79856375.02 2445529.76 13.704 -11.209 1.492 .976 42.565 96.951
> 79856351.02 79856399.02
>
> 339 19 79862542.19 2445529.83 13.706 -11.238 1.492 .976 42.567 96.928
> 79862518.19 79862566.19
>
> 339 27 79868737.28 2445529.91 13.709 -11.266 1.492 .977 42.569 97.405
> 79868713.28 79868761.28
>
> 339 36 79874904.18 2445529.98 13.712 -11.295 1.492 .977 42.570 97.382
> 79874880.18 79874928.18
>
> 339 45 79881083.18 2445530.05 13.714 -11.323 1.492 .977 42.572 97.359
> 79881059.18 79881107.18
>
> 368 367 27 81087172.42 2445544.01 14.252 -16.695 1.503 1.061 42.436
> 92.237 81087148.42 81087196.42
>
> 367 30 81093338.99 2445544.08 14.255 -16.721 1.503 1.061 42.433 92.218
> 81093314.99 81093362.99
>
> 367 33 81099504.81 2445544.15 14.258 -16.747 1.503 1.062 42.430 92.698
> 81099480.81 81099528.81
>
> 368 19 81130987.98 2445544.52 14.273 -16.881 1.504 1.064 42.416 92.599
> 81130963.98 81131011.98
>
> 368 22 81136593.44 2445544.58 14.276 -16.905 1.504 1.065 42.413 92.580
> 81136569.44 81136617.44
>
> 368 26 81142774.31 2445544.65 14.279 -16.931 1.504 1.065 42.410 92.561
> 81142750.31 81142798.31
>
> 369 2 81148963.75 2445544.72 14.282 -16.957 1.504 1.066 42.407 93.041
> 81148939.75 81148987.75
>
> 369 8 81155144.91 2445544.80 14.285 -16.984 1.504 1.066 42.405 93.022
> 81155120.91 81155168.91
>
> 389 389 8 82021150.24 2445554.82 14.717 -20.491 1.521 1.136 41.819
> 89.381 82021126.24 82021174.24
>
> 389 14 82027343.81 2445554.89 14.720 -20.514 1.521 1.136 41.813 89.363
> 82027319.81 82027367.81
>
> 389 19 82033537.15 2445554.96 14.723 -20.538 1.521 1.137 41.808 89.345
> 82033513.15 82033561.15
>
> 389 26 82039730.88 2445555.03 14.727 -20.562 1.521 1.137 41.803 89.826
> 82039706.88 82039754.88
>
> 389 31 82046201.37 2445555.11 14.730 -20.587 1.521 1.138 41.797 89.808
> 82046177.37 82046225.37
>
> 390 34 82089207.50 2445555.61 14.752 -20.751 1.522 1.141 41.759 89.680
> 82089183.50 82089231.50
>
> 391 2 82095390.09 2445555.68 14.755 -20.775 1.523 1.142 41.753 90.162
> 82095366.09 82095414.09
>
> 391 7 82101574.27 2445555.75 14.759 -20.798 1.523 1.142 41.747 90.144
> 82101550.27 82101598.27
>
> 391 13 82107749.53 2445555.82 14.762 -20.822 1.523 1.143 41.742 90.626
> 82107725.53 82107773.53
>
> 421 421 10 83399973.15 2445570.78 15.468 -25.267 1.560 1.263 40.269
> 85.403 83399949.15 83399997.15
>
> 421 16 83406167.56 2445570.85 15.471 -25.285 1.560 1.263 40.261 85.385
> 83406143.56 83406191.56
>
> 421 23 83412361.80 2445570.92 15.475 -25.304 1.561 1.264 40.252 85.867
> 83412337.80 83412385.80
>
> 421 30 83418556.84 2445570.99 15.478 -25.323 1.561 1.265 40.244 85.849
> 83418532.84 83418580.84
>
> 421 35 83424751.15 2445571.06 15.482 -25.342 1.561 1.265 40.236 85.832
> 83424727.15 83424775.15
>
> 421 41 83431383.14 2445571.14 15.486 -25.362 1.561 1.266 40.227 86.313
> 83431359.14 83431407.14
>
> 422 29 83468042.03 2445571.57 15.506 -25.472 1.562 1.270 40.177 86.208
> 83468018.03 83468066.03
>
> 422 34 83474235.73 2445571.64 15.510 -25.491 1.563 1.270 40.168 86.190
> 83474211.73 83474259.73
>
> 493 491 31 86442399.77 2445605.99 17.283 -31.342 1.693 1.618 35.138
> 76.062 86442375.77 86442423.77
>
> 491 38 86448584.78 2445606.06 17.287 -31.348 1.694 1.618 35.126 76.541
> 86448560.78 86448608.78
>
> 492 41 86491978.73 2445606.56 17.313 -31.388 1.696 1.624 35.042 75.893
> 86491954.73 86492002.73
>
> 492 49 86498048.00 2445606.63 17.317 -31.393 1.696 1.625 35.030 76.373
> 86498024.00 86498072.00
>
> 493 12 86510412.90 2445606.78 17.324 -31.404 1.697 1.627 35.006 76.330
> 86510388.90 86510436.90
>
> 493 18 86516596.90 2445606.85 17.328 -31.410 1.697 1.628 34.994 76.309
> 86516572.90 86516620.90
>
> 493 25 86522780.71 2445606.92 17.332 -31.415 1.697 1.628 34.982 76.788
> 86522756.71 86522804.71
>
> NOTES:
>
> 1\. UTCS and JD in columns 4 and 5 are the times that the IRAS
> boresite crossed the comet.
>
> 2\. RA and DEC (B1950) are the coordinates of the comet at the time of
> crossing.
>
> 3\. RHO and DELTA are the heliocentric and geocentric distance of the
> comet at the time of
>
> crossing.
>
> 4\. ELONGATION is the solar elongation of the comet at the time of
> crossing.
>
> 5\. UTCS(begin) and UTCS(end) are the beginning and ending times of
> the scan.

## References

Aumann, H.H., Fowler, J.W., Melnyk, M., 1990, \"A Maximum Correlation
Method for Image Construction of IRAS Data\", Astron. J. 99, 1674-1681.

Beichman, et al, 1988, 'IRAS Catalogs, Vol 1. Explanatory Supplement'.

Cohen, M., Walker, R.G., Barlow, M.J., Deacon, J.R., 1992, "Spectral
Irradiance Calibration in the Infrared. I. Ground-based and IRAS
Broadband Calibrations", Astron. J. vol. 104, no. 4, pp1650-1657.

Fowler, J.W. and Aumann, H.H., 1994, "Science with High Spatial
Resolution Far-Infrared Data, Proceedings of a Workshop Held 14-16 June
1993", JPL Publication 94-5, (S.Terebey and J. Mazzarella, Eds.).

Melnyk, M., 1990, \"Technical Reference to the Full Resolution Survey
Coadder (FRESCO)\", IPAC User\'s Guide, Ed.4, Part VR, California
Institute of Technology.

Melnyk, M. and Rice, W, 1991, \"High Resolution Processing\", IPAC
User\'s Guide, Ed.4, Part VI, California Institute of Technology.

Moshir, M., 1986, \"Accessing Detector Response Function Data\", IPAC,
Interoffice Memo, 240-86-103 (1).

Rice, W., 1993, "An Atlas of High Resolution IRAS Maps of Nearby
Galaxies", Astron. J. Vol 105, pp 67-96.