IRAS Explanatory Supplement
X. The Formats of the IRAS Catalogs and Atlases
D. Extended Emission
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- Introductory Comments
- Map Projections and Transformation Equations
- 16.5° Images
- Galactic Plane Maps
- Low-Resolution All-Sky Maps
- Zodiacal Observation History file
- Coordinate Overlays
D.1. Introductory Comments
The extended emission data are presented as maps of the infrared sky at two different scales in all four wavelength bands. The entire sky surveyed is mapped with 2' pixels at an effective resolution of 4'-6' in 212 16.5° × 16.5° fields and also with an effective resolution of l° in a single field. A special map of the region within ± 10° of the Galactic plane was also made at 4'-6' resolution. All of these maps are available in both digital and photographic formats. In addition, data from the survey averaged in a ½° × ½° beam is available in time ordered form. The details of the presentation of each of these products are described below. The methods used to produce the products were described in Section V.G. All the map projections used are described below.
The survey covered most parts of the sky several times and the extended emission data have been separated for the reasons outlined in Section V.G.1. The data released in Nov. 1984 includes the 188 fields in the 75% of the sky covered in the third sky coverage, along with the associated Galactic plane and low-resolution all-sky maps. Subsequent releases include a small part of the sky covered by the "minisurvey" done at the beginning of the mission (Section III.C.11) and the first and second coverages, each of about 95% of the sky.
Three separate map projections were used. The descriptions
below provide enough information for the user of the IRAS data.
More information can be found in
Richardus and Adler (1972).
The gnonomic projection used for 16.5° images produces
a geometric projection of the celestial sphere onto a tangent
plane from a center of projection at the center of the sphere.
Each individual field has its own tangent projection plane with
the tangent point at the center of the field. This projection
is neither conformal (angle preserving) nor equivalent (equal
area) but does have the property that all straight lines in the
projection are great circles on the sphere. All projections were
done so that the sky coordinate associated with a pixel refers
to the position at the center of the pixel. For the 16.5°
fields the maximum distortion of angles is 0.6° and the
maximum distortion of area is 6%. The area distortion is approximately
proportional to the inverse cube of the cosine of the angular
displacement from the center of the field. The distortion is in
the sense to make extended areas cover more sq. arcminute pixels
than their true solid angles would require. This results in overestimating
fluxes when integrating sources within fixed intensity
contours.
The transformation equations for conversion between line
and sample number in the map and right ascension and declination
on the sky are shown below.
Forward:
(X.D.1)
(X.D.2)
Reverse:
(X.D.3)
where (X) and (X) are the declination and right ascension of the
field center. The arctangent functions for (X) and (X) must be
four quadrant arctangents.
The Lambert normal equivalent cylindrical project was used
to provide an equal area projection of the sky within 10°
of the Galactic plane. The projection cylinder is tangent to the
celestial sphere at the Galactic equator and the projection proceeds
by projecting radially outward from each point on the polar axis
of the Galactic coordinate system in a plane parallel to the equatorial
plane. The maximum angular distortion (deviation of bearing)
is 0.9°. The equal area property of the transformation
preserves photometric accuracy when integrating fluxes for an
extended source.
The transformation equations are:
Forward:
(X.D.4)
Reverse:
(X.D.5)
where (X) and (X) are Galactic latitude and longitude and subscript
zero denotes the field center.
The Aitoff equal area projection was used to provide a photometrically
correct map of the entire celestial sphere. Galactic coordinates
were chosen as a convenient and natural coordinate system. The
transformation equations are:
Forward:
(X.D.6) (X.D.7)
Reverse:
(X.D.8)
where (X) and (X) are Galactic longitude and latitude and subscript
zero denotes the field center.
The 16.5° images the high-resolution presentation
of the IRAS sky survey in image form. Two hundred twelve (212)
16.5° × 16.5° fields cover the whole sky with field
centers spaced by approximately 15°. The three sky coverages
of the full mission are presented as three separate sets of 212
maps, with
some maps not included in the third coverage (Table X.D.1). A
list of plate numbers vs. plate centers comprises
Appendix X.2
and a map of plate locations is given in
Fig. X.D.1. An individual
map consists of 499 × 499 array 2' × 2' pixels into which the IRAS
survey data were mapped using a gnomonic projection (described
in Section X.D.2.a).
The 16.5° images are available as
photographic prints and as digital magnetic tape. The formats
of these two forms are described below. Detailed descriptions
of the procedures used to produce the maps are given in
Section V.G.
The compression, clipping and scaling were accomplished
by first extracting the fifth root of the surface brightness to
compress the dynamic range of the data. A histogram of the the
root map was made and the pixel values were shifted and scaled
into the 0 - 255 range so as to saturate the lower and upper one
percent of the histogram. The approximate surface brightness value
of any pixel can be recovered by first comparing the density of
the pixel of interest to the grey scales which show every 17th
pixel value from zero to 255. The shift and scale are removed using the 0
DN = X Jy sr-1 and 255 DN = Y Jy sr-1 information in the label
(see the sample label below).
The complete formula is:
(X.D.9)
Final calibration factors were not applied to the third
sky coverage data before production of the photo products. Therefore,
the intensities obtained using the procedure above on the third
coverage may not agree with intensities found on the magnetic
tape versions of the maps. The magnetic tape version uses the
final IRAS catalog calibration and should be used in case of discrepancy.
Intensities obtained
from the third coverage photo products can be approximately corrected
to the final calibration by multiplying the intensity derived
from a photograph by the following factors:
The first, second and mini-survey coverage photos were corrected
to the final calibration.
The coordinate system of each map is arranged so that when
viewed with the printing in the label right side up north is up
and east is to the left at the field center, which is adopted
as pixel (0, 0). In this orientation the horizontal rows of pixels
are by convention called lines and the pixels within each line
are called samples. Line numbers increase from top to bottom
and sample numbers increase from left to right. The line numbers
of the top and bottom lines are given in the label as TOP and
BOTTOM, respectively. Similarly the left and right extreme sample
numbers are given as LEFT and RIGHT. With this information and
the tic marks along the sides of the image area the line and sample
coordinates of any pixel can be determined for application of
the inverse map projection formulae given above in
Section X.D.2.
The tic marks also allow alignment of the coordinate overlay
grids as described in Section X.D.7.
Color composite negative transparencies in 4 × 5 inch format
of each sky plate field have been produced by recording the 100
µm map in red (positive), the 60 µm map in green and the
12 µm
map in blue. These color versions of the data are not intended
for quantitative analysis. The shift and scale information in
the label is difficult to read and no attempt has been made to
produce a consistent color balance among the plates. In one plate
a particular hue will indicate one ratio to 100 µm to 60 µm to
12 µm brightness and in another plate the ratio for that hue will
be somewhat different.
Sample Label from 16.5° Image Photograph
First line:
Second line:
Third line:
Fourth line:
The magnetic tape form of the 16.5° images contains
the calibrated surface brightness data in 499x499 arrays of 2' × 2'
pixels recorded in the FITS format. The article by
Wells et al.
(1981) in conjunction with the label records of each tape file
gives a detailed description of the format of each map image.
A brief description of the format follows and a listing of a
sample FITS label can be found in Appendix X.3.
One sky coverage consists of 27 tapes of 6250 bpi (bits per
inch) density. The third coverage has only 24 tapes with a total
of 188 plates. Each plate consists of four surface brightness
maps and four statistical weight maps, one of each for each wavelength
band. The plates are ordered on the tapes by plate number and
within a plate the image files are ordered: 12 µm brightness,
12 µm weight, 25 µm brightness, 25 µm weight, 60 µm
brightness,
60 µm weight, 100 µm brightness and 100 µm weight. The
first
two records of each file contain the label, then the image appears
as a stream of pixel values divided into 2880 byte records without
regard for line length. The stream begins with the smallest line
and smallest sample number and the sample number increases fastest.
The last record is padded to 2880 bytes with zeros. Four-byte
integers are used for brightness image data numbers and 2-byte
integers for weight images, high order byte first. All this and
other information necessary to successfully regenerate a map is
contained in the FITS label records described in
Appendix X.3.
The ½° × ½° beam data contained in the Zodiacal
History file described below was split into the three separate
sky coverages and assembled into three all-sky maps with an Aitoff
equal area projection in Galactic coordinates. Two fields of
each sky coverage were produced; one centered on the Galactic
center and one centered on the Galactic anti-center. The pixel
arrays consist of 325 lines of 649 samples
each. Galactic north is in the direction of decreasing line number
(up) and Galactic east in the direction of decreasing sample number
(left). The all-sky maps are available in both photographic and
FITS tape forms. The formats of the photographic and tape forms
of all-sky maps are very similar to those of the 16.5° images
(see
Section X.D.3) with the differences described in the labels
of the photographs and tape files. Coordinate overlays described
in
Section X.D.7 are available for the all-sky maps.
For convenience in the analysis and treatment of background
emission from interplanetary dust (zodiacal emission) and other
extremely large scale emission features, the survey data were
averaged to ½° × ½° beam size and along with pointing
information was preserved as a time ordered data set containing
all three sky coverages of the survey. This file is available
on magnetic tape written with the format described in
Appendix X.4.
A set of coordinate overlays for the photographs is available
as photographic negative transparencies in the 5 inch sq. format.
The scale is identical to the corresponding map product so the
overlays will be the correct size if enlarged by the same factor
as the map. One overlay is provided for each declination zone
from -30° to +30° where the overlays for zones of
opposite sign are obtained by rotating the grids through 180°.
Five overlays are provided for each declination zone between 45°
and 75° to accommodate the fact that integer hour
meridians cross the plates in these zones in five different configurations.
Again the overlay for the zone of opposite sign is obtained by
rotating the grid 180°. All integer hour meridians are
labeled 00M. The hour of right ascension should be determined
from the position of the plate center given in the label on the
photograph. The plate numbers to which a particular overlay pertains
are printed in the lower right cornerof the overlay. The overlays
are aligned by matching the two triangular fiducials along each
edge of the overlay with the two large map border tics which straddle
the center of each side of the map. The two overlays for the
polar regions are similarly aligned with the fiducials and tics.
The correct orientation makes the lettering on the overlay read
the same way as the lettering in the plate label.
One overlay is used for all Galactic plane maps. It is aligned
with the same method as the sky plates. One orientation of the
overlay is used for even numbered fields and has 0° as
the center longitude; the other orientation, used for all fields,
has 5° as the center longitude. The tens digit of the true
longitude should be obtained from label of the picture.
The overlays for the low-resolution all-sky maps come in
only two varieties, (X) = 0.0° in the center and (X) =
180.0° in the center. Alignment of the overlays is similar
to that for the other maps.
D.2. Map Projections and Transformation Equations
D.2.a Gnomonic Projection - 16.5° Images
define:
scale
= 30 pixels/degree
A
= cos(X) × cos(X - X)
F
= scale × (180/(X))/[sin(X) × sin(X) + A × cos(X)
then
LINE
= -F × [cos(X) × sin(X) -- A × sin(X)]
SAMPLE
= -F × cos(X) × sin(X -- X)
define
X
= SAMPLE(scale × 180/(X))
Y
= LINE/(scale × 180/(X))
(X)
= arctan [(X2 + Y2) ½ ]
(X)
= arctan(-X/Y)
XX
= sin(X) × sin(X) × cos(X) + cos(X) × cos(X)
YY
= sin(X) × sin(X)
then
(X)
= arcsin [sin(X) × cos(X) - cos(X) × sin(X) × cos(X)]
(X)
= (X) + arctan(YY/XX)
D.2.b Equivalent Cylindrical Projection - Galactic Plane
Fields
define
scale
= 30 pixels/degree
then
LINE
= -scale × 180/(X) × sin(X)
SAMPLE
= -scale × (X - X)
(X)
= (X) - SAMPLE/scale
(X)
= -arcsin [LINE/(scale × 180(X)]
D.2.c. Aitoff Projection - Low-Resolution All-Sky Maps
define
scale
= 2 pixels/degree
(X)
= arccos [cos(X) × cos(X - X)/2]
0
= arcsin [cos(X) × sin({X - X}/2)/sin(X)]
then
SAMPLE
= -4 × scale × 180/(X) × sin(p/2) × sin(X)
LINE
= ± 2 × scale × 180/(X) × sin(X)/2) × cos(X)
define
Y
= -LINE/(2 × scale × 180/(X))
X
= -SAMPLE/(2 × scale × 180/(X))
A
=(4 - X2 - 4 × Y2) ½
then
(X)
= 180/(X) × arcsin(A × Y)
(X)
= (X) + 2 × 180/(X) × arcsin[A × X/(2 × cos(X))]
D.3 16.5° Images
Table X.D.1
47 95 130
60 96 131
70 97 132
71 107 143
72 108 144
83 118 154
84 119 115
94 120 168
D.3.a. Prints of 16.5° Images
Photographic black and white negative transparencies were
produced from the digital map data with a film recorder. All
four bands of each field were reproduced side by side in a rectangular
format approximately 5 inches sq. intended for enlargement to
16 inches by 20 inches. Two hundred fifty-six (256) brightness
levels were available with the film recorder and the brightness
range in each band of each field was individually compressed,
clipped and scaled to fit within these 256 levels.
12 µm 0.84
25 µm 0.80
60 µm 0.80
100 µm 0.69
IRAS SKYFLUX HCON: 3 FIELD: 153 DEC:-30 RA: 10:00 25 MICRON
R.A. & DEC GNOMONIC PIXEL: 2.00 ARCMIN JD:2445654.25-2445660.25
TOP:-249 BOTTOM: 249 LEFT:-249 RIGHT: 249 1 TIC = 5 PIXELS
0DN= 4.28E+ 2 JY/SR 255DN= 5.38E+ 2 MJY/SR 5TH ROOT DATE:84/08/10
D.3.b Tapes of 16.5° Images
D.4. Galactic Plane Maps
For convenience in dealing with the Galactic plane the survey
data within 10° of the Galactic plane were remapped from
the into a set of images in Galactic coordinates to cover the
full circle of the Galaxy. This remapping from the 16.5°
images resulted in a slight degradation in resolution even though
the pixel size was the same in both sets of maps. Twenty-four
16.7° × 20° fields cover the Galactic plane with field
centers at integral multiples of 15° Galactic longitude.
The three sky coverages of the survey were separated into three
sets of maps. The image format is 499 lines of 599 samples each,
projected from Galactic coordinates with an equal area cylindrical
projection (see
Section X.D.2.b). Galactic plane maps are available
in both photographic and FITS tape formats. Two 6250 bpi tapes
of 12 maps each hold the 24 Galactic plane maps. The differences
in the FITS label between the 16.5° images and the
Galactic plane maps are noted in the description and listing of
the FITS label in
Appendix X.3. No statistical weight images are
included for the Galactic plane maps. Statistical weight information
may be obtained from the 16.5° maps. Coordinate overlays
described in
Section X.D.7 are available for the Galactic plane
maps.
D.5. Low-Resolution All-Sky Maps
D.6. Zodiacal Observation History file
D.7. Coordinate Overlays
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