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The unprojection-reprojection approach to add the pixel offsets is more
accurate than simple offset addition to projected position, in particular
far away from the equator of the coordinate system. If we look at the radio
projection (its standard FITS name is Global Sinusoidal, abbreviated into
GLS) of the full sky shown in Fig.
, we can see that one can
expect strong distortions near the pole. Note that the distortions depend
on the declination of the object and NOT on the declination of the
projection center3.4. In other words, the
plane of projection is not tangent to the projection center, but to the
equator instead. This is directly linked to the mathematical formula of the
radio projection
where (
) is the projection center, (
) the object
absolute coordinates, and (
) its offsets in the projected
map. The key point in this projection is that
is a function of
and not
. Hence, the deformation for wide fields of view will depend
both on the distance to the projection center and the source declination!
That's why the radio projection is deprecated and IAU recommends to replace
it by the Sanson-Flamsteed projection (abbreviated in SFL).
Figure:
Radio projection of the full sky (right ascension from -12
to 12 hours, declination from -90 to 90 degrees), for four
projection centers (marked with a blue cross) at 0 right ascension
and 0, 30, 60, 90 degrees declination. The parallels (resp. the
meridians) are spaced by 30 degrees (resp. 2 hours).
|
The distortions near the pole may thus have a non-negligible impact on
observations. Figures
to
show the
effect in different conditions. The geometry of the multi-beam array shows
no visible distortions, even one degree away from the source position, when
the source position is located on the equator. However, the distorsions of
the array geometry increase with the distance to the projection center when
the source is located at high declination. Moreover, for the same source
coodinates, the deformation at high source declination depends on the right
ascension of the projection center (cf. Fig.
), but they are independent of the
projection center declination (cf. Fig.
)!
Figure:
Effects of the radio projection on observations with HERA
for source centers at 4h, 12h, 20h Right Ascension and 0, 44, 88
degrees declination (blue crosses). In this case, the
projection center is aligned on the source center. The green
polygon shows the shape of a
square degree field in
sky spherical coordinates. In addition, the red parallelograms
show the resulting shape of a
square multi-beam
array as a function of the distance from the source center.
Finally, the parallels (resp. meridians), shown as black dashed
lines, are separated by 0.5 degree (resp. 1 degree).
|
Figure:
Same as Fig.
, except that the projection
center is located 15 degrees south the source center. The
deformations are independent of the declination of the projection
center!
|
Figure:
Same as Fig.
, except that the projection
center is located 1 hour angle west from the source center. The
deformations depend on the right ascension of the projection center.
|
Next: In practice: Effect on
Up: Offsets of multi-pixel receiver
Previous: Computing the pixel coordinates
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Gildas manager
2023-06-01