Definition of the pointing offsets (getting the sign correct)
jan,2004
It seems that every time I try
to correct for a pointing error, I have to figure out the sign of the pointing
error as reported by the various routines. The pointing error is computed
using the heiles calibration scans and by using the turret scans. Below
is a description of the errors for each.
In the examples, x,y (or azComputed, zaComputed)
will be the offsets of the pattern relative to the center of the pattern.
The center of the pattern is the "computed" position of the source using
the ra,dec transformation to az,za and any current pointing model. The
"measured" position of the peak will be the position in each strip that
is centered on the actual peak that was found by fitting a 2d gaussian
to the data. When doing the fitting, the offset that is added to the computed
values must make the measured center be at 0.
Turret scan error definition.
The turret scans fits to the functions:
z(x,y)=A*exp((xx0)**2/sigx**2)*exp((yy0)**2/sigy**2)

x, y are the az,za offset positions of the motion centered on 0 (actually
turret, za).

X0, Y0 are reported as the error.
Let's use y,y0 (za position) to determine the sign of the error.

If there is no pointing error, then y0 is 0 and the measured peak is at
y=0.

If the peak comes after the center of the pattern (say at y=1.5) then y0
will be positive (1.5) so that (yy0)=0 so we have the gaussian
peak be at (yy0)=0.
So the turret scans are reporting zaErr=(measured  computed) position.
Since the pointing model adds the model value to the computed position,
you want to added the zaErr to the model value so you point at the measured
position:
zaPos= zaComputed + modelErr= zaComputed + zaErr=zaComputed+(zaMeasuredzaComputed)=zaMeasured.
So for turret scans, Add the az,za error to the pointing model.
Note: the routines that report the turret scans errors automatically
correct for the difference in azimuth motion and turret motion. What is
reported is the actual azimuth error.
Calib scan error definition:
Atoms technical memo 20004 (Main beam and first
sidelobe parameters for arecibo's receiver systems) describes the calib
scan fitting. eq 4a,4b on page 4 define the az,za offsets that are fit
as:
azoffOfFit=azComputed + deltaAz
zaOffOfFit=zaComputed + deltaZa
deltaAz and deltaZa are the values that are reported as the az,za pointing
errors.

If there is no pointing error then deltaAz,deltaZa equals 0.

If the peak comes after the center of the pattern (say zaComputed of 1.5)
then deltaZa must be negative (1.5) to make zaOffToFit be 0 at the center
of the beam.
So the calib scans are returning zaErr=zaComputed(0)  zaMeasured(1.5).
When putting these errors back into the model you need:
zaPos=zaComputed + modelErr= zaComputed  zaErr=zaComputed(zaCompzaMeas)=zaMeas
So for the calib scans, Subtract the az,za error from the current pointing
model.
Note:
I also verified this in the g2dcurv fitting code.
home_~phil