fit lband gain(az,za) and compare pitch, roll, focus losses
Aug. 2000 (last modified 02oct00)
The lband gain measurements (sefd,tsys,gain
jul/aug00) were fit to a function of azimuth and zenith angle.
The fit was:
g(az,za)=g0 + g1*za+g2*(za-14)^2 + g3*(za-14)^3 + g4*cos(az)
g6*cos(2az) + g7*sin(2az) + g8*cos(3az) + g9*sin(3az)
... the (za-14) terms are only used for za > 14 degrees.
The fit can be used for:
exploring why the telescope gain is lower than the theoretical value
(11-12 K/Jy) at lband.
calibrating lband telescope data.
The degradation in gain from the theoretical value can come from
misalignment of the mirrors and feed. These can be broken down into parts
that are dependent and independent of az,za.
errors caused by irregularities in the mirrors (primarily the main dish).
blockage of the structure.
The maxim measured gain of 9 K/Jy is about 20% below the expected value.
Looking at the above list:
Az,za independent: mounting of the dome on the azimuth arm, mounting of
the secondary, tertiary, and feed relative to each other (assuming gravity
changes with za are small).
Az,za dependent : motion of the dome relative to the
primary. Affected by the azimuth and elevation rail shimming, and horizontal
motion of the platform do to the platform support cables and the unbalanced
maximum pointing errors of say 15 asecs at lband is a 2% loss.
irregularities in the secondary, tertiary are measured to be small.
blockage .. this one i'm not sure of.. my guess is the 11-12 K/Jy includes
That leaves us with the primary surface irregularities and the motion of
the feed relative to the paraxial surface. The feed motion was measured
using a theodolite and tilt sensors. The primary surface is in the process
of being measured using photogrametry.
The symmetries of the platform includes a 3az term do to the 3 towers.
The primary surface and its support system has no obvious 3az term.
To check the validity of the gain measurements, pitch/roll/focus measurements,
and the gain loss computation from the aoant program I compared the 3az
term from the fit to the 3az term from the measured gain. These should
have the same phase and amplitude (unless we've screwed up or left something
computing the pitch,roll, focus losses:
A fit in (az,za) was made to the pitch, roll, focus measurements.
The pitch and roll errors were computed for the source tracks and added
in quadtrature. This value was used in the aoant program to compute the
pr loss. The focus loss along the source tracks was computed using a 24"
full width half maximum gaussian. This was scaled from an sband focus curve
(12.5*2)/1.74 * 21/12.6 = 24 inches fwhm focus
12.5*2 fwhm sband in tiedown inches,
1.74 tiedown inches/platform inch
21/12.6 = the ratio of the wavelengths (cos
of za was ignored).
The focus loss was then multiplied by the pr loss. This gave
a fractional loss from prf. To scale this to K/Jy, the prf fractional loss
was multiplied by an idealized curve that included spill over gain:
gainIdeal=8.5 K/Jy (0 to 15 deg za), then linear
ramp 8.5 -> 8.5*.8 (15 to 20 deg za)
This computed gain was then fit using the same formula as the measured
data above. The 1az, 2az, and 3az components were plotted. You would expect
the 3az loss to come from only the pitch,roll, focus losses (if we did
the pitch, roll, focus measurement and computation correctly).
gainPRF=fractionalGainPRF * gainIdeal:
The fit results:
Fig 1 shows the average gain (polA+polB)/2 plotted by source for the 4
frequencies :1405,1460,1290, and 1370 Mhz. To compute the gain, the source
flux and the cal values are needed (as well as the measurement).
The first 14 and last 2 sources have large gain variations with frequency.
These source used the lband narrow receiver where there is only a single
cal measurement at 1420 Mhz. Using this same value for 1460,1290, and 1370
causes large errors. The 5 sources towards the end with little gain dispersion
by frequency were taken with the lband wide receiver where the cal values
have been measured at these frequencies.
Fig 2 plots the average gain versus za. The + are for the azimuth (feed)
on the north part of the dish and * is the azimuth (feed) in the south
part of the dish. The gain in the north part of the dish is better than
Fig 3 is the average gain by sample for the 1405 Mhz data vs za. The fit
to the gain(az,za) is over plotted as a solid line. The rms residuals
are .25 K/Jy.
Fig 4 is the measured gain minus the fit vs za. The symbols +/* mark
the feed in the north/south portion of the dish.
Fig 5 has the data-fit to az,za versus azimuth in black. The data - fit
to only za is over plotted in red. The rms of the fit degrades from .25
K/Jy to .44 K/Jy when the azimuth dependence is left out. You can also
see a gain difference in the northern (az=360) and southern (az=180) portions
of the dish.
Fig 6 shows the fractional gain do to pitch, roll, focus errors vs za.
These values were measured with the theodolite/tilt sensors and then computed
using the aoant program. The loss approaches 9% at high za.
Fig 7 shows the 1az, 2az, 3az terms for the fit to the data (solid line)
and the 1az,2az,3az terms for the pitch,roll,focus gain (dashed line).
The values for the complete data fit is at the top of the page and the
fit to the pitch,roll,focus is at the bottom.
North/south gain difference , 1az term:
The north part of the dish has a higher gain than the south. Looking at
plot the south west side is worse than the southeast (sband showed
the southeast fill area to be the worst). The 1az term measures this north,
south difference (fig 6.) An amplitude of .4 K/Jy is .4/9K/Jy =.04 degradation.
The prf gain does not show much 1az term. prf 1az terms come from
a residual platform tilt (the tiedown cables are not the correct length).
A 4% degradation would require a .18 degree residual tilt. Using the tilt
sensors to measure the 1az term we are pretty sure that this is not the
case. So the 1 az term is probably coming from north/south differences
in the dish surface irregularities or horizontal translations of the platform
relative to the dish. If you assumed it was just a focus error of 2*4%
(peak to peak), then at lband you would need to go 4 inches out of focus.
The prfgain has very little 2az gain. The measured 2az term could be interacting
with the za dependence. For sources that come near 18 deg dec, they will
have strong za dependence spaced by about 180 degrees. If the za part of
the fit does not completely remove this dependence, then you could end
up getting a 2az term.
The 3az term in the data is .3 K/Jy or a .3/9 = 3.3% loss at lband. The
phase of the measured 3az term aligns with the prf (pitch/roll/focus) phase
which shows that we've got the phase of the prf 3az term correct.
The 3az prf amplitude of .14 K/Jy is .14/.33 = 40% of the measured
value. Assuming the measured 3az gain term is correct, we have
underestimated the prf 3az term. The measurement of the 3az prf term
is pretty straight forward since it comes from the 3az term of the theodolite/tilt
sensor measurements. The 3az prf error sits on top of any constant
prf error. Since the error is nonlinear in prf, any errors in the estimation
of the constant term could explain the difference in the amplitude.
The fit is for 1405 Mhz average gain (polA+polB)/2 , gain polA, and gain
PolB in K/Jy. The za is in degrees and the (za-14) terms are only used
for za > 14 degrees.
gainavg(az,za) = 8.78131
-.11062 *za + ( .00183)*(za-14)^2 +(-.00310)(za-14)^3
+ .37864*cos(1az) + ( .16833)*sin(1az)
-.10007*cos(2az) + ( .02403)*sin(2az)
-.26800 *cos(3az)- (.14245)*sin(3az)
The fits to gainPola and gainPolB in K/Jy were:
gainpolA(az,za)= 8.92204 -(0.11083)*za +( 0.00214)*(za-14)^2 +(-0.00342)(za-14)^3
+ .41611*cos(1az) + ( 0.18207)*sin(1az)
-0.10120*cos(2az) + ( 0.02740)*sin(2az)
-0.30386*cos(3az) + (-0.14610)*sin(3az)
gainpolb(az,za)= 8.64057 -(0.11041)*za +( 0.00152)*(za-14)^2 +(-0.00278)(za-14)^3
+0.34117*cos(1az) + ( 0.15459)*sin(1az)
-0.09894*cos(2az) + ( 0.02066)*sin(2az)
-0.23214*cos(3az) + (-0.13879)*sin(3az)
How good is the fit for calibrating data:
Errors in the gain measurement come from the measurement technique, the
source fluxes, and the cal values used. The rms of the fit was .25 K/Jy
(.25/9= 3%). This probably includes the errors in the source fluxes. The
data was taken with the lband narrow and lband wide receivers which have
different cals. Two sources were measured using both systems. The
ratio of the gains were gainlbw/gainlbn = 1.05. Assuming the gains are
the same (even though the horn illumination is a bit different) then the
cals differed by 5%. This is a systematic error. The lbw gain values were
scaled to the lbn scale (decreased by 5% since there were many more lbn
measurement than lbw). On the other hand, the lbw cal is 5 times larger
than the lbn cal (10,1.9) so it is probably a better cal to use.
Converting the cals to Janskies:
A large uncertainty in the above measurement is the value of the cal in
Kelvins. If the cals are stable over long periods of time, then we can
use the size of the cal itself as the temperature unit and bypass the uncertainty
in the kelvins/cal. The conversion is: (K/Cal)/(gainK/Jy) =
Jy/Cal. So take the measured calVal and divide it by the gain in K/Jy to
get Jy per cal. Most of this data was taken with the lbn cal but
a fraction of it was taken with the lbw cal and then scaled to the gains
we got with lbn cal. You should probably only use these equations with
the lbn cal.
Frequencies other than 1400 Mhz:
The large variation in gains for the 1290,1370, and 1460 Mhz makes it doubtful
that the lbn cal is a constant over this frequency range so the gain in
K/Jy is incorrect. It is still valid to compute the cal in Jy using the
gain(az,za) equations for each of these frequencies and the 1420Mhz cal
value (since that is what was used to compute the K/Jy gains). These gains
(1290,1370,1460) will be provided separately.
processing: x101/callb/Aug00/fig_fitazza.pro ..