Results of the August 1994 Pointing
Measurements on the 140ft Telescope After the Recabling of the Feed Legs
Ronald J. Maddalena
September 9, 1994
In this memo I discuss the results of both the prime focus and Cassegrain
pointing measurements I made in August on the 140ft telescope. The observations
were taken after the recabling of the telescope's feed legs in an attempt to see
if the recabling has changed any of the coefficients in the pointing model.
Before reading this memo, you should read the pointing memo I wrote in
August, 1992 describing the revised pointing model I came up with and have been
using for the 140ft. If you don't have the memo I can provide you with a copy.
Note that I am using the definition of coefficients of the memo.
I had one prime focus run at 5 GHz (beam width = 6'), a Cassegrain run at
18.5 GHz ( beam width = 1.6') which was cut short because of weather, and a
Cassegrain run at 8.1 GHz ( beam width = 3.6'). The 18.5 and 8.1 GHz runs used
different Cassegrain feed locations (22.5 and 202.5 degrees, respectively) with
the lateral focus and deformer mechanisms working.
The derived coefficients for the three runs and the current values of the
coefficients in the H316 are:
Prime focus (6 cm): 
Derived coefficients: 
Old coefficients: 

D1 =  2.32 ± 0.12  2.40 ± 0.05 
D2=  0.60 ± 0.07  0.47 ± 0.04 
D3=  2.26 ± 0.15  2.31 ± 0.06 
D4=  1.01 ± 0.11  0.94 ± 0.08 
D13=  2.08 ± 0.38  1.30 ± 0.14 
D14=  1.12 ± 0.25  1.15 ± 0.10 
D15=  2.54 ± 0.39  0.81 ± 0.15 
D16=  0.13 ± 0.12  0.22 ± 0.08 
D20=  0.35 ± 0.22  0.33 ± 0.08 
D21=  0.55 ± 0.24  0.58 ± 0.11 
Number of points = 438 rms = 6.4" (H.A.) 9.3" (Dec)
Cassegrain focus (1.6 cm  Position: 22.5  lateral focus on): 
Derived coefficients: 
Old coefficients: 

D1 =  2.57 ± 0.34  2.40 ± 0.05 
D2=  1.46 ± 0.16  0.47 ± 0.04 
D3=  1.97 ± 0.39  2.31 ± 0.06 
D4=  6.68 ± 0.15  6.79 ± 0.05 
D13=  2.43 ± 0.57  1.30 ± 0.14 
D14=  0.38 ± 0.66  1.15 ± 0.10 
D15=  2.30 ± 0.63  0.81 ± 0.15 
D16=  11.90 ± 0.23  11.95 ± 0.06 
D20=  0.28 ± 0.43  0.33 ± 0.08 
D21=  0.32 ± 0.71  0.58 ± 0.11 
Number of points = 138 rms = 6.6" (H.A.) 10.9" (Dec)
Cassegrain focus (3.6 cm  Position 202.5  lateral focus on): 
Derived coefficients: 
Old coefficients: 

D1 =  2.05 ± 0.11  2.40 ± 0.05 
D2=  1.08 ± 0.06  0.47 ± 0.04 
D3=  2.57 ± 0.13  2.31 ± 0.06 
D4=  7.17 ± 0.08  6.79 ± 0.05 
D13=  0.29 ± 0.25  1.30 ± 0.14 
D14=  1.35 ± 0.21  1.15 ± 0.10 
D15=  1.91 ± 0.26  0.81 ± 0.15 
D16=  12.42 ± 0.09  11.95 ± 0.06 
D20=  0.34 ± 0.14  0.33 ± 0.08 
D21=  0.26 ± 0.21  0.58 ± 0.11 
Number of points = 703 rms = 11.9" (H.A.) 10.7"
(Dec)
As I note in my 1992 memo, I've assumed D5, the refraction coefficient, has a
value of 1.02, as has been proven over and over again throughout the years. The
units of the coefficients are arcminutes (as are their 1 sigma errors) and the 1
sigma rms values of the residuals of the fit are in arcseconds.
I will now discuss the values I have found for the coefficients. Note that
the following discussion illustrates why I strongly suggested in GBT memo 112
(as did von Hoerner in GBT memo 110) that one must understand why the terms
exist in the pointing model and why it is important to choose wisely where one
makes pointing measurements. A nonphysical model would have made the following
analysis difficult at best and impossible in some cases.
You could ignore any changes in D1, D13, and D15 (either between runs or
between old and derived coefficients) since these coefficients depend upon the
receiver placement. Any changes in these coefficients are monitored by the PVLS
calculation whenever a receiver is mounted.
The D1 coefficients are consistent between the old and derived coefficients. The
weighted average of the D1 values is: D1 = 2.34 ± 0.04.
The D13 and D15 terms, however, have changed drastically between what is in the
H316 and what I have derived. Most likely, the recabling has changed the
collimation of the telescope in H.A. (but not in Dec). We could leave these
values as is in the H316 and hope that the PVLS calculations will take out the
change in the D13 and D15 coefficients. Or, better yet, we can use the weighted
average of the new values: D13 = 1.02 ± 0.20 and D15 = 2.12 ± 0.20.
All three runs give values to D3, D20, and D21 that are consistent between
the runs and consistent with the old coefficients. The weighted average of old
and newly derived values are: D3 = 2.34 ± 0.05; D20 = 0.33 ± 0.07; and D21 =
0.51 ± 0.09.
The D4 and D16 coefficients should differ between Cassegrain and prime focus
(and if the lateral focus is on or off  in our case, the lateral focus was
on). The old and derived values are consistent for prime focus and give a
weighted average of: D4 = 0.97 ± 0.06 and D16 = 0.19 ± 0.07.
But I'm slightly worried about why the D4 and D16 coefficients at 3.6 cm and
1.6 cm runs differ significantly from each other and why the 3.6 cm values
differ from the old values. If the lateral focus mechanism is out of center or
misadjusted I would expect to see difference due to the different feed locations
of the two measurement sets. If I had more 1.6 cm observations I would be in a
better position to decide whether it is the feed position that has caused the
difference. If I ignore the possible cause of the discrepancies, I get for a
weighted average: D4 = 6.88 ± 0.04 and D16 = 12.09 ± 0.05
I have not been able for years to make measurements at Cassegrain focus with the lateral focus mechanism off. To infer what we should use when the lateral focus is off, I must use a single measurement set I collected many years ago and I tentatively suggest we use: D4 = 1.07 and D16 = 0.21. These values could be grossly in error.
The D14 coefficient for the prime focus and 3.6 cm runs are consistent with
each other and with the old coefficients. However, the coefficient for the 1.6
cm run is very different.
I think I can explain the differences between the determinations of the
coefficients. The correlation matrix for the 1.6 cm run indicates a strong (90%)
correlation between the D14 and D21 coefficients. The D14 and D21 coefficients
are for the terms that look like:
H.A. = D14 * sin(Dec) + D21 * sin(Dec) * cos(H.A.) .
Apparently, when one looks at the sampling on the sky, the 1.6 cm run did not
have enough points at high H.A. so the linear leastsquare fitting routine could
not come up with independent determinations of the two coefficients. That is,
the sampling on the sky was not adequate. [Note that I designed the observing
file at 1.6 cm so as to provide adequate sky coverage but the weather shut us
down early.] The other runs have lower correlation coefficients between the D14
and D21 terms because they had significantly more points at high H.A.
I have taken a weighted average of the D14 coefficients for the 3.6 and 6 cm
runs with that previously determined and suggest we use: D14 = 1.18 ± 0.08.
The D2 coefficient is for the term:
Dec = D2 * sin(H.A.)
and arises theoretically from the misalignment of the polar axis. Thus,
physically, the D2 coefficient should be identical between prime and Cassegrain
focus observations. It should be one of the best determined and most consistent
of the coefficients.
The D2 coefficient, however, remains a puzzle. The prime focus measurements
give a coefficient that is consistent with the existing H316 coefficients so
there's no problem there. But the coefficient has inconsistent values for the
Cassegrain runs.
The Cassegrain D2 coefficient is well determined (as one can see from the low
rms errors on the coefficients and the low cross correlation coefficients
between the D2 term and all others). The coefficient doesn't change in the
middle of a run since I can take subsets of the data and derive the same
coefficients. Thus, while the derived values are not in question, the
inconsistencies are in question.
As I noted in my memo from 1992, the D2 coefficient for Cassegrain
observations seems to fluctuate. D2 either has a value close to 0.45 or
sometimes something around 1.30! It's as if something changes and makes the
coefficient take on a different value for a time and then something changes
again and the coefficient returns to its 'correct' value. The change never
happens during an observational run, only between runs.
What can be 'flopping' around between runs? It can't be polar alignment since
we would see these occasional changes in prime focus pointing runs as well. What
changes between Cassegrain runs? Does the coefficient have a different value for
the two Cassegrain feed positions? These questions were asked in my 1992 memo
and they still remain unanswered.
These are the first pointing measurement I have been able to make in over a
year and a half. I used to have time during VLBI runs to make these observations
but the recent VLBI schedules are so full I can no longer make such
measurements. As I suggested in 1992, and reiterate here, we need more pointing
measurements to try to look for correlations between coefficient values and the
physical state of the telescope (receiver used, position on the Cassegrain
house, state of the lateral focus and deformer, etc.). Without such measurements
I have no hope of solving the D2 problem.
As per my 1992 memo, I suggest we prepare the operator to change the value of
the D2 coefficient whenever a change in value is suspected. The weighted average
values we should use are:
D2 (when the telescope is behaving) = 0.50 ± 0.03
D2 (when it is not) = 1.15 ± 0.03
I am currently debating whether to add an additional term to the pointing
equation. I was able to determine what the term should look like by feeding the
residuals from the fit into the 2d graphics routines of UniPops.
The term I am thinking of adding is the D19 term from the 1992 memo:
H.A. = D19 * cos(Dec) * cos(H.A.)
and it theoretically comes about from any possible eccentricity in the H.A.
encoders. If I fit the 3.6 cm data for the above coefficients and for D19 I get:
D1  D4 = Same as above since these are terms
and I have not changed them.
D13 = 0.09 ± 0.26 D14 = 1.84 ± 0.27 D15 = 2.22 ± 0.28 D16 = 12.48 ± 0.09 D19 = 0.65 ± 0.23 D20 = 0.28 ± 0.15 D21 = 0.76 ± 0.28 
Number of points = 701 rms = 10.3" (H.A.) 10.7" ()
Note that the new fit changes some of the other coefficients significantly
and that the rms of the residuals in H.A. is reduced by a significant 2".
If you read Herrero's memo from 1972 on the 140ft pointing curve, as well as
von Hoerner's memos from 19751976, there is an additional term (what I call
D18) that deals with H.A. encoder eccentricity plus two terms for the encoder
eccentricity (D5 and D6). But fitting for these three additional coefficients do
not reduce the rms of the residuals and the determined values for the added
coefficients either have a high rms error or have large cross correlation
coefficients.
If I perform the same fit for the prime focus, I get very different D19
values (0.09 ± 0.30). For the 1.6 cm Cassegrain run I get a value that is not
well determined (0.31 ± 0.74). In both cases, the rms of the residuals are not
improved. As stated in the 1992 memo, the D19 coefficient has always been
ignorable.
I need more pointing measurements in order to decide whether it would be wise
to add the new term to the pointing model and to decide what value the
coefficient should have.
The best determined values for the pointing coefficients we should now be
using in the H316 are:
D1=  2.34 ± 0.04 
D2 =  0.50 ± 0.03 
D3=  2.34 ± 0.05 
D4=  0.97 ± 0.06 
D13 =  1.02 ± 0.20 
D14 =  1.18 ± 0.08 
D15 =  2.12 ± 0.20 
D16 =  0.19 ± 0.07 
D20 =  0.33 ± 0.07 
D21 =  0.51 ± 0.09 
D1=  2.34 ± 0.04 
D2 =  0.50 ± 0.03 (when the telescope is behaving) 1.15 ± 0.03 (when it is not) 
D3=  2.34 ± 0.05 
D4=  6.88 ± 0.04 (lateral focus on) 1.07 (lateral focus off) 
D13 =  1.02 ± 0.20 
D14 =  1.18 ± 0.08 
D15 =  2.12 ± 0.20 
D16 =  12.09 ± 0.05 (lateral focus on) 0.21 (lateral focus off) 
D20 =  0.33 ± 0.07 
D21 =  0.51 ± 0.09 
Only the D13 and D15 coefficients have noticeably changed after the recabling.
The D4 and D16 coefficients for when the lateral focus mechanism is off are
extremely rough estimates. We maybe have some problems with the D4 and D16
coefficients at Cassegrain focus and we have a major lack of understanding
concerning the D2 coefficient at Cassegrain focus. More measurements and time
are needed to determine what is going on with these coefficients and whether or
not I should add a D19 term to the pointing model.