A proposed correction for the elevation pointing

The table below shows the recent data : the columns show

1. the dataset - by date
2. the FE
3. the number of data (N>10 for inclusion)
4. the raw rms scatters in daz
5. the raw rms scatters in del
6. the slope of the best fit line in the del - vs- (Tf-Tb) plane
7. the rms scatter of del about this line
8. the slope of the best fit line in the del - vs- 0.5*(Tf+Tb) plane
9. the rms scatter of del about this line

      1       2  3     4   5        6         7         8          9

  dataset    FE  N    raw rms    del-vs-  new_rms     del-vs-   new_rms
                      daz del    (Tf-Tb)            0.5*(Tf+Tb)

  970416-17   B 13    0.7 1.3   2.5 +- 3.1   1.2    0.7 +- 0.2    0.8
  970420      S 15    1.3 2.3   4.7 +- 1.0   1.4    1.1 +- 0.2    1.1  
  970422_23   A 16    1.3 1.9       --        -         --         -    
  970424_01   A 12    0.5 1.6  -6.0 +- 2.5   1.3    1.2 +- 0.5    1.3
  970425      S 11    0.5 1.7 -13.0 +- 2.7   1.0    2.4 +- 0.4    0.7
  970425-26   S 17    1.2 2.2  -4.1 +- 1.9   1.9    1.0 +- 0.2    1.2
  970426_17   S 16    1.6 2.3   4.6 +- 2.1   2.0    1.4 +- 0.2    1.0

[ The data of 970422_23 do not cover a sufficiently large span of antenna temperature to make any sense of this fitting procedure. ]

Given the increased confidence in the recent models (see below), the raw rms scatters in del are disappointing when compared with those in daz. This suggests some systematic error unconnected with the track model or pointing model. A poor atmosphere might make the refraction corrections erroneous, but such is not particularly indicated, and poor seeing might be equally deleterious to daz. For those data covering the periods when thermal changes are sufficently large (this eliminates 970422_23), the systematic trends of del-vs-time suggest that the effect is thermal, and the first order response is to correct temp_slope, relating del to (Tf-Tb). The relationships between del and (Tf-Tb) for each dataset are given in column 6 and the resulting scatters in column 7, but they show that any suggested change to temp_slope is not well defined. However, the relationships of del to 0.5*(Tf+Tb) (the average leg temperature) are relatively self similar (see column 8) and give superior residual scatters (column 9) :

                The weighted mean of the these slopes is           1.1 +- 0.2,

and is in the sense that del is currently +ve when (Tf+Tb) is +ve, so del needs to be made more negative when (Tf+Tb) is +ve in order to correct for this effect. (It's so easy to get these signs confused).

Similarly, and graphically, a slope of 1.0 +- 0.1 results from analysis of the concatenated SCUBA data. The raw data show a very strong trend of del with time, but the plot of del-vs-(Tf-Tb) does not indicate a problem with the current value of temp_slope at the 3-sigma significance level, and any correction based on this weak trend would not significantly improve the scatter. However, the relationship between del and 0.5*(Tf+Tb) is significant at the 8-sigma level, with a coefficient of 1.0 ("/deg).

[ NB : the multiplying factor for (Tf+Tb) alone is then 0.5 ],

The resulting scatter about the line (2.1" rms) is worse than in the individual datasets because of the concatenation and the loss of information about drifts in the collimation.

The range of (Tf+Tb) covered in each dataset varies from about 2 degrees to about 6 degrees, but there is no correlation between the individually derived values of temp_mean_slope (?) and the temperature range covered.

Conclusion
I suggest that a correction to del of this form and size (1.0"/degree) be incorporated into the TEL task.

Confidence
This analysis is possible only because of high levels of confidence in the inclinometry system, which generates the track model, and in pointing with SCUBA, which generates the 7-parameter telescope model. The improvement in the pointing of JCMT was always going to be a bootstrap process, with each improvement relying on the elimination of some previous limiting uncertainty. I think we have been generating decent track models for some time - even if there is still some residual, minor uncertainty in the calculation of YAW. Now, SCUBA has the sensitivity with which we can rapidly acquire high S/N images of sources of unambiguous position. ALL these factors are necessary for the production of a good pointing model, and it is a relief to have more of the pieces in place.

The Future
Future updates to either temp_slope (? shall we now call it temp_diff_slope ?) or to temp_mean_slope will require plotting del residuals in this way against both (Tf-Tb) and 0.5*(Tf+Tb), in order to establish which coefficient, if any, needs correction.

The use of the antenna LEG temperatures in the role of ANTENNA temperatures has always been a cause for concern inasmuch as there is the possibility of a time lag between one and the other. However, even during extreme thermal changes, as experienced during pointing on 25 April, when, between 18:00 and 20:00 the mean leg temperature dropped from 8 degrees C to 4 degrees C, and (Tf-Tb) fell from +0.4 to -0.5 , the elevation residuals did not show any behaviour that might be attributable to lag.

However, temperature data from the dish (backing structure ?) is occasionally taken by Fred Baas for use in the surface upgrades program, and analysis of these data and contemperaneous leg temperatures will be made to provide insight into any possible thermal lag. Should any significant lag exist, a further upgrade to these pointing algorithms could be necessary. However, this would require that we

• either have to estimate the future temperature of the antenna based on the current temperatures of the legs,
• or that we read the antenna (dish ?, backing structure ?) temperatures and use those as our real-time working temperature.

Return to POINTING REPORTS

Iain Coulson
28 April 1997