A sequence of HARP H10-centred FIVEPOINTs were obtained at CO:3-2 (345GHz) on irc+10216 and CRL618

1. EL=35 : with 33 < Elevation < 37 and the K-mirror parameters all set to zero,
2. EL=43 : with 41 < Elevation < 45 and the K-mirror parameters (x0, y0, x1, y1, x2, y2) set to ( 1.1, 1.1, 4.4, -0.5, 0.0, 0.0).
3. EL=54 : with 56 > Elevation > 52 and the K-mirror parameters all set to zero,
4. EL=49 : with 51 > Elevation > 47 and the K-mirror parameters (x0, y0, x1, y1, x2, y2) set to ( 1.1, 1.1, 4.4, -0.5, 0.0, 0.0).

  #    UT          x0 = y0 = x1 = y1 = x2 = y2 = 0

  76 15:03         daz= -2.80, del= -1.36
                   Start of kmirror pointing tests. Zero coefficients.
  78 15:14         IMG angle 100, PA 68
  79 15:18         IMG angle 50, PA 17
  80 15:23         IMG angle 0, PA -34
  81 15:27         IMG angle -50, PA -86
  82 15:32         IMG angle -100, PA -137
  83 15:36         Regular fivepoint.  setoff 0 -5
                   kmirror rotated 90 degrees since last regular pointing.
  84 15:41         Regular pointing. Rejected by mistake; error was small: 1.63, -0.16

                   x0= 1.1, y0= 1.1, x1= 4.4, y1= -0.5
  86 15:48         IMG angle 100, PA 59
  87 15:53         IMG angle 50, PA 9
  88 15:57         IMG angle 0, PA -42
  89 16:02         IMG angle -50, PA 93
  90 16:06         IMG angle -98, PA -143
  91 16:10         Regular pointing.   daz= 1.48, del= 0.13
  92 16:17         Regular pointing.   daz= 4.66, del= 0.67

                   Zero coefficients.
  93 16:22         IMG angle 100, PA 43
  94 16:26         IMG angle 50, PA -6
  95 16:31         IMG angle 0, PA -54
  97 16:36         IMG angle -50, PA -103
  98 16:41         IMG angle -100, PA -153
  99 16:45         Regular pointing daz= -0.99, del= 1.96

                   x0= 1.1, y0= 1.1, x1= 4.4, y1= -0.5
 100 16:49         IMG angle 100, PA 48
 101 16:54         IMG angle 50, PA 0
 102 16:58         IMG angle 0, PA -49
 103 17:02         IMG angle -50, PA -98
 104 17:07         IMG angle -100, PA -147
 105 17:11         Regular pointing. daz= 1.59, del= 0.38

The results of the centroid fitting are as follows:

   #      AZ       EL     PA  IMG_ROT=2K X(daz) Y(del) 

00078  86.6836 32.9783   67.94  100.93    1.87  1.11 
00079  87.0379 34.0600   16.84   50.91    0.66 -0.96 
00080  87.3696 35.0808  -34.14    0.95   -1.82 -1.27 
00081  87.7147 36.1414  -86.10  -49.94   -3.54  0.53 
00082  88.0411 37.1282 -137.03  -99.89   -2.70  2.65 

00086  89.4464 41.1636   58.89  100.06   -3.77  1.38
00087  89.8158 42.2000    8.95   51.16   -3.33  1.68 
00088  90.1873 43.2390  -42.08    1.17   -2.77  2.35 
00089  90.5578 44.2607  -93.10  -48.83   -1.62  1.50  
00090  90.9322 45.2654 -143.03  -97.75   -2.31  0.33

00093 305.9051 56.1146   43.02   99.16   -0.71  4.32 
00094 305.3985 55.2864   -5.92   49.40    2.39  3.68 
00095 304.9192 54.4479  -53.96    0.52    3.19 -0.91
00097 304.3487 53.3510 -102.91  -49.53   -0.18 -3.57 
00098 303.9720 52.5505 -152.95 -100.37   -3.27 -2.47

00100 303.2696 50.7992   47.98   98.81   -3.48  2.75  
00101 302.9585 49.9392    0.09   50.06   -4.44  1.93     
00102 302.6693 49.0787  -48.96    0.14   -3.49  2.39    
00103 302.4106 48.2371  -97.90  -49.64   -2.11  0.68  
00104 302.1808 47.4041 -146.93  -99.50   -3.82 -0.30

The data are shown below, where the black arcs in each case are those where the K-mirror coefficients were set to zero, and the red 'arcs' are those using the parameter set (x0, y0, x1, y1, x2, y2) = ( 1.1, 1.1, 4.4, -0.5, 0.0, 0.0):

The qualitative reduction in pointing residuals is clear - although some (hopefully cosmetic) issues, such as the zero-point offsets of the corrected data, need addressing - and may lead to further understanding. The 'zero-coefficent' data (EL=35 and EL54) have raw observed RMS errors of (2.0",1.4") and (2.3", 3.2") while the (corrected ?) datasets (EL=43 and EL=49) have RMS errors of (0.8",0.7") and (0.8",1.1"), respectively. The uncorrected data separately (EL=35 and EL=54) and together lend themselves to the arc-fitting technique for determining the K_mirror parameters described previously:

   Opt.       xc    yc     x0     y0     xd     yd         Az-rms-El
  EL=35     -0.8    1.3   -1.1    1.1    0.9   -1.1   |   0.2    0.1
  EL=54     -1.3    0.8   -1.1   -1.7    1.6    1.6   |   0.3    0.6
 together   -1.1    1.1  -14.4   -3.9  -10.6    7.2   |   0.4    0.7
 current      -      -     1.1    1.1    4.4   -0.5   |    -      -

Despite the jarringly large coefficent values in the joint ('together') solution, it fits the EL=35 and EL=54 data equally well. There would appear to be severe redundancy in the data if such distant parts of solution-space can provide such a 'good' fit.

20071018
I add here solutions obtained from the 15 AZ/EL HARP pointings obtained serendipitously during UT20071001 (the largest dataset of its kind in a while):

   Opt.       xc    yc     x0     y0     xd     yd    flex  |   Az-rms-El
 20071001   -4.5   -5.8    2.7   -2.5    2.9    0.3   -0.7  |   1.6   2.3
 20071001   -4.5   -6.3    1.5   -4.2    0.9   -0.4     -   |   1.5   2.3
 20071001   -3.9   -6.0     -      -     2.2    3.3     -   |   1.6   2.5

The elevations covered the range 27 to 77, and the K-mirror angle(K)/IMG_ROT(=2K) varies between -25 and +37 (-50 and +75). Raw rms's in (daz,del) were (1.7",3.6"), so the improvement in residuals is impressive. However, while the second of these solutions is rather similar to the solution of all-sky data of 20070823 it is an awful fit to the arcs of UT20071005, above.

Conclusions
There is a clear improvement between data taken uncorrected and data taken with the proffered parameter set, but it is not possible to see any consistent pattern in the solutions that would have obtained from either the individual (uncorrected) datasets or their combination. It may be that they are too similar in elevation . . .

I am also concerned that the activities between the arc-sets (the acceptance of 'regular pointings', for instance) has invalidated the combination of the 'uncorrected' datasets. 'Regular' pointings ## 83 84 91 92 99 were (accepted?) NO NO YES YES YES. This introduces offsets of (6.14", 0.80") between the EL=35 and EL=54 sets that could skew their combined result ('together' in the table above). Subtracting (and adding) these offsets from the EL=54 data before solving 'together' produces instead

   Opt.       xc    yc     x0     y0     xd     yd         Az-rms-El
  EL=35     -0.8    1.3   -1.1    1.1    0.9   -1.1   |   0.2    0.1
  EL=54     -1.3    0.8   -1.1   -1.7    1.6    1.6   |   0.3    0.6
 together   -1.1    1.1  -14.4   -3.9  -10.6    7.2   |   0.4    0.7

 offs subt  -7.4   -0.1   -0.8   -7.0   -1.2   -2.8   |   0.3    0.5
 offs added  4.8    1.5   -1.1   -0.3    2.4    2.9   |   0.3    0.6
 current      -      -     1.1    1.1    4.4   -0.5   |    -      -

And - a minor point in light of the above - the timing of these datasets was not optimal, and so the elevation range covered is smaller than desired; as mentioned above it might allow solutions from almost any part of the parameter-space being searched.