|
|
| Home | Problem Reports | Operations Schedule | Weather | Data Archive |
|
|
Grant M. Hill April 11, 2000 Introduction Procedure Results and Discussion Conclusions Introduction When coarse mirror alignment is performed at CCAS using the burst/anti-burst code, the burst and anti-burst images provide detailed knowledge of individual mirror profiles as seen in the laser light from CCAS. Historically we have not used this information other than to measure EE(50) and EE(80) of a few of them to crudely log single mirror image quality. The reader is reminded that although EE(50) and EE(80) are valuable indicators of image quality, they provide limited information about actual profile shapes. The opportunity exists to use the detailed profiles of all the mirrors to numerically reconstruct the stacks. Such an exercise has the potential to yield much valuable information and be of utility when studying the on-sky performance of the primary mirror. Some of the questions to be studied include:
Procedure For a given stack obtained at CCAS, the stack is fit by a Moffat function, yielding the Moffat FWHM and Moffat beta parameters. The reader is referred to the accompanying document on Moffat functions for a description of such fitting. The burst and anti-burst images that were used in creating the given stack are then measured to create a library of single mirror profiles. A given library consists of 91 pairs of MFWHM and beta values. Not all mirrors can be measured because there is some de-focus as a result of camera viewing angle. Enough in-focus mirrors can be measured in each of the four images to provide a statistical sample though and these are multiplied if necessary to provide 91 mirrors. I have written some code which generates a set of 91 random numbers on the interval 0 to 360. All values on this interval are equally likely. A number from this set is assigned to each mirror. Each mirror now has three numbers, MFWHM, beta and an angular direction in which it is displaced from center of the stack. The underlying assumption is that stacking errors have no preferential direction. The roundness of the stacks would seem to support this. A second piece of code I have written generates 91 random numbers but this time with a mean of zero and a Gaussian distribution. Each mirror now has four numbers with the addition of the magnitude of its displacement along the direction assigned above. It is equally likely that this magnitude is negative as positive. The underlying assumption here is that the stacking errors are random and can be approximated by a normal distribution. An artificial stack can now be created by combining the 91 single mirror profiles at the 91 random locations generated above. The sum of these profiles yields the stack. This artificial stack produced by combining individual mirror profiles can be compared to the fit to the real stack. The routines which generate the locations of the mirrors and creates the artificial stack are embedded in a downhill symplex routine that minimizes the chi-squared difference between the artificial stack and the fit to the real stack. The two free parameters are the sigma of the Gaussian distribution and a multiplicative normalizing factor to account for the varying intensity of the real stack. A single running of this code thus provides a measurement of the stacking errors needed to reproduce the given stack from the library of individual mirror profiles. Since the directions and magnitudes of the individual mirror errors are generated randomly, one needs to run the code a number of times to get more statistically significant results.
I have chosen 17 stacks with varying EE(50) obtained during 2000 February and March and generated artificial stacks as described above. I have done this a half dozen times for each stack to get some indication of uncertainties. Figure 1 shows the resulting stacking errors as a function of measured EE(50). Results and Discussion We can now examine some of the questions posed in the introduction. Not unexpectedly, there is a correlation between the size of the stacking errors (found via modeling) with the measured EE(50) of the actual stack. The straight line fit in Figure 1, has a correlation coefficient of 0.89 which for the data shown, implies that the chance of no correlation is less than 0.05 percent. For the range of EE(50) values typical of present stacking, the stacking errors are on the order of a third to half an arcsecond in sky coordinates. In other words, if CCAS were to work, it should generate tips and tilts which when summed in quadrature would be of order this large in sky coordinates. We have not extensively studied the size of measurement error in the burst/anti-burst process, but on the two occasions we have measured it, it has been of the order of 0.2 arcseconds. If this number is accurate, it would appear that measurement error is a significant source of stacking error. The implication is that the potential exists for improvement in stacking by reducing measurement error. How much improvement? To get some idea, let us say that we can reduce measurement error by a factor of two. This is the sort of improvement one might expect by using four burst images and four anti-burst images instead of the current one each. I have assumed that for each of the stacks modeled, measurement error contributes 0.2 arcseconds to the stacking error found via modeling. Additionally, I have assumed that the measurement error combines in a root-sum-square sense with other errors (of indeterminate origin) to yield the total error found through modeling. This allows a new total error to be calculated assuming a measurement error of 0.1 arcseconds. Each of the model stacks was then regenerated with the new total errors. Figure 2 shows the expected reduction in EE(50) that results. The average reduction is 0.10 ± 0.01 arcseconds. Another question one might ask is, what are the best stacks we can possibly obtain given the current dome seeing? In other words what is the theoretical limit for EE(50) in the case of zero stacking errors? I have regenerated each of the stacks using the 17 libraries of single mirror profiles stacked perfectly atop each other, i.e. zero dispersion. Figure 2 shows the results. Notice that the resulting values of EE(50) can be roughly described as having a constant value of 0.65 arcseconds for those stacks which actually had a measured value less than 1.2. After that one presumably sees the effects of dome seeing as the values rise. Two exceptions are the points corresponding to actual measured EE(50) of 1.08 and 1.21 arcseconds. When the single mirror profiles from those two stacks are stacked perfectly atop one another they still give quite high values of EE(50). In other words, for those two stacks, the dome seeing was bad but the stacking was good. Notice in Figure 1, that for those same two stacks, the modeling indicated low stacking errors. Now in reality, we will never achieve absolutely perfect stacking. There will always be some error. For the sake of argument, let us say that stacking errors on the order of 0.1 arcsecond are achievable. For the seven stacks with the best dome seeing, (indicated by the open circles in Figure 2,) I have regenerated the stacks from the libraries of single mirror profiles using a dispersion of 0.1 arcseconds. The resulting stacks have an average EE(50) of 0.72 ± 0.01 arcseconds. Conclusions A number of conclusions can be drawn from this study:
The numerical modeling discussed here is necessary to study the
on-sky performance of the HET using the so-called hex burst test.
With images of the stack and individual mirrors obtained on-sky
we need to know how to combine the single mirror profiles for
comparison to the stack image. Modeling the stack as seen
at CCAS using the single mirror profiles (as seen at CCAS) should
yield the parameters needed to correctly combine the on-sky single mirror
profiles for comparison to the on-sky stack. In turn, this should
allow evaluation of the performance of the spherical aberration corrector
optics, tracker, PFIP, primary mirror combination.
If the combination of individual
mirror profiles yields something very similar to the stack, the implication
is that dome seeing is our biggest problem. If not, then the
entire optical path needs to be examined.
Top of Page Return to Technical Reports List |
Created: see
report date above Send comments to: webmaster@het.as.utexas.edu |
