ODI, WIYN, and image quality

Daniel was right - the monsoon is on its way out.  It was clear and the seeing was good last night - around 0.5 arcsec plus or minus all night.  Among other things, I did some experiments that Pieter van Dokkum had suggested to me - to begin to understand observationally the potential gains of OT shifting with ODI.  The idea is as follows.  When you are doing OT shifting, you are taking each very short exposure of a source, shifting it according to some measure of its "center", and adding it to the accumulated image.  We are expecting to be able to do OT shifting between about 10 and 30 Hz, so 50 milliseconds is a good starting point for each individual exposure.  Pieter's suggestion was to look at an exposure of 50 milliseconds and measure the image quality.  If it is much better than a longer exposure, you know that there is a lot to be gained from OT shifting; if it isn't, then there isn't much potential gain.  One can take this one step further and use a sequence of short exposures to compare the differences between coherent and local guiding by comparing the shifts that you derive from objects over the whole field.

So, what I did was find a field near the galactic plane with lots of bright stars (to have something to measure in a 50 ms exposure).  I took a 10 second exposure, a 5 minute (guided, but not OT shifted) exposure, then 55 50 ms exposures, and then another 10 second exposure.  I haven't got all the way through the analysis, but the initial results are interesting.

The two 10-second exposures had average PSF FWHMs of 0.430 and 0.512 arcseconds, which themselves average to 0.47 arcseconds.  The 5-minute exposure has an average PSF FWHM of 0.452 arcseconds, pretty close to the 0.430 of the 10 second exposure taken immediately before it.

The 55 short exposures have the following distribution of FWHM values (I have only measured one star so far):

The average is 0.425 arcseconds, only a little better than the 0.47 that one might get from 10 second exposures over this same time period, but the spread is quite large.  So what is going on?  Two things.  First, when the PSF is spread out, its central peak is not as tall.  When you combine two PSFs, the resulting PSF will not have the average FWHM, it will be smaller than that.  Second, the PSFs that have large FWHMs tend to have multiple speckles visible and the FWHM is pushed to larger values.  In the image here, the left frame shows a typical large FWHM image, while the right frame shows a typical small FWHM image. (Note also the CTE problem evident in the faint tails going up from each image.  These will not appear in well exposed images - even those that are OT shifted.)

As a quantitative test of this, I took four frames, two with small FWHM (0.245 and 0.248) and two with large FWHM (0.675 and 0.567) values.  The average of these is 0.434, close to the average of the entire set of 55.  I then shifted these frames so that their brightest pixels were aligned.  I averaged them and measured the PSF: 0.26 arcseconds.  This is the ultimate promise of local guiding.  How much of it can be gotten from coherent guiding is still to be determined. 

Todd

UPDATE - I found a simple way to do this shift and add for the whole set of 55 frames.  The resulting PSF FWHM is 0.33 arcseconds.

UPDATE 2 - Daniel correctly points out that, in real OT shifting, you are using the image from 50 ms ago to predict the shift now.  I can't model that in my experiment, since each image took 30 seconds to read out. So, my experiment is a best case, and there may be an additional contribution to the degradation of the PSF.