Ellipticity Measurements

In February 2001, Tony Tyson and his group showed us some ellipticity maps of their Mosaic images. Ellipticity of each star is measured, as per SExtractor's definitions (see the User Manual), and plotted as vectors showing both amplitude 'e' and angle 'pa'. By definition:

e = 1 - B/A, where B and A are the semi-minor and semi-major axis lengths. So a perfectly round image has an ellipticity of 0 and e=0.1 means the major axis is 10% longer than the minor axis.

Some trends were quite unusual (see example) and obviously contained precious information about image quality. In May, we obtained our first engineering images with specific telescope parameters (like ADC on/off, M1 corrections on/off, etc...) in order to study the effects methodically. We have taken more data since then at various opportunities, sometimes with the complicity of the CTIO Mosaic engineering team. Based on Dave Wittman's (Bell Labs) original programs, Dara Norman (CTIO) has built up additionnal tools to calculate the mean ellipticity vector in the field, substract it from all the stars and do combined plots showing the data before and after substraction. There has been a substantial support from both Dave and Dara to get these tools running and they are now working very efficiently and robustly. Sincere thanks to both of them. The programs and a README file explaining how to use them can be found in /ua76/boccas/4m/ellipticity/.

These ellipticity plots have allowed us to investigate deeper mostly 2 issues: the effects of the ADC in the image quality, and a method to build astigmatism lookup tables for M1. Most images are 10sec unguided R filter exposures (unless written otherwise).


ADC effects:

The Atmospheric Dispersion Corrector (ADC) is part of the Prime Focus Corrector (PFC). It consists of 2 rotating pairs of cemented prisms as descibed in this paper. These are fairly large piece of refractive optics (40cm in diameter) that can introduce wavefront distorsion if their surfacing has residual aberrations and/or if their mounting introduce stress into the glass. We conducted tests near the zenith (so that any gravity effect is azimuthally uniform and no dispersion has to be compensated) by rotating the prisms and observing the ellipticity patterns.
* One prism rotating, one fixed:

* Both prisms rotating together maintaining the neutral 180deg angle difference:


Astigmatism lookup tables:

Since the active optics were implemented on the Blanco 4m telescope, we have been building the PF lookup tables with the Hartmann screen method. We have used a few times curvature sensing with EF too. Both techniques are applied on one on-axis star only, mostly because of the time needed for the data reduction with our existing software tools. The ellipticity maps have revealed in some cases that measuring one star in the center of the field is not appropriate to determine the best overall correction for the entire field. The ellipticity approach, because it does a statistical analysis of all the stars in the field in a fairly short time, yields the precise information of the optimum correction to apply to compensate astigmatism. Other aberrations at PF can not be measured (nor corrected) by this technique but astigmatism is the dominant static telescope aberration that needs to be corrected, thus the ellipticity measurements are best suited for that task.

A Mean Ellipticity Vector MEV (for the entire field) above 0.04 indicates that there is some astigmatism worth correcting. The existence of a MEV > 0.04 means:


  • To the observer: the focus chosen is wrong, because remember that there is no ellipticity in the best focus (astigmatism 'waist')! See this mscfocus output plot for example: there was a 3.5um tweak and both best fwhm and lowest ellipticity happen at the same focus.

Example: through-focus sequence of 6 images taken with steps of 75um and a forced astigmatism (M1 tweak) of 1um at 0deg (10sec, R, ADC off, corr off, zenith). One can clearly see the 90deg rotation (from horizontal to vertical in this case) of the astigmatism/ellipticity pattern when going through focus. From the ellipmap program we get:

Image Focus e pa fwhm
obj019 15875 0.07 7 2.71
obj018 15800 0.04 2 2.21
obj017 15725 0.02 106 2.18
obj016 15650 0.10 84 1.91
obj020 15575 0.08 91 2.71
obj021 15500 0.15 87 2.52


The image with least astigmatism is the 3rd one (obj017) but it is the 4th image (obj016) that has the best fwhm. Based on the pattern of the plots, it seems like there would be an intermediate focus (about 15760) between the 2nd and 3rd images where the ellipticity would be lower in average (i.e. rounder images). Thus in this case we would conclude that the best fwhm focus (15650) is different from the 'roundest' focus (15760). Furthermore, an 'mscfocus' analysis of the focus sequence corresponding to these 6 images yields a best focus of 15704 at 1.83".

  • To the CTIO staff: as long as the frame was taken at the best focus, there is astigmatism in that particular direction of the sky and the lookup table doesn't correct it, so it needs some improvement!


 M.B., 30 Sept 01