Roddier Test (1)

A new software tool for the analysis of star test images has recently became available. Its name is roddier test http://www.astrosurf.com/tests/roddier/roddier.htm .
What the software does is essentially to "reverse engineer" a couple of star test digital images to find what the wavefront should be to produce them.
The principle of operation is based on pointwise evaluation of brightness differences which yields information about wavefront curvature. With some calculations (numerical solution of a Poisson equation) the wavefront is then estimated.
We can think of the roddier software as a tool which quantitatively evaluates star test images.

The traditional way of evaluating star tests is based on experiance and comparison with artificial star test images (e.g. see Suiter book, Aberrator or S. Khoeler diffract.r). Expert testers can say whether an optics is excellent, good, fair, sufficient or bad. People and experts, when evaluating the traditional way, are all aware of the uncertainties that are intrinsic in the evaluation.

The roddier software gives a new way to assess optical quality. A recent thread on an italian amateur astronomer forum made me understand that, unlike the traditional way, people are not so aware of the many possible pitfalls in using the method. Most people do not understand that the roddier method is a "measurement system". Issues like accuracy, and repeatability are paramount.
The roddier software have been demonstrated to fairly match with interferometric tests as well as it was successful into reconstruction the aberrations of artificial star tests. Thus people tend to "believe" to the "numbers" given by the method and do not understand the many possible pitfalls and improper use.
When making measurements it is in fact paramount to deeply understand the principle of operation, the parameters that may interfere o fake the measurements and to develop proper estimates and bounds for the accuracy. People tend to believe that a "meter" gives "exact" numbers. The roddier "meter" is much more complex than a tape measure. Among the many factors that may false results are: improper brightness scale of the images and incorrect estimation of their defocus. It is very important to make multiple measurements in order to estimate the repeatablity of the resultas. Moreover, the evaluation of accuracy and systematic error has to be addressed by use of complementary methods. For example if one resizes the intra-extra focal images he may introduce a systematic error in the estimation of their defocus (if he does not correct the pixel size). This error can be however easily pointed out by counting the numebr of rings or by comparison with artifical star images at the estimated defocus.
Before entering in examples (left top next posts) of the use of the roddier test it is thus very important to understand the possible pitfalls.

I here show an (exaggerated) example of improper use (the software is fine, it is the user who fails).

Let us try to ask this question: what is the correction of the Moon surface?

Well I used the roddier software (which has been tested against interferometer, so I believe in it!!) to evaluate the ptv and rms of the moon surface. I took two full moon pictures (the extrafocal is top down), and gave them to the software. Amazingling it returnes that the Moon surface has 0.0 PTV and 0.0 rms. Thus the Moon is perfect, as Cremonini said ( http://http://en.wikipedia.org/wiki/Cesare_Cremonini_(philosopher) When Galileo claimed he had discovered mountains on the Moon, Cremonini was one of the scholars who sternly refused to even check through the telescope, alleging that Aristotle had definitely proved that the Moon could only be a perfect sphere).