[Aavso-photometry] Sources of accuracy and precision in photometric measurements

[Michael Newberry]

Hi Radu,

Thanks for your comments. They are well reasoned. I have added comments 
which expand what I said earlier in light of your remarks (at the > level).

Regards,

Michael

>> 1. Sky estimation:
[...]

> Mode does have good outlier-rejection properties. There is however one
> big issue with it: it's badly defined in the presence of noise. by
> definition, the mode is the peak of the intensity distribution (the most
> frequent value). with a limited number of samples and in the presence of
> noise, it's obvious from just looking at the distribution that the peak
> is not the value one wants. So various authors use different ways of
> estimating the mode - which does pose a problem: how do you know the
> properties of a particular method of mode-ing? in many cases you don't.
>
> My second problem with mode is that it's quite bad with a tilted
> background: for an uniform tilt, the distribution of values is uniform -
> the mode cannot be defined at all!
>

I agree with the essence of your points about the mode. This is what I meant
about the huge difference between the concept of the mode and actually
implementing its measurement in real data.  As I said, "one man's mode is
not another man's mode. It depends on whether the calculation is robust in
the presence of noise and tiled background. Mira uses a fairly robust
algorithm that is insensitive to noise. When the background is tilted, 
indeed, the mode becomes smeared by
convolution with a rectangle function. And once again, the calculation has
to be robust. If the background is tilted so much that it affects Mira's
mode results then I would suggest people not be trying to to aperture
photometry on the image in the first place.


>> 2. Partial Pixels:
[...]

> Ah, but apportioning the flux of a pixel to an aperture based on the
> fraction of the area inside the aperture is only "exact" if the pixels
> were uniformly sensitive _and_ uniformaly illuminated. In any practical
> case (particularly with smallish apertures), especially the second
> hypothesis is far from being true. So in this case we are left with
> determining whether the error introduced by using some approximation of
> true circular or elliptical apertures is significant compared to error
> introduced by sampling. My tests have shown me that there is a
> detectable improvment in using "true" apertures vs whole pixels, but do
> detectable improvment over the simplified "irregular polygon" algorithm
> of iraf phot. The author of phot also seem to be holding the same view.
> I have to say however that in these days of plentyful computing
> resources, there is not much justification in rejection an even
> marginally superior algorithm on the basis of complexity alone.
> Yes, with big fat stars

It all depends on the ratio of PSF size to pixel size. With stars are large
relative to the PSF, i.e., "poor seeing" or poor sampling, you and the
author of RPHOT are correct about using a trapezoidal approximation. But
this claim becomes progressively less valid as you reduce the ratio of PSF /
Pixel. As you say, the exact aperture solution is not perfect in that case
either, but it gives you a better result with greater magnitude consistency
than from using trapezoidal approximations as in RPHOT.

>>
>> 3. Centroiding noise:
[...]
>
> No argument on this: centroiding is very important unless one has the
> luxury of being able to use rather large apertures (and even then).
>
> Radu