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

[Radu Corlan]

> >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.

Well, average combined with outlier rejection works pretty well in these 
cases; so does full-frame background fitting.

> 
> 
> >>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.

I have to differ here. what i meant is that the error due to sampling 
rises much faster than errors due to shape approximations especially 
when undersampling. That being said, i'd love to be proven wrong ;-).

Radu

> 
> >>
> >>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
> 
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-- 
Radu Corlan      

   You can still escape the "Gates" of Hell!
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