[Aavso-photometry] Sources of accuracy and precision inphotometric measurements

[Michael Newberry]

(Cross posted from the main discussion group)

Hi Brian,

I have embedded followup reposnses to some of the items you mention.

----- Original Message ----- 
From: "Brian D. Warner" <brian at minorplanetobserver.com>
To: "AAVSO Discussion group" <aavso-discussion at aavso.org>
Sent: Thursday, December 15, 2005 1:18 AM
Subject: [AAVSO-DIS] Software for variable star work


> Since it was the mention of my software that got this thread going and 
> both Mike
> and Richard have commented, I thought I would throw in my nickel's worth 
> to the
> discussion.
>
> Regarding background subtraction,
[ with a star contaminating the sky annulus...]
> Using Mike's standard of how the instrumental magnitude is
> affected, I measured several stars where another star that was about 0.5m
> brighter was and was not included in the sky annulus. The difference in IM 
> of the
> target was 0.001-0.003m. It was not until I included a star with an IM 
> about 1.2m
> brighter that the target IM changed by 0.012m.
>

    Of course, your bias in that case was smaller but you were probably 
using a larger annulus that the one I used in Mira. Mine contained only a 
few hundred pixels. In doing high-precision backgound estimation, a bigger 
aperture can be misleadingly "better". The larger the number of pixels 
inside the sky annulus, the better can be the rejection of contaminating 
star(s) and thus the lower the magnitude bias in your star's magnitude. This 
makes the appearance of increasing the accuracy of the magnitude. However, 
there is another type of systematic error that plagues photometry. Remember: 
you want to estimate the background underneath the object, not underneath 
somewhere else, and the background is neither "perfectly" flat nor free of a 
diffuse background and lumpy distribution of fainter things. The more pixels 
in the sky annulus, the further away it samples pixels. That tends to reduce 
accuracy of the background correction by measuring it less locally to the 
star in question. These are competing issues---which magnitude bias is 
worse...

> Canopus has used ensemble photometry - in the sense of multiple 
> comparisons -
> since it was first written by allowing up to five comparisons to be 
> averaged for
> a single reference. For now, it's a simple average, with no weighting,
[...]

    Of all the programs available, Mira has maximum versatility in this 
regard---always has. It handles any number of target objects and any number 
of standards (with or without ensemble weighting), in any number of images. 
When doing time series (or otherwise measuring an image set), the numbers of 
objects and standards do not have to be the same for each image.

[...]

> As for errors, Canopus handles only one of the general types mentioned by 
> Mike.
> Specifically, errors are computed based on SNR converted to magnitudes 
> using
> Howell's formula and adding the errors of each comp in quadrature as well 
> as that
> of the target. The complete formula is provided in two of the output file 
> headers
> so that there is no doubt how the error is computed.

    Which "Howell's formula" are you talking about? Is it the sigma(m) = 
1.0857 / S/N or the complete magnitude error formula I published in 
Astronomical Journal, January 1991?

Regards,

Michael Newberry