[Aavso-photometry] Photometric transformation coefficients - general concepts

[Michael Koppelman]

Very nice, Tom. I've been thinking about this, too, because people  
seem to think that transformations are some dark magic where you need  
to look up a special formula in a book. You don't need to -- you can  
easily rediscover transformations yourself from first principles.

A transformation is way to mathematically take one unique value and  
transform it into another unique value. All linear transformations  
have the same form:

y = mx + b

where "m" is the slope of the function and "b" is the offset. In  
photometry we use all sort of greek letters and subscripts but the  
formula is just this simple -- you multiply your magnitude by a slope  
and add or subtract an offset. That's it! The "transformation  
coefficients" are just fancy names for the slope and offset. You can  
easily find m and b by plotting y versus x and fitting a line. The  
equation for that line is your transform.

As Tom mentions, the types of things we seek to correct can vary.  
There are many systematic effects that can be removed by  
transformations and the devil is in the details. That's what makes it  
fun!

M.


On Jun 18, 2009, at 11:37 PM, Tom Krajci wrote:

> Solution #4: Measure brightness of stars with your 'imperfect'  
> filters/CCD/scope/atmosphere, and compare your results to 'catalog'  
> values. Analyze the differences, and you'll probably find that they  
> are repeatable and consistent. Then, apply a difference correction  
> to your measurements and they should (pretty closely) match the  
> 'catalog values.'