Photometry Calculations

The math used by MaxIm DL's photometry tool to calculate magnitude and error values from the raw data is described in this section. These calculations were revised from their original implementation as of MaxIm DL Version 6.21.

Determining Target Object Magnitude

Every target object's standard magnitude is computed from its instrumental magnitude (i.e. its measured magnitude) and an ensemble of N reference stars as a weighted average of their differential magnitudes, relative to the catalog values of each reference star.

We assume you have means to determine an object's intensity and signal to noise ratio (SNR) by processing relevant image pixel values. (MaxIm DL performs this step whenever an object is tagged, and these results depend upon the size of the aperture and annulus rings.)

If I is the intensity of an object in an image, and t is the exposure time of that image, then

Let , where

is the instrumental magnitude of reference star , and
is the catalog magnitude of

Let the 1-sigma SNR-based uncertainty be defined as

Let be the weight factor arising from the SNR of reference star .

Let , where N is the number of reference stars.

Then the standard magnitude of the object is given by

   

It is this value () that is plotted on the graph as the object's magnitude, and is exported as MAG in the AAVSO format and "Magnitude (Centroid)" in the CSV format.

Calculating Error

Let the SNR-based magnitude error be defined as:

Let c be the preferred minimum ensemble size, which MaxIm DL sets to 3.

Let be the magnitude error we seek, exported as MAGERR in the AAVSO format, and "Error" in the CSV format.

For N = 1

   , the SNR-based magnitude error (see above).

For N < c

Let , the SNR-based magnitude error of the target object.

Let , where is the SNR-based magnitude error for reference star .

In other words, this is the sum in quadrature of object error and average reference star SNR-based errors.

For N >= c

We use the standard deviation of target magnitude computed with respect to each reference star:

,

where are the standardized magnitudes of the object for each reference star i and  is their average.

It is this value that is exported as MAGERR in the AAVSO format, and "Error" in the CSV format.