Photometrica

About the organization

Photometrica.org is a non-profit organization that provides an expanding suite of analytical tools for the online analysis of astronomical CCD images, that supports the work of amateur astronomers, students and researchers, to provides a shared, virtual workspace for distributed teams, and to bridge the amateur and professional communities in collaborations that advance science.

Contact Information

Photometrica was developed by Geir Klingenberg, Norway. It is owned and operated by Geir Klingenberg and Michael Kran, California USA. You can reach us by mail; use michael and/or geir, both with extension @photometrica.org.

About the software

Currently Photometrica is mainly an aperture photometry software program that analyses remote CCD images online. We are however continously working on expanding its analytical capabilities, and it will in the near future support other common task.

The main steps involved in the aperture photometry analysis process are:

Centroid determination
Sky fitting
Aperture integration
Final magnitude estimate
Error estimation

Centroid determination:

The centroiding algorithm is based on the DAOPHOT FIND algorithm in IRAF (1987PASP...99..191S). In short, it goes something like this:

When the image is clicked a region centered on the click is scanned for star centroids
The size of this region is determined from the aperture size
A unit height Gaussian is fitted to every pixel in the region, based on that pixel's surrounding pixels. The fit tend to be good for pixels that happens to be in a star center, bad otherwise.
A sharpness criteria is calculated to separate stars from hot pixels and cosmic rays.
The pixel with the best fit is selected as the final centroid.

Finally the exact star center is calculated using center of mass calculations on the marginals, see the IRAF specification at http://iraf.noao.edu/docs/photom.html.

Sky fitting

Photometrica uses the following outlier rejection algorithm to remove high valued pixels in the sky annulus (from stars, hot pixels etc.):

Calculate the mean and standard deviation of the ADUs in the annulus.
Remove all pixels with ADU greater than 3 * std.
Repeat until no more pixels are rejected

Then the sky glow is estimated using the mode:

mode = 3 * median - 2 * mean

This is the value subtracted from each pixel in the aperture.

Aperture integration

The star signal (instrumental magnitude) is estimated as

-2.5 * LOG( SUM( ADU - Sky ) / exptime )

where the sum runs over all pixels in the aperture. That is, for each pixel that is fully contained inside the aperture, the software sums the pixels ADU, subtracted the estimated sky background (from step 2). The sum is divided by exposure time to get total intensity pr second before it is converted to the magnitude scale.

Along the rim of the aperture there are pixels that are only partially inside the aperture. If the distance from a given pixel to the centroid is less than the aperture radius - 0.5, it is included in the sum as described above. If the distance is greater than the aperture radius + 0.5 the pixel is excluded. If the distance is in between, a fraction of (ADU - Sky) is included, proportional to the amount of the pixel inside the aperture.

This is an approximate algorithm, but works fairly well. It is similar to the aperture integration algorithm in PHOT IRAF module, see http://iraf.noao.edu/docs/photom.html.

Final Magnitude Estimate: Calculating the instrumental magnitude of a target, It, and a comp star Ic, as described in the sections above, the magnitude estimate of the target is given as

V = It - Ic + C

where C is the known magnitude of the comp star. If we use more than one comp star, we get instrumental magnitudes I1, I2, ..., In. And hence n estimates of the targets magnitude, V1, V2, ..., Vn. Photometrica calculates the final magnitude as the average of these n estimates.

Error Estimation

In an ensemble solution with more than two comp stars, the magnitude is estimated as the average of the individual comp stars estimate, and the error is taken as the standard deviation of this sample. This error estimate will cover all error sources.

If one or two comp stars are used, the error estimate is based on the SNR of each measurement (the target measurement and the comp stars measurements). The standard error of a measurement is defined as

2.5 * LOG(1 + 1 / SNR)

where LOG is the 10 based logarithm, and SNR is defined as

S / Sqrt(S / (G + Ns * Std^2 * (1 + 1 / Nr)))

S: Total ADU in aperture
Ns: Number of pixels in aperture
Nr: Number of pixels is sky annulus
Std: ADU standard deviation in sky annulus
G: Gain of the CCD detector

For more information see the AAVSO CCD Observing Manual and 'Handbook of CCD Astronomy' by Steve B. Howell, 2000.

Finally, the standard error of each measurement is squared and summed, and the error estimation is the square root of this number.

Limitations

Since Photometrica is based on aperture photometry, it has the limitations of this method. In particular this means that one has to be careful when working in crowded fields, and when there is large variations in the sky level, such as for a star close to a galaxy center.

Aknowledgement

This software uses source code created at the Centre de Données astronomiques de Strasbourg, France.

Plate solving is done by