Photometrica is a GRAS proprietary, browser based, scientific software analysis
application; a tool that provides the ability for GRAS subscribers to perform instant
photometric analysis of images taken with the remote telescopes at
GRAS. Currently this system is only available at the GRAS New Mexico facility
but will soon become available at all locations. Access to this service is provided
at extra cost.
The GRAS Photometrica imaging software system, performs, on-the-fly, plate solving
and calibration. The processed images are then uploaded to the Photometrica server,
where they can be analyzed, and the pertinent data extracted. Once the correct data
is acquired the observer is free to use the built-in reporting resources to populate,
distribute and submit the appropriate reports to the specified reporting authorities
using the required formats. Unless otherwise required, there is no need to download
the images.
Only the user has access to this data, and no results of your analysis are stored,
so you can be assured that the privacy of your observations are secure.
About the Calibration System
GRAS has developed a sophisticated system that automatically generates calibration
files, and images that is being analysed in Photometrica has been calibrated. This
is a huge time-saver compared to other systems. Here are the details of how the
calibration system works:
Each dawn and dusk the systems will automatically acquire flats under the correct
weather conditions.
In case of heavy cloud or rain and it's night time the systems will automatically
acquire bias and dark frames.
Each dark, flat and bias sub frame generated will be saved into a master holding
library and will be used to generate the master darks, flats and bias frames.
Each dark, flat and bias will be made up of a minimum of 3 to a maximum of 40+ sub
frames, the amount of sub frames going into the master is mainly dependant on weather
conditions. All these details are saved in the FITS header and can be seen in Photometrica.
Sub frames will be deleted after they are 14 days old.
Each sub flat will have bias scaled dark applied, then each sub will be normalized
and all subs median combined, so no additional calibration is needed to use the
master flats.
All darks and bias subs will be median combined to generate the master dark and
bias.
At around 12 noon local system on each Sunday and Wednesday each system will refresh
and generate its master calibration library which will be used to .
In case the optical train of a system is changed the calibration frames will have
to be re-done. It might take some time to generate flats for all filters (depending
on the weather). Photometrica will display a warning if the image is not properly
calibrated.
Methodology
Photometrica performs aperture photometry on the CCD images. The main steps involved
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.
Contact Information
Photoemtrica is developed by Geir Klingenberg at BMO Software and Global Rent-a-Scope.
If you have questions or comments please send an e-mail to geir.klingenberg _at_
gmail.com.
This software uses source code created at the Centre de Données astronomiques de Strasbourg, France.
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