Photometric Performance and Characteristics of the GRAS Science Scopes

This page provides a number of photometric quality measures for the GRAS telescope systems. All images relevant for this report have been calibrated by the GRAS Automated Calibration System, and magnitudes reduced using Photometrica. The results are thus representative for the GRAS photometry system as a whole.

Only differential aperture photometry is considered. Direct any questions to Geir Klingenberg.

1 Summary and Conclusion
2 GRAS Science Telescopes
3 Transformation Coefficients
4 Accuracy
5 Precision
6 How to use this page
7 Appendix A: Details for accuracy calculations
8 Appendix B: Details for precision calculations

Summary and Conclusion

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The photometric performance of the GRAS scopes is very good. Tests have shown that an accuracy of 0.02 magnitudes and a precision of about 4 mmag can be achieved under fair conditions and with high SNR, using differential photometry with a single comparison star. Better or worse results may be experienced depending on the sky quality and air mass of observation. Using more than one comparison star (ensemble photometry) might also improve the results.

The need for transforming observations to a standard system varies among the scope, but for most projects transformation is not needed. G5 is very close to the standard system, while G2 is in most need of transformation. In general R and I observations gives more error if untransformed than does V observations.

GRAS Science Telescopes

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Photometric telescopes are those that minimally have a V-filter. For technical specifications, see the telescopes page.

Transformation Coefficients

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N is the number of nights used to determine the coefficients. The stated values are the average of each nights result.

Fields used are SA110 and M67, and the methods and calculations are described in detail in the photometry book of Henden and Kaitchuck.




The chart above gives you an idea of what error to expect if not transforming your observations. The values are for the special case of having a color difference of 1 between the target and the comparison star.

For instance, assume we use G1 to estimate the V-band magnitude of a star. We use a comparison star whose B-V color index is 1 less that the star we want to measure. Then, reading from the chart, we can on average expect an accuracy that is about 0.04 less than if we did transform.

An untransformed R-band measurement using G2 will, on average, be as much as 0.17 mags off.

If the color difference is halved, so is the loss of accuracy.

Accuracy

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The chart show each scope’s estimated accuracy as a function of SNR.

Accuracy is taken as the absolute error between the measured magnitude of a standard (or secondary standard) star compared to its catalog value. Another standard star was used as comparison, and regular differential photometry applied. SNR is the signal-to-noise ratio of the faintest of the two stars. The observations were made at an air mass of 1.2 – 1.4, with various exposure times pr image to get a wide range of SNR.

Note that these results are approximate, and that other levels of accuracy can be experienced depending on sky quality, air mass, exposure time and other factors.

Also note that a single comparison star was used. Better results may be obtained using ensemble photometry (multiple comparison stars).

Detailed information can be found here.

Precision

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The chart show each scope’s estimated precision as a function of SNR.

Here precision is taken as the standard deviation of the magnitude difference between two stars in a series of 20 to 30 images. SNR is the signal-to-noise ratio of the faintest of the two stars. The observations were made at an air mass of 1.2 – 1.4, with 120 second exposure time pr image.

Note that these results are approximate, and that other levels of precision can be experienced depending on sky quality, air mass, exposure time and other factors.

Also note that a single comparison star was used. Better results may be obtained using ensemble photometry (multiple comparison stars).

Detailed information can be found here.

How to use this page

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Evaluating photometric quality of the systems is equivalent to evaluating its measurement errors. Two error measures are considered: accuracy and precision.

If a measurement is of high accuracy it is close to the true value of what is being measured. If the precision is high as well, repeated measurements will be close to that value, with little scatter. The scatter will be less with higher precision. Take a look here for more info about these terms.

Ideally, we would like our photometry to be as accurate and precise as possible. But the requirement depends on your particular project.

If your project is monitoring a long period variable star, with perhaps one measurement a week which will be mixed with observations from other observers, your primary concern is accuracy. If the star is faint, the precision might be low, but averaging measurements from several images can still give you high accuracy. Furthermore, the demand for high accuracy increases with decreasing amplitude of the observed phenomenon. Also, for the highest possible accuracy observations should be transformed.

But if your interest lies in timing events such as planetary transits, or finding the period of a short period pulsating star, you might not be that concerned whether the true average magnitude is 10.3 or 10.4 (that is, accuracy). But you want to catch the (possibly tiny) magnitude changes the star produce, so you need high precision.

As an example, the figure below shows an actual exo-planet transit observed with G2. The dip in the light curve might not have been detectable if the noise in the measurements were just a bit larger (lower precision).

Appendix A: Details for accuracy calculations

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Images of varying exposure time of the standard field SA110 and the secondary standard field NGC7790 were acquired using a photometric V filter. Then, a relatively bright comparison star was selected in each image, with large SNR. The magnitude of all other standard stars was calculated using this comparison star, and transformed using the transformation coefficients given on this page. The absolute error, given as the absolute difference between the cataloged value and the calculated value, is plotted against the SNR in the charts below.

Note that the chart scales differ.

SNR is the SNR of the fainter of the two stars, as the noise in the fainter stars measurement will dominate the error. So with a SNR of about 100, we can read from the charts an error of about 0.06 magnitudes for G4, and 0.05 for G5. These are conservative estimates.

Note that, in general, better results can be obtained by using several comp stars, or by averaging several consecutive measurements.

To create the chart in the Accuracy section, all observations but those with the largest error in its SNR range was removed, and a power equation fitted to the remaining data. This to give conservative error estimates. The resulting equations are

G1: E = 2.171 * SNR^-0.866
G2: E = 1.059 * SNR^-0.725
G4: E = 1.090 * SNR^-0.669
G5: E = 0.672 * SNR^-0.652

These equations can be used to give a conservative error estimate by plugging in the SNR of the faintest star.

Appendix B: Details for precision calculations

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Precision was measured by taking a number of images of a star field with non-varying stars, in this case SA110 and NGC7790. A single star with high SNR was selected as comparison star. Then, regular differential aperture photometry was applied to as many stars as possible in each image. Since each star is constant, this should result in flat light curves. Ideally, each measure of the same star should yield the same value, but in real life there will always be a slight variation around the mean value. This variation, measured by the standard deviation, is taken as the systems precision and is plotted in the charts below.

Note that the chart scales differ.

20 - 30 R-band images was taken with each scope, at an air mass ranging from 1.4 to 1.2. Each image exposure was 120 seconds.

One important factor that influences precision is scintillation (twinkling). As this effect is dependent on air mass, better or worse results than those shown here can be experienced. Also, long exposure times tend to average out noise from scintillation. So less precision is expected for short exposures.

A power curve was fitted to the data for each scope. The resulting equations are:

G1: P = 0.194 * SNR^-0.559
G2: P = 0.676 * SNR^-0.719
G4: P = 0.332 * SNR^-0.668
G5: P = 0.190 * SNR^-0.548

These equations can be used to estimate precision by plugging in the SNR of the faintest star.