Sequence-Specific Photometric Transformation Using Ensemble-Based Linear Regression

Science Smart Telescope Photometry
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I have only recently begun following this forum, and I find the ideas shared here very interesting.

Dr. Brian Kloppenborg suggested that I share this approach here with the Smart Telescope Working Group.

I also own a Celestron Origin telescope, which I primarily use for live online astronomy presentations. Recently, however, I have started experimenting with photometric observations using the Origin, mainly targeting RR Lyrae and δ Cephei type variables.

In parallel with this, I continue to perform photometric measurements using Newtonian telescopes mounted on equatorial mounts, equipped with a monochrome CMOS camera (ZWO ASI1600MM Pro), ASIAIR control, and non-standard (ZWO New LRGB) filters. During the reduction of these observations, I developed a method to convert instrumental magnitudes into standard magnitudes.

The essence of the method is the following:

For each image series, I perform ensemble differential photometry on all stars within the field of view that have known standard magnitudes listed on AAVSO charts, and I determine their instrumental magnitudes.

For the non-variable stars, the instrumental magnitudes obtained from the ensemble photometry are averaged over the entire duration of the observing sequence. Since these stars are constant in time, averaging reduces measurement noise, while the standard deviation provides a useful characterization of the internal stability of the observing sequence and the observing conditions.

Each star thus contributes a single data point consisting of its averaged instrumental magnitude and its corresponding standard magnitude. These data points form the basis of a linear regression. From this regression, I determine the transformation equation valid for the given observing sequence, which I then directly use to convert the variable star’s instrumental magnitude into a standard magnitude.

The primary goal of this approach is to determine the standard magnitude of the observed variable star within a given observing sequence with the highest possible internal consistency.

The correlation coefficient obtained from the linear regression and the residual scatter provide immediate, quantitative feedback on the internal precision of the observing sequence and indicate the level of scientific use for which the results may be suitable.

In this approach, I do not treat the transformation as a constant system parameter, but rather as a local fitting problem: for each observing sequence, I determine an empirical relationship fitted to the standard stars present in the field of view.

Conceptually, this sequence-level fitting may be related to the nightly coefficient strategies currently discussed within the STWG, although implemented here at the level of a single observed field.

I would be interested to learn whether similar sequence-specific transformation strategies are being considered within the current STWG workflow.

If this is of interest, I would be happy to return with a more detailed and mathematically

Best regards,

Vilmos Tekler

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The only potential problem I see with this approach is that the errors of the magnitudes and colour indices of AAVSO comparison stars are often larger than the corresponding errors in AAVSO photometric standard stars.

Therefore, the transformation coefficients derived from comparison stars may not be as accurate as those calculated from photometric standards. If this is the case, and particularly since you are using non-scientific filters for photometry for which TCs may for some filters be very different from those of scientific filters, it would be advantageous to get the ‘best’ transformation coefficients possible.

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Hi Vilmos,

Thanks for bringing this topic up.

If I’m not mistaken, this approach was also proposed by Bruce L. Gary (CCD Transformation Equations). I tried it for last couple of years for observing short period variables (e.g. Lyrids).

The main outcome for me was: the numbers of comparison stars in the sequence is crucial.

My setup is rather modest (150 mm Newtonian, ZWO ASI585MM Pro + filter wheel), as well as viewing conditions (backyard at Seattle suburbia). So far the only target I’m satisfied is SZ Lyncis, which has a dozen of comparison stars inside 60 arcsec FOV. I was able to achieve uncertainty about 30 mmag for V, 50 mmag for B and Rc.

Measurements of stars with lesser number of comparison stars produce very noisy data.

It would be very nice if you publish the details of your approach. My algorithm (quite straightforward) is here: vsopy-pkg/src/vsopy/phot/transform.py at dev · dmitrymu/vsopy-pkg · GitHub .

Best regards,
Dmitry (MDMD)

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Vilmos:
Thank you for experimenting with this and for sharing what you’ve found.

You’ve done a couple of things that I find interesting:

  • You are averaging instrumental magnitudes. It’s never occurred to me to do that, mostly because I’m so used to miserable sky conditions that I expect transient cloud cover all the time. But the technique that you’re using is commonly used by research-class observatories with well-understood sky conditions for exactly the reasons that you’ve noted. It has to be used with caution, though, if you have a long time series where airmass/extinction is changing noticeably throughout the sequence.
  • By limiting your regression fitting to a single field in the sky, you eliminate some of the field-to-field issues that happen when you combine all data across a single night. When the STWG does a linear fit across an entire session’s worth of observations, we are doing it to extract two sets of information: the correction coefficients for our color/vignetting/airmass correction algorithms, and a set of zero points for our images. We are rarely using existing AAVSO photometric sequences, since we get “better” results using APASS or ATLAS Refcat-2 catalog data (either of which is more homogeneous than the AAVSO sequences). Right now we find ourselves trying to get “more stars, more stars” into those regressions (looking for 10,000 to 100,000 points from each session) in order to average out errors.

Please continue doing what you’re doing – and sharing your results with us!

– Mark