The Quick Binzel Reduction Method
This method for reducing to standard magnitudes is called the "Binzel Method" because it was suggested by Dr. Richard Binzel of MIT and written up in the Minor Planet Bulletin, "A Simplified Method for Standard Star Calibration", 2004, MPB 32, pp. 93-95. The original implementation of the method is covered in the second edition of "A Practical Guide to Lightcurve Photometry and Analysis" by B.D. Warner.
The Quick Binzel Method is a hybrid of Binzel method meant for "one-shot" photometry of targets, not time-series work. This can be used to get quick, reasonably good magnitude estimates of targets, by using the 2MASS BVRI conversion formulae on UCAC2 or 2MASS stars (see "MPO2M - 2MASS Catalog" on pg. 23). If the field includes stars from the LONEOS or User Star catalogs, those can be used instead for more accurate measurements.
Quick Binzel makes use of the hidden transforms found when using the Transforms method. The hidden transforms are the relationship between a catalog color index magnitude and the instrumental color index. For example, the hidden transform can convert a v-r to V-R.
By incorporating the color index information, the Quick Binzel method removes most of the color dependency of your system and so finds a more accurate estimate of the differential magnitude of the target minus a given comparison.
The comparison star standard magnitudes are found by measuring a number of stars in a field against their catalog values when taking an image in a given filter, e.g., V. For each star, the average of the catalog value minus the instrumental magnitude is found. In a perfect world, this value would be identical for all comparison stars. Since it is not, the average and standard deviation of that average are found. For each instrumental magnitude then, that average is added to it to find the reduced magnitude of the target. When several comparisons are used, then the average and standard deviation of those reduced magnitudes is found. The total error is the two standard deviations added in quadrature, i.e.,
TotalErr = sqrt(sqr(Error1) + sqr(Error2))
The color index of the target is found by averaging several instrumental color index values and then using that value in the hidden transform for that color index to find the standard color index. The error is the standard deviation of the average of those reduced color indices.
Before you can use the Quick Binzel method, keep in mind several points.
1. This method works only with the V-R color index, therefore, if you're also finding the color index of the target, you must have at least one, preferably three, images in V and R.
2. Establish a good v-r to V-R transform (the "hidden transform") using the Transforms method on a good standard field, i.e., Landolt or high-quality Henden field (M67 is a good choice when available).
3. Establish a good K'vr first-order extinction.
The first of these requirements can be met by spending two or three good nights every three or four months getting the required images. The VR hidden transform should be very stable and so you can take the average of the several nights to use for all the reductions for a given season.
The K'v and K'r values, of course, change nightly. However, under most circumstances, the differential value, i.e., K'vr, should be fairly stable and which comes into play during this reduction method. You can find seasonal averages for these values and use them for the reductions as well. Of course, you should be careful not to assume too much too often. For example, large forest or brush fires can push smoke high into the atmosphere that go across many miles and so change the differential value significantly.
The good news is that since all measurements are in the same field of view, the errors due to differential air mass can be ignored as long as you're not working too near the horizon.
See the Users Guide for a tutorial on running the Quick Binzel method.
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