The purpose of observing variable stars is to obtain measures of their numerical magnitudes from time to time. My extensive experience has been with the observing program administered by the American Association of Variable Star Observers (AAVSO), headquartered at Harvard College Observatory in Cambridge, Massachusetts, using star charts provided by the AAVSO, each showing each variable star and several comparison stars calibrated with visual magnitudes. Last I know, which was way back in 1970, the AAVSO was administering programs covering several different types of variable stars - long-term, intermediate term, short-term, irregular, eclipsing , and RR-Lyrae.
It's not clear how you propose to use a ccd and a wedge with an altitude-azimuth mounting. The only method I've used in measuring the magnitudes of variable stars was visual, using pairs of comparison stars with known magnitudes bracketing the magnitude of the variable star between pairs of comparison stars. For example, if I judged visually that the brightness of the variable star was between those of comparison stars A and B with calibrated magnitudes 10.3 and 10.8 but closer to that of A than to B, I'd record the magnitude of the variable star by interpolation as either 10.4 or 10.5. If I judged the one of three comparison stars with an intermediate magnitude to exactly match that of the variable star, so much the better. A crucial consideration in any case was uniformity of the telescope field in the sense that a given star would appear to have the same brightness regardless of its position in the field. This would also be a critical consideration for a ccd. Also, the ccd must have uniform color sensitivity: red and blue stars of the same visual magnitude need to produce images of the same density on the ccd. This is not the case for ordinary photographic film.
If you use an alt-azimuth-mounted telescope with a ccd and a wedge to record an image of the field including two comparison stars, you need to assure that the exposure is short enough so that the tracks of all three relevant star images will be of equal length on the ccd.
You also need to assure that the image of a given star is measured as having the same magnitude regardless of the location of its image on the ccd.
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