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C. Analysis of the Dark Tests


Figure 10 is a plot of the mean dark current against exposure time for two sets of temperature data in the useful range (T = -10 degrees C and T = -20 degrees C) with different symbols showing data at different temperatures. The lines are weighted, one-sided linear least-squares fits to the data, using exposure time as the independent parameter. Linear fits are an excellent representation of the data. The fit line for T = -20 degrees C is

and for T = -10 degrees C the fit is

where D is the dark rate in counts per pixel and t is the exposure time in minutes. The linearity of the dark rate holds for all temperatures tested (extending to temperatures substantially warmer than are likely to yield useful astronomical data). Notice also that, within the scatter in the measurement, the data are consistent with a constant dark rate (counts per pixel per unit time) at a given temperature. Thus, for example, a bias-corrected ten-minute dark frame obtained at T = -20 degrees C will have half the total counts per pixel as a twenty-minute dark frame at T = -20 degrees C. I shall return to this point when discussing general strategies for obtaining darks.

  • Figure 10: Dark rate plotted against exposure time for T = -20 degrees C (squares, dotted line) and T = -10 degrees C (six-pointed stars, dashed line).

    Figure 11 shows the final result of the set of dark tests. It is a plot of the dark rate (counts per pixel per minute) as a function of detector temperature for the set of dark tests all obtained by PBE on the dates indicated in the figure. Several essential points are clear from this figure.

  • Figure 11: Dark rate as a function of detector temperature for dark frames obtained on five separate dates from mid-winter through mid-summer.

  • First, there is no evidence of any night-to-night systematic offsets in the dark rate to within the scatter in the data. Thus one can reliably expect to understand what the dark rate of a given exposure should be (to within the intrinsic scatter) if one knows the detector temperature at the time of the exposure.

  • Second, the dark rate is a very strong function of temperature at detector temperatures T > -10 degrees C. Recall that these data have been bias corrected. Thus, in agreement with the conclusions from Section 2, good quantitative work will be very difficult, if not impossible to do unless T_D < -10 degrees C.

  • Third, for T_D < -10 degrees C, there is a well behaved, linear trend of the dark rate as a function of temperature. This is shown in Fig. 11 by a set of the linear least-squares fits. The solid line is a weighted fit with the detector temperature as the independent parameter. It has the form

    The dotted line is an unweighted fit with the detector temperature as the independent parameter. It has the form

    The dashed line is an unweighted ordinary bisector fit. It has the form

    All of these fits provide an excellent description of the data. Thus the dark current of our detector is relatively well-behaved.

    Finally, even at T < -10 degrees C, there is a scatter of about +/- 1 ADU at fixed temperature. This means that, although an observer can use these results to guide his or her strategy for calibration, one cannot expect to obtain a good dark correction simply by scaling a "master dark" to a given temperature and integration time. Good dark correction with our system will require the observer to obtain darks every night, and at every detector temperature used for actual sky observations.


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    Updated: 2009 August 20 [pbe]