Statistics of Accumulating Signal

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Hubble Space Telescope, Hst, Space Telescope Science Institute, Nicmos

Scientific paper

NICMOS detectors accumulate charge which can be read non-destructively. The charge accumulation is a Poisson process, and readout noise is present. Here, formulae are presented for the variance (i.e., "error") of two estimators of the underlying rate of accumulation of charge, or "countrate," subject to these two processes only. The formulae are tested using Monte-Carlo simulations and are applied to the standard NICMOS MULTIACCUM sequences using the known NICMOS dark properties. These algorithms are essentially the current one employed by calnica, least-squares fit of a straight line, and the previous version, weighted mean of first differences. The usual formula for the error on the slope of the least-squares straight line is inapplicable because data points are not independent of previous data points. Also, the usual formula for the error on the weighted mean is inappropriate because of the presence of readout noise (which cancels out to a degree depending on the timing intervals). The results can be used to infer: (i) the least-squares fit algorithm gives a significantly better estimate of the countrate than the weighted mean of first differences, in the readnoise dominated regime (ii) the uncertainty goes down approximately linearly with exposure time in the readnoise dominated regime which suggests longer integrations should be used where possible (iii) Multiple Initial and Final reads (MIFs) improve the uncertainty by about 20% in regions of the detector where ampglow is small (cf. other sequences) (iv) there is little difference otherwise between any of the standard MULTIACCUM sequences. Tables are provided to allow optimal choice of sequence, and to show the characteristics of the uncertainties of MULTIACCUM data in various circumstances.These variances represent fundamental theoretical limits on the utility of the algorithms. Additional noise sources include cosmic rays and inaccuracies in the shading correction. A fairly high sensitivity to cosmic rays suggest using as many readouts as possible, but the consequent accumulation of ampglow can add significant noise.

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