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Analytical Model and Maximum Accuracy of Fluctuating Return Pulse Arrival Time Measurement in Satellite Laser Ranging (SLR)


M.A. Sadovnikov

In satellite laser ranging systems using photodetectors with sensitivity sufficient for single photon counting, basic error sources in return pulse arrival time measurement are fluctuations of primary photoelectron number and emergence time at the pulse duration interval as well as transit time fluctuation of primary photoelectrons during their multiplication in the photodetector. To achieve a submillimeter ranging accuracy it is necessary to increase the laser transmitter pulse repetition frequency (PRF) and to use photo detectors operating in a single-electrons receive mode. For estimation of the maximum achievable measurement accuracy in this operation mode, for the first time analytical expressions were obtained describing the random and systematic ranging errors with fluctuating single-electron and multi-electron return pulses. A basic hypothesis for the analytical measurement model is that in photodetectors with a high internal gain (sufficient for single photoelectron detection) the return pulse arrival time is a sum of the first photoelectron emergence time in the return pulse and of the pulse transit time in the photodetector. It is shown that with a sufficiently small average number of photoelectrons in a pulse, the return pulse intensity fluctuations practically do not affect the measurement systematic error value. It is also shown that the systematic error of measurement may be reduced to a given level by reducing the average number of photoelectrons in a pulse and by increasing the pulse repetition frequency (PRF). Estimations are presented of the achievable measurement accuracy and of the minimum required PRF.

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