Output signal electrons from photomultiplier tubes (PMTs) have neither a Gaussian nor a Poisson distribution because of changes induced by multiplication when the number of input signal photons and dark electrons is fewer than ~100. Therefore the assumption of a Gaussian distribution of signal electrons cannot be used in simulations for space lidar observations with PMTs, for which the number of return signal photons is normally small. A theory is introduced for analog detection with PMTs that have Poisson-distributed secondary-electron emission at each dynode stage. The theory is validated by straightforward numerical simulations. It is shown that the multiplication in PMTs is a multiply stochastic Poisson process and that the distribution of output signal electrons can be interpreted basically as Neyman type A. Analysis by the threshold method of cloud detection with a space lidar shows considerable difference between a Gaussian approximation and the exact distribution. The result indicates that the threshold level must be optimized for the exact distribution. Return signals were simulated for a proposed space lidar, and cloud detection with the threshold method was demonstrated.

© 2002 Optical Society of America

[Optical Society of America ]

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