Angle measurement uncertainty statistical distribution of pulsed laser quadrant photodetector

Abstract

As a positionsensitive detector, laser quadrant photodetector(QPD) is widely used in the areas such as laser guidance, laser radar and space optical communication. In the echoed laser pulse detection mode, the laser pulse signal arrived at the QPD photosensitive surface is changed in pulse amplitude, pulse width and pulse waveform due to the influences of target characteristic, atmospheric transmission and other complex factors. In addition, there are random noises in QPD itself and the signal processing circuit. These factors will have an uncertainty effect on the angle measurement accuracy of the QPD. However, the study on the statistical distribution of digital angle measurement of pulsed laser QPD has not been carried out so far. To investigate this angle measurement statistical distribution, the channel of laser angle measurement circuit and the echoed laser spot on QPD photosensitive surface should be modeled first. A measurable signal model in one quadrant of QPD processing circuit channel is established based on the type of random noise and the type of desired ideal signal. The random noise model is considered to be a Gaussian distribution, and the ideal laser pulse signal is considered to have the Gaussian or inverted parabolic distribution in the time domain. Taking into account the QPD symmetry, the statistical distributions of angle measurement value αy for five different spot centers are calculated by the Monte Carlo simulation method within the range θ0∈[0,π/4], under the conditions of different signal distribution types in the time domain, different total peak powers of the spots, different ideal signal widths at half maximum, and different standard deviations of equivalent noise voltage probability density. Simulation results show that the statistical distribution of the measured angle αy value is a normal distribution, and is influenced by the above-mentioned conditions, especially by the signaltonoise ratio in one quadrant. QPD possesses higher angular accuracy as the spot center is closer to the axis center. While the spot center is not closer to the axis center, the mean of statistical distribution of the QPD measurement angle αy is always less than the ideal angle measurement value. Therefore, in order to improve the angle measurement accuracy of the pulsed laser QPD for digital purpose, laser pulse transmit power should be increased, or the noise of each circuit channel of QPD should be reduced, or the laser pulse width should be increased by modulating appropriately.