<title>Analysis of the noise equivalent angle of various tilt-estimation algorithms in the presence of Poisson and Gaussian noise</title>

Abstract

This paper addresses the problem of estimating the noise equivalent angle (NEA) of several tilt estimation algorithms resulting from including zero-mean Poisson and Gaussian noise. The Poisson noise is due to both photon shot noise and the photoelectric conversion. The readout noise of the detector is assumed to be Gaussian. There are no simple means to relate the noise on the detector to the noise in the measurement. More signal increases the signal-to-noise (SNR) and decreases the NEA. The 2D signal density profile strong influences the NEA. Three different profiles will be analyzed: a Gaussian spot, a top hat, and a simulated missile. The analysis will be performed as a function of total signal. The simulation of these three profiles will be based on using a constant base image with added noise. The variation in the tilt estimate is due to the added noise since each frame would be identical otherwise. The variation as a function of total signal is performed by scaling the base image. Experimental data is analyzed to determine the SNR by dividing the mean by the rms. This data was taken at several different intensity levels so that the total counts would change. Finally, the results from the simulations and the experimental data are compared. The dominant noise not simulated is due to scintillation. Currently, it seems that this last noise source dominates both of the sources included in the simulation.