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The analytical calculation of the bit error rate (BER) of digital optical receivers that employ avalanche photodiodes (APDs) is challenging due to 1) the stochastic nature of the avalanche photodiode's impulse-response function and 2) the presence of intersymbol interference (ISI). At ultrafast transmission rates, ISI becomes a dominant component of the BER, and its effect on the BER should be carefully addressed. One solution to this problem, termed the bit-pattern-dependent (PD) approach, is to first calculate the conditional BER given a specific bit pattern and then average over all possible bit patterns. Alternatively, a simplifying method, termed the bit-pattern-independent (PI) approach, has been commonly used whereby the average bit stream is used to calculate the distribution of the receiver output, which, in turn, is used to calculate the BER. However, when ISI is dominant, the PI approximation is inaccurate. Here, the two approaches are analytically compared by analyzing their asymptotic behavior and their bounds. Conditions are found to determine when the PI method overestimates the BER. The BER found using the PD method exponentially decays with the received optical power, whereas for the PI approach, the BER converges to a constant, which is unrealistic. For an InP-based APD receiver with a 100-nm multiplication layer, the PI method is found to be inaccurate for transmission rates beyond 20 Gb/s. [ABSTRACT FROM PUBLISHER]

The mean avalanche current impulse response in an avalanche photodiode exhibits an initial transient and then grows or decays, above or below breakdown, at exponential rates which depend only on the probability distributions of the electron and hole ionization events. The process continues while the electric field profile remains unchanged by the applied bias or the evolving space charge. Below breakdown the distribution in the avalanche duration also exhibits an initial transient and then decays exponentially at the same rate as the mean current. Below breakdown the standard deviation in current decays exponentially at one half of the rate of the mean current, while above breakdown it grows exponentially at the same rate as the mean. Consequently the jitter in a Geiger mode avalanche photodiode becomes independent of time after the initial transients have decayed away. This behavior is quite general and independent of the electric field profile or of the presence of heterojunctions in the multiplication region. Using simple models for carrier transport we find the predicted enhancement in the velocity to ionization of those carriers which ionise shortly after their ballistic dead space significantly speeds up the avalanche dynamics in short devices. [ABSTRACT FROM AUTHOR]

We report on engineering impact ionization characteristics of In0.53Ga0.47As/Al0.48In0.52As superlattice avalanche photodiodes (InGaAs/AlInAs SL APDs) on InP substrate to design and demonstrate an APD with low k-value. We design InGaAs/AlInAs SL APDs with three different SL periods (4 ML, 6 ML, and 8 ML) to achieve the same composition as Al0.4Ga0.07In0.53As quaternary random alloy (RA). The simulated results of an RA and the three SLs predict that the SLs have lower k-values than the RA because the electrons can readily reach their threshold energy for impact ionization while the holes experience the multiple valence minibands scattering. The shorter period of SL shows the lower k-value. To support the theoretical prediction, the designed 6 ML and 8 ML SLs are experimentally demonstrated. The 8 ML SL shows k-value of 0.22, which is lower than the k-value of the RA. The 6 ML SL exhibits even lower k-value than the 8 ML SL, indicating that the shorter period of the SL, the lower k-value as predicted. This work is a theoretical modeling and experimental demonstration of engineering avalanche characteristics in InGaAs/AlInAs SLs and would assist one to design the SLs with improved performance for various SWIR APD application. [ABSTRACT FROM AUTHOR]

A computationally efficient method for image registration is investigated that can achieve an improved performance over the traditional two-dimensional (2-D) cross-correlation-based techniques in the presence of both fixed-pattern and temporal noise. The method relies on transforming each image in the sequence of frames into two vector projections formed by accumulating pixel values along the rows and columns of the image. The vector projections corresponding to successive frames are in turn used to estimate the individual horizontal and vertical components of the shift by means of a one-dimensional (1-D) cross-correlation-based estimator. While gradient-based shift estimation techniques are computationally efficient, they often exhibit degraded performance under noisy conditions in comparison to cross-correlators due to the fact that the gradient operation amplifies noise. The projection-based estimator, on the other hand, significantly reduces the computational complexity associated with the 2-D operations involved in traditional correlation-based shift estimators while improving the performance in the presence of temporal and spatial noise. To show the noise rejection capability of the projection-based shift estimator relative to the 2-D cross correlator, a figure-of-merit is developed and computed reflecting the signal-to-noise ratio (SNR) associated with each estimator. The two methods are also compared by means of computer simulation and tests using real image sequences.

We describe a new, to our knowledge, scene-based nonuniformity correction algorithm for array detectors. The algorithm relies on the ability to register a sequence of observed frames in the presence of the fixed-pattern noise caused by pixel-to-pixel nonuniformity. In low-to-moderate levels of nonuniformity, sufficiently accurate registration may be possible with standard scene-based registration techniques. If the registration is accurate, and motion exists between the frames, then groups of independent detectors can be identified that observe the same irradiance (or true scene value). These detector outputs are averaged to generate estimates of the true scene values. With these scene estimates, and the corresponding observed values through a given detector, a curve-fitting procedure is used to estimate the individual detector response parameters. These can then be used to correct for detector nonuniformity. The strength of the algorithm lies in its simplicity and low computational complexity. Experimental results, to illustrate the performance of the algorithm, include the use of visible-range imagery with simulated nonuniformity and infrared imagery with real nonuniformity.

A statistical algorithm has been developed to compensate for the fixed-pattern noise associated with spatial nonuniformity and temporal drift in the response of focal-plane array infrared imaging systems. The algorithm uses initial scene data to generate initial estimates of the gain, the offset, and the variance of the additive electronic noise of each detector element. The algorithm then updates these parameters by use of subsequent frames and uses the updated parameters to restore the true image by use of a least-mean-square error finite-impulse-response filter. The algorithm is applied to infrared data, and the restored images compare favorably with those restored by use of a multiple-point calibration technique.

The performance of neural networks for which weights and signals are modeled by shot-noise processes is considered. Examples of such networks are optical neural networks and biological systems. We develop a theory that facilitates the computation of the average probability of error in binary-input/binary-output multistage and recurrent networks. We express the probability of error in terms of two key parameters: the computing-noise parameter and the weight-recording-noise parameter. The former is the average number of particles per clock cycle per signal and it represents noise due to the particle nature of the signal. The latter represents noise in the weight-recording process and is the average number of particles per weight. For a fixed computing-noise parameter, the probability of error decreases with the increase in the recording-noise parameter and saturates at a level limited by the computing-noise parameter. A similar behavior is observed when the role of the two parameters is interchanged. As both parameters increase, the probability of error decreases to zero exponentially fast at a rate that is determined using large deviations. We show that the performance can be optimized by a selective choice of the nonlinearity threshold levels. For recurrent networks, as the number of iterations increases, the probability of error increases initially and then saturates at a level determined by the stationary distribution of a Markov chain.