A New Approach for Computing the Bandwidth Statistics of Avalanche Photodiodes

A new approach for characterizing the avalanche-buildup-time-limited bandwidth of avalanche photodiodes (APDs) is introduced which relies on the direct knowledge of the statistics of the random response time. The random response time is the actual duration of the APD’s finite buildup-limited random impulse response function. A theory is developed characterizing the probability distribution function (PDF) of the random response time. Recurrence equations are derived and numerically solved to yield the PDF of the random response time. The PDF is then used to compute the mean and the standard deviation of the bandwidth. The dependence of the mean and the standard deviation of the bandwidth on the APD mean gain and the ionization coefficient ratio is investigated. Exact asymptotics of the tail of the PDF of the response time are also developed to aid the computation efficiency. The technique can be readily applied to multiplication models which incorporate dead space and can be extended to cases for which the carrier ionization coefficient is position dependent

Multiplication theory for dynamically biased avalanche photodiodes: new limits for gain bandwidth product

Novel theory is developed for the avalanche multiplication process in avalanche photodiodes (APDs) under time-varying reverse-biasing conditions. Integral equations are derived characterizing the statistics of the multiplication factor and the impulse-response function of APDs, as well as their breakdown probability, all under the assumption that the electric field driving the avalanche process is time varying and spatially nonuniform. Numerical calculations generated by the model predict that by using a bit-synchronous sinusoidal biasing scheme to operate the APD in an optical receiver, the pulse-integrated gain-bandwidth product can be improved by a factor of 5 compared to the same APD operating under the conventional static biasing. The bit-synchronized periodic modulation of the electric field in the multiplication region serves to (1) produce large avalanche multiplication factors with suppressed avalanche durations for photons arriving in the early phase of each optical pulse; and (2) generate low avalanche gains and very short avalanche durations for photons arriving in the latter part of each optical pulse. These two factors can work together to reduce intersymbol interference in optical receivers without sacrificing sensitivity

Shift Estimation Algorithm for Dynamic Sensors With Frame-to-Frame Variation in Their Spectral Response

This study is motivated by the emergence of a new class of tunable infrared spectral-imaging sensors that offer the ability to dynamically vary the sensor\u27s intrinsic spectral response from frame to frame in an electronically controlled fashion. A manifestation of this is when a sequence of dissimilar spectral responses is periodically realized, whereby in every period of acquired imagery, each frame is associated with a distinct spectral band. Traditional scene-based global shift estimation algorithms are not applicable to such spectrally heterogeneous video sequences, as a pixel value may change from frame to frame as a result of both global motion and varying spectral response. In this paper, a novel algorithm is proposed and examined to fuse a series of coarse global shift estimates between periodically sampled pairs of nonadjacent frames to estimate motion between consecutive frames; each pair corresponds to two nonadjacent frames of the same spectral band. The proposed algorithm outperforms three alternative methods, with the average error being one half of that obtained by using an equal weights version of the proposed algorithm, one-fourth of that obtained by using a simple linear interpolation method, and one-twentieth of that obtained by using a nai¿ve correlation-based direct method

Projection-based image registration in the presence of fixed-pattern noise

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

Theory of photon coincidence statistics in photon-correlated beams

The statistics of photon coincidence counting in photon-correlated beams is thoroughly investigated considering the effect of the finite coincidence resolving time. The correlated beams are assumed to be generated using parametric downconversion, and the photon streams in the correlated beams are modeled by two partially correlated Poisson point processes. An exact expression for the mean rate of coincidence registration is developed using techniques from renewal theory. It is shown that the use of the traditional approximate rate, in certain situations, leads to the overestimation of the actual rate. The error between the exact and approximate coincidence rates increases as the coincidence-noise parameter, defined as the mean number of uncorrelated photons detected per coincidence resolving time, increases. The use of the exact statistics of the coincidence becomes crucial when the background noise is high or in cases when high precision measurement of coincidence is required. Such cases arise whenever the coincidence-noise parameter is even slightly in excess of zero. It is also shown that the probability distribution function of the time between consecutive coincidence registration can be well approximated by an exponential distribution function. The well-known and experimentally verified Poissonian model of the coincidence registration process is therefore theoretically justified. The theory is applied to an on-off keying communication system proposed by Mandel which has been shown to perform well in extremely noisy conditions. It is shown that the bit-error rate (BER) predicted by the approximate coincidence-rate theory can be significantly lower than the actual BER obtained using the exact theory

Reduction of Quantum Noise in Transmittance Estimation Using PhotoneCorrelated Beams

The accuracy of optical measurements at low light levels is limited by the quantum noise of the source and by the random nature of the interaction with the measured object. The source noise may be reduced by use of nonclassical photon-number squeezed light. This paper considers the use of two photon-correlated beams (generated, for example, by spontaneous parametric downconversion) to measure the optical transmittance of an object. The photons of each beam obey a random Poisson process, but are synchronized in time. One beam is used to probe the object while the other is used as a reference providing information on the realization of the random arrival of photons at the object. The additional information available by such measurement may be exploited to improve the accuracy of the measurement. Various estimators, including the maximum likelihood estimator, are considered and their performance is evaluated and compared with the measurement based on single-beam conventional (Poisson) source and maximally squeezed (fixed photon number) source. The performance advantage established in this paper depends on parameters such as the intensity of the source, the transmittance of the object, the quantum efficiency of the detectors, the background noise, and the degree of correlation of the photon numbers in the two beams

Bit Error Rates for Ultrafast APD Based Optical Receivers: Exact and Large Deviation Based Asymptotic Approaches

Exact analysis as well as asymptotic analysis, based on large-deviation theory (LDT), are developed to compute the bit-error rate (BER) for ultrafast avalanche-photodiode (APD) based optical receivers assuming on-off keying and direct detection. The effects of intersymbol interference (ISI), resulting from the APD\u27s stochastic avalanche buildup time, as well as the APD\u27s dead space are both included in the analysis. ISI becomes a limiting factor as the transmission rate approaches the detector\u27s bandwidth, in which case the bit duration becomes comparable to APD\u27s avalanche buildup time. Further, the effect of dead space becomes significant in high-speed APDs that employ thin avalanche multiplication regions. While the exact BER analysis at the generality considered here has not been reported heretofore, the asymptotic analysis is a major generalization of that developed by Letaief and Sadowsky [IEEE Trans. Inform. Theory, vol. 38, 1992], in which the LDT was used to estimate the BER assuming APDs with an instantaneous response (negligible avalanche buildup time) and no dead space. These results are compared with those obtained using the common Gaussian approximation approach showing the inadequacy of the Guassian approximation when ISI noise has strong presence

An Analytical Approximation for the Excess Noise Factor of Avalanche Photodiodes with Dead Space

Approximate analytical expressions are derived for the mean gain and the excess noise factor of avalanche photodiodes including the effect of dead space. The analysis is based on undertaking a characteristic-equation approach to obtain an approximate analytical solution to the existing system of recurrence equations which characterize the statistics of the random multiplication gain. The analytical expressions for the excess noise factor and the mean gain are shown to be in good agreement with the exact results obtained from numerical solutions of the recurrence equations for values of the dead space reaching up to 20% of the width of the multiplication region

Maximizing Service Reliability in Distributed Computing Systems with Random Node Failures: Theory and Implementation

In distributed computing systems (DCSs) where server nodes can fail permanently with nonzero probability, the system performance can be assessed by means of the service reliability, defined as the probability of serving all the tasks queued in the DCS before all the nodes fail. This paper presents a rigorous probabilistic framework to analytically characterize the service reliability of a DCS in the presence of communication uncertainties and stochastic topological changes due to node deletions. The framework considers a system composed of heterogeneous nodes with stochastic service and failure times and a communication network imposing random tangible delays. The framework also permits arbitrarily specified, distributed load-balancing actions to be taken by the individual nodes in order to improve the service reliability. The presented analysis is based upon a novel use of the concept of stochastic regeneration, which is exploited to derive a system of difference-differential equations characterizing the service reliability. The theory is further utilized to optimize certain load-balancing policies for maximal service reliability; the optimization is carried out by means of an algorithm that scales linearly with the number of nodes in the system. The analytical model is validated using both Monte Carlo simulations and experimental data collected from a DCS testbed

Information theoretic approach for assessing image fidelity in photon-counting arrays

The method of photon-counting integral imaging has been introduced recently for three-dimensional object sensing, visualization, recognition and classification of scenes under photon-starved conditions. This paper presents an information-theoretic model for the photon-counting imaging (PCI) method, thereby providing a rigorous foundation for the merits of PCI in terms of image fidelity. This, in turn, can facilitate our understanding of the demonstrated success of photon-counting integral imaging in compressive imaging and classification. The mutual information between the source and photon-counted images is derived in a Markov random field setting and normalized by the source-image’s entropy, yielding a fidelity metric that is between zero and unity, which respectively corresponds to complete loss of information and full preservation of information. Calculations suggest that the PCI fidelity metric increases with spatial correlation in source image, from which we infer that the PCI method is particularly effective for source images with high spatial correlation; the metric also increases with the reduction in photon-number uncertainty. As an application to the theory, an image-classification problem is considered showing a congruous relationship between the fidelity metric and classifier’s performance