arXiv subjects

Aaron J. Hendrickson

Publications and source records attributed to Aaron J. Hendrickson.

5 recordsLinked to original sources

arXiv2026

Valley-peak modulation in phase space: a law-invariant VPM and its theta-function structure

Valley-peak modulation (VPM) was introduced as a metric for quantifying read noise in deep sub-electron read noise (DSERN) CMOS image sensors. In its original amplitude-domain definition VPM depends on both read noise and quanta exposure, yet Starkey and Fossum demonstrated exposure-independent approximations valid in the DSERN regime. Here we identify the invariant object those approximations probe, and find its invariance extends beyond exposure to the electron-number law itself. A phase mapping quotients the sensor model by the integer electron lattice, yielding a wrapped-Gaussian density parameterized only by read noise and admitting lattice-sum and Jacobi theta-function representations. The invariant is the theta ratio $R=\vartheta_4(q)/\vartheta_3(q)$ with nome $q$, of which any VPM is a contrast normalization; the existing approximations are low-order truncations of its lattice sums, and the amplitude-domain metric converges to its phase-space counterpart at large exposure. A closed-form inverse for read noise in terms of VPM follows from elliptic integrals. The identification yields a moment method of characterization: conversion gain and read noise are estimated jointly from the modulus of the empirical characteristic function of the raw gray values, without specifying the number law, and with leading-order precision depending on it only through its variance.

physics.ins-det↗

arXiv2025

Initialization-robust characterization of deep sub-electron read noise pixels via annealed PCH-EM

We present an annealed Photon Counting Histogram Expectation Maximization (PCH-EM) algorithm for maximum likelihood characterization of Deep Sub-Electron Read Noise (DSERN) pixels. The annealed variant mitigates initialization-dependent convergence to suboptimal local optima of the likelihood function while achieving uncertainties substantially lower than the Photon Transfer (PT) method in the DSERN regime. Although the annealing principle is optimizer-agnostic, we pair it with PCH-EM for tractability; a single temperature parameter and simple cooling schedule suffice, without re-deriving the original EM update equations. Simulations across varied starting points show more stable parameter estimates with equal or better final likelihoods than the baseline. While designed for DSERN, the method applies across read-noise regimes and matches PT performance outside DSERN. Practically, the method enables reliable characterization of DSERN devices, including direct calibration from raw gray counts to electron counts for photon number resolving applications.

physics.ins-det↗

arXiv2025

Beyond Discretization: A Continuous-Time Framework for Event Generation in Neuromorphic Pixels

A novel continuous-time framework is proposed for modeling neuromorphic image sensors in the form of an initial canonical representation with analytical tractability. Exact simulation algorithms are developed in parallel with closed-form expressions that characterize the model's dynamics. This framework enables the generation of synthetic event streams in genuine continuous-time, which combined with the analytical results, reveal the underlying mechanisms driving the oscillatory behavior of event data presented in the literature.

stat.AP↗

arXiv2024

Photon Counting Accuracy in Digital Image Sensors

A statistical model for data emanating from digital image sensors is developed and used to define a notion of the system level photon counting accuracy given a specified quantization strategy. The photon counting accuracy for three example quantization rules is derived and the performance of each rule is compared.

physics.ins-det↗

arXiv2024

PCH-EM: A solution to information loss in the photon transfer method

Working from a Poisson-Gaussian noise model, a multi-sample extension of the Photon Counting Histogram Expectation Maximization (PCH-EM) algorithm is derived as a general-purpose alternative to the Photon Transfer (PT) method. This algorithm is derived from the same model, requires the same experimental data, and estimates the same sensor performance parameters as the time-tested PT method, all while obtaining lower uncertainty estimates. It is shown that as read noise becomes large, multiple data samples are necessary to capture enough information about the parameters of a device under test, justifying the need for a multi-sample extension. An estimation procedure is devised consisting of initial PT characterization followed by repeated iteration of PCH-EM to demonstrate the improvement in estimate uncertainty achievable with PCH-EM; particularly in the regime of Deep Sub-Electron Read Noise (DSERN). A statistical argument based on the information theoretic concept of sufficiency is formulated to explain how PT data reduction procedures discard information contained in raw sensor data, thus explaining why the proposed algorithm is able to obtain lower uncertainty estimates of key sensor performance parameters such as read noise and conversion gain. Experimental data captured from a CMOS quanta image sensor with DSERN is then used to demonstrate the algorithm's usage and validate the underlying theory and statistical model. In support of the reproducible research effort, the code associated with this work can be obtained on the MathWorks File Exchange (Hendrickson et al., 2024).

physics.ins-det↗