arXiv subjects

David P. Haefner

Publications and source records attributed to David P. Haefner.

8 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

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↗

arXiv2023

A comparative study of methods to estimate conversion gain in sub-electron and multi-electron read noise regimes

Of all sensor performance parameters, the conversion gain is arguably the most fundamental as it describes the conversion of photoelectrons at the sensor input into digital numbers at the output. Due in part to the emergence of deep sub-electron read noise image sensors in recent years, the literature has seen a resurgence of papers detailing methods for estimating conversion gain in both the sub-electron and multi-electron read noise regimes. Each of the proposed methods work from identical noise models but nevertheless yield diverse procedures for estimating conversion gain. Here, an overview of the proposed methods is provided along with an investigation into their assumptions, uncertainty, and measurement requirements. A sensitivity analysis is conducted using synthetic data for a variety of different sensor configurations. Specifically, the dependence of the conversion gain estimate uncertainty on the magnitude of read noise and quanta exposure is explored. Guidance into the trade-offs between the different methods is provided so that experimenters understand which method is optimal for their application. In support of the reproducible research effort, the MATLAB functions associated with this work can be found on the Mathworks file exchange.

physics.ins-det↗

arXiv2023

Experimental Verification of PCH-EM Algorithm for Characterizing DSERN Image Sensors

The Photon Counting Histogram Expectation Maximization (PCH-EM) algorithm has recently been reported as a candidate method for the characterization of Deep Sub-Electron Read Noise (DSERN) image sensors. This work describes a comprehensive demonstration of the PCH-EM algorithm applied to a DSERN capable quanta image sensor. The results show that PCH-EM is able to characterize DSERN pixels for a large span of quanta exposure and read noise values. The per-pixel characterization results of the sensor are combined with the proposed Photon Counting Distribution (PCD) model to demonstrate the ability of PCH-EM to predict the ensemble distribution of the device. The agreement between experimental observations and model predictions demonstrates both the applicability of the PCD model in the DSERN regime as well as the ability of the PCH-EM algorithm to accurately estimate the underlying model parameters.

physics.ins-det↗

arXiv2023

Photon Counting Histogram Expectation Maximization Algorithm for Characterization of Deep Sub-Electron Read Noise Sensors

We develop a novel algorithm for characterizing Deep Sub-Electron Read Noise (DSERN) image sensors. This algorithm is able to simultaneously compute maximum likelihood estimates of quanta exposure, conversion gain, bias, and read noise of DSERN pixels from a single sample of data with less uncertainty than the traditional photon transfer method. Methods for estimating the starting point of the algorithm are also provided to allow for automated analysis. Demonstration through Monte Carlo numerical experiments are carried out to show the effectiveness of the proposed technique. In support of the reproducible research effort, all of the simulation and analysis tools developed are available on the MathWorks file exchange [1].

physics.ins-det↗

arXiv2023

On the optimal measurement of conversion gain in the presence of dark noise

Working from a model of Gaussian pixel noise, we present and unify over twenty-five years of developments in the statistical analysis of the photon transfer conversion gain measurement. We then study a two-sample estimator of the conversion gain that accounts for the general case of non-negligible dark noise. The moments of this estimator are ill-defined (their integral representations diverge) and so we propose a method for assigning pseudomoments, which are shown to agree with actual sample moments under mild conditions. A definition of optimal sample size pairs for this two-sample estimator is proposed and used to find approximate optimal sample size pairs that allow experimenters to achieve a predetermined measurement uncertainty with as little data as possible. The conditions under which these approximations hold are also discussed. Design and control of experiment procedures are developed and used to optimally estimate a per-pixel conversion gain map of a real image sensor. Experimental results show excellent agreement with theoretical predictions and are backed up with Monte Carlo simulation. The per-pixel conversion gain estimates are then applied in a demonstration of per-pixel read noise estimation of the same image sensor. The results of this work open the door to a comprehensive pixel-level adaptation of the photon transfer method.

physics.optics↗