Computing Electronic Gain for Detectors Read Out Up-The-Ramp: a Consistent and Nearly Unbiased Estimator

Determining the electronic gain, which converts detected light into measurable digital signals, is fundamental to accurately interpreting astronomical images and understanding the relationship between signal strength and noise. Timothy D. Brandt from the Space Telescope Science Institute, along with colleagues, presents a novel method for calculating this crucial gain from images acquired using a ‘up-the-ramp’ technique, where detectors are read repeatedly without resetting. This likelihood-based approach fully utilises each measurement, assuming an ideal detector subject to noise, and extends to accommodate slight nonlinearities in the light-to-signal conversion. The team demonstrates that this method provides a reliable and unbiased estimate of the gain, and importantly, successfully applies it to data from the Wide-Field Instrument on the Roman Space Telescope, revealing that pixel-to-pixel gain variations explain much of the observed pixel response in flatfield images.

This approach fully utilizes individual detector readings, initially assuming an ideal detector subject to photon noise and Gaussian read noise, and extends to incorporate slight nonlinearities in the relationship between detected photoelectrons and measured counts, enhancing accuracy in real-world applications. Accurate gain calibration is crucial for precise photometric measurements and scientific analysis of astronomical data, and the WFI, a large-format infrared instrument, presents challenges in achieving uniform and accurate calibration across all pixels due to the mission goals of studying dark energy and exoplanets, which demand high photometric precision. The researchers developed a maximum likelihood estimation (MLE) method to determine the gain for each pixel, a statistical approach that finds the gain value that best fits the observed data. The method utilizes ramp data, a series of images taken with increasing integration times, allowing for a more robust estimation of the gain and read noise while incorporating various noise sources, including Poisson noise from the signal, read noise from the detector, and dark current noise.

Validating the method using data from the WFI’s test detectors, the researchers achieved a median uncertainty of approximately 3. 5% in the pixel-by-pixel gain measurements, revealing significant spatial variations in gain, particularly in regions where the epoxy layer used to protect the detector was deposited differently. This work will be incorporated into the WFI’s calibration pipeline to automatically generate gain maps for all detectors, and the methodology could be adapted for calibrating other large-format infrared detectors, paving the way for high-precision astronomical observations.

Ramp Reads Precisely Determine Detector Gain

This work presents a new likelihood-based method for determining the electronic gain, the conversion between detected photoelectrons and recorded digital numbers, in astronomical images. The team developed a technique that utilizes data from “up-the-ramp” reads, where detectors are read multiple times without resetting, to precisely calculate gain and account for detector noise. Experiments demonstrate that this approach delivers a consistent and nearly unbiased estimate of the gain, even when slight nonlinearities exist in the relationship between photoelectrons and measured counts. The researchers validated their method using synthetic data, generating 100 simulated “ramps” each with 30 reads. Analysis of the resulting likelihood distributions revealed that interpreting the likelihood as a probability density in the logarithm of gain and read noise yields a remarkably Gaussian form, allowing for accurate determination of both gain and read noise by evaluating the likelihood at only nine combinations of values, significantly reducing computational cost. Further investigation focused on characterizing the probability distribution of the gain itself, demonstrating that the marginalized posterior distribution of the gain is accurately Gaussian and can be fully characterized using the quadratic form, and confirming the computational efficiency of this method scales linearly with the number of pixels, ramps, and reads, making it practical for analyzing large datasets.

Likelihood Gain Estimation For Nondestructive Readout

This work presents a new likelihood-based method for determining the electronic gain of detectors read out nondestructively, a technique known as up-the-ramp sampling. Building upon the established photon transfer method, this approach utilizes all available data reads and incorporates a correct covariance matrix, offering improved statistical power and accuracy. The method successfully accounts for variations in photon rates between exposures by marginalizing over the unknown count rate in each pixel, simultaneously constraining both gain and read noise. 5%, revealing that much of the spatial variation observed in flatfield images can be attributed to variations in gain.