Photon Transfer Curve Research Articles

Characterization and Optimization of Skipper CCDs for the SOAR Integral Field Spectrograph

We present results from the characterization and optimization of Skipper charge-coupled devices (CCDs) for use in a focal plane prototype for the Southern Astrophysical Research Integral Field Spectrograph (SIFS). We tested eight Skipper CCDs and selected six for SIFS based on performance results. The Skipper CCDs are 6k × 1k, 15 μm pixels, thick, fully depleted, p-channel devices that have been thinned to ∼250 μm, backside processed, and treated with an anti-reflective coating. We demonstrate a single-sample readout noise of <4.3 e− rms pixel−1 in all amplifiers. We optimize the readout sequence timing to achieve a readout noise of 0.5 e− rms pixel−1 after 74 non-destructive measurements, which can be accomplished in a region covering 5% of the detector area in a readout time of <4 minutes. We demonstrate single-photon-counting in all 24 amplifiers (four amplifiers per detector) with a readnoise of σ N ∼ 0.18 e− rms pixel−1 after N samp = 400 samples, and we constrain the degree of nonlinearity to be ≲1% at low signal levels (0 e− to 50 e−). Clock-induced charge (CIC) remains an important issue when the Skipper CCD is configured to provide a large full-well capacity. We achieve a CIC rate of <1.45 × 10−3 e− pixel−1 frame−1 for a full-well capacity of ∼900 e−, which increases to a CIC rate of ∼3 e− pixel−1 frame−1 for full-well capacities ∼40,000–65,000 e−. We also perform conventional CCD characterization measurements such as charge transfer inefficiency (3.44 × 10−7 on average), dark current (∼2 × 10−4 e− pixel−1 s−1), photon transfer curves, cosmetic defects (<0.45% “bad” pixels), and charge diffusion (point-spread function < 7.5 μm) to verify that these properties are consistent with expectations from conventional p-channel CCDs used for astronomy. Furthermore, we provide the first measurements of the brighter-fatter effect and absolute quantum efficiency (≳80% between 450 and 980 nm; ≳90% between 600 and 900 nm) using Skipper CCDs.

Characterization of a C‐RED One camera for astrophotonical applications

AbstractTo better understand the impact of the avalanche gain applied in the detector technology and apply this technology in our in‐house astrophotonic projects, we have characterized a C‐RED One camera and produced a stable and reliable method for calculating the system gain at any desired avalanche gain setting. We observed that depending on how the system gain is obtained, multiplying the system gain times the avalanche gain may not accurately produce a conversion factor from electrons to ADUs. As the acquisition of a photon transfer curve (PTC) was possible at different avalanche gain levels, several PTCs at low avalanche gain levels were acquired. Consequently, a linear fit was produced from the acquired system gain as a function of the avalanche gain setting. Through the linear fit, the effective system gain was calculated at any desired avalanche level. The effective system gain makes possible to accurately calculate the initial system gain without the ambiguity introduced by the nonlinearity of the system. Besides, the impact of the avalanche gain on the dynamic range was also analyzed and showed a stable behavior through the measured avalanche range.

StarDICE

Context. The Hubble diagram of type-Ia supernovae (SNe-Ia) provides cosmological constraints on the nature of dark energy with an accuracy limited by the flux calibration of currently available spectrophotometric standards. This motivates new developments to improve the link between existing astrophysical flux standards and laboratory standards. Aims. The StarDICE experiment aims to establish a five-stage metrology chain from NIST photodiodes to stars, with a targeted accuracy of 1 mmag in griz colors. We present the first two stages, resulting in the calibration transfer from NIST photodiodes to a demonstration 150 mpixel CMOS sensor (Sony IMX411ALR as implemented in the QHY411M camera by QHYCCD). As a side-product, we provide full characterization of this camera, which we believe to be of potential interest in astronomical imaging and photometry and specifically discuss its use in the context of gravitational wave optical follow-up. Methods. A fully automated spectrophotometric bench was built to perform the calibration transfer. The sensor readout electronics was studied using thousands of flat-field images from which we derived stability, high-resolution photon transfer curves (PTC), and estimates of the individual pixel gain. The sensor quantum efficiency (QE) was then measured relatively to a NIST-calibrated photodiode, in a well-defined monochromatic light beam from 375 to 1078 nm. Last, flat-field scans at 16 different wavelengths were used to build maps of the sensor response, fully characterizing the sensor for absolute photometric measurements. Results. We demonstrated statistical uncertainty on QE below 0.001 e−/γ between 387 nm and 950 nm, the range being limited by the sensitivity decline of the tested sensor in the infrared. Systematic uncertainties in the bench optics are controlled at the level of 1 × 10−3 e−/γ. Linearity issues are detected at the level of 5 × 10−3 e−/γ for the tested camera and require further developments to fully correct. Uncertainty in the overall normalization of the QE curve (without relevance for the cosmology, but relevant to evaluate the performance of the camera itself) is 1%. Regarding the camera we demonstrate stability in steady state conditions at the level of 32.5 ppm. Homogeneity in the response is below 1% RMS across the entire sensor area. Quantum efficiency stays above 50% in most of the visible range, peaking well above 80% between 440 nm and 570 nm. Differential nonlinearities at the level of 1% are detected. A simple two-parameter model is proposed to mitigate the effect and found to adequately correct the shape of the PTC on half the numerical scale. No significant deviations from integral linearity were detected in our limited test. Static and dynamical correlations between pixels are low, making the device likely suitable for galaxy shape measurements.

3D noise photon transfer curve.

A photon transfer curve (PTC) is used to determine fundamental detector noise parameters such as read noise, conversion gain, and fixed pattern noise. Here, the method for determining a PTC is expanded to include 3D noise parameters. 3D noise PTC provides more insight into detector noise and is treated as the next logical step to classical PTC. However, it induces several new challenges in analyzing the results, specifically the fitting of seven, or more, variance curves compared to the one (total variance) or two (temporal and fixed pattern variance) prior. Therefore, a general measurement model is created, which provides a new method to separate out all the classical terms, such as DSNU and PRNU, but can also handle high gain cameras with a noise factor. This method is then verified using Monte Carlo simulations and applied to a commercial machine vision camera. In addition, the effects of lens vignetting and non-uniformity correction (NUC) are explored, along with a comparison of the single pixel PTC.

A review of IEEE P2020 noise metrics

The IEEE P2020 standard addresses fundamental image quality attributes that are specifically relevant to cameras in automotive imaging systems. The Noise standard in IEEE P2020 is mostly based on existing standards on noise in digital cameras. However, it adjusts test conditions and procedures to make them more suitable for cameras for automotive applications, such as use of fisheye lenses, 16-32 bit data format in operation in high dynamic range (HDR) mode, HDR scenes, extended temperature range, and near-infrared imaging. The work presents methodology, procedures and experimental results that demonstrate extraction of camera characteristics from videos of HDR and other test charts that are recorded in raw format, including dark and photo signals, temporal noise, fixed-pattern noise, signal-to-noise ratio curves, photon transfer curve, transaction factor and effective full well capacity. The work also presents methodology and experimental results for characterization of camera noise in the dark array and signal falloff.

Accurate Determination of Conversion Gains of SVOM VT CCDs Based on a Signal-Dependent Charge-Sharing Mechanism

The signal-variance method and the photon transfer curve method are the most valuable tools for calculating the conversion gains of charge-coupled device (CCD) detectors. This paper describes the phenomena that arise in the conversion gain measurements of space multi-band variable object monitor (SVOM) visible telescope (VT) CCDs, where the results of the signal-variance method increase with the image gray level, and the results of the photon transfer curve method appear with nonlinearity, which is caused by the signal-dependent charge sharing mechanism of back-illuminated CCDs. A numerical simulation model based on random variables was adopted to analyze the influence of the mechanism on the gain determination. The model simulates all the signals and noise in the flat field image, including the photon signal and photon-shot noise, readout noise, fixed pattern noise, and the signal-dependent charge-sharing signal, and it demonstrated agreement with the experimental data. Then, we proposed a quadratic polynomial curve-fitting formula for the photon transfer curve, and we quantitatively analyzed the relationship between the fitting coefficients and the gain, the signal-dependent charge sharing coefficient, and the full well capacity using the control variable method. Finally, the formula was used to accurately determine the conversion gains of SVOM VT CCDs.

Compensation of Signal-Dependent Readout Noise in Photon Transfer Curve Characterisation of CMOS Image Sensors

The signal independence of the noise induced by the analogue signal processing chain in CMOS imagers is important for measurement accuracy when applying the photon transfer technique. This brief shows the implications of signal-dependent readout noise on the photon transfer method, and proposes a methodology to minimize its sensitivity to cameras with non-flat electronic readout noise. This noise can in some cases be signal-dependent, which alters the Photon Transfer Curve (PTC) used for evaluating photodiode array performance. A modulated PTC changes the imager transfer constant, which could lead to inaccurate parameter calculations. We reveal that the typical application of single-point calculation for the sense node to ADC sensitivity constant near the full well diode capacity is insufficient. This brief proposes a methodology for compensation of signal-dependent readout noise using multi-point measurements in the low-light segment of the PTC curve, which improves control over calculations using the PTC method.

Image sensor correction algorithm for photon transfer curve based on neural network

Pattern noise and nonlinearity are common problems in many image sensors that limit their performance. We present an algorithm based on neural network to correct pattern noise and nonlinearity of the image sensor when the gray value approaches the saturation point to improve the linear range and image contrast of image sensors. The photon transfer curve (PTC) of each pixel is evaluated through a photographic test with an image sensor at different exposures. Assuming that the PTC of the ideal image sensor is a proportional function, the nonlinear region of the PTC of each pixel is corrected to the targeted curve using a neural network. The experimental results show that the image contrast and dynamic range of the corrected image can be significantly improved while the pattern noise of the corrected image is also effectively removed. In addition, the algorithm corrects the damaged pixels of the image sensor.

Brighter-fatter Effect in Near-infrared Detectors. I. Theory of Flat Autocorrelations

Weak gravitational lensing studies aim to measure small distortions in the shapes of distant galaxies, thus placing very tight demands on the understanding of detector-induced systematic effects in astronomical images. The Wide-field Infrared Survey Telescope will carry out weak lensing measurements in the near-infrared using the new Teledyne H4RG-10 detector arrays, which makes the range of possible detector systematics very different from traditional weak lensing measurements using optical CCDs. One of the nonlinear detector effects observed in CCDs is the brighter-fatter effect (BFE), in which charge already accumulated in a pixel alters the electric field geometry and causes new charge to be deflected away from brighter pixels. Here we describe the formalism for measuring the BFE using flat-field correlation functions in infrared detector arrays. The autocorrelation of CCD flat fields is often used to measure the BFE, but because the infrared detector arrays are read out with the charge “in place,” the flat-field correlations are dominated by capacitive cross-talk between neighboring pixels (the interpixel capacitance, or IPC). Conversely, if the BFE is present and one does not account for it, it can bias correlation measurements of the IPC and photon transfer curve measurements of the gain. We show that one can compute numerous cross-correlation functions between different time slices of the same flat exposures, and that correlations due to IPC and BFE leave distinct imprints. We generate a suite of simulated flat fields and show that the underlying IPC and BFE parameters can be extracted, even when both are present in the simulation. There are some biases in the BFE coefficients up to 12%, which are likely caused by higher-order terms that are dropped from this analysis. The method is applied to laboratory data in the companion Paper II.

Experimental Verification of the Impact of Analog CMS on CIS Readout Noise

In this article, the impact of the combination of the column-level gain and the correlated multiple sampling (CMS) on the noise of CMOS image sensor (CIS) readout chains is first analyzed. The theory is then validated experimentally with CIS readout chains embedding two different pixels, a variable gain column-level amplifier (CLA) and a passive switched-capacitor (SC) CMS circuit. The noise measurements include photon transfer curves (PTCs) for different gains and pixels and they show reasonably well that CMS reduces the 1/f noise by about 33% for order 8 as expected theoretically.

The shape of the photon transfer curve of CCD sensors

The photon transfer curve (PTC) of a CCD depicts the variance of uniform images as a function of their average. It is now well established that the variance is not proportional to the average, as Poisson statistics would indicate, but rather flattens out at high flux. This “variance deficit”, related to the brighter-fatter effect, feeds correlations between nearby pixels that increase with flux, and decay with distance. We propose an analytical expression for the PTC shape, and for the dependence of correlations with intensity, and relate both to some more basic quantities related to the electrostatics of the sensor, which are commonly used to correct science images for the brighter-fatter effect. We derive electrostatic constraints from a large set of flat field images acquired with a CCD e2v 250, and eventually question the generally-admitted assumption that boundaries of CCD pixels shift by amounts proportional to the source charges. Our results show that the departure of flat field statistics from the Poisson law is entirely compatible with charge redistribution during the drift in the sensor.

A Quantitative Analytical Framework for Photon Transfer Curve-Based Preflight Characterization of the Indian Remote Sensing Imaging Systems

Preflight performance characterization of spaceborne imaging systems offers high-quality images for scientific applications. A key challenge in the laboratory characterization process is to identify the candidate signal chains requiring performance optimization. For the Indian Remote Sensing (IRS) imaging systems, light transfer characterization has been identified as a standard process for performance characterization. Photon transfer curve (PTC) is another powerful and widely used tool to characterize the imaging systems in terms of camera gain ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$e^{-}$ </tex-math></inline-formula> /DN), read noise ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$e^{-}$ </tex-math></inline-formula> ), charge-to-voltage conversion factor (CVF), signal-to-noise ratio, mean–variance linearity, and so on. There have been no detailed investigations on the PTC characteristics of the IRS imaging systems. We present here PTC-based characterization studies on two high-resolution IRS imaging systems, namely, Cartosat-1 and Cartosat-2. For this, a quantitative analytical framework has been developed, which enables comparative studies among multiple signal chains by applying various statistical measures on the PTC derived parameters. This framework provides not only a quantitative assessment of performance deviations but also enables performance traceability up to detector level. Taken together, our analysis shows that all the signal chains have well behaved PTC characteristics, and performance deviations are less than 10%. In particular, performance traceability is established by the close match of the system-level CVF values within the detector manufacturer’s specified range. Studies on the adequacy of linear approximation of the PTC curve reveal large residual errors in the lower dynamic range due to an increase in read noise floor. The analytical framework developed here can significantly help optimize future IRS imaging systems.

Analysis and Design of a CMOS Ultra-High-Speed Burst Mode Imager with In-Situ Storage Topology Featuring In-Pixel CDS Amplification.

This paper presents an in-situ storage topology for ultra-high-speed burst mode imagers, enabling low noise operation while keeping a high frame depth. The proposed pixel architecture contains a 4T pinned photodiode, a correlated double sampling (CDS) amplification stage, and an in-situ memory bank. Focusing on the sampling noise, the system level trade-off of the proposed pixel architecture is discussed, showing its advantages on the noise, power, and scaling capability. Integrated with an AC coupling CDS stage, the amplification is obtained by exploiting the strong capacitance to the voltage relation of a single NMOS transistor. A comprehensive noise model is developed for optimizing the trade-off between the area and noise. As a proof-of-concept, a prototype imager with a 30 µm pixel pitch was fabricated in a CMOS 130 nm technology. A 108-cell memory bank is implemented allowing dense layout and parallel readout. Two types of CDS amplification stages were investigated. Despite the limited memory capacitance of 10 fF/cell, the photon transfer curves of both pixel types were measured over different operation speeds up to 20 Mfps showing a noise performance of 8.4 e−.

Exploring the Brighter-fatter Effect with the Hyper Suprime-Cam

Abstract The brighter-fatter effect has been postulated to arise due to the build up of a transverse electric field, produced as photocharges accumulate in the pixels’ potential wells. We investigate the brighter-fatter effect in the Hyper Suprime-Cam by examining flat fields and moments of stars. We observe deviations from the expected linear relation in the photon transfer curve (PTC), luminosity-dependent correlations between pixels in flat-field images, and a luminosity-dependent point-spread function (PSF) in stellar observations. Under the key assumptions of translation invariance and Maxwell’s equations in the quasi-static limit, we give a first-principles proof that the effect can be parameterized by a translationally invariant scalar kernel. We describe how this kernel can be estimated from flat fields and discuss how this kernel has been used to remove the brighter-fatter distortions in Hyper Suprime-Cam images. We find that our correction restores the expected linear relation in the PTCs and significantly reduces, but does not completely remove, the luminosity dependence of the PSF over a wide range of magnitudes.

Quantitative evaluation method of the threshold adjustment and the flat field correction performances of hybrid photon counting pixel detectors

A simple method is proposed in this work for quantitative evaluation of the quality of the threshold adjustment and the flat-field correction of Hybrid Photon Counting pixel (HPC) detectors. This approach is based on the Photon Transfer Curve (PTC) corresponding to the measurement of the standard deviation of the signal in flat field images. Fixed pattern noise (FPN), easily identifiable in the curve, is linked to the residual threshold dispersion, sensor inhomogeneity and the remnant errors in flat fielding techniques. The analytical expression of the signal to noise ratio curve is developed for HPC and successfully used as a fit function applied to experimental data obtained with the XPAD detector. The quantitative evaluation of the FPN, described by the photon response non-uniformity (PRNU), is measured for different configurations (threshold adjustment method and flat fielding technique) and is demonstrated to be used in order to evaluate the best setting for having the best image quality from a commercial or a R&D detector.

Characterisation of a novel reverse-biased PPD CMOS image sensor

A new pinned photodiode (PPD) CMOS image sensor (CIS) has been developed and characterised. The sensor can be fully depleted by means of reverse bias applied to the substrate, and the principle of operation is applicable to very thick sensitive volumes. Additional n-type implants under the pixel p-wells, called Deep Depletion Extension (DDE), have been added in order to eliminate the large parasitic substrate current that would otherwise be present in a normal device. The first prototype has been manufactured on a 18 μm thick, 1000 Ω .cm epitaxial silicon wafers using 180 nm PPD image sensor process at TowerJazz Semiconductor. The chip contains arrays of 10 μm and 5.4 μm pixels, with variations of the shape, size and the depth of the DDE implant. Back-side illuminated (BSI) devices were manufactured in collaboration with Teledyne e2v, and characterised together with the front-side illuminated (FSI) variants. The presented results show that the devices could be reverse-biased without parasitic leakage currents, in good agreement with simulations. The new 10 μm pixels in both BSI and FSI variants exhibit nearly identical photo response to the reference non-modified pixels, as characterised with the photon transfer curve. Different techniques were used to measure the depletion depth in FSI and BSI chips, and the results are consistent with the expected full depletion.

Characterization of a sCMOS-based high-resolution imaging system

The detection system is a key part of any imaging station. Here the performance of the novel sCMOS-based detection system installed at the ID17 biomedical beamline of the European Synchrotron Radiation Facility and dedicated to high-resolution computed-tomography imaging is analysed. The system consists of an X-ray-visible-light converter, a visible-light optics and a PCO.Edge5.5 sCMOS detector. Measurements of the optical characteristics, the linearity of the system, the detection lag, the modulation transfer function, the normalized power spectrum, the detective quantum efficiency and the photon transfer curve are presented and discussed. The study was carried out at two different X-ray energies (35 and 50 keV) using both 2× and 1× optical magnification systems. The final pixel size resulted in 3.1 and 6.2 µm, respectively. The measured characteristic parameters of the PCO.Edge5.5 are in good agreement with the manufacturer specifications. Fast imaging can be achieved using this detection system, but at the price of unavoidable losses in terms of image quality. The way in which the X-ray beam inhomogeneity limited some of the performances of the system is also discussed.

CMOS图像传感器光子转移曲线辐照后的退化机理

CMOS图像传感器光子转移曲线辐照后的退化机理

Assessing low-light cameras with photon transfer curve method

Low-light camera is an indispensable component in various fluorescence microscopy techniques. However, choosing an appropriate low-light camera for a specific technique (for example, single molecule imaging) is always time-consuming and sometimes confusing, especially after the commercialization of a new type of camera called sCMOS camera, which is now receiving heavy demands and high praise from both academic and industrial users. In this tutorial, we try to provide a guide on how to fully access the performance of low-light cameras using a well-developed method called photon transfer curve (PTC). We first present a brief explanation on the key parameters for characterizing low-light cameras, then explain the experimental procedures on how to measure PTC. We also show the application of the PTC method in experimentally quantifying the performance of two representative low-light cameras. Finally, we extend the PTC method to provide offset map, read noise map, and gain map of individual pixels inside a camera.

Detection Statistics in Geiger-Mode Avalanche Photodiode Quad-Cell Arrays With Crosstalk and Dead Time

The detection statistics of Geiger-mode photodetector subarrays with a combination of reset-time blocking loss and optical crosstalk are investigated. Closed-form expressions are obtained for the means and covariances of the numbers of counts in $2 \times 2$ subarrays (quad cells) used in Shack–Hartmann wavefront sensors. The predicted wavefront sensing precision is compared with that obtained with a charge-coupled device-based wavefront sensor with readout noise. The results of the theory are also used to predict photon transfer curves for the Geiger-mode device and these are compared with experiment.