The H4RG-10 detectors in the Roman Wide Field Instrument (WFI) display a number of non-ideal effects, including transient responses to changes in illumination, interactions between neighboring pixels, and illumination-dependent nonlinearity.  This article summarizes these effects and provides approximate quantitative characterizations for the WFI detectors.

An ideal detector accumulates signal linearly in response to constant illumination, faithfully preserves the spatial structure of the incident light, and exhibits noise that is fully described by Gaussian read noise and Poisson photon noise. Real detectors deviate from this ideal behavior in several ways. Some effects, such as classic nonlinearity and pixel-to-pixel variations in response and gain, are discussed in the Sources of Pixel to Pixel Variation article. This article addresses additional, significant sources of non-ideal detector behavior.  

Persistence and Burn-In

When the illumination incident on a pixel changes, the pixel takes some time to respond to the new illumination level. Following an increase in illumination, the first exposure accumulates signal at a lower rate than subsequent exposures as charge traps within the pixel fill. Conversely, after a period of high illumination, subsequent exposures exhibit a gradually decreasing rate of signal accumulation as the traps slowly empty.  These equilibration effects are known as hysteresis.  Both burn-in and persistence can be characterized using the Roman Calibration System (RCS), by imposing controlled changes in detector illumination and measuring the resulting detector response.

Burn-In 

To quantify burn-in, we use a series of three sequential 174-second exposures obtained after suddenly increasing the flatfield illumination level supplied by the RCS. Assuming that burn-in is a sharply decreasing function of time, we first apply a classic nonlinearity correction and then subtract the third (final) exposure from the first. We then measure the average count rate across the 18 WFI detectors by subtracting the values in each successive pair of reads. For example, the difference in linearity-corrected counts between the second and first reads provides an estimate of the count rate at the midpoint between these reads. We normalize our measured read-by-read count differences by the approximate signal rate itself to provide a unitless measure of burn-in. For example, if the difference between the second and first reads corresponds to 1010 counts/second while the average across all reads and ramps is 1000 counts per second, our dimensionless measure would be 1.01, for a 1% excess. We perform this analysis at two count rates: first at ≈50 electrons per pixel per second and then at a higher count rate of ≈ 900 electrons per pixel per second. 

The Figure of Mean Measured WFI Burn-In figure shows the dimensionless burn-in measured. Burn-in is well-approximated by an exponential decay with a characteristic timescale of approximately 20 seconds. The magnitude of the effect, expressed in our dimensionless units, is a weak function of illumination level, suggesting that burn-in is more problematic for absolute flux measurements than for relative flux measurements. Quantitatively, burn-in is likely to be a ~0.1% systematic if uncorrected. Error bars in the figure are derived from the scatter amongst the 18 WFI detectors. Since burn-in disproportionately affects early reads, shorter exposures will show larger impacts on derived count rates. While the figure shows detector-averaged behavior, individual pixels on some detectors may exhibit stronger-than-average effects.

Persistence 

Persistence is quantified using a series of ten 174-second exposures taken immediately after saturating the detectors during ground testing. A dark reference exposure taken after the detectors had remained unilluminated for many hours is subtracted. We then measure the difference between successive reads as a function of time since saturation. We use telemetry measurements of the state of the LEDs in the Relative Calibration System (RCS) to define time zero as the moment the RCS LEDs were switched off (accurate to about 1 second). 

The Figure of Measured WFI Persistence shows persistence behavior over approximately 30 minutes following saturation. Measurements begin about 20 seconds after saturation, at which point the persistence level is ≈1 electron per pixel per second. The amplitude varies significantly across detectors, by a factor of ≈5 between the detector with the strongest persistence (WFI04) and those with the weakest persistence. Persistence also varies spatially within individual detectors (not shown in the figure), sometimes with large regions of pixels exhibiting systematically higher persistence. These pixels represent a pixel family more prone to persistence than others. The worst large-scale regions of WFI04 are a factor of ≈2-3 worse than that detector’s average, and ≈10 times worse than the best-performing detectors on the WFI.

After saturation, the persistence decays as 1/t. This behavior is the same for all detectors, both those that show high persistence and those that show low persistence. This functional form is consistent from the earliest measurable times (≈20 seconds post-saturation) and 30 minutes post-saturation. Earlier measurements are not available due to a minimum number of full-frame resets enforced between WFI exposures, which require nearly 15 seconds. 

The 1/t decline in persistence is much shallower than an exponential, implying that some degree of persistence may remain detectable many exposures after saturation. Assuming a background count rate of several 0.1 electrons per pixel per second, persistence will fall to the background level 1-5 minutes after saturation, and to 10% of the background level by ≈30 minutes after saturation. Given the simplicity of the functional form of persistence, it may be possible to model and remove it in individual exposures if the time of last saturation is accurately known. Persistence correction is not performed as part of standard prompt data processing because persistence depends on the full illumination history of each pixel. Correcting or flagging persistence would therefore require coupling information across multiple WFI exposures and may be implemented in future data release products if required by science use cases.

Interpixel Capacitance (IPC)

When a pixel is read out, electrical coupling with neighboring pixels causes the recorded value to include small contributions from adjacent pixels. The measured signal is therefore a weighted average of the pixel’s true value and those of its nearest neighbors. The dominant contribution arises from the pixel being read out, while each of the four nearest neighbors contributes approximately 2%.

The Measured WFI Interpixel Capacitance figure shows the average IPC measured for detector WFI01 based on the reference file available in the Calibration Reference Data System (CRDS). When a pixel is read out, about 92% of the recorded signal is charge accumulated on that pixel, while most of the remaining 8% is from the pixel's four nearest neighbors.  

IPC has two primary effects. First, the image recorded by the detector is the image that would be observed in the absence of IPC convolved with the IPC kernel. Even in the absence of IPC, the image on the detector represents the convolution of the sky scene with the effective PSF, where the effective PSF itself is the convolution of the optical PSF with the pixel response function (Anderson & King 2000). The associativity of the convolution operator means that we can think of IPC as modifying the effective PSF, making it slightly broader (decreasing the angular resolution of the instrument). Given the relatively small magnitude of IPC in the WFI detectors, its impact on observed images is modest. The Figure of Effect of IPC on the PSF illustrates this effect on the PSF as simulated by STPSF .

The second primary effect of IPC is the introduction of spatial correlations in photon noise because a fraction of the signal, including its associated noise, is shared among adjacent pixels. As a result, photon noise appears to be slightly lower in each individual pixel, while remaining unchanged when summed over a large aperture. If desired, this noise correlation may be accounted for when measuring photometry and astrometry from WFI images. It is possible to reduce, but not eliminate, IPC-induced correlated noise by convolving the data with a kernel that designed to partially reverse the effects of IPC. However, noise arising from the readout process itself (i.e. read noise) is intrinsically uncorrelated between pixels. A kernel that decorrelates photon noise will correlate read noise to a comparable extent. For this reason, and because a true deconvolution is impossible for a finite-sized detector, there is no kernel that can fully remove the effects of IPC, even if the IPC kernel is perfectly known and constant across the detector.

Charge Diffusion 

When a photon creates an electron-hole pair, the hole can diffuse away from where it was created before it is trapped in a pixel’s potential well. Sometimes, a hole can be created in one pixel but recorded in a neighboring pixel. Thus, charge diffusion acts to spatially broaden the signal seen on the detector. Charge diffusion is similar to IPC (discussed above) in its visual effect on images, but since the charge itself is moving, charge diffusion does not spatially correlate noise as IPC does. In practice it is nearly indistinguishable from spacecraft jitter and/or from a broadening of the PSF due to optical effects. 

Charge diffusion was measured for three H4RG detectors, two of which are currently placed in the WFI focal plane (Givans et al. 2022). The measured length scale for diffusion was ≈3 microns, or ≈0.3 WFI pixels, assuming a Gaussian functional form for the diffusion length. As a result, charge diffusion will meaningfully impact the size of the WFI PSF beyond what would be predicted from an optical model of the telescope and instrument like that implemented in  STPSF . 

Brighter-Fatter Effect (BFE) 

As a pixel accumulates charge, its electrical properties change. If two adjacent pixels have accumulated different amounts of charge, a photoelectron or hole excited in the pixel with more charge may become increasingly likely to drift over to its neighbor. This is because the accumulation of signal changes the voltage across the pixel’s depletion region where charges are trapped, which in turn changes the size of the depletion region. A pixel approaching saturation has a smaller physical region where charge can be trapped; it is likely to lose a photoelectron to a neighboring pixel with a larger depletion region. This process, where a photoelectron is trapped in a different pixel from where it was generated due to contrasting electrical properties between those pixels, is known as charge migration. As a result, a pixel will tend to decrease in count rate as it accumulates charge, while its less-illuminated neighbor will tend to increase in count rate. Charge migration is conceptually similar to charge diffusion (discussed above). Charge diffusion is a linear process, independent of the accumulated charge in each pixel, while the brighter-fatter effect is analogous but nonlinear because it does depend on the accumulated charge in each pixel and the difference in that charge between pixels.

The brighter-fatter effect described above only occurs if the detector is illuminated nonuniformly, e.g., by a star. For a uniformly illuminated detector, adjacent pixels will have very nearly the same accumulated charge. Charge diffusion will still apply, but the diffusion probabilities between adjacent pixels will be symmetric. Under nonuniform illumination, the brightest pixel will accumulate signal more slowly as the detector integrates, while its neighbors will accumulate signal more rapidly, as the brightest pixel's depletion region shrinks and the pixel becomes increasingly likely to lose charge to its neighbors. The result is that the photoelectrons become more spread out spatially the further we go up the ramp. Since this process depends on the accumulated charge, it is more significant for brighter stars at fixed integration time and is sometimes called the brighter-fatter effect. 

The brighter-fatter effect in H4RG detectors like those on the WFI has been measured in laboratory data where the detector is illuminated with a grid of small spots. While these spots are not PSFs (they are actually an interference pattern from pinhole grids), we will refer to them here as if they were PSFs. An inset from an image resulting from this setup is shown in the left panel of the Figure of Laboratory Measurements of the Brighter-Fatter Effect. The spots on the detector are undersampled by a factor ≈2, similar to the sampling expected for WFI imaging data. The right panel, from Paine et al. (in prep), shows the brighter-fatter effect. It is calculated by first performing a classic nonlinearity correction measured with uniform illumination and then measuring the size of the "effective PSF" in the differences between pairs of reads. As the detector integrates, the sizes of the spots increase by ≈10%. The size of the spots is never constant as a function of peak counts; the brighter-fatter effect is never negligible.

For WFI processing, the brighter-fatter effect means that the point-spread function depends on the accumulated signal: it differs between bright stars and faint stars, and it differs even for the same star at different points in the ramp. The impact of the brighter-fatter effect will be larger on inferred shape than on flux, as charge mostly moves from one pixel to another rather than being lost to recombination. The mitigation of the brighter-fatter effect in post-processing is a topic of ongoing research. 

Count Rate Dependent Nonlinearity (CRNL)

The RDox article on Sources of Pixel to Pixel Variation discusses classic nonlinearity: the nonlinear relation between accumulated signal on a pixel and the integrated light that was incident on that pixel. Classic nonlinearity applies to uniformly illuminated data. As such, neither IPC nor BFE are relevant. It is possible that a classic nonlinearity correction will produce a linear accumulation of signal at many levels of illumination, but that these linear accumulations will not retain the true ratio of illuminations seen by the detector. For example, suppose that a detector is illuminated at a level I and then at a level 10 × I. Neither ramp will show a linear accumulation of signal in the raw data. A classic nonlinearity correction might produce a linear accumulation of signal in both cases, but the slopes of these signal ramps might have a ratio that differs from 10. Such a difference, subject to the assumption that the nonlinearity correction produces a linear accumulation of signal under both illumination levels, is called count rate dependent nonlinearity, or CRNL. CRNL is sometimes also referred to as flux-dependent nonlinearity, or FDNL.

CRNL is difficult to measure because the true ratio of intensities incident on the detector is itself difficult to measure with high precision. In the example above, we might not be able to verify that we indeed illuminated the detector at a level I and then at a level precisely ten times as high. If we use a different sensor like a photodiode to calibrate the intensity, we must take care to ensure the linearity of this sensor. We also need to guard against the spectrum of illuminating light changing as its intensity changes; this could easily happen for real lamps. To enable another calibration method of CRNL, the WFI uses combinatorial flux addition (CFA), a process of sequentially turning on LEDs individually and then in tandem. This approach still requires an extremely precise classic nonlinearity correction potentially derived together with the CRNL.

Work to characterize the CRNL for the WFI is ongoing, but has found that the effect is small, ≲0.5% over four orders of magnitude of flux. A more precise characterization is specified in the WFI science requirements in order to meet the precision photometry requirements of the supernova cosmology survey (see Deustua et al. 2021 for a discussion).

References

• "Toward High-Precision Astrometry with WFPC2. I. Deriving an Accurate Point-Spread Function", Anderson & King 2000
• "The Roman Space Telescope Relative Calibration System and the Dark Energy Figure of Merit", Deustua et al. 2021
• "Quantum Yield and Charge Diffusion in the Nancy Grace Roman Space Telescope Infrared Detectors", Givans et al. 2022 
• "Characterization of brighter-fatter effect in a Roman detector and implications for weak lensing cosmology", Paine et al. 2025