Sources of Pixel to Pixel Variation
An ideal detector will record a constant accumulation of signal under constant illumination, with gain referring to the ratio of photoelectrons to measured signal. Real detectors, like the H4RG-10s on the Roman Space Telescope's Wide Field Instrument (WFI), will deviate from this behavior. Detector properties like gain, nonlinearity, and saturation will all differ from pixel to pixel. These variations, captured by the flatfield and described on this page, cause the signal observed by a detector to show structure absent in the sky scene.
Pixels in Roman's WFI will see different levels of signal, and will behave differently as they accumulate charge. This article summarizes several sources of that variation together with the approaches used to calibrate pixels to the intensity incident on the detector. After these calibrations, the image seen by the WFI should much more accurately reflect the scene on the sky.
This article does not include all effects that modify the scene as it appears on the detector. For example, interpixel capacitance effectively smooths the image as the value recorded for a pixel is modified by the values of its neighbors, while the effective size of a pixel can change with its electrical properties as it accumulates charge. The effects discussed on this page — nonlinearity, flatfields, and saturation — will modify the signal seen by a uniformly illuminated detector. Corrections for these effects are included as part of the Exposure Level Pipeline.
Note
Linearity and Saturation
A pixel under constant illumination will not accumulate signal at a constant rate. This is due to the combination of many effects. For example, a linear accumulation of charge on a capacitor will not produce a linear accumulation of voltage across a capacitor, and the digitization of voltage can also be nonlinear. A pixel also has a finite amount of charge that it can accumulate, at which point it “saturates” and its recorded signal no longer increases with time until it is reset.
The actual signal recorded by a pixel under uniform accumulation is shown in the Figure Showing Nonlinear Behavior of a Pixel. The Roman WFI detectors may be read out many times without being reset, with the pixel value recorded at each of these reads. Signal is measured as a data number (DN; also called digital number); the conversion between DN and physical units like photoelectrons and holes must be derived from observational data. In the Figure Showing Nonlinear Behavior of a Pixel, a pixel is shown to reach digital saturation, i.e., it stops accumulating signal when its voltage exceeds the value that corresponds to 65535 (the largest 16-bit unsigned integer).
Figure Showing Nonlinear Behavior of a Pixel
Accumulated signal as a function of time for a single pixel on the WFI subject to constant illumination. This pixel's signal increases nearly linearly at first. As it accumulates charge, its signal accumulation rate increasingly deviates from a constant. This pixel stops accumulating signal (though not necessarily charge) at the largest 16-bit unsigned integer, 65535; at this point it has reached digital saturation.
The Nonlinearity Correction
A nonlinearity correction should take the signal recorded by a uniformly illuminated pixel and transform it into a corrected signal that accumulates at a constant rate. This nonlinearity correction for the WFI is a polynomial function of the measured signal that transforms the measured counts into a linearized signal. Every pixel on every detector will have its own nonlinearity correction derived from a sequence of exposures extending into saturation.
The nonlinearity correction described above is often referred to as classic nonlinearity. There are also effects that will cause a pixel to deviate from a linear accumulation of signal under constant but nonuniform illumination. For example, a pixel that has already accumulated substantial charge will have differing electrical properties from neighbors that have received less illumination, leading to a change in effective pixel area. The more strongly illuminated pixel accumulates charge more slowly while its immediate neighbors accumulate charge more rapidly. This is referred to as the brighter-fatter effect. It is also possible that, even after applying a classic nonlinearity correction, a pixel under twice the illumination will not accumulate signal at twice the rate. Deviations of this nature are referred to as count-rate dependent nonlinearity. The discussion in this article is limited to the classic linearity correction, which can be measured by uniformly illuminating a detector and measuring its response up-the-ramp.
The algorithm used to derive the nonlinearity correction is described in Brandt (2025) with the correction for integral nonlinearity (INL) described in Brandt and Perera (2025). The Figure Demonstrating the Nonlinearity Correction for a Sample Pixel shows 5500 individual reads from 100 ramps, showing both the measured signal and the corrected signal for different polynomial correction orders. A first-order correction (the yellow line) is insufficient; a nonlinearity correction must indeed be applied.
The characterization of the nonlinearity correction is still ongoing, and the order for the correction for the WFI has not yet been determined. Details of the correction will continue to be added in future RDox publications.
Figure Demonstrating the Nonlinearity Correction for a Sample Pixel
The first panel uses red dots to show each individual read in 100 ramps of 55 reads each. The colored lines show the best-fit nonlinearity corrections of different polynomial orders ranging from 1 (for no nonlinearity correction) to 8. The second panel shows the same information, but with the yellow (linear; order 1) fit subtracted from all lines and points to emphasize the deviations from linearity.
Saturation
A pixel may or may not have its signal accumulation rate instantly go to zero at saturation. If a pixel’s signal extends to digital saturation (65535 units, the largest possible value of a 16-bit unsigned integer), then its signal may suddenly become constant (see Figure of Saturation Behavior in Three Pixels). If a pixel cannot hold enough charge to reach this signal, then its signal accumulation rate will decrease more gradually. Some pixels will reach digital saturation abruptly, some will reach digital saturation only after their count rates have substantially decreased as they approach full well, and some pixels will be unable to store any more charge before they reach digital saturation.
For the purposes of Roman calibration, we will take “saturation” to mean the signal level beyond which the nonlinearity correction is considered to be unreliable. It does not correspond to the maximum counts recorded by a pixel. As a practical matter, the “saturation” level adopted for the WFI is within 5-10% of the largest value ever recorded by a pixel. Unsaturated reads are corrected as described above and saturated reads are discarded when fitting a pixel’s charge accumulation rate.
Figure of Saturation Behavior in Three Pixels
Saturation behavior in three pixels. One, shown in blue stars, reaches digital saturation while the count level is still increasing steadily. The ramp shown in green pentagons reaches digital saturation only after the count rate has nearly plateaued, while the ramp shown in orange circles never reaches digital saturation.
Saturation and Neighboring Pixels
When a pixel saturates by filling its well (which could come after digital saturation), it can no longer store charge, but photoelectrons (or electron holes) can still be generated by impinging photons. These photoelectrons or holes can then be trapped in neighboring pixels and appear as signal there (see the Figure of Saturation and Neighboring Pixels). A pixel’s charge accumulation rate can increase when its neighbor saturates, so that its signal no longer accurately reflects the intensity of light illuminating that pixel. This effect has been seen in other infrared detectors, including Hawaii-2RG detectors similar to (but smaller than) the H4RG-10 detectors used for the WFI (see discussion in Brandt et al. 2017 for Hawaii-2RG). For the WFI, we consider a read to be saturated, and unusable for fitting a pixel’s count rate, if it exceeds that pixel’s adopted saturation value or if any of its immediate neighbors have reached their saturation values.
Figure of Saturation and Neighboring Pixels
Behavior of a pixel's neighbors when that pixel saturates: the lines show the ramps of the pixels in the inset, with colors matching the colors in the inset. When the central pixel saturates by filling its well (which occurs after digital saturation in this case), its neighbors record the excess charge and show an increase in their count rate.
Flatfields
Two pixels that receive the same illumination will not accumulate signal at the same rate, even after applying the appropriate nonlinearity corrections. There are three main reasons for this: (1) pixels can vary in effective size as a result of the manufacturing process; (2) the gain — the ratio of accumulated signal in digital number (DN) to the signal in electrons or holes — will differ from pixel to pixel; and (3) the probability that a pixel records a photon depends on its electrical properties and coatings. The latter effect means that pixel-to-pixel variations can be wavelength-dependent.
The Roman WFI will uniformly illuminate its detectors with the Roman Calibration System (RCS) in order to produce flatfields that correct for the differing responses pixel-by-pixel. After applying the nonlinearity correction described above, flatfields will be produced at six wavelengths corresponding to the six different-colored LEDs in the RCS. These flatfields will include pixel-to-pixel gain variations, quantum efficiency variations, and differences in effective pixel size (see the Figure Showing the Effect of Flatfielding for an example). The distinction between these effects is unimportant for the WFI, apart from their implication that a different flatfield must be produced for each wavelength of illumination.
Figure Showing the Effect of Flatfielding
The first panel shows the measured count rates in a region of a single WFI detector illuminated in a mode that produces a small amount of scattered light. The middle panel shows the measured count rates in a mode that provides very uniform illumination of the WFI; this serves as the flatfield. The last panel demonstrates how dividing by the flatfield clearly shows the structure in the left image (note the different color scale). The vertical bars visible in the middle and left images correspond to distinct readout channels in the H4RG detector.
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References
- "Data reduction pipeline for the CHARIS integral-field spectrograph I: detector readout calibration and data cube extraction", Brandt et al. 2017
- "Computing the Electronic Gain for Detectors Read Out Up-the-ramp", Brandt 2025
- "A Classic Nonlinearity Correction Algorithm for Detectors Read Out Up-the-ramp", Brandt 2025
- "Integral Nonlinearity in Roman-WFI Detector Data", Brandt and Perera 2025