Instrumental noise such as dark current, read noise, and $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ noise have been characterized for the Wide Field Instrument (WFI) detectors.  This article describes these sources of noise and how they are currently treated in processing.  

Dark Current

Dark current found in WFI exposures is a combination of internal detector current, residuals biases, and the thermal background. It describes the signal detected in the absence of external light, e.g., with the dark element in place (see WFI Optical Elements). During the non-destructive readout, it also generates a Poisson noise contribution, which is usually very small.

From ground testing, WFI darks have been obtained to measure the dark current in each detector and the results are show in the Figure of Dark Signal in WFI.  Dark current has been determined after rejection of bad pixels by measuring the slopes of a series of resultants, known as sampling up the ramp, that form an exposure. Based on the low temperatures and detector environment, WFI detectors have extremely low dark current values (Betti et al. 2025). Measurements taken over multiple ground-tests have found that the dark current is stable to < 0.5% (dark current < 0.5 electrons per second) in each detector for > 99% of the pixels in the detector (see WFI Ground Testing Campaigns). The average dark signal for all 18 detectors is 0.016 electrons per second under thermal vacuum conditions, well below the median dark current operability requirement of 0.05 electrons per second (Betti et al. 2025). The thermal background may be different in orbit, and the dark current will be regularly monitored throughout the Mission (see On-Orbit Calibration Plan).

The dark signal is subtracted from an observation exposure using the dark current subtraction step of the exposure_pipeline in romancal . 

Read Noise 

Read noise refers to the pixel-to-pixel signal variation introduced by the detector's electronic systems during the readout process. It is caused by instrumental effects such as amplifier fluctuations, analog-to-digital conversion errors, and thermal variations. Unlike shot noise, which scales with signal level, read noise is a stochastic process largely independent of the signal and presents itself as a constant noise floor. In low signal regimes, such as dark exposures, read noise often dominates the noise budget.

Read noise is estimated by measuring the dispersion of the residuals from the linear fit to a pixel’s ramp. We measure the standard deviation of the residuals as the read noise in units of data number (DN). For the WFI, we quantified this instrumental effect during thermal vacuum (TVAC) test campaigns using a total noise test and the results are shown in the Figure of Read Noise in the WFI. Across all detectors, most pixels have a read noise measured between 5 DN and 6 DN (Betti et al. 2025). The On-Orbit Calibration Plan summarizes how dark exposures will be used to monitor this quantity throughout the mission.

The read noise reference file is used together with the gain reference file in the ramp fit step of the exposure_pipeline in romancal to estimate the noise in each pixel while fitting slopes to the data. 

1/f Noise 

During the non-destructive readout of the WFI detectors, drifts in the bias voltage can cause fluctuations that show a temporal correlation with a $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ power law.  This $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ noise is a form of correlated read noise, and is added by the detector readout system to digital images at low spatial frequencies. It appears as horizontal banding in the fast-read (row) direction of the detectors as shown in the left panel of the Figure of 1/f Noise in WFI Data. In Fourier space, the noise is best described by a $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ power spectrum as is shown in the Figure of 1/f Noise Power Law in WFI Data. As a result of the banding structure, this noise introduces biases into observations, wherein spurious structure is added to the signal, preferentially oriented along the detector x direction, and potentially altering the brightness and shape of astronomical sources.

The $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ noise can be reduced using differential readouts and utilizing the reference pixels along the edge of the detector (for more information see the Readout and Reference Pixels section of the Description of the WFI article). However, the $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ noise is not optimally removed using this image space method, as correlations between pixels are not fully treated and the reference output is insufficiently subtracted. Instead, the Improved Roman Reference Correction (IRRC) has been developed to remove this correlated noise by using the fact that in Fourier space, the noise is not correlated and can be well modeled as shown in the Figure of 1/f Noise Power Law in WFI Data. 

The IRRC works on a single read level to calculate a correction to the $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ noise that is then applied to each pixel up-the-ramp. Along the edge of each detector is a set of 4-pixel-wide reference rows and columns that are identical to regular ones except they are not exposed to light and are designed to track changes in bias voltage. Additionally, the Roman WFI detectors have a 33rd amplifier, which is a completely virtual amplifier, containing pixels with a single reference voltage and designed to quantify high-frequency electronic variations. The reference pixels are only sensitive to the electronic noise, and are used to create a model of the correlated $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ noise. 

The main assumption for the IRRC is that the $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ noise is independent of time, and is uncorrelated in Fourier space. Then, using the fact that regular or normal pixels ($//<![CDATA[ \begin{array}{l}n\end{array} //]]>$) are identical to reference pixel when not exposed to light, they can be represented by a linear combination of the reference amplifier ($//<![CDATA[ \begin{array}{l}a\end{array} //]]>$) and the reference columns ($//<![CDATA[ \begin{array}{l}l\end{array} //]]>$ and $//<![CDATA[ \begin{array}{l}r\end{array} //]]>$). In Fourier space, the noise in the regular pixels can therefore be modeled as the linear combination of the noise in the reference pixels, and can be modeled in the equation below: 

where $//<![CDATA[ \begin{array}{l}Fn\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}Fa\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}Fr\end{array} //]]>$, and $//<![CDATA[ \begin{array}{l}Fl\end{array} //]]>$ are the Fourier transforms of the regular, reference amplifier, right, and left pixels, respectively, and $//<![CDATA[ \begin{array}{l}\alpha\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}\zeta\end{array} //]]>$, and $//<![CDATA[ \begin{array}{l}\gamma\end{array} //]]>$ are the coefficients for the reference amplifier, right, and left reference pixels, respectively.  By solving the linear least square relation for the Fourier transform of the normal pixel that minimizes the noise in the reference pixels, a set of optimized frequency dependent coefficients ($//<![CDATA[ \begin{array}{l}\alpha\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}\zeta\end{array} //]]>$, $//<![CDATA[ \begin{array}{l}\gamma\end{array} //]]>$ ) can be determined.  These weights are then used to develop a model of the noise in any observation using the refpix step of exposure_pipeline in romancal , which subtracts the $//<![CDATA[ \begin{array}{l}1/f\end{array} //]]>$ noise model on a per-resultant level.

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References

• "Properties and characteristics of the WFIRST H4RG-10 detectors", Mosby et al. 2020
• "Simple improved reference subtraction for H4RG, H2RG, and H1RG near-infrared array detectors", Rauscher et al. 2022

• "Characterization of Roman Detectors Darks Data acquired with Leach and ACADIA Controllers", Petric et al. 2023

• "Resolving the dark current anomaly in the Nancy Grace Roman Space Telescope focal plane", Mosby et al. 2024
• "Summary of the Nancy Grace Roman Space Telescope flight detector performance", Mosby et al. 2025

• "Application and Characterization of IRRC on Roman/WFI TVAC1 Data", Betti et al. 2024

• "The Statistical Properties of Dark Ramps for the Roman-WFI Detectors", Betti et al. 2025