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arxiv: 2604.26114 · v1 · submitted 2026-04-28 · 🌌 astro-ph.IM

Recognition: unknown

Charge diffusion and modulation transfer function in a Nancy Grace Roman Space Telescope detector

Emily Macbeth , Katherine Laliotis , Christopher M. Hirata , Christopher Merchant
Authors on Pith no claims yet

Pith reviewed 2026-05-07 14:12 UTC · model grok-4.3

classification 🌌 astro-ph.IM
keywords charge diffusionmodulation transfer functionRoman Space Telescopeinfrared detectorsweak lensinghyperbolic secantlaser speckleMTF
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The pith

Charge diffusion in a Roman Space Telescope detector follows a hyperbolic secant profile rather than Gaussian, with a per-axis width of 0.328 pixels and no detectable wavelength dependence from 850 to 2000 nm.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures the modulation transfer function of charge diffusion in a flight-lot Roman infrared detector by illuminating it with a laser speckle pattern at multiple near-infrared wavelengths. Several functional forms are tested against the data, including Gaussian and hyperbolic secant profiles as well as a more general drift-diffusion model. The hyperbolic secant form fits the observations acceptably on its own and is strongly preferred over the Gaussian, yielding a consistent width across the tested band. This characterization supplies a concrete correction term that can be folded into image simulations and data pipelines for weak gravitational lensing analyses.

Core claim

Laser speckle data from a Roman detector are used to extract the modulation transfer function contribution from charge diffusion. Fits show that a hyperbolic secant profile describes the measurements with a standard deviation of 0.3279 pixels per axis and no extra free parameter, while a Gaussian profile is disfavored; the general drift-diffusion model collapses to the sech case. The width shows no measurable change over 850–2000 nm, and the resulting model is inserted into mission simulations to guide weak lensing survey strategy and pipeline development.

What carries the argument

Hyperbolic secant (sech) charge diffusion profile extracted from speckle-pattern MTF data, which captures the spatial distribution of charge spread in the detector pixels.

If this is right

  • The sech model can be adopted directly in Roman image simulations and data processing pipelines without additional free parameters.
  • Weak lensing shear measurements can incorporate this fixed diffusion scale to reduce one source of systematic error in galaxy shape estimates.
  • Detector modeling across the Roman near-infrared band is simplified because diffusion shows no wavelength variation between 850 and 2000 nm.
  • Survey strategy and exposure-time calculations for the mission can use the reported MTF to set requirements on pixel sampling and dithering.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The physical transport process in these detectors may intrinsically produce sech-like tails rather than Gaussian wings, which could be checked by comparing to detailed carrier transport simulations.
  • Similar infrared arrays on other space telescopes might be re-analyzed with a sech template to see whether the same functional form emerges.
  • Reducing non-linearity residuals in future calibration campaigns would shrink the dominant systematic floor and allow tighter constraints on the diffusion width.
  • On-orbit star or galaxy images from Roman could be stacked to test whether the ground-measured sech width reproduces the observed point-spread function core.

Load-bearing premise

The laser speckle pattern isolates charge diffusion in the MTF measurement without significant contamination from other detector effects such as non-linearities.

What would settle it

An independent MTF measurement on the same detector using a sharp point-source or knife-edge target that yields either a statistically better Gaussian fit or a diffusion width differing by more than the reported systematic uncertainty would falsify the sech preference.

Figures

Figures reproduced from arXiv: 2604.26114 by Christopher Merchant, Christopher M. Hirata, Emily Macbeth, Katherine Laliotis.

Figure 1
Figure 1. Figure 1: The setup for this experiment, at the Detec￾tor Characterization Laboratory at NASA Goddard Space Flight Center. Fourier modes of high frequencies are indistinguishable from low frequencies. Using the double-slit, for which this issue is not present due to discrete peaks in Fourier space because of slit separation, avoids further compli￾cations with measurements. Aperture Slit spacing Slit width d (mm) w (… view at source ↗
Figure 2
Figure 2. Figure 2: These panels show a 512 × 512 pixel portion of the entire array’s display. Each panel is an individual frame of the speckle pattern realizations over time, F1 being the earliest and F5 the latest. The signal, measured in data numbers (DN), builds up between each frame and the interference fringes tend towards zero. The large-scale structure is consistent between each frame, with the patterns becoming more … view at source ↗
Figure 3
Figure 3. Figure 3: These panels show the same region of the detector as represented in view at source ↗
Figure 4
Figure 4. Figure 4: Visual representation of the autocorrelation of two top hat functions. The center triangle is centered at a spatial frequency of u = 0 cyc/pix. The outer two triangles are the same width and about half the height of the center triangle. They are centered at the spatial frequencies of the fringes of the pattern. periment. The feature of the power spectrum centered at a spatial frequency of zero is unsuppres… view at source ↗
Figure 5
Figure 5. Figure 5: Examples of the 1D power spectra, in log scale, of the speckle data in three aperture arrangements, AP3, AP7, and AP10. For each aperture, we show 5 panels ranging from the bluest wavelength (850 nm, top) to the reddest (2000 nm, bottom). Within each panel, there are 64 rows of data indicating the 512 × 512 subregions in the detector array. The plot ranges from u = 0 to u = 1 cyc/pix on the horizontal axis… view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of the binning of the MTF2 values and the spatial frequencies, u, using the original fitting method, measured in the 850 nm wavelength. The top row represents the MTF2 values, the bottom row represents the fitted spatial frequencies, and each column represents a different aperture arrangement (AP1 through AP12). Each sub-panel shows results from an 8 × 8 grid of regions on the detector array,… view at source ↗
Figure 7
Figure 7. Figure 7: Contour plots of χ 2 for a range of values for the parameters h and ξ in the general model for F1-2. The left plot showcases a complete view of the valley centered at a value of ξ = 0. The right plot is a zoomed in and rescaled view, focused on the genuine minimum χ 2 value. These plots were created using the data from the first two frames of the experiment. valley seen in the left plot of view at source ↗
Figure 8
Figure 8. Figure 8: MTF measurements acquired from SCA 21536 using the data from the first two frames of the experiment. Solid circles show the fit of the MTF and spatial frequency, while open circles indicate the points where a forced fit was used. The general charge diffusion model (this work) is shown as a solid line. Special case models and the model of the MTF without a contribution from charge diffusion are shown as var… view at source ↗
Figure 9
Figure 9. Figure 9: Dependence of the width of the diffusion￾dominated case of charge diffusion on the wavelength. All five experimental wavelengths are used, and a line was fit through the data. The shaded regions display the error of the fit, with the lighter region within 2σ and the darker within 1σ. The slope of the line is consistent with zero within 2σ, indicating a lack of dependence on wavelength. will seek to charact… view at source ↗
Figure 10
Figure 10. Figure 10: The geometry and symbols used in Appendix A (not to scale). The diffusing inner surface of the integrating sphere is divided into pixels j. Light from each pixel passes through the aperture plane, and then on to the detector plane. The light arriving at the aperture can be treated as a superposition of plane waves. If there is a single incident plane wave E(r) = E0e iknˆ·r (where nˆ is the direction of pr… view at source ↗
Figure 11
Figure 11. Figure 11: The solution domain of the differential equation, Eq. (B35). The illuminated surface (and anti-reflection coating) are at top, and the p − n junctions at which charge is collected are at the bottom. Then we have a differential equation for the number density of holes in the detector: 0 = ∂ ∂z  µ dΦ dz n˜ + D ∂n˜ ∂z  − 4π 2 view at source ↗
Figure 13
Figure 13. Figure 13: MTF data from frames 1-5 used to fit the gen￾eral model, likely including the most significant nonlinear ef￾fects. The closed points were found using the original fit, while the open points are the forced fit to the spatial frequencies. The MTF model without charge diffusion and the special case models are displayed. The residuals of the robust model are plotted at the bottom, indicating periodic behavior… view at source ↗
Figure 14
Figure 14. Figure 14: Measured and predicted MTF for aperture 7 in the 1550 nm in 64 regions. The values are plotted with respect to the values of the distortion matrix to indicate how the MTF varies with spatial frequency. The predicted MTF has a slope of -0.377 ± 0.000095, with an intercept of 1.15 ± 0.000094. The slope of the measured MTF is -0.46 ±0.10 with an intercept of 1.22 ± 0.10. The measured slope and intercept is c… view at source ↗
read the original abstract

The Nancy Grace Roman Space Telescope (Roman) is an observatory motivated by the search to understand dark energy, exoplanets, and general astrophysics. Roman will bring unprecedented amounts of precision to weak gravitational lensing measurements, which necessitates an improved understanding of instrumental signatures in star and galaxy images. One feature is the modulation transfer function (MTF), which includes contributions from charge diffusion in Roman's infrared detector arrays. As part of the detector characterization effort, a detector from the flight lots (but ultimately not selected for flight) was illuminated with a laser speckle pattern. We present an analysis of the laser speckle data, including MTF measurements in several wavelengths. We fit several models for the charge diffusion profile, including: (i) a Gaussian profile; (ii) a hyperbolic secant (sech) profile; and (iii) a general drift-diffusion model that includes the Gaussian and sech as limiting cases. We find that the sech model produces an acceptable fit with no need for the additional parameter and is strongly preferred over the Gaussian. The standard deviation per axis of the sech profile is $0.3279^{+0.0043}_{-0.0042}$(stat)$\pm0.0093$(sys) pixels, with the systematic error dominated by non-linearities. We find no detectable wavelength dependence over the range from 850--2000 nm. The model informs survey strategy for weak lensing measurements and has been included in simulations used to develop the data processing pipelines for the Roman mission.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript analyzes laser speckle data from a Roman Space Telescope H4RG detector to measure the MTF arising from charge diffusion. Three models are fitted to the data: a Gaussian profile, a sech profile, and a general drift-diffusion model that encompasses both as limits. The sech model is reported to provide an acceptable fit with no requirement for the extra parameter, and is strongly preferred over the Gaussian; the fitted per-axis standard deviation is 0.3279^{+0.0043}_{-0.0042}(stat) ± 0.0093(sys) pixels, with systematics dominated by non-linearities. No wavelength dependence is detected over 850–2000 nm. The resulting model is incorporated into Roman weak-lensing simulations.

Significance. If the laser-speckle MTF measurements isolate charge diffusion to the stated precision, the work supplies a concrete, empirically calibrated diffusion kernel that directly improves the fidelity of Roman weak-lensing image simulations and pipeline development. The explicit comparison of three nested physical models and the separation of statistical and systematic uncertainties are strengths; the result is immediately usable for survey-strategy studies.

major comments (3)
  1. [§4 (Model comparison and fitting)] §4 (Model comparison and fitting): The claim that the sech model is 'strongly preferred' and that the general drift-diffusion model requires no additional parameter rests on a model-selection statistic whose sensitivity to the dominant systematic (non-linearities) is not quantified. A test in which the non-linearity correction parameters are varied within their uncertainty and the resulting change in the selection metric (AIC, BIC, or likelihood ratio) is reported would directly address whether the preference is robust.
  2. [§3.2 (MTF extraction from speckle power spectra)] §3.2 (MTF extraction from speckle power spectra): The central assumption that the measured power spectrum reflects only charge diffusion is load-bearing for both the model preference and the quoted width. The manuscript acknowledges that non-linearities dominate the systematic error budget, yet no explicit propagation of residual non-linearity residuals into the shape of the MTF (or into the fitted diffusion width) is presented. A quantitative bound on the bias this could induce in the sech-versus-Gaussian comparison is required.
  3. [Results section (wavelength dependence)] Results section (wavelength dependence): The statement of 'no detectable wavelength dependence' is reported without the per-band fit values, the number of independent wavelengths, or the statistical power of the test once the systematic floor is included. These details are needed to evaluate whether the null result is limited by the non-linearity uncertainty rather than by the data.
minor comments (2)
  1. [Abstract] Abstract: the numerical result is clearly stated, but the units 'pixels' should be attached explicitly to the quoted standard deviation for immediate readability.
  2. [Figure captions] Figure captions (e.g., those showing MTF curves and residuals): axis labels and legend entries should be enlarged or clarified so that the Gaussian versus sech comparison is legible in print.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful and detailed review. The comments highlight important aspects of robustness in our model selection and uncertainty analysis, and we will revise the manuscript to incorporate additional quantitative tests and details as outlined below.

read point-by-point responses

  1. Referee: The claim that the sech model is 'strongly preferred' and that the general drift-diffusion model requires no additional parameter rests on a model-selection statistic whose sensitivity to the dominant systematic (non-linearities) is not quantified. A test in which the non-linearity correction parameters are varied within their uncertainty and the resulting change in the selection metric (AIC, BIC, or likelihood ratio) is reported would directly address whether the preference is robust.

    Authors: We agree that demonstrating the robustness of the model preference against variations in the non-linearity correction is valuable. In the revised manuscript, we will add the suggested test to §4: the non-linearity parameters will be varied within their uncertainties, the power spectra re-derived, and the AIC, BIC, and likelihood ratios recomputed for the Gaussian, sech, and drift-diffusion models. This will confirm whether the strong preference for the sech model persists. revision: yes

  2. Referee: The central assumption that the measured power spectrum reflects only charge diffusion is load-bearing for both the model preference and the quoted width. The manuscript acknowledges that non-linearities dominate the systematic error budget, yet no explicit propagation of residual non-linearity residuals into the shape of the MTF (or into the fitted diffusion width) is presented. A quantitative bound on the bias this could induce in the sech-versus-Gaussian comparison is required.

    Authors: We acknowledge that an explicit bound on bias from residual non-linearities in the MTF shape and model comparison would strengthen the presentation. We will add to §3.2 a quantitative estimate obtained by injecting simulated residual non-linearity effects (at the level of the systematic floor) into the power spectra, refitting the models, and reporting the induced shift in the sech-versus-Gaussian likelihood ratio and fitted width. This bound will be included in the revised text. revision: yes

  3. Referee: The statement of 'no detectable wavelength dependence' is reported without the per-band fit values, the number of independent wavelengths, or the statistical power of the test once the systematic floor is included. These details are needed to evaluate whether the null result is limited by the non-linearity uncertainty rather than by the data.

    Authors: We will expand the Results section to include the per-band fitted diffusion widths (with uncertainties), the number of independent wavelengths (eight bands spanning 850–2000 nm), and a calculation of the statistical power of the wavelength-dependence test when the systematic floor is folded in. This will clarify that the null result is not limited by the non-linearity uncertainty. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central result is direct empirical fit to external laser speckle MTF data.

full rationale

The paper illuminates a Roman detector with laser speckle patterns, measures the resulting MTF at multiple wavelengths, and performs least-squares fits of three charge-diffusion models (Gaussian, sech, and a general drift-diffusion model whose limiting cases recover the first two) to those data. The reported sech width, its statistical and systematic uncertainties, and the model-preference conclusion are all direct outputs of this fit; no equation, self-citation, or parameter-renaming step reduces the final numbers to quantities already fitted or assumed inside the same analysis. Systematic error is explicitly traced to detector non-linearities rather than absorbed into the functional form, and the absence of wavelength dependence is likewise a direct observational result. The derivation chain is therefore self-contained against independent external measurements.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The measurement rests on the domain assumption that charge diffusion is adequately described by one of the three tested functional forms and that the speckle data cleanly isolates this effect; the reported width is obtained by fitting rather than derived from first principles.

free parameters (1)
  • sech profile standard deviation = 0.3279 pixels
    Fitted directly to the observed MTF from speckle data to quantify the charge diffusion width.
axioms (1)
  • domain assumption Charge diffusion in the detector can be represented by Gaussian, sech, or drift-diffusion profiles
    Invoked when comparing the three models to the speckle MTF data.

pith-pipeline@v0.9.0 · 5585 in / 1425 out tokens · 68671 ms · 2026-05-07T14:12:40.044276+00:00 · methodology

discussion (0)

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