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REVIEW 3 major objections 4 minor 20 references

Skipper CCD readout time optimization for astronomical applications

T0 review · 3 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read For any target readout noise, a Skipper CCD has a uniquely fastest combination of integration time and sample count—and that optimum can be predicted from the sensor's measured noise spectrum rather than tuned by hand.

desk verdict A genuinely useful engineering model for Skipper readout-time optimization, with a validated central prediction, but the t_Skip scaling claim rests on simulation outside the model's validated range. read the letter →

arxiv 2607.20126 v1 pith:FBAR5MAB submitted 2026-07-22 astro-ph.IM physics.ins-det

Johannes Wüthrich , Andrin Fazan , Sean MacBride , Marcelle Soares-Santos This is my paper
classification astro-ph.IMphysics.ins-det PACS 95.55.Aq
keywords SkipperCCDreadoutnoisetimecorrelateddoublesamplingpowerspectraldensitymulti-samplingcharge-transferastronomicaldetectors
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper shows that the age-old trade-off in Skipper CCDs—more samples mean lower noise but longer readout—has a mathematically predictable sweet spot. The authors model the readout chain as a transfer function acting on the sensor's measured noise power spectral density, and demonstrate that for any target readout noise there is a combination of correlated-double-sampling integration time and number of skipper samples that minimizes total readout time. That optimum, they argue, sits where the integration time becomes comparable to the per-sample charge-transfer time, and it barely moves as the target noise changes. Because readout time directly eats into telescope exposure time, being able to predict this optimum from a noise spectrum rather than measuring it per device is what makes Skipper CCDs practical for astronomy.

What carries the argument

The mechanism is a frequency-domain transfer function that combines correlated double sampling with the averaging of repeated skipper samples. CDS acts as a filter whose magnitude is 2 sin(π t_i f) sin(π(t_i + t_Skip) f)/(π t_i f); repeated samples add narrow-band rejection around that lobe. Integrating the squared transfer function against the one-sided noise PSD—white noise plus a 1/f term with fitted corner frequency and exponent, per Eq. (6)—yields the readout noise for any (t_i, N_Skip). The workhorse insight is that increasing t_i shifts the transfer-function lobe to lower frequencies and therefore admits more 1/f noise, while increasing N_Skip narrows the lobe without shifting it, whi

What would settle it

Measure the readout noise of a Skipper CCD across t_i and N_Skip while deliberately injecting a narrowband noise tone at, say, 300 kHz—inside the regime where the assumed PSD model is wrong—and check whether the predicted optimal (t_i, N_Skip) from Eq. (6) still matches the measured minimum readout time. A mismatch would show the simple PSD fit is not sufficient to predict the optimum on all devices.

Watch

Extended reading notes

Core claim

The central claim is that the readout noise of a Skipper CCD is a calculable function of two operational parameters—CDS integration time and the number of nondestructive samples—through a transfer-function model built on the sensor's intrinsic noise PSD. Fitting the model to short noise measurements yields a PSD per readout channel, and evaluating the model at many parameter combinations then produces readout-noise contours in the (samples, readout-time) plane. Each contour for a fixed target noise has a clear minimum readout time, with the minimum occurring near a single integration time that depends mainly on the per-sample charge-transfer time and not on the target noise. This explains a

Load-bearing premise

The paper's predictions stand only if a single white-plus-1/f noise model with one corner frequency and one exponent, fitted from a few short measurements, accurately represents the sensor's noise spectrum across the full range of integration times and sample counts; the authors note the real spectrum deviates at high frequency due to pickup noise.

Editorial extensions

If this is right

  • Astronomers can now pick (t_i, N_Skip) for a target readout noise from a sensor's measured PSD, without time-consuming empirical scans.
  • The optimal integration time is essentially independent of the target noise; what changes with target noise is only the number of samples, so the operating-point search decouples into two simple steps.
  • Minimizing the per-sample charge-transfer time t_Skip both shortens readout and shifts the optimum to shorter integration times, making dedicated fast-clock readout electronics more valuable than further noise optimization in the amplifier path.
  • For t_Skip → 0 the optimum disappears: readout time decreases asymptotically as t_i is shortened and N_Skip raised, implying the ultimate speed limit of Skipper readout is set by charge-transfer physics, not by noise filtering.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extension: if the same PSD-based optimization transfers to other multi-sampling detectors (e.g., multi-amplifier sensing CCDs), the design rule 'sample many times, integrate briefly' may generalize to all readout architectures where averaging suppresses white noise without adding 1/f noise.
  • Extension: a directly testable prediction is that the optimum integration time scales with t_Skip; measuring readout-time contours on two Skipper CCDs whose t_Skip differs by a known factor would confirm this scaling.
  • Extension: for future fast-readout systems, the model suggests that pushing t_Skip below roughly a microsecond—while watching for secondary effects like clock-induced charge and charge-transfer inefficiency—is a higher-leverage engineering target than reducing the amplifier's white noise floor.
  • Extension: the model's success despite unmodeled pickup noise above 500 kHz hints that the 1/f-dominated band below 100 kHz largely sets the optimum, but this needs confirmation on sensors with different pickup profiles.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper develops an analytical model for Skipper CCD readout noise as a function of the CDS integration time t_i and the number of skipper samples N_Skip, using the CDS transfer function that includes the finite per-sample charge-transfer time t_Skip and a white-plus-1/f noise PSD model. The PSD parameters are fitted per quadrant from measured readout noise versus t_i for N_Skip = 1, 2, 3, 5 on an Oscura Microchip Skipper CCD. The model is then used to compute readout-time isocontours for target noise levels, revealing an optimal t_i that minimizes the readout time for each target noise. The predictions are compared to direct measurements for t_i from 2 to 20 microseconds and N_Skip up to 100, reporting agreement within 20%. The paper further simulates the effect of shorter t_Skip values, concluding that the optimum shifts to shorter t_i and that minimizing t_Skip is key to fast Skipper readout.

Significance. The model is physically well-founded and the explicit inclusion of t_Skip in the CDS transfer function is a useful correction for Skipper CCDs where t_Skip is not negligible. The experimental validation on a real device is a strength, as is the use of a clock-accurate readout-time model. If the framework is confirmed on other devices, it would allow readout optimization from a measured PSD rather than from exhaustive empirical scans. However, the quantitative prediction of the t_Skip-scaling relies on a simulation in a regime where the PSD model is admitted to be inaccurate, and the validation lacks uncertainty quantification, so the generality of the central claims is not yet fully established.

major comments (3)
  1. [§4, Fig. 4] The central conclusion that reducing t_Skip shifts the optimum and is key to fast readout is supported quantitatively only by simulations with t_Skip ≈ 0.6 μs and 0.0 μs, using t_i values as low as 0.7 μs. The experimental validation in §3 is limited to t_i ≥ 2 μs, and the PSD model of Eq. (5) is stated to deviate from the true PSD above 500 kHz because of pickup noise. For t_i = 0.7 μs, the CDS passband extends well beyond 500 kHz, so the predicted optimum and the magnitude of the readout-time reduction in Fig. 4 may be artifacts of the omitted pickup component. This is load-bearing for the main claim. Please either validate the model at short t_i, incorporate the measured pickup component into the PSD model, or explicitly restrict the claim to the qualitative behavior.
  2. [§3, Fig. 2] The validation is reported as agreement 'to within 20%' without any uncertainty quantification. The measured isocontours are derived from noise measurements with no error bars, and the fitted PSD parameters (S_white, f_c, α) are presented without uncertainties. Since the central claim is that the optimal operating point can be predicted from the PSD, the precision of the predicted optimum (the t_i at which readout time is minimal) must be quantified. Please report uncertainties on the fitted parameters and measured isocontours, and propagate them to the predicted optimum.
  3. [§4, after Fig. 3] The statement 'Since both noise components scale as 1/√N_Skip' is used to conclude that the optimal t_i is essentially independent of the target noise. This scaling is not derived from Eq. (6) for the 1/f component; the Skipper samples are correlated for low-frequency noise, and the effective scaling with N_Skip depends on α and on the CDS transfer function. Figure 3b is suggestive but covers only the fitted PSD of one quadrant. Please provide a derivation or a numerical check over the relevant range of α and f_c, or qualify the claim as approximate for the measured device. As written, this unsupported step weakens the generality of the 'optimum independent of target noise' conclusion.
minor comments (4)
  1. [Fig. 1a and Fig. 4] Units are missing the micro sign: 'Integration Time [ s]' should be 'µs', and labels such as 'tSkip 0.6 s' and 'ti: 0.7 s' should read '0.6 µs' and '0.7 µs'.
  2. [Eq. (1)] The factor 2 in the t_Skip and t_i terms is not explained. State explicitly that it accounts for shifting the charge into and out of the sense node and for the baseline plus signal integrations.
  3. [Notation throughout] The number of skipper samples is written inconsistently as N_Skip in the text and NSkip in equations and figures. Please use a single notation.
  4. [Fig. 3 caption] The phrase 'the same is not true for the 1/f component' is ambiguous. Clarify whether the 1/f noise component depends on the total integration time N_Skip·t_i or on N_Skip separately.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the optimum emerges from a calibrated noise model and is validated on independent N_Skip data.

full rationale

The paper's derivation is not circular. It builds a transfer-function noise model (Eqs. 2–6), fits the PSD shape parameters (S_white, f_c, α) to measured readout noise vs. CDS integration time for N_Skip ∈ {1,2,3,5} (Sec. 3, Fig. 1), and then uses that fitted model to compute readout-noise isocontours and locate the readout-time minimum. The fitted parameters are inputs, but the predicted optimum is not a direct re-fit of the optimum: it emerges from the combination of Eq. 1 (readout time), Eq. 6 (noise integral), and the assumed PSD. The model is tested against independently measured isocontours at N_Skip up to 100, with agreement to within 20% (Sec. 3, Fig. 2). The conclusion that the optimum is set by t_Skip is a consequence of the time-budget equation and the transfer function, not a restatement of an input. The t_Skip→0 simulation in Fig. 4 is an extrapolation, and the sub-µs regime is outside the validated t_i range and the PSD model's known validity (the paper itself notes pickup >500 kHz in Sec. 3); that is a correctness/robustness concern, not circularity. The wording 'predicted rather than determined experimentally' overstates the independence of the PSD calibration, but the central result is not forced by definition or by self-citation.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central prediction rests on a fitted empirical PSD rather than a fully parameter-free first-principles derivation. The main axioms are standard signal-processing and noise models; no new physical entities are introduced.

free parameters (3)
  • S_white (white noise PSD level) per quadrant = Q1: 11.2 m e/√Hz; Q2: 7.8; Q3: 8.0; Q4: 7.6 (from Fig. 1b)
    Fitted to measured readout noise σ(t_i) for N_Skip∈{1,2,3,5}; the entire readout-time prediction uses this fitted noise floor.
  • f_c (1/f corner frequency) per quadrant = Q1: 7.0 kHz; Q2: 19.7 kHz; Q3: 19.7 kHz; Q4: 23.2 kHz (from Fig. 1b)
    Fitted as part of the PSD model; determines where 1/f noise starts dominating and shapes the optimum t_i.
  • α (1/f exponent) per quadrant = Q1: 2.1; Q2: 1.7; Q3: 1.7; Q4: 1.6 (from Fig. 1b)
    Fitted as part of the PSD model; changes the frequency weighting of 1/f noise and the optimal integration time.
assumptions (5)
  • standard math Wiener–Khinchin theorem
    Used in Eq. (6) to calculate readout noise as integral over the product of transfer function magnitude-squared and the one-sided noise PSD.
  • domain assumption Noise is stationary and CDS is a linear time-invariant filter
    Section 2: the signal is decomposed into s_charge(t) + s_noise(t), with s_noise(t) stationary, allowing the CDS transfer function formalism.
  • domain assumption Noise PSD has the form S(f) = S_white (1 + (f_c/f)^α)
    Eq. (5) — a standard empirical model for FET noise in CCDs; the authors acknowledge the real PSD deviates at >500 kHz due to pickup, so predictions rest on this approximate shape.
  • domain assumption Both white and 1/f noise components scale as 1/sqrt(N_Skip)
    Section 4: used to argue that the optimal t_i is independent of the target noise. For correlated 1/f noise this scaling is only approximate; the quantitative model uses the full transfer function.
  • domain assumption Readout time decomposes as Eq. (1): total time is sum of row shift, serial shift, per-sample sense-register shifts and CDS integrations, and drain time
    Standard CCD timing model; assumes per-sample overhead (charge transfer in/out) adds 2 N_Skip t_Skip per pixel.

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Cite this review

Pith. "Pith review of Skipper CCD readout time optimization for astronomical applications." pith.science (2026). https://pith.science/paper/FBAR5MAB

@misc{pith2026260720126,
  author       = {Pith},
  title        = {Pith review of: Skipper CCD readout time optimization for astronomical applications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FBAR5MAB}},
  note         = {Machine review of arXiv:2607.20126}
}
read the original abstract

Skipper CCDs enable the reduction of CCD readout noise by non-destructively measuring the individual pixel charge packets multiple times. This readout noise reduction has attracted considerable interest in the astronomical community, particularly in spectroscopic surveys targeting faint objects at high redshifts. However, noise reduction via repetitive sampling leads to an unavoidable increase in readout time, often to prohibitive levels. To enable their use in astronomical applications, the optimal operation regime of Skipper CCDs must be determined, balancing noise improvement and readout time. Traditionally, such optimization has been carried out empirically for each CCD architecture. We present a general optimization scheme derived from first principles and experimentally verified in the laboratory using a Skipper CCD as used by the Oscura experiment. While the existence of an optimal combination of correlated double-sampling integration time and number of Skipper samples for reaching a given readout noise level at minimal readout time has previously been observed empirically, we model this trade-off analytically based on the intrinsic noise power spectral density of the sensor, allowing the optimal operating point to be predicted rather than determined experimentally for each architecture. We further show that the location of this optimum is governed by the per-sample charge-transfer time, whose minimization is therefore key to achieving fast Skipper CCD readout.

Figures

Figures reproduced from arXiv: 2607.20126 by the authors.

Figure 1
Figure 1. Extraction of the underlying noise PSD by fitting the noise model ( [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Simulated (solid lines) and measured (dotted lines) readout noise isocontours for the Oscura Microchip [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Individual readout noise components (white noise and [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Simulated readout time and readout noise for two cases with shorter [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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