Scope and evidence
A nightside optical photometer at 550 km can be studied with explicit transport and counting models. Useful orbital yield and reliable source-depth classification still require measured source populations, realistic cloud constraints and a characterised receiver.
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Emitted photons → directional atmospheric delivery → entrance aperture → optics → registered photoelectrons → accepted event.
Cloud escape, nadir radiance and detector counts are different quantities. An observed spacecraft fluence already includes atmospheric delivery; applying cloud attenuation again would count that loss twice.
Finding a 3 ms pulse does not guarantee enough photons in its first 30 µs to estimate the rise. A useful accepted event also needs a meaningful 777 nm upper limit, receiver linearity and an association with the intended source population.
Initial question / A1
A newly executed scalar Monte Carlo model follows photons in a finite cloud and estimates their arrival at a nadir observer. Realistic tabulated ice angular scattering and a matched-mean HG approximation are compared under the same declared geometry.
Total and overlying optical depths are distinct. At/above cloud top, overlying cloud depth is zero while reflection from below can still change the signal. Error bars: batch Monte Carlo standard error where available.
Delay is relative to the straight source–observer light flight. The analytic unscattered contribution is a point mass at zero; a histogram bin is not its physical width. Time overflow and photon truncation are reported, not silently normalised away.
Input: exp(−t/3 ms) × [1−exp(−t/τr)] for t≥0, calibrated to the selected intrinsic 10–90% rise and unit peak. Each output curve is normalised to its own peak to compare shape; it cannot show gain or attenuation. Time excludes the straight source–observer flight. This is a hypothetical source, not a recovered intrinsic waveform of the published events. Mean analogue convolution does not establish a Poisson likelihood for filtered samples.
The earlier spherical-particle/HG runs are retained for traceability. Their assumed emitted pulse is not a measured intrinsic waveform, and their geometry differs from the new finite-cloud model.
A2 / C7–9
The measured waveform combines source emission, photon travel paths and the receiver. The new classifier compares received-waveform shapes; it does not validate a real cloud-depth label.
Hypothetical linear rise to a plateau. The optional one-pole response is a deterministic analogue mean illustration; it is not used to claim independent-Poisson statistics after analogue filtering.
Exact integration over each sampling bin; reconstructed 10–90% crossings use interpolation at bin midpoints. These curves omit photon noise and real pulse-shape variability.
Independent simulation trials with the declared fitting/selection rules. Intervals quantify Monte Carlo sampling, not real event-population uncertainty. A low error among accepted events must be read together with its acceptance fraction.
B4–6 / C8 / E16–17 / G21
*Illustrative union-bound allocation over 50,000 starts/s × 3 window families × 86,400 observing seconds. It does not model particle bursts, changing backgrounds or the operational trigger.
Exact Poisson critical counts and mean signal for 95% detection probability. Total response is assumed linear with independent counts. Source fluence is at the aperture, after propagation. This is not a mission completeness curve.
Assumed admitted 337 nm band brightness and projected field filling. No Kp or lunar-phase forecast is implied. Subtracting a background mean does not remove the random photon arrivals.
A red nondetection is an upper confidence limit. Classifying an event additionally requires a validated thermal-alternative red/UV bound, matching field/time acceptance and a responsive unsaturated red receiver.
C7–11 / D12–15 / F18–20
Effective-index coating approximation. Telecentricity controls chief rays but leaves a finite ray cone. The area bound assumes lossless passive optics in air; it is not a lens prescription.
Not a reconstructed nitrogen spectrum or a flight-filter optimum. Source width, coating model and peak transmission are assumed. The earlier molecular-strength/population mapping remains unvalidated and is not promoted into the design.
The horizontal ratio is already weighted by the full scene spectrum and detector response. Required OD applies over that leak range. A vendor OD specification over a short UV interval gives no automatic visible/NIR guarantee.
NEP = Eγ √(2 F Rdark) / η, in W Hz⁻½, for an ideal primary-count shot-noise model with a one-sided spectrum. No sky, amplifier/read noise, afterpulses or radiation forecast. The curves are assumptions, not PMT/SiPM/CMOS/APD specifications.
Device defects, temperature, gain, particle interactions and optical contamination affect different parts of the receiver. A supplier name, a hermetic package or an unrelated approval is not full flight qualification. A calibration LED alone does not separate LED ageing, optical loss and photon-efficiency drift.
Controlled mathematical tests
Vacuum above a Lambert surface; no cloud residence time. Rise is 10–90% of the final plateau of an indefinitely sustained ramp-to-plateau input. The zero-height case is a limiting kernel. These results are not fits to observed NBE rise populations.
Semi-infinite homogeneous diffusion with uniform absorption. The same L²/D can give the same PDE response at different depths. Parabolic diffusion has nonphysical pre-flight tails; unflagged cases are not automatically valid early-time transport.
Quasi-static mean of a hypothetical 17 ns nonparalyzable counter. This is an uncorrected mean-response diagnostic, not a model of corrected MMIA data or a stochastic noise-restoration method.
Normalised bright-enough population weights above a 95%-power mean-count cut. Slopes are assumptions; this is neither a full detection-probability integral nor an orbital event rate. More field also admits more background.
Complete original scope
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Established principles, conditional computations, measured heritage and mission validation are different states. The initial transmission question was unnumbered; original question labels are retained.
Reproducibility and provenance
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Versioned deliverables
Standalone corrected assessment of the full original scope, with equations, results, uncertainties, remaining gaps and detailed sources.
Open technical PDFFull plain-language explanation of the measurement chain, new calculations, corrections and remaining empirical requirements.
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