MOTCamSimulator

Analytical noise model, benchmark plots and an interactive dashboard for imaging CaF MOT fluorescence (606 nm) with seven candidate cameras: Hamamatsu ORCA-Quest 2 and ORCA-R2, Thorlabs Zelux CS165MU, Teledyne Kinetix, Andor iXon Ultra 888, Andor CB2 High Res and CB2 High Speed 7.1F.

Quick start

Open CaF_MOT_Camera_Comparison.nb in Mathematica / Wolfram 14.x. Everything is pre-evaluated; click Enable when asked about dynamic content to activate the dashboard.

Section	What it answers
1 Noise engine	Optics, cloud, camera database, SNR functions
2 Primary benchmark	Integrated SNR vs molecule number for every camera and binning; where each saturates
3 SNR definitions	Peak-pixel vs top-hat vs matched-filter SNR; precision on number and on cloud width
4 Visibility	Molecules needed before the cloud shows in a single raw frame, vs binning
5 Resolution	Object-space pixel size and resolution elements across the cloud, vs binning
6 Dashboard	Interactive synthetic image, cross-section fit and metrics card
7 Thresholds	Table + CSV of molecules for SNR = 3 / 10 per camera, readout mode and binning
8 Tests	The verification suite

Dashboard controls: camera, readout mode, binning (only the bins the camera supports), log10 molecules, scattering rate, exposure, background multiplier, noise seed. The image is one random realisation chosen by the seed — keep it fixed while changing other controls, step it to "take another shot". The metrics card is analytic except the rows marked "from frame" and the fitted width. Sliders update on release.

Files

File	Purpose
CaFCameraNoise.wl	The model: physics, camera database, plots, dashboard and tests, in Wolfram package-cell format. Edit this.
GenerateCaFComparisonNotebook.wls	Builds and evaluates the notebook from the .wl, runs the tests, exports the CSV and figures.
regenerate.sh	Finds wolframscript and runs the generator.
CaF_MOT_Camera_Comparison.nb	Generated notebook — never edit by hand, it is overwritten.
CaF_MOT_Camera_Thresholds.csv, verification/*.png	Produced locally by the generator (thresholds table; every key figure as PNG). Not tracked in git.

Change the physics

All inputs are top-level parameters in CaFCameraNoise.wl, Section 1:

Parameter	Section	Default	Meaning
cloudFWHM	1.2	2.8 mm	measured MOT FWHM (object space); σ, aperture and fields of view derive from it
scatteringRate	1.2	1e6 /s	photons scattered per molecule per second — assumed, replace with the measured value
baselineScatterRate, backgroundMultiplierDefault	1.2	39 /s/px, 4	laser-scatter background per 6.5 µm pixel — unverified
exposureTimeNominal	1.2	20 ms	exposure for all benchmark plots and tables
imagingLensRadius, imagingLensEFL	1.1	20 mm, 28.6 mm	second lens (Comar 29 AF 40); sets the limiting stop and the magnification
viewportClearRadius	1.1	Infinity	set to the viewport semi-diameter if it clips before the lenses
workingPointMolecules	3	1e4	molecule number used in the summary tables

Then regenerate:

./regenerate.sh

(~30 s; equivalent to wolframscript -file GenerateCaFComparisonNotebook.wls, the script also looks inside /Applications/Wolfram.app and /Applications/Mathematica.app if wolframscript is not on your PATH). It rebuilds the notebook, CSV and figures and prints PASS/FAIL for the 41 verification tests; exit code 1 if any fail.

Add a camera

Append an entry to cameraDatabase (Section 1.3). All keys are required:

"Vendor Model (type)" -> <|
   "ShortName" -> "Model", "Type" -> "sCMOS",
   "PixelsX" -> 2048, "PixelsY" -> 2048, "PixelPitch" -> 6.5,     (* um *)
   "QE" -> 0.80,                                                     (* at 606 nm, not the peak *)
   "ReadNoiseRMS" -> 1.0,                                            (* e- rms, primary mode *)
   "ReadNoiseModes" -> <|"Mode name" -> 1.0|>,                       (* every quoted mode *)
   "DarkCurrent" -> 0.1,                                             (* e-/pixel/s at operating temperature *)
   "FullWell" -> 30000,                                              (* e-, only used for saturation markers *)
   "BinningType" -> "Software",                                      (* label only *)
   "HardwareBinLimit" -> 1,      (* 1 = digital binning only, Infinity = on-chip at every bin (CCD/EMCCD), 2 = on-chip 2x2 then digital *)
   "SupportedBins" -> {1, 2, 4, 8},
   "ENF" -> 1.0,                                                     (* Sqrt[2] for EMCCD with gain *)
   "Notes" -> "Where the numbers came from."|>

Read the QE off the vendor's curve at 606 nm — the headline peak is usually at 500–550 nm and can be 10 points higher. Regenerate; the camera appears in every plot, table and the dashboard.

One-off calculations

Get["CaFCameraNoise.wl"];
cam = cameraDatabase["Thorlabs Zelux CS165MU (Compact CMOS)"];

integratedSNRMolecules[cam, 4, 10^4]        (* top-hat SNR, 4x4 bin, 1e4 molecules, nominal conditions *)
peakPixelSNR[cam, 4, 10^4]                  (* single-shot visibility *)
visibilityMolecules[cam, 4, 5]              (* molecules needed for peak-pixel SNR = 5 *)
minimumMolecules[cam, 1, 3]                 (* molecules for integrated SNR = 3 *)
snrEstimators[cam, 1, 10^4]                 (* peak / top-hat / matched-filter SNR, dN/N, dSigma/Sigma *)
noiseFloorBreakdown[cam, 1, 0.02, 4., 4.]    (* read vs scatter vs dark variance, dominant term *)

Every function has a long form with explicit exposure (s), background multiplier, read noise (e⁻) and scattering rate (/s); see Sections 1.4–1.5 of the .wl.

How the model works

• Signal: nSig = nMol × scatteringRate × tExp × etaGeom × T × fAperture photons arrive inside the 2σ integration aperture (86.5 % of the cloud's fluorescence); signal electrons are nSig × QE. All axes are in molecules (10 to 10⁶).
• Optics: LA1401-A collector (2", EFL 59.8 mm) at its BFL of 49.1 mm, Comar 29 AF 40 imaging lens (40 mm, EFL 28.6 mm). The Comar is the limiting stop, giving a geometric efficiency of 3.69 % (5.59 % would be the unvignetted 2" lens). Magnification M = f2/f1 = 0.478: a pixel of pitch p samples p/M at the MOT. Cloud geometry is kept in object space; background and dark electrons use the physical sensor pixel area and do not scale with M.
• Noise per superpixel: shot noise on signal, background and dark electrons, plus read noise sigmaRead × b / Min[b, HardwareBinLimit]; a factor 2 on all signal-independent terms accounts for subtracting an identical off-target reference. Software binning sums b² independent reads, so it leaves the aperture-integrated read noise unchanged — only on-chip binning lowers it. It does raise the peak-pixel SNR in proportion to b, which is what matters for seeing the cloud in a single shot.
• Three SNRs: peak-pixel (visibility), top-hat over the 2σ aperture (the conventional integrated SNR), and the matched filter (inverse-variance, profile-weighted), whose variance is the Cramér–Rao bound on the molecule number. δN/N and δσ/σ follow from the Fisher information.
• Regimes: the log-log slope is 1 where a signal-independent term (read noise, laser scatter or dark current) dominates and ½ once signal shot noise dominates; the regime table in Section 2 says which term sets the floor for each camera. Filled markers show where the peak superpixel reaches full well.