Bragg integration: a CCD rotation sweep's sigmas at the measured gain, intensities in photons

The pre-scan measures the gain of an SMV/marCCD detector (background variance per unit mean) but the
integrator used it only for the background clip: sigma, var_bkg, the strong-spot flag (I/sigma >= 5)
and the profile-vs-box-sum guard (10 box sigmas) all treated one ADU as one photon, so on a Saturn
(g 4.7-5.8) the guard sat at ~4.5 true sigma. The new BraggIntegrationSettings::PixelGain (set by
rugnux from the same measurement, rotation only, at max(1, g)) takes every variance the engine forms
at the gain, and Finalize converts I, sigma, bkg and var_bkg to photons, which is what the merge's
variance model (var_bkg + I) assumes. CPU and CUDA engines; Metal runs the CPU code for this. Gain 1
(every photon-counting input, ADSC/marCCD whose measured ratio is below 1, and stills) is bit-identical.

Battery --only, 12 open-arm CCD/background-dominated sets vs the base build (987e812e2), GPU:
the six Saturn sets (g 4.7-5.8) all improve - guard fallbacks 4.1-17.3% -> 1.2-6.1%,
anomalous peak height 3mc4 x1.10, 3p85 x1.02, 3r6o x1.06, 5cc8 x1.03, 5uth x1.05, 5vml x1.04;
R_meas 0.880-0.993x on all six; R_model shell-scaled better on 5/6 (5cc8 +0.0005); ISa 5uth +1.5%,
5vml +15%, 3p85 +3%, the twinned 3mc4/3r6o -5%/-1%. 6cee, 6i3j, 6v2r, 7kcn, 8v4j, 9jzo unchanged.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_015CeEGgpKdfkCTJb3YNMJcu

image_analysis/bragg_integration/BraggIntegrationEngine.cpp

@@ -118,6 +118,7 @@ BraggIntegrationEngine::BraggIntegrationEngine(const DiffractionExperiment &expe
     // longer overrides it for broadband data.
     bkg_clip_nsigma = settings.GetBackgroundClipNSigma();
     bkg_pixel_gain = settings.GetBackgroundPixelGain();
+    pixel_gain = settings.GetPixelGain();
     bkg_trim = bkg_clip_nsigma > 0.0f ? 0.0f : settings.GetBackgroundTrimFraction();
 
     // Overlap treatment. Ownership is decided out to the fit grid's half size, which is where the
@@ -265,10 +266,11 @@ std::vector<Reflection> BraggIntegrationEngine::Finalize(const std::vector<Refle
         if (!fr.ok)
             continue;
         Reflection refl = predicted[i];
-        refl.I = fr.I;
-        refl.sigma = fr.sigma;
-        refl.bkg = fr.bkg;
-        refl.var_bkg = fr.var_bkg;
+        // In photons: the engine measured in ADU, with variances already taken at the gain.
+        refl.I = fr.I / pixel_gain;
+        refl.sigma = fr.sigma / pixel_gain;
+        refl.bkg = fr.bkg / pixel_gain;
+        refl.var_bkg = fr.var_bkg / (pixel_gain * pixel_gain);
         if (fr.has_observed) {
             refl.observed_x = fr.observed_x;
             refl.observed_y = fr.observed_y;