Noise and saturation

add_noise_and_digitize() applies the wcc_etc noise model to the rendered source image, following the ETC’s semantics exactly so that measured SNRs match ETC predictions.

The model

Starting from the source-only image in electrons:

  1. Sky + dark. Uniform per-pixel rates (zodiacal background and dark current from the ETC) times exptime are added, giving the clean expectation image image_clean.

  2. Saturation cap. The per-frame expectation image_clean / n_reads is compared against the full-well depth and the ADC ceiling (adc_max × gain); the expectation is capped at the smaller of the two (times n_reads), and the per-pixel boolean satmask records which pixels hit the limit.

  3. Poisson noise on the (capped) expectation.

  4. Read noise, Gaussian with variance scaling as n_reads (each coadded frame contributes one read).

  5. Digitization. Electrons are divided by the gain, the bias level is added, and the result is clipped to [0, n_reads × adc_max] ADU.

With add_noise=False, steps 3 and 4 are skipped and image_e equals the capped expectation of step 2 (image_clean where nothing saturates), which is what a photometric closure test wants.

Three products come out of this: the truth image_clean (noiseless expectation, e-), the pre-digitization realization image_e (e-, may be negative) and the delivered frame image_adu (what the camera would hand you). Photometry only ever sees the delivered frame, converted back to electrons as (ADU - bias) * gain, so a SimulatedField and the FITS file written from it give identical measurements. Note that both WCC sensors carry bias = 0 in the ETC, so the zero clip removes negative read-noise excursions from the delivered frame; a low-background sky therefore measures slightly above its expectation, on every path alike.

n_reads semantics

n_reads follows the ETC convention of coadded frames: the total exposure time is split into n_reads equal frames that are summed. Consequences:

  • saturation is evaluated per frame, so splitting a long exposure into more reads is the way to keep bright stars unsaturated;

  • read-noise variance grows linearly with n_reads;

  • the ADU ceiling of the summed image is n_reads × adc_max.

Per-star saturation flags

The FITS/output catalog carries a per-star saturated column computed by star_saturated(). It flags a star if any saturated pixel lies within 32 px of its center. A window is needed, rather than the central pixel alone, because the defocused PSFs are centrally depressed: a bright star can saturate its ring while its central pixel stays below full well (the 2-wave ring extends to ~29 px).

Quick example

from wcc_sim import simulate_field

field = simulate_field(291.0, 44.5, sensorfilter="zwo:r", focus=2,
                       exptime=90, n_reads=1, seed=42, shape=(1024, 1024))
n_sat_px = field.saturation_mask.sum()
sat_stars = field.catalog[field.catalog["saturated"]]

# Same field, 9 reads: per-frame exposure drops from 90 s to 10 s
field9 = simulate_field(291.0, 44.5, sensorfilter="zwo:r", focus=2,
                        exptime=90, n_reads=9, seed=42, shape=(1024, 1024))

Every noise-model quantity used is recorded in field.params (and the FITS header): gain, read_noise, dark_e_s, sky_e_s, well_depth.