Spectrophotometric Standard Star Calibration (SSSC)

No-QE-curve color calibration. SSSC solves the camera's true effective response R(λ) from the stars already in the image — compared against real measured spectra from the Gaia mission — rather than taking a sensor QE curve as an input. Filter curves stay as inputs; everything else (sensor QE at operating temperature, AR coating, optics, atmosphere) is absorbed into R(λ) and solved empirically. Each run on the same filter+camera combination refines the solution and seeds the next.

Published method. SSSC is a SetiAstro invention, documented in a formal whitepaper:
Marek, F. (2026). Spectrophotometric Standard Star Calibration: An Empirical System-Response Approach to Astrophotographic Color Calibration. Zenodo. doi:10.5281/zenodo.23107662. Wiki page: GitHub Wiki.

1. Using the tool

Three buttons across the top row set up and run the calibration: Step 0 plate-solves the active frame, Step 1 fetches calibrator stars and their spectra, and Step 2 runs the SSSC solver on the measured stellar photometry. The dialog remembers the last filter/sensor selections and the Camera / Rig label — so continuing a long-term calibration on the same equipment is just “open, Step 1, Step 2”.

Step 0 — Plate solve

SSSC needs a plate solution to map pixels to sky coordinates. If the active document already has a WCS it's used directly; otherwise the Step 0 button runs the plate solver in-place and refreshes the WCS. Step 1 will offer to call Step 0 for you if you skip ahead.

Step 1 — Fetch stars & spectra

Mechanically identical to the SFCC fetch step (same auto-σ SEP waterfall, same bulk Gaia-library match, same SIMBAD query, same B−V letter inference, same synthetic Johnson B/V/R via gaiaxpy) — see the SFCC doc for the plot interpretation. Choose a White Reference SED for diagnostics (G2V by default; it does not affect the solved R(λ)).

The shared panel — filters and the Camera/Rig label

Three rows configure the optical chain:

R / G / B Filter — the channel filter curves. Reliable interferometric data for these is published by every reputable filter vendor, so filter curves are an input to SSSC — the only input it takes about the optics.
LP/Cut 1 & 2 — any light-pollution or cut filters in the light path. These multiply into all three channels.
White Reference — the SED defining “neutral grey” for the diagnostic residual plot. Default G2V.
Camera / Rig — free-text label such as IMX492 · EdgeHD f/7. Together with the filter selections this uniquely identifies the imaging train, and separates the saved R(λ) history per sensor/optical train so that solutions from different rigs sharing a filter set don't mix. Leave blank if you only have one setup.
Notice there is no sensor QE picker — that's the whole point. SSSC is solving for the QE, so it can't be an input.

The SASP Viewer button opens the same curve explorer used by SFCC (see its documentation for details) — useful for sanity-checking a custom filter curve you just imported with Add Curve….

Step 2 — Run SSSC calibration

The main action, with the standard options alongside:

BG Neutralize — run the Background Neutralization tool before the solve and again on the final output, so a channel pedestal doesn't contaminate the stellar ratios.
Star σ + Auto — identical to the SFCC detection threshold control. Auto waterfall is on by default.
Advanced → R(λ) ctrl pts — resolution of the Stage-3 solved response curve, per channel:
- 8 — default, good for 200–600 stars.
- 12 — finer, ∼600+ stars.
- 16 — high resolution, ∼1000+ stars.
More points on too few stars fits noise, not your system. Leave at 8 unless you have a dense field.
Advanced → M(Σ) ctrl pts — max stars used for photometry (default 500). Stars are chosen brightest-first with Gaia-spectrum stars prioritized; dim stars add noise, not accuracy.

Session memory — the long game

SSSC accumulates calibration quality across runs. Every solve is saved, keyed on the filter + camera combination, into the Gaia XP sqlite cache:

The current filter+camera combination is shown as an 8-character session id next to the Close button along with the number of prior runs for that id and a summary of the last one (“Session 7a3f2b1c · 4 prior runs · last: Stage 3 · 487 stars”).
When Step 2 runs and a prior Stage-3 solution exists for the current session, the new solve seeds its optimizer from the prior session's per-channel control points — so the next run starts close to the previous solution and refines from there rather than re-solving from scratch.
Clear History wipes all saved solutions for the current session id (with confirmation). Use it when the optical train changes and the accumulated curve is no longer physically valid.

Over several nights of imaging with the same rig, the solution converges to your actual rig-specific R(λ) — a measurement no datasheet could give you. See §2.7 for the convergence endgame.

Reading the diagnostics (four-panel figure)

After Step 2 the lower pane shows four panels; the suptitle names the stage reached, star count, and per-stage RMS waterfall:

Panel 1 — Solved R(λ) per channel

The headline plot. For Stage 3 each channel's own solved R(λ) is drawn as a solid colored line (R red, G green, B blue) inside its filter passband, with the three filter transmission curves shaded faintly behind. For Stage 1/2 a single stitched dashed grey composite is drawn instead, because the stages don't solve for the detailed shape. If a manufacturer QE curve is passed in (not by default), it's overlaid in dashed amber for comparison. This panel is the plot that replaces the QE datasheet: it's what the solver saw, through this camera, on this night. A healthy Stage 3 result shows three smooth response lobes, one per channel, each covering its own filter without wild spikes or dropouts.

Panel 2 — Residuals before / after

Scatter of fractional residuals (meas/exp − 1) in R/G and B/G ratio space vs expected ratio, four series: dark circles for before correction (what the raw image showed), lighter triangles for after. The before clouds should sit off the zero line (that's the colour error SSSC is fixing); the after triangles should collapse to a tight band on zero. The horizontal dashed line is the perfect-calibration reference. If a residual slope or curvature remains, Stage 3 is still converging — another run on the same rig will tighten it further.

Panel 3 — Calibration quality by stage (the waterfall)

A horizontal bar chart with one row per bootstrap stage, bar length = fractional-residual RMS, shorter is better. Stages that ran show as coloured bars with their RMS number; a green ▼ delta annotation on the right side of a row quantifies the improvement over the previous stage. Stages that did not run show as faint placeholder bars with an italic note (“need 142 more stars” or “Requires DR4 + multi-night airmass data”). The small monospace block at the bottom right of this panel reports the final gains k_R, k_G=1, k_B and the B−V span of the calibrator population — the two numbers that gate stage selection.

Panel 4 — Calibrator spectral coverage

Histogram of the B−V colour index of the valid calibrator stars, with the actual range used marked by two orange dashed lines. A good Stage 3 field looks like a broad hump covering roughly -0.3 to +1.8 — hot O/B stars pin the blue edge of each filter, cool K/M stars pin the red edge, together they triangulate the shape of R(λ). If the title says “need N more stars for Stage 3” this panel is where you'll see whether to point at a denser field (add stars) or a wider colour spread (add span).

After apply

Step 2 commits the calibrated image as an “SSSC Calibrated” step; the metadata records the stage reached, star count, residual RMS, gains, B−V range and session id for traceability. A completion dialog repeats the headline numbers and tells you how many more stars (if any) stand between you and Stage 3 on the next run.

2. Technical details

RGB only. The core departure from SFCC: SSSC never multiplies by a sensor QE curve. Instead it treats the per-channel system response R_c(λ) as the unknown and solves it from the measured photometry of stars with known Gaia XP spectra. The filter transmission is the only published optical datum that enters the solver.

Third-party data used. Gaia DR3 XP calibrated spectra (ESA/DPAC) via gaiaxpy; the Pickles 1998 stellar flux library and SIMBAD (CDS Strasbourg) as fallbacks when no XP spectrum is available; SEP for source extraction. The empirical system-response solver, the bootstrap-stage machinery, the hat-basis control-point parameterisation, the directional coordinate descent, the session-cache seeding scheme, and every SSSC-specific guard below are SetiAstro's own work — see the published whitepaper for the formal derivation.

2.1 The model

For every star i and channel c ∈ {R, G, B}:

\mathrm{measured}_c \;=\; k_c \,\int f_{\mathrm{star}}(\lambda)\,T^{c}_{\mathrm{filter}}(\lambda)\,R(\lambda)\,d\lambda

where f_star(λ) is the Gaia XP calibrated spectrum (interpolated onto the 3000–11000 Å, 1 Å grid), T_filter^c is the published filter transmission (combined with any LP/cut filters), R(λ) is the unknown effective system response the solver is after, and k_c is a per-channel scalar gain. R(λ) absorbs everything the manufacturer QE curve cannot tell you — true sensor QE at operating temperature, AR coating transmission, mirror and lens throughput, flattener, and atmospheric extinction at the time of observation.

2.2 Bootstrap-stage selection

The solver automatically picks the richest stage the data supports. Two numbers decide: N = valid calibrator stars, and Δ(B−V) = (B−V)_max − (B−V)_min = colour span of the population:

Stage = 3 if N ≥ 200 AND Δ(B-V) ≥ 1.5 2 if 50 ≤ N < 200 1 if N < 50

Every stage is strictly more expressive than the one below it, so Stage 3 must beat Stage 2's RMS to be kept — a strict-improvement guard reverts to Stage 2 if the Stage 3 fit regresses (§2.5).

2.3 Stage 1 — scalar per-channel gains

The baseline. Compute measured and expected band ratios meas_RG = R_meas/G_meas, exp_RG = S_R/S_G (and likewise for B/G); the scalar gain that minimises per-star residual is the median ratio of ratios:

k_c=\mathrm{median}_i\!\left(\frac{\mathrm{meas}_{c/G}^{(i)}}{\mathrm{exp}_{c/G}^{(i)}}\right)

with k_G = 1 (G is the reference), each gain clipped to [0.1, 10]. Equivalent to a traditional scalar SPCC white balance — but computed with no QE curve.

2.4 Stage 2 — color-dependent band response

Same three-model fit as SFCC §2.4 (slope-only closed form, affine least-squares, quadratic polyfit), scored by fractional-residual RMS and selected per channel. The important difference is that the expected integrals S_c are now computed with filter × LP only — no QE curve enters anywhere.

Two SSSC-specific guards protect against the pathological-field blow-ups that can occur with very wide B−V populations (carbon stars, extreme mismatches):

Quadratic validation — the fitted quadratic must stay positive on both the sigma-clipped subset and the full population; coefficients must be finite and bounded (|a_q| < 10^6). If any check fails, quadratic is rejected and the slope/affine winner stands.
Degenerate-fit fallback — if the chosen model's final RMS on the full population exceeds 10^6 or is non-finite, SSSC reverts to the Stage-1 scalar RMS so the reported number stays meaningful rather than reporting a bogus explosion.

2.5 Stage 3 — full R(λ) solver

The main SSSC contribution. For each channel independently SSSC solves for a piecewise-linear R_c(λ) parameterised by N_ctrl control points inside the filter's passband:

R_c(\lambda)=\sum_{j=1}^{N_{\mathrm{ctrl}}} r_j^{(c)}\,\Lambda_j(\lambda)

where Λ_j are tent (hat) basis functions on the ctrl_wl grid. Precomputed per-star weight matrices turn the spectral integrals into one matrix-vector product per channel:

\hat{S}^{c}_i=\sum_{j=1}^{N_{\mathrm{ctrl}}} W_{ij}^{(c)}\,r_j^{(c)}\,,\quad W_{ij}^{(c)}=\int f_i(\lambda)\,T^{c}_{\mathrm{filter}}(\lambda)\,\Lambda_j(\lambda)\,d\lambda

Per-channel passband thresholds

Control points cover the wavelength range where T_filter^c is above a per-channel fraction of its peak:

Channel	Threshold	Rationale
R	`0.30`	Tight enough to exclude cross-channel leakage, loose enough to cover the steep astro-filter rolloffs.
G	`0.707` (half-power)	OSC Bayer green filters have a secondary red lobe that would otherwise contaminate G integrals. The half-power clip removes it. Also applied to the G integrals used in Stage 1/2 ratio math so the baseline gains don't inherit the leak either.
B	`0.30`	Same as R.

Loss and coordinate descent

The loss is the sum of squared fractional residuals in colour-ratio space — the same space Stage 1 and Stage 2 are evaluated in, so all three RMS numbers are directly comparable in the waterfall plot:

\mathcal{L}(\mathbf{r})=\sum_i\!\left(\frac{\mathrm{meas}_{R/G}^{(i)}}{k_R\hat{S}^{R}_i/\hat{S}^{G}_i}-1\right)^{\!2}+\sum_i\!\left(\frac{\mathrm{meas}_{B/G}^{(i)}}{k_B\hat{S}^{B}_i/\hat{S}^{G}_i}-1\right)^{\!2}

A directional coordinate descent optimises r_j^(c): for each control point, probe UP first (×1.1 then ×1.2) and take the best improving step; only if neither helps, probe DOWN (×0.9, ×0.8); else stay:

r_j^{(c)}\leftarrow\mathrm{argmin}_{s\in\{1.1,\,1.2,\,0.9,\,0.8,\,1\}}\mathcal{L}\!\left(\,\ldots,\;s\cdot r_j^{(c)},\;\ldots\right)

Up to 60 sweeps; converges when no point moved on a full sweep or the loss change drops below 10^-4. The up-first ordering makes refinement sweeps (seeded from a prior solve) cheap — a point already near its optimum typically settles in one or two probes.

Prior-session seeding

When the session cache (§2.6) has a prior Stage-3 solve for this session_id, the solver seeds x_0 from that solve's per-channel control points, interpolated onto the current ctrl grid:

r_j^{(c),\mathrm{init}}=R^{(c)}_{\mathrm{prior}}\!\left(\lambda_j^{(c)}\right)\quad\text{if}\;N_{\mathrm{ctrl}}^{\mathrm{prior}}=N_{\mathrm{ctrl}}\;\text{and}\;\mathcal{L}_{\mathrm{seed}}\leq 5\,\mathcal{L}_{\mathrm{flat}}

Three checks gate the seed:

Prior must have ctrl_points stored (older cache entries with only the stitched composite are rejected — the composite is a filter-weighted average across channels and maps poorly back to individual control points, producing runaway RMS).
N_ctrl must match exactly — the W-matrix hat-function scale depends on hat width, which depends on N_ctrl. An 8-pt prior into a 16-pt solver has a ∼2× scale mismatch.
Prior residual RMS must be below 2.0.
The seeded x_0's loss must be no more than 5× the flat Stage-2 operating-point loss. If a prior is incompatible for any other reason, this catches it and starts fresh instead.

Strict-improvement guard

Stage 3 is strictly more expressive than Stage 2, so it must match or beat it on RMS. If it doesn't — bad seed, pathological field, or any other reason:

\mathrm{if}\;\mathrm{RMS}_3>\mathrm{RMS}_2\;\Rightarrow\;\mathrm{revert\ to\ Stage\ 2}

and the rejected ctrl_points are not written to the cache (so a bad solve can't poison the next session's seed). SSSC never regresses.

What drives the pixel correction

Even for a Stage 3 solve, the per-pixel correction applied to the image uses the Stage 2 quadratic coefficients — the same pivot-at-median application as SFCC. Stage 3's full R(λ) drives the diagnostics panel and seeds the next session; it does not go directly to pixels. This is deliberate: the piecewise-linear R(λ) on 8–16 control points can have mild oscillation that is harmless in integral space (the diagnostic) but would be loud when evaluated per pixel. The Stage 2 quadratic is well-conditioned and inherits all the gain information that matters for colour.

2.6 Session identity & the response cache

Each solve is tagged with an 8-character session id derived from the filter+camera configuration:

\mathrm{session\_id}=\mathrm{SHA256}\!\left([R,G,B,\mathrm{LP}_1,\mathrm{LP}_2,\mathrm{cam}]\right)[:8]

Deliberately independent of any QE curve name — SSSC is solving for QE, so it cannot be a key. The SessionResponseCache is a table in gaia_xp_cache.sqlite storing the full JSON-serialised SystemResponse for every run (gains, control points, per-stage RMS, timestamp, B−V range). Each save appends; the Clear History button issues a DELETE WHERE session_id = ?.

2.7 Stage 4 (future) — hardware/atmosphere separation

Not yet shipped. With Gaia DR4 (fainter XP coverage, so ∼10× more calibrators per field) and multi-session data spanning a range of airmasses, R(λ) decomposes as:

R(λ) = R_hardware(λ) × R_atmosphere(λ, X)

Hardware stays stable night-to-night (sensor, coatings, optics, filters); atmosphere varies with airmass X and conditions. Imaging the same rig across many nights at different airmasses lets the solver isolate R_hardware(λ) and lock it in permanently. From then on every calibration is Stage 2 speed with Stage 3+ accuracy, using your measured hardware curve instead of a datasheet guess. The curve also tracks aging naturally — mirror oxidation, filter wear, and optical changes appear as drift in R_hardware(λ) over time.

DR4 migration points in the code (filter-list bump to G ≤ 16.5, gaiadr3 → gaiadr4 query change, lowered Stage-3 star threshold, Stage-4 solver path, airmass header ingestion) are flagged in the module header for the forthcoming port.