---
title: Scene Modeling Photometry (SMP)
url: https://www.emergentmind.com/topics/scene-modeling-photometry-smp
type: topic
---

# Scene Modeling Photometry (SMP)

Scene Modeling Photometry (SMP) is a pixel-level, generative approach to transient photometry in which the entire scene around a supernova is modeled directly on the original exposures rather than on resampled or subtracted images. In the Roman context, the method is explicitly identified with what Holtzman et al. (2008) called “scene modeling” photometry, and in the ZTF context it is described as a maximum-likelihood fit of a parametric model containing the SN PSF, a common host-galaxy light distribution, sky/background, per-epoch astrometric mapping, and photometric scaling derived from stars [2102.05069] [2509.04073]. Across both implementations, the central idea is stable: a static host and a time-variable point source are fit jointly in pixel space over many epochs, so that host subtraction, PSF handling, calibration transfer, and uncertainty propagation are all embedded in one forward model.

## 1. Conceptual definition and mathematical structure

In its Roman formulation, the “scene” is the combination of a time-variable point source, a static host-galaxy light distribution, and a per-image spatially flat background. The forward model predicts the expected counts in every pixel of every exposure from a set of parameters that includes galaxy spline coefficients, SN fluxes, SN position, small astrometric shifts, and sky levels, with the observed image taken to be model plus noise [2102.05069].

The galaxy component for image \(i\) at detector pixel \((x,y)\) is written as
\[
G_i(x,y) =
G\!\left(\mathcal{A}_i (x^{11}, y^{11}) + \Delta \alpha_i,\,
\mathcal{D}_i (x^{11}, y^{11}) + \Delta \delta_i \right)
\otimes \mathrm{PSF}_i(x^{11}, y^{11})\big|_{x, y},
\]
where \(G(\alpha,\delta)\) is the underlying time-independent galaxy surface brightness, \((x^{11},y^{11})\) are coordinates on an 11× oversampled grid, \(\mathcal{A}_i,\mathcal{D}_i\) are the WCS transforms, \(\Delta\alpha_i,\Delta\delta_i\) are small image-by-image astrometric corrections, and \(\mathrm{PSF}_i\) is the PSF including convolution with the pixel response. The full Roman pixel model is
\[
M_i(x,y) =
G_i(x, y) +
\frac{F_i}{A(x, y)}\,\mathrm{PSF}_i\!\big(x - x^{\mathrm{SN}}_i,\,
y - y^{\mathrm{SN}}_i\big) + s_i,
\]
with \(F_i\) the SN flux in image \(i\), \(A(x,y)\) the local pixel area on the sky, and \(s_i\) the constant sky level. Statistically, the model is \(D_i(x,y)=M_i(x,y)+N_i(x,y)\), with fitting performed by minimizing a weighted \(\chi^2\) over all images and pixels [2102.05069].

The ZTF implementation uses an equivalent scene-modeling logic, but with a different parameterization. Its core model is
\[
Y_{ip} = R_i \left[ f_i \,\psi_i\bigl(\vec{x}_p - \vec{T}_i(\vec{x}_{\mathrm{SN}})\bigr)
+ K_i \otimes G\bigl(\vec{T}_i^{-1}(\vec{x}_p)\bigr) + S_i \right],
\]
where \(i\) indexes exposures and \(p\) pixels within the cutout. Here \(f_i\) is the SN flux, \(\psi_i\) the per-exposure PSF, \(G(\vec{x})\) the static host galaxy in a reference frame, \(K_i\) the kernel mapping the reference-frame PSF to the exposure PSF, \(S_i\) an additive sky term, \(R_i\) a scalar photometric scale, and \(\vec{T}_i\) the geometric transform from reference frame to exposure [2509.04073].

In both cases, SMP is therefore not merely a fitting convenience but a generative statistical model of the measurement process. A plausible implication is that its defining feature is the preservation of the native data model—PSF, WCS, pixel response, and background—rather than the creation of a derived difference image on which photometry is performed afterward.

## 2. Distinction from image subtraction and classical PSF photometry

Traditional supernova photometry commonly uses image resampling plus subtraction, or PSF/aperture photometry on host-subtracted stacked images. Those approaches require accurate resampling and PSF matching. The Roman study argues that they are problematic for the Wide Field Instrument because the data are undersampled, with PSF FWHM after pixel convolution ranging from \(0.127''\) to \(0.166''\), or \(1.16\) to \(1.51\) pixels depending on band, and because the survey will often have a single, undithered exposure per filter per epoch [2102.05069].

The failure mode identified for resampling-based approaches is aliasing and correlated errors. In the Roman simulations, a drizzle-like resampling approach with a square kernel of \(\mathrm{pixfrac}=0.3\) for references, followed by PSF photometry on subtracted images, performs much worse than scene modeling on the noise-free data: residuals correlate strongly with the galaxy second derivative, showing over-smoothing and aliasing [2102.05069]. The contrast is structural. Forward modeling constructs a high-resolution scene on the sky, convolves once with a high-resolution PSF and pixel response, then samples at the native pixel grid for each exposure, respecting exact pointing and rotation.

The ZTF comparison emphasizes a different set of limitations in difference imaging. In DR2 forced photometry, a single sky position is estimated from alerts, a ZOGY difference image is created for each exposure, and a fixed PSF at the fixed SN position is fit on the difference image with only the amplitude free. The paper identifies three limitations in that implementation: a fixed, non-spatial PSF on difference images; a fixed SN position based on the alert pipeline; and the inability to apply the same method to stars, since stars are not present in the difference image. As a result, stars are calibrated on science images with one pipeline, while SNe are measured on difference images with another, breaking the direct SN–star flux comparison [2509.04073].

This contrast addresses a common misconception: SMP is not simply a more elaborate variant of subtraction. The Roman and ZTF descriptions both treat it as a method that works directly on calibrated science frames and uses all available pixels, including host-galaxy morphology and background structure, rather than only the difference signal [2102.05069] [2509.04073].

## 3. Parameterizations, fitting strategy, and calibration logic

The Roman implementation fits, for each filter, a 2D spline galaxy model \(G(\alpha,\delta)\) on a uniform grid of spline nodes in sky coordinates, a single sky position for the SN, an independent flux parameter \(F_i\) for each image, a per-image constant sky level \(s_i\), and per-image small astrometric shifts \(\Delta\alpha_i,\Delta\delta_i\). The node spacing is 2 nodes per PSF FWHM, described as roughly Nyquist sampling of the PSF-convolved galaxy. The modeled region is a circular patch around the SN, and the galaxy model is forced to go to zero at the edge of this patch to break degeneracy between galaxy pedestal and sky background [2102.05069].

Roman PSFs are generated with WebbPSF and convolved with ideal square \(0.11''\) pixels. The model uses 11× oversampling, with the galaxy defined on a \(0.01''\) grid and the PSF sampled on the same oversampled grid. The supersampling strategy is stated to ensure the 2D spline is represented with \(\sim 10^{-4}\) accuracy after convolution, sufficient for millimagnitude-level SN photometry. Optimization uses Levenberg–Marquardt least squares, with uncertainties and covariances of the flux parameters coming from the LM covariance matrix and validated empirically via pull distributions. The paper explicitly states that there is no MCMC and no explicit regularization term added to the cost function [2102.05069].

The ZTF pipeline begins from detrended quadrant images, masks, and WCS. For each SN and band it selects on-frames in rest-frame phase \(-50<\Phi<+100\) days and adds off-frames outside \(-50<\Phi<+200\) days, with at least six times more off-frames and at least 100 in total, to constrain the host galaxy model. Pre-processing includes SExtractor source detection, sky background construction in object-masked regions, inverse-variance pixel weight maps based on sky variance and flat-field, and cross-matching to GAIA eDR3 and Pan-STARRS1 for PSF training, astrometric refinement, and photometric alignment [2509.04073].

Its PSF model follows Astier et al. (2013): an analytic core, usually a Moffat profile, plus a pixelized residual grid, both varying smoothly with position. For undersampled data, the analytic PSF part is integrated over each pixel using a 3-point Gaussian quadrature. Astrometric transforms are built from GAIA positions and proper motions, with relative transforms defined as \(\vec{T}_i=\vec{P}_i\circ\vec{P}_{\rm ref}^{-1}\). Photometric alignment is done through a global linear model
\[
m_{ij} = m_j + zp_i,\qquad
R_i = 10^{0.4(zp_i-zp_{\rm ref})},
\]
with the typical uncertainty on \(zp_i-zp_{\rm ref}\) reported as \(<0.8\) mmag [2509.04073].

A distinctive feature of the ZTF formulation is the insistence that the same flux estimator be used for SNe and for calibration stars. In SMP, the same PSF model, astrometric transforms, kernels, and weighting scheme are used to fit the SN plus galaxy and to fit field stars with galaxy fixed to zero. The paper presents this symmetry as a key cosmology requirement because the average SMP flux of a star becomes the natural anchor for calibration, placing stars and SNe on the same instrumental system [2509.04073]. This suggests that SMP is as much a calibration architecture as a host-subtraction method.

## 4. Validation on Roman undersampled imaging

The Roman validation uses simulated data designed to approximate about \(10\%\) of a full Roman SN survey: 2,061 simulated SNe Ia and 762,570 image cutouts around SNe or host galaxies in the \(Z087\), \(Y106\), \(J129\), \(H158\), and \(F184\) filters, with a 5 observer-frame day cadence over a year and visits rotated by about \(5^\circ\) relative to the previous visit [2102.05069]. Host galaxies are drawn from the VELA cosmological simulations and provide oversampled, SED-informed mock images in Roman filters; SN light curves are generated with SALT2-Extended via SNCosmo, with redshifts uniform in \(z\) between 0.7 and 2.0 and SN positions drawn from a probability map proportional to the slightly smoothed \(Y106\) host image [2102.05069].

The validation strategy is multi-layered. First, the authors examine galaxy modeling errors against local second derivatives of the host surface brightness, arguing that curvature rather than gradient is the relevant diagnostic. Figures 5 and 6 are summarized as showing no trend of noise-free residuals with local Laplacian, indicating that the spline grid with 2 nodes per FWHM is adequate and does not need to be finer [2102.05069]. Second, they study pull distributions,
\[
\mathrm{pull}=\frac{F_{i,\mathrm{rec}}-F_{i,\mathrm{true}}}{\sigma_{i,\mathrm{rec}}},
\]
whose means and medians are consistent with zero except in \(Z087\) at some magnitudes, while the dispersions are near unity at bright magnitudes and rise to about \(1.1\) at faint magnitudes in \(Z087\) and \(Y106\), implying that uncertainties are underestimated by \(\lesssim 10\%\) there [2102.05069].

Third, they analyze flux bias versus magnitude. For noise-free images, all filters show biases at the \(\approx 1\) mmag level across most of the magnitude range, with somewhat larger biases at the very faint end, likely due to small galaxy subtraction residuals and the \(\sim 0.1\%\) limitation of the reprojection step. For images with noise, \(Y106\), \(J129\), \(H158\), and \(F184\) remain extremely close to unity in the average scaling between true and observed flux, while \(Z087\) shows a consistent bias of order 2 mmag across much of the magnitude range [2102.05069]. The abstract summarizes the band-level result as biases at the millimagnitude level in the four red filters and larger \(\sim 2\)–3 millimagnitude biases in \(Z087\), all meeting the 0.5% Roman inter-filter calibration requirement [2102.05069].

At the light-curve level, SALT2-Extended fits to the recovered multiband photometry show distance-modulus residuals \(\Delta\mu=\mu_{\rm rec}-\mu_{\rm true}\) whose mean and median in redshift bins are consistent with zero at the few mmag level, with dispersion increasing with redshift as expected. Sensitivity tests using \(\partial \mu/\partial m_{\rm zp,band}\) indicate that for 5-band Roman light curves the per-band sensitivities are typically \(|\partial\mu/\partial m_{\rm zp,band}|\lesssim 1\), so a 5 mmag calibration bias in any single band would generally translate into \(\le 5\) mmag distance-modulus bias per SN. Since the measured photometric biases are \(\le 1\)–3 mmag, their impact is described as safely below Roman’s systematic-error budget from calibration [2102.05069].

These results also bear directly on the specific challenge of undersampling. Roman’s WFI will often have one undithered exposure per filter per epoch, so per-epoch images cannot be Nyquist-sampled by dithering. The paper’s conclusion is that undersampling can be handled by defining the model in sky coordinates, supersampling the galaxy and PSF, and fitting many epochs jointly, including numerous reference images [2102.05069].

## 5. ZTF implementation and the requirement of a common instrumental system

The ZTF SN Ia DR2 paper places SMP in the setting of a large optical survey with 3628 spectroscopically confirmed Type Ia supernovae discovered during the first 2.5 years of operation, with DR2 light curves originally based on forced photometry on difference images. The motivation for reprocessing with SMP is explicit: precision cosmology requires control of total systematic error on SN fluxes at the few \(\times 10^{-3}\) level, or approximately \(0.1\%\) in flux per band, whereas the difference-image approach delivers \(\sim 1\)–2% photometry, sufficient for population and rate studies but not for that calibration target [2509.04073].

Operationally, the SMP processing is large-scale. Across DR2, the selected data amount to approximately \(3.2\) million quadrants, about \(179\) TB, or \(11.6\%\) of all ZTF quadrants over that period. A complete SMP processing run requires 2–3 weeks at CC-IN2P3 using up to approximately 2000 cores. On a single 3 GHz core, the SN fit takes \(\lesssim 100\) s even for high-cadence SNe. Two full iterations produced about 9493 light curves for 3582 SNe, with failures at the \(\sim 2.6\%\) level occurring mainly in crowded Galactic-plane fields or poorly sampled \(i\)-band light curves [2509.04073].

The paper’s technical emphasis falls on repeatability and calibration. Using SMP star light curves, the authors measure a weighted RMS as a function of magnitude. In \(g\) band, free-PSF repeatability for bright stars has a floor of approximately 10 mmag, while SMP repeatability is worse by approximately 2 mmag, which the paper identifies as the expected penalty of fixing positions under finite astrometric noise. The reported astrometric residuals relative to GAIA are \(\sigma_x\sim 0.08\) pixel and \(\sigma_y\sim 0.04\) pixel for bright stars, and for a Gaussian PSF the approximate flux bias is
\[
\frac{\Delta f}{f}=\frac{1}{4}\frac{\delta x^2+\delta y^2}{\sigma_{\rm seeing}^2},
\]
yielding about 2 mmag flux bias on average and 3–4 mmag at best seeing [2509.04073].

The direct comparison between SMP and DR2 forced photometry is revealing. Differences in magnitudes per point, defined as SMP minus DR2, have mean offsets of approximately 30 mmag in \(g\), 50 mmag in \(r\), and 20 mmag in \(i\), with DR2 fluxes on average brighter than SMP. When both light-curve sets are fit with SALT2.4, stretch \(x_1\) and time of maximum \(t_{\rm max}\) are consistent, and color \(c\) differs by only about 10 mmag. However, the derived distance modulus offset is about 90 mmag, with SMP distances larger than DR2. The paper interprets this as evidence that DR2 absolute calibration and/or linearity are not yet at the level required for precision cosmology [2509.04073].

The calibration chain itself is formulated through time-averaged SMP instrumental magnitudes of stars matched to PS1:
\[
\hat{m}_{{\rm SMP},i}=m_{{\rm cal},i}+\alpha\,\mathrm{col}_i+\delta zp(\vec{x}_i)+zp_{\rm SMP}.
\]
The fits reveal strong color terms consistent with ZTF bandpasses that are approximately 6 nm bluer in \(g\), 14 nm redder in \(r\), and 15 nm redder in \(i\) than PS1, together with 10–20 mmag non-linearities over 14–18 mag in calibration residuals versus magnitude [2509.04073].

## 6. Systematics, limitations, and broader significance

A central lesson from the ZTF study is that SMP does not eliminate instrumental systematics by itself. The paper identifies a new sensor effect, dubbed the “pocket effect,” which distorts the PSF in a flux-dependent manner and produces non-linearities of a few percent in photometry. Its signatures include serial-direction astrometric residuals that depend on star magnitude, strong variation of PSF skewness in \(x\) with brightness while \(y\)-skewness remains essentially constant, strong CCD-to-CCD variation, background dependence that makes the effect strongest at low sky background and nearly absent above about 6000 ADU sky, and a worsening after a readout waveform upgrade in November 2019 [2509.04073].

The photometric consequences are substantial. On low-background frames, comparisons of PSF and aperture magnitudes show that some CCDs are nearly unaffected, while strongly affected CCDs exhibit 8% peak-to-peak variations across the magnitude range in \(m_{\rm PSF}-m_{\rm aper}\), and even modestly affected CCDs show 1–2% peak-to-peak non-linearities. The paper concludes that the pocket effect alone can induce approximately 1–7% photometric non-linearities, far above the 0.1% target, and that both DR2 and current SMP are affected because they share the same raw images and detrending [2509.04073].

The stated remedy is a pixel-level correction applied during detrending, before PSF modeling and SMP. The correction must be sensor-dependent and time-dependent, reflecting pre- and post-2019 readout conditions. The authors do not provide the final model in the paper, but describe the intended strategy as measuring flux-dependent PSF shape and centroid shifts versus position and background, building a forward model of charge redistribution along the serial register, and inverting it to deconvolve deferred charges at the pixel level [2509.04073].

Roman’s limitations are different and more controlled. The validation assumes perfect knowledge of the PSF, perfect calibration of detector effects such as nonlinearity and IPC, no SED dependence in the PSF, and otherwise accurate WCS apart from fitted small shifts. The paper therefore positions its results as a validation of the forward-modeling algorithm under idealized instrumental knowledge, not as an end-to-end demonstration under all real-world systematics [2102.05069]. A plausible implication is that the Roman results establish the intrinsic adequacy of scene modeling for undersampled imaging, while the ZTF results demonstrate that cosmology-grade performance also requires sensor physics, bandpass modeling, and calibration control at the pixel level.

Within the broader SMP literature, the Roman paper explicitly connects its implementation to Holtzman et al. (2008) for SDSS-II, Astier et al. (2013) for SNLS, Brout et al. (2019) for DES, Rodet et al. (2008), and Bongard et al. (2011). The shared philosophy is joint fitting of a static galaxy plus variable SN directly in pixel space across multiple epochs. The differences lie in the galaxy basis and instrumental regime: Roman uses a 2D spline basis with nodes at about \(0.5\) FWHM spacing and is centered on undersampled, space-based PSFs with changing roll angles, whereas ZTF uses a pixelized host model in a ground-based survey and foregrounds the requirement that stars and SNe be measured with the same estimator [2102.05069] [2509.04073].

Taken together, these studies define SMP as a methodological framework for precision transient photometry rather than a single algorithmic template. In Roman simulations it delivers millimagnitude-level SN flux biases—\(\lesssim 1\) mmag in \(Y106\), \(J129\), \(H158\), and \(F184\), and about 2–3 mmag in \(Z087\)—meeting the stated inter-filter calibration requirement [2102.05069]. In ZTF, it provides a statistically powerful and calibration-consistent alternative to difference-image forced photometry, but also exposes unresolved non-linearity, bandpass, and absolute-calibration problems that currently prevent both the legacy DR2 light curves and the present SMP measurements from being used for precise cosmological analyses [2509.04073].

Source: https://www.emergentmind.com/topics/scene-modeling-photometry-smp