Read the residuals in deblending and difference images

Separate two questions before comparing methods

Deblending assigns overlapping light to sources within an image. Time differencing compares observations to find new, disappearing or changing emission. A steady neighbor can bias aperture photometry yet cancel in an ideal difference. A variable neighbor leaves a signal.

For every panel, identify whether it shows an observation, model, difference or filtered detection score. A visually small residual does not guarantee correct individual source fluxes. Several allocations can predict similar combined images.

Distinguish the ZOGY difference from its detection score

In section III.1, mark the assumptions: registered images, known profiles, calibration and background, and independent, approximately Gaussian background-dominated noise. Section IV.1 ties optimality to those conditions.

Read section III.6 with two separate notes for the difference image and point-source detection statistic. The latter combines pixels using a source profile and needs its associated uncertainty. Section III.3 adds bright-source noise and other corrections. A residual near a bright star needs that treatment before interpretation as a new source.

Check sections VIII.1–VIII.4 for background, profile, sampling and registration. Figure 5 provides a real-image test. Use its caption to identify the processing in each panel and inspect structure near bright sources.

Reading: Zackay, Ofek & Gal-Yam (2016), Proper image subtraction, arXiv:1601.02655v2

Derive a simple difference limit yourself

Take two background-subtracted observations with identical calibration and identical profiles. An unchanged sky should have zero mean after direct subtraction. If the two pixel noises are independent, their variances add. This check does not require the full Fourier method.

Now shift one image slightly to the right. A constant star produces a positive residual on one side and a negative one on the other. Reducing the shift reduces the pattern. Registration errors can leave a structured residual around a steady star.

D_i=N_i-R_i,\qquad\mathbb E[D_i]=0,\qquad\operatorname{Var}(D_i)=v_{N,i}+v_{R,i}

The special case assumes a static sky, identical calibration and profiles, and independent noise. It checks signs and units, without reproducing the complete paper algorithm.

Use color as another source-separation clue

Turn to scarlet section 2 and figure 1. Each component has a spatial morphology and a list of band amplitudes; the observed prediction includes the relevant profile convolution. Color supplies information beyond a single blended image.

In section 2.3, note exactly where positivity, symmetry and monotonicity are imposed. Sections 2.4 and 2.5 address noise and profiles. Return to figure 1 and compare data, model and residuals for signs of a missing component.

The authors’ Core Concepts documentation distinguishes a component from an observation and a frame. Masked pixels can have zero weight, and observations can have different band profiles. The factorized model keeps one component’s spectrum constant across its spatial extent; strong color gradients make that assumption worth checking.

Reading: Melchior et al. (2018), scarlet, arXiv:1802.10157v2 · scarlet authors, Core Concepts

Check the software after the paper

The pinned Rubin Science Pipelines w_2026_41 ip_diffim overview describes Alard–Lupton kernel matching, several convolution modes and decorrelation options. A method paper and a software task with a similar purpose need not implement the same algorithm.

Save templates, science images, masks, variances, profiles, registration choices and software versions. Inject known changes and measure recovery against both brightness and neighbor distance. Test bright- and dark-background regions separately.

Reading: Rubin Science Pipelines w_2026_41, ip_diffim overview

Carry the reasoning to faint extended emission

A faint extended source spreads light across many pixels. A small shared background error accumulates over that area. Treating it as independent pixel noise and taking a square root underestimates the common bias.

For $n$ pixels sharing a sky error $\Delta B$ , the total bias is $n\Delta B$ . Independent-noise standard deviation generally grows only as $\sqrt n$ . The different scaling explains why more area can expose calibration errors.

For the next result, record component assignments, background estimation, pixel correlations, the statistic used to display residuals and injected-source recovery. The output here is a reading route through fixed papers and products; a full-size science-pipeline reproduction would additionally require its calibrated images and execution record.