---
title: "Direct imaging, from glare to a spectrum"
description: "Follow sampled coronagraph images through self-subtraction, spectral recovery and three actual GPI exposures."
canonical_url: "https://sandboxphysics.com/stories/direct-imaging/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/direct-imaging/"
last_modified: "2026-11-03"
---

AC22 · Direct imaging

# Direct imaging, from glare to a spectrum

Sandbox Physics · 2026-10-28

A faint source turns through a stellar halo. Follow its photons into the camera, measure what subtraction removes, then extract a spectrum from synthetic and real data.

[01 · L1 The faint point that turns beside a star Follow a faint companion through stellar glare, and see why subtracting the glare also changes the companion light.](https://sandboxphysics.com/stories/direct-imaging/the-point-that-turns/) [02 · L1 From a pupil wave to counted camera pixels Derive a finite-band coronagraph image from complex amplitudes, a fixed angular pixel grid and photon counting.](https://sandboxphysics.com/stories/direct-imaging/from-pupil-to-pixels/) [03 · L2 Why subtracting a halo also subtracts a companion Derive angular and spectral self-subtraction, including the two-frame Gaussian limit and a measured five-channel response.](https://sandboxphysics.com/stories/direct-imaging/rotation-and-self-subtraction/) [04 · L3 Recover a spectrum without losing its uncertainty Fit a full spectral response, profile source position and test empirical covariance with independent complete acquisitions.](https://sandboxphysics.com/stories/direct-imaging/recovering-a-coupled-spectrum/) [05 · L3 Extract a contrast spectrum from three GPI exposures Download exact public Beta Pictoris GPI ranges, check the headers and satellite spots, and test a sparse contrast extraction.](https://sandboxphysics.com/stories/direct-imaging/betapic-gpi-tutorial/) [06 · L4 Read the papers that separate speckles from companions Read fixed KLIP, spectral-covariance, IFS-extraction and wavefront-control papers with their assumptions and measured results in view.](https://sandboxphysics.com/stories/direct-imaging/reading-speckles-and-wavefront-control/)

## Sources and calculation scope

1. [Marois et al., Angular Differential Imaging (2006)](https://arxiv.org/abs/astro-ph/0512335v1)

   Fixed v1, observing geometry and reference subtraction. Field rotation supplies diversity between an astronomical source and pupil-fixed structure.

2. [Soummer, Pueyo & Larkin, KLIP (2012)](https://arxiv.org/abs/1207.4197v1)

   Fixed v1, Sections 2.1–2.3 and 3.1, Equations 5–12, Figures 1–2. The reference library, eigenimages and projection define a particular subtraction operator.

3. [Pueyo, Detection and Characterization of Exoplanets Using Projections on Karhunen–Loève Eigenimages (2016)](https://arxiv.org/abs/1604.06097v1)

   Fixed v1, Sections 2.1–2.5, 3.1–3.3 and 4.1–4.2; Appendix E, Equations E18/E20, and Appendix F, Equations F8–F12. Source contamination changes the reference basis. The illustrative J-band spectra use synthetic injections.

4. [Mawet et al., Fundamental Limitations of High Contrast Imaging Set by Small Sample Statistics (2014)](https://arxiv.org/abs/1407.2247v1)

   Fixed v1, Sections 3.1–3.3 and 4.1, Equations 7–10. Read the resolution-element count and assumptions before converting a statistic into a tail probability.

5. [Greco & Brandt, The Measurement, Treatment, and Impact of Spectral Covariance and Bayesian Priors in Integral-Field Spectroscopy of Exoplanets (2016)](https://arxiv.org/abs/1602.00691v1)

   Fixed v1, Section 2, Equations 1–6; Sections 3.1–3.2, Equations 7–8. Spectral covariance changes the weighting of broad spectral structures.

6. [Bonnefoy et al., Physical and orbital properties of beta Pictoris b (2014)](https://arxiv.org/abs/1407.4001v1)

   Fixed v1, Section 2 and Table 1. Nineteen J-band exposures, satellite-spot calibration and the adopted stellar spectrum belong to the published analysis; the tutorial selects three later-reduced public cubes.

7. [GPI Data Pipeline 1.4.0 data formats](https://docs.planetimager.org/pipeline/ifs/dataformats.html)

   SCI/DQ extensions, quality-bit definitions, coordinates and exposure metadata. Raw cards are preserved; old CDELT values and the explicitly inaccurate PAR\_ANG card are not used for sky orientation.

8. [Jason Wang and contributors, original public GPI data commit](https://github.com/semaphoreP/pyklip/tree/72a7517b1a34bdc29c33211f2ef591ddff64dcf9/tests/data)

   Pinned author-repository commit from 9 August 2016. S20131210S0092, S0099 and S0111; exact SCI/DQ ranges and original headers have SHA256 checks. Software BSD licensing does not establish a data-specific redistribution grant.

9. [Samland et al., Spectral cube extraction for the VLT/SPHERE IFS (2022)](https://arxiv.org/abs/2210.06390v1)

   Fixed v1, Sections 3.4, 4.2–4.3, 4.6, 5.2–5.3 and 6. Raw-detector PSFlet fitting and spectral cross-talk occur upstream of the already-reduced GPI cubes used here.

10. [Haffert et al., Implicit electric field Conjugation: Data-driven focal plane control (2023)](https://arxiv.org/abs/2303.13719v1)

    Fixed v1, Sections 2.1–2.4 and Equations 1–22. Pairwise probes and empirical control matrices change coherent stellar leakage before the science image is recorded.

11. [Haffert et al., On-sky dark-hole diggin’ with implicit Electric Field Conjugation on MagAO-X (2026 preprint)](https://arxiv.org/abs/2607.08146v1)

    Fixed July 2026 v1, four pages, Sections 2–2.1 and 3–4, Figures 1–3. Keep internal-bench suppression, on-sky contrast ratios and future goals distinct. This source is treated as a preprint.