AC22 · Direct imaging
Direct imaging, from glare to a spectrum
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.
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.
02 · L1From a pupil wave to counted camera pixels
Derive a finite-band coronagraph image from complex amplitudes, a fixed angular pixel grid and photon counting.
03 · L2Why 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.
04 · L3Recover a spectrum without losing its uncertainty
Fit a full spectral response, profile source position and test empirical covariance with independent complete acquisitions.
05 · L3Extract 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.
06 · L4Read 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.
Sources and calculation scope
- Marois et al., Angular Differential Imaging (2006)
Fixed v1, observing geometry and reference subtraction. Field rotation supplies diversity between an astronomical source and pupil-fixed structure.
- Soummer, Pueyo & Larkin, KLIP (2012)
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.
- Pueyo, Detection and Characterization of Exoplanets Using Projections on Karhunen–Loève Eigenimages (2016)
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.
- Mawet et al., Fundamental Limitations of High Contrast Imaging Set by Small Sample Statistics (2014)
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.
- Greco & Brandt, The Measurement, Treatment, and Impact of Spectral Covariance and Bayesian Priors in Integral-Field Spectroscopy of Exoplanets (2016)
Fixed v1, Section 2, Equations 1–6; Sections 3.1–3.2, Equations 7–8. Spectral covariance changes the weighting of broad spectral structures.
- Bonnefoy et al., Physical and orbital properties of beta Pictoris b (2014)
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.
- GPI Data Pipeline 1.4.0 data formats
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.
- Jason Wang and contributors, original public GPI data commit
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.
- Samland et al., Spectral cube extraction for the VLT/SPHERE IFS (2022)
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.
- Haffert et al., Implicit electric field Conjugation: Data-driven focal plane control (2023)
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.
- Haffert et al., On-sky dark-hole diggin’ with implicit Electric Field Conjugation on MagAO-X (2026 preprint)
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.