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Sandbox Physics
Direct imaging, from glare to a spectrum

L1 · Direct imaging

The faint point that turns beside a star

A real companion follows the turning sky; many bright speckles stay with the telescope pupil. Watching which point moves gives astronomers a way to separate a faint world from the glare around its star.

The star spreads across the camera

Imagine photographing a small lamp beside a car headlight at night. Covering the brightest part of the headlight helps, but scattered light still reaches the lamp. A telescope has a related problem. A star is concentrated into a small central image, yet diffraction and tiny optical errors spread some of its light into a broad halo.

A coronagraph reduces that stellar light before it reaches the science camera. In a Lyot coronagraph, a small mask blocks the bright central focus, and another aperture removes light redistributed near the edge of a reimaged pupil. A companion arrives from a slightly different direction, so much of its light follows a path around the central mask.

The remaining halo has bright knots called speckles. Slight differences in the distance light travels across a mirror change where waves reinforce each other. A knot can look remarkably like the compact image of a companion. Better angular resolution sharpens the knot as well as the planet.

Reading: Marois et al. · Soummer

Let the sky supply the motion

During pupil-tracking observations, the instrument keeps its pupil pattern in a nearly fixed orientation. Earth continues to rotate. The sky then turns across the detector, taking a companion around the stellar position. Over an observing sequence, the planet draws a short arc through a halo that changes more slowly.

Astronomers use the sequence to estimate the stellar background, subtract that estimate from each frame, then turn the residual frames back to a common sky direction. Companion light comes together at one position. Many instrumental features spread out. This procedure is angular differential imaging, usually shortened to ADI.

The motion happens because the observing coordinates turn. An apparent arc lasting half an hour is not half an hour of visible planetary orbital motion. Keeping that distinction makes the camera sequence much easier to read.

Reading: Marois et al.

The reference has seen the companion too

Suppose the companion scarcely moves between frames. The estimated background now includes a bright point in nearly the same place every time. Subtraction removes that point along with the halo. More rotation helps because each frame puts the source on different camera pixels.

This loss is called self-subtraction. It often leaves a positive core with negative shapes beside it. The negative patches mark places where the reference contained companion light; they are part of the processing response. Summing every pixel of that signed image can therefore give a very misleading measure of the source brightness.

One practical remedy is to add a faint source with known brightness to the original frames and process the enlarged sequence again. The recovered light tells us how the chosen procedure responds at that location. If the reference is learned from the data, the added source can change that reference as well. The calibration has to follow that change.

Reading: Pueyo

A real sequence from Beta Pictoris

On 10 December 2013, the Gemini Planet Imager observed the young giant planet Beta Pictoris b in the near-infrared J band. Bonnefoy and colleagues described nineteen exposures in their 2014 analysis. Each exposure was already a small stack of images at different wavelengths, so the source could be followed both around the star and through its colors.

An unrelated background star also follows the turning sky. Repeated astrometry tests whether a source belongs to the target system. Beta Pictoris b has a particular advantage here: its location can be compared with images from other instruments and dates. In the small public sample used by the companion tutorial, three exposures span about twenty degrees of field rotation. Their headers, satellite calibration spots and sky orientation can all be checked before extracting a spectrum.

The teaching camera uses its own synthetic observations so that source brightness, optical errors and noise are known. The real-data tutorial returns to the telescope files. These two paths meet at the same question: how much source light survives the procedure used to reveal it?

Reading: Bonnefoy et al. · Jason Wang and contributors

Keep the colors attached to the light

A spectrum measures brightness across wavelength. It can show broad changes caused by a cool atmosphere, but image processing also changes those brightnesses. Some methods compare wavelengths after resizing the images so that stellar speckles line up. A companion moves during that resizing, and light from one channel can influence several recovered channels.

The useful endpoint is a spectrum accompanied by its measured processing response and uncertainty. A striking point starts the investigation. Following its motion and accounting for its light lets the investigation continue.

Reading: Greco & Brandt · Bonnefoy et al.

Try the observation

Watch a companion turn, then nearly erase it

  1. Watch A companion turns, and follow the hollow handle through the sampled camera frames.
  2. Switch to Almost no rotation. Compare the source in the camera with its much smaller processed aperture response.
  3. Predict what will happen closer to the star, then try Near the mask edge.

Sources and calculation scope

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

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