Blocking starlight

Blocking starlight

1. History. Bernard Lyot invented the coronagraph in 1930 to study the Sun's corona without an eclipse; a focal-plane mask blocks the disc and a "Lyot stop" removes the diffracted light (Lyot 1939). SOHO's LASCO coronagraphs show the same idea every day (Brueckner et al. 1995). The Sun scene above is an illustration based on LASCO, not a LASCO image.
2. Coronagraph families. Lyot-type amplitude masks, apodised pupils and phase masks such as the vortex. The key figure is the inner working angle, in units of λ/D (Mawet et al. 2012). Earth at 10 pc sits 0.1″ from its star: about 5.3 λ/D for a 6 m telescope at 550 nm [calc].
3. Adaptive optics and speckles. A deformable mirror flattens the turbulent wavefront hundreds of times a second. What remains are speckles; angular differential imaging lets the sky rotate while speckles stay fixed, so they can be subtracted (Marois et al. 2006).
4. Starshade. A flower-shaped screen flown far in front of a telescope (Cash 2006). The Roman Starshade Rendezvous concept: 26 m at 26,000 km; HabEx: 52 m at about 76,600 km (HabEx Final Report).
5. Nulling interferometry. Two telescopes combined half a wave out of phase cancel the star on a dark fringe while an off-axis planet sits on a bright one (Bracewell 1978; the LIFE concept, Quanz et al. 2022).

Coronagraph families, plane by plane

Each family below is drawn as four planes of one optical train. The intensities are computed, not painted: Fraunhofer optics of an ideal, monochromatic telescope with a clear circular pupil, shown on a log stretch from the star's peak down to a millionth. The mask and stop sizes, the apodiser and the planets' brightness are illustrative and say so.

Illustrationnot to scale; after Lyot 1939

1. Lyot coronagraph. An opaque disc in the focal plane blocks the core of the star's image. What it does not remove is the light its edge diffracts, which the next lens sends to the rim of the re-imaged pupil; a Lyot stop slightly smaller than the pupil catches that rim (Lyot 1939). With a 4 λ/D disc, closing the stop from 150% to 80% of the pupil cuts the starlight at 8 λ/D from 6.7×10⁻⁵ to 1.8×10⁻⁷ of the star's peak (no coronagraph: 7.8×10⁻⁵) [calc], while a planet well outside the disc keeps 64% of its light, the stop's area.
2. Apodised pupil. Instead of a mask, the pupil's transmission tapers to its edge, so the image has no sharp edge to ring from. For A(ρ) = (1 − ρ²)² the brightest ring near 5 λ/D falls from 7.8×10⁻⁴ to 1.2×10⁻⁶ of the clear pupil's peak [calc], but only 1/(2n + 1) = 20% of the light gets through and the core is wider. Real apodisers (shaped pupils, prolate and APLC designs) are optimised numerically; this taper is illustrative.
3. Vortex phase mask. A transparent mask whose phase winds around its centre (e^(2iθ), charge 2) moves an on-axis star's light outside the re-imaged pupil: for an ideal charge-2 vortex on a clear circular aperture the field there is exactly zero inside the pupil and (1/ρ)² outside it [calc], so a stop just inside the pupil removes the star. Phase masks are the family that works closest to the star (Mawet et al. 2012); real vortices leave residuals from wavefront errors and the star's finite size.
4. Adaptive optics and ADI. A deformable mirror turns the seeing halo into a sharp core, but quasi-static speckles λ/D wide remain. With the instrument's pupil fixed, the sky and the planet turn through the night while the speckles stay; the median of the sequence models the speckles, and each frame minus it, turned back by its field rotation and stacked, keeps the planet (Marois et al. 2006). The frames on the stage are synthetic. On the sky, GPI reaches about 10⁻⁴ raw contrast at 0.4″ in 60 s and more than ten times deeper after an hour of ADI (Bailey et al. 2016).

The contrast ladder

HR 8799's planets on the canvas use exoplanet.eu's semi-major axes and eccentricities; their orientation on the sky is illustrative, and time is compressed. Contrasts from different instruments are measured at different separations, wavelengths and significances, so the rungs are not directly comparable.

1,216 of the 8,049 planets with a stored distance in exoplanet.eu were found by imaging (the first method listed). Show them on the Galaxy map ›

peak 118 (2024)

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