O067 · AC22 · A point that turns

Direct Imaging beside Stellar Glare

Is that faint point a companion or a speckle? A companion follows the rotating sky; instrumental speckles tend to stay with the pupil. Subtracting the stellar halo also removes companion light and mixes spectral channels. Known-source injections measure that response. Noise, position and PSF uncertainty determine how well the spectrum can be recovered.

Watch a faint source turn through a fixed stellar halo, then measure how subtracting that halo changes its spectrum.

Rotation displacement $4.23\,\lambda_{\rm ref}/D$

Processed aperture response $0.687$

Extracted middle-channel contrast $0.00124$

Nominal comparison-ring statistic $189$

Let the sky turn

Total field rotation

50

\Delta\psi\;[{}^{\circ}]

Brightness relative to star

0.002

c

Source separation

5

\rho\;[\lambda_{\rm ref}/D]

Camera band

Drag the hollow handle to place a synthetic companion.

Replaying the saved default observation.

Subtraction and optical errors

ProcessingStatic optical-path RMS

20

W_{\rm rms}\;[\mathrm{nm}]

Evolving optical-path RMS amplitude

2

W_{{\rm var},\rm rms}\;[\mathrm{nm}]

Photon-noise seed

22022

s_{\rm noise}

KL modes removed

1

K

Five top-hat bands, eighteen one-second exposures spaced two minutes apart. Prescribed optical-path patterns are not a reproduced atmosphere or AO loop. A channel contrast is constant across its narrow band.

The circular pupil, focal mask and Lyot stop use area quadrature. The 512-point Fourier grid and 64-sample pupil are checked against independent finer calculations. Below three reference angular units, the camera remains available while spectral inference is withheld.

Derivation, calibration and real GPI tutorial

Model assumptions

Synthetic scalar Lyot-coronagraph observations use an eight-metre circular pupil, five finite J-band channels, prescribed static and evolving optical-path errors, photon counting and read noise. One acquired cube supplies the camera replay, ADI or SDI processing and finite-injection response. Source angle is enlarged by the camera display; rotation represents pupil-tracking field rotation, not orbital motion. The pupil, mask, Lyot stop and final camera are conjugate planes in the preserved Optical bench mode. The observing model is a teaching instrument, not the GPI optical prescription or an adaptive-optics controller. Aperture spectra use empirical comparison-ring covariance plus estimated source photon noise; the quoted statistic is nominal and not a global detection probability. Source-dependent KLIP, small comparison samples, position and PSF uncertainty require the separate validation in the course. Real GPI observations are analyzed in a local-download tutorial; observed pixels are not embedded here while their redistribution terms remain unresolved.

The residual and spectrum use the same synthetic detector frames. The dashed spectrum shows the prescribed input for comparison.

After subtraction and derotation

Recovered contrast spectrum

Each injected band changes the output

What the uncertainty includes

The aperture estimate conditions on the chosen source position and adopted PSF. Mean-ADI and mean-SDI photon propagation is exact for their fixed numerical operators. Data-dependent KLIP uses finite source-photon resampling with its basis recomputed. Neither removes uncertainty in a covariance estimated from a few correlated comparison patches. The course tests this with independent complete acquisitions, a spatial–spectral position profile and PSF mismatch.

Start with the essentials

Focus question: How much of a companion survives subtracting a reference made from its own images?
One-sentence intuition: A reduction acts on the source as well as the halo. Calibrate the complete operator, including its source-dependent reference, before interpreting a spectrum.

Core mathematical model

Optical-path error makes phase

\phi_\lambda=2\pi W/\lambda

Path error and wavelength use the same length unit. Path error is not mirror surface displacement.

Count photons before subtracting

D_{t\ell p}\sim\operatorname{Poisson}\!\left[N_\star(p_{\star,t\ell p}+c_\ell p_{{\rm s},t\ell p})+b\right]+\mathcal N(0,\sigma_{\rm r}^2)

The camera PSFs retain coronagraph and finite-field losses; they are not renormalized to unit transmitted flux.

Calibrate a coupled spectrum

\widehat{\boldsymbol c}=(A^{\mathsf T}C^{-1}A)^{-1}A^{\mathsf T}C^{-1}\boldsymbol y

The response columns come from separate channel injections before all processing. Singular response directions cannot be measured by this inverse.

Common difficulties

A bright residual is not a probability

Typical misconceptionA large local statistic directly gives the probability that a planet is real.

Better mental modelComparison samples are few and correlated; a blind search adds trials. The tutorial keeps the nominal statistic separate from null experiments.

A known injection does not create new observations

Typical misconceptionAdding an empirical PSF to a real cube simulates an independent observation with all its noise.

Better mental modelIt measures conditional processing response on that frozen background. Independent photon and speckle realizations need separate simulations.

Run the experiment

01
Watch a rotating source
Open A companion turns. Drag its hollow cyan handle; the source is a synthetic input, not a detected position marker.
What to observe: The sampled camera source follows the same field rotation used in derotation.
02
Lose most of its light
Choose Almost no rotation, then compare the processed aperture response.
What to observe: A reference sees nearly the same source in every frame, so subtraction removes nearly all of it.
03
Mix the channels
In the advanced group choose spectral plus angular subtraction and inspect the response matrix.
What to observe: An injection into one band can change several extracted bands; diagonal throughput correction alone misses that effect.

Direct Imaging beside Stellar Glare

Follow the point, then account for the light

Core mathematical model

Optical-path error makes phase

Count photons before subtracting

Calibrate a coupled spectrum

Common difficulties

A bright residual is not a probability

A known injection does not create new observations

Run the experiment

Watch a rotating source

Lose most of its light

Mix the channels

Related experiments and articles

From stellar glare to a companion spectrum