Coherent Differential Imaging

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Overview

Direct imaging of exoplanet (planets around other stars) is a significant challenge due to the extreme contrast level between exoplanets and the stars they orbit. For example, at optical wavelengths, Earth is about 10 billion times fainter than the Sun. To successfully image exoplanets imaging systems must overcome this high contrast.

The current and future instruments designed to image exoplanets therefore include “Extreme Adaptive Optics”: active wavefront control systems that constantly optimize the wavefront in the instrument to maintain high contrast imaging capability. Even with this approach, there is still too much starlight to image the most interesting planets, so calibration techniques are required to separate planet light from the much brighter starlight.

Speckle Control and Calibration

Directly imaging exoplanets requires an optical system able to deliver high contrast images, using wavefront sensing techniques to measure and control starlight in a region of interest, usually located a few diffraction elements from the star. Using focal plane images to sense residual residual errors (refered to as speckle control) is a powerful approach to meet this challenge, as it offers fundamental advantages compared to more conventional pupil-plane wavefront sensing: high sensitivity and absence of non-common path errors. Focal plane images can also be used to separate coherent light (starlight due to wavefront errors) from incoherent light which contains exoplanet images(s), a technique refered to as coherent differential imaging (CDI).

Self-calibrating Coherent Differential Imaging

With Coherent Differential Imaging (CDI), the deformable mirror in the system is modulated to induce a corresponding modulation in the focal plane image speckles. This modulation is measured by a high speed camera, and processed to separate the light that is coherent (starlight) from incoherent light (planet light). The fundamental difference between these two components is that the coherent light reacts to small motions of the deformable mirror by interference, while the incoherent light does not.

The technique is described in the simulation shown in Figure 2. To obtain very high performance, even in the presence of calibration errors, the deformable mirror (DM) probes are linear combinations of two master DM probes, This allows the algorithm to fully constrain the incoherent light measurement, yielding photon-noise limited detection of exoplanets in speckles 100x to 1000x brighter, even with large (> 10%) model uncertainties.

Figure 2 shows Speckle wavefront sensing (SWFS) and coherent differential imaging (CDI) principle. Monochromatic imaging of a faint companion with an apodized pupil is considered here in the presence of wavefront errors.

• (a): Apodized pupil amplitude profile, log scale (top left image) and deformable mirror probes. Five probes, including the nominal unperturbed DM state, are considered in this example. Probes 1 to 4 are designed to add coherent light in a rectangular area extending from 4 to 20 λ/D in x, and from 0 to 20 λ/D in y.
• (b): PSF in the absence of wavefront error, with no companion and probe 1 applied (top left). The five images acquired with the 5 DM probes are shown in the presence of a wavefront aberration and with the companion. The Companion (contrast 5e-8) is about 20x fainter than speckles due to wavefront errors, so it is not visible without image processing. The dashed green rectangle shows the area of the focal planet modulated by the DM probes, and for which FPWFS and CDI algorithms are applied.
• (c): For each pixel within this area, the FPWFS/CDI algorithm converts the 5 intensity measurements in an estimate of complex amplitude conherent light and incoherent light. Since measured intensity is the incoherent sum of incoherent light and the square modulus of coherent complex amplitude, the process is equivalent to fitting a 2D parabola to the 5 measurements. The location of the measurement evaluation points in the real/imaginary plane, shown in green, are known from a model of the optical system and DM probes. The location of the parabola minima in the real/imaginary plane is the coherent light component, and the parabola value at this location is the incoherent light component.
• (d): When this algorithm is applied to each pixel within the zone of interest, the original intensity image (top left) can be decomposed in coherent light component (real part: top right, imaginary part: bottom left) and an incoherent residual revealing the companion (bottom right). The brightness scale in the final bottom right image is 10x finer than the original intensity image. Noise in this final image is dominated by photon noise in the 5 input images.