KEYWORDS: Signal to noise ratio, Point spread functions, Optical spheres, Stars, Detection and tracking algorithms, Data modeling, Adaptive optics, Computer simulations, Coronagraphy, Electronic filtering
Direct, ground-based exoplanet detection is an extremely challenging task requiring extreme adaptive optics (AO) systems and very high contrast. Dedicated planet hunters, such as SPHERE and GPI have been designed with these requirements in mind. Despite this, direct detection is still limited due to the presence of residual speckles. Smith et al.<sup>1</sup> described a maximum likelihood estimation technique for the detection of exoplanets in speckle data in which the planet appears to rotate about a host star when observing with an alt-az telescope. We propose the adaptation of this technique to operate on multi-spectral data, such as produced by the integral field spectrographs present on both SPHERE<sup>2</sup> or GPI.<sup>3</sup> As the speckle pattern approximately scales smoothly with wavelength, it is possible to resample data to a single reference wavelength in which speckles will remain fixed in the wavelength dimension while any companions that are present will exhibit radial motion in a predictable manner. We simulate data comparable to SPHERE and with this we compare the performance of our algorithm with another multi-spectral detection technique; spectral deconvolution. We compare the techniques using a ROC (Receiver Operating Characteristic) analysis.
We derive a physical model of the on-axis PSF for a high contrast imaging system such as GPI or SPHERE. This model is based on a multi-spectral Taylor series expansion of the diffraction pattern and predicts that the speckles should be a combination of spatial modes with deterministic chromatic magnification and weighting. We propose to remove most of the residuals by fitting this model on a set of images at multiple wavelengths and times. On simulated data, we demonstrate that our approach achieves very good speckle suppression without additional heuristic parameters. <p> </p>The residual speckles<sup>1, 2</sup> set the most serious limitation in the detection of exo-planets in high contrast coronographic images provided by instruments such as SPHERE<sup>3</sup> at the VLT, GPI<sup>4, 5</sup> at Gemini, or SCExAO<sup>6</sup> at Subaru. A number of post-processing methods have been proposed to remove as much as possible of the residual speckles while preserving the signal from the planets. These methods exploit the fact that the speckles and the planetary signal have different temporal and spectral behaviors. Some methods like LOCI<sup>7</sup> are based on angular differential imaging<sup>8</sup> (ADI), spectral differential imaging<sup>9, 10</sup> (SDI), or on a combination of ADI and SDI.11 Instead of working on image differences, we propose to tackle the exo-planet detection as an inverse problem where a model of the residual speckles is fit on the set of multi-spectral images and, possibly, multiple exposures. In order to reduce the number of degrees of freedom, we impose specific constraints on the spatio-spectral distribution of stellar speckles. These constraints are deduced from a multi-spectral Taylor series expansion of the diffraction pattern for an on-axis source which implies that the speckles are a combination of spatial modes with deterministic chromatic magnification and weighting. Using simulated data, the efficiency of speckle removal by fitting the proposed multi-spectral model is compared to the result of using an approximation based on the singular value decomposition of the rescaled images. We show how the difficult problem to fitting a bilinear model on the can be solved in practise. The results are promising for further developments including application to real data and joint planet detection in multi-variate data (multi-spectral and multiple exposures images).