Evaluar en campo las características morfológicas de las plantas de B.

High contrast imaging observing strategies and data analysis are structured around the need to remove speckle noise from the images. Many advances and discoveries in the field have occurred due to superior observing styles and reduction algorithms, without recourse to new instrumentation, and it is possible that more breakthroughs will allow archival datasets to be reanalyzed to reveal new planets and disks.

1.4.5.1 Hardware discrimination techniques

Speckles look very similar to planets, but there are some differences in the light that goes into a speckle and the light that goes into a planet. Speckles are generated by optical errors and composed of starlight, and planets are composed of planet light.

One possible exploit is that speckles look different at different wavelengths. More precisely, the position of a speckle is determined both by the spatial frequency of the error on the optical surface, and the wavelength of light. That means that when viewed at different wavelength, speckles will appear at different locations. Planets will stay fixed, since they are determined by angular position on the sky, not wavelength. Said another way, the angular separation of two objects does not depend on the wavelength used to view them. Using this wavelength-dependent information to separate speckle and planet light is called “simultaneous spectral differential imaging,” or SSDI (Marois et al., 2000; Racine et al., 1999). Of course, to use SSDI, observations at multiple wavelengths are required. It cannot be done at a single wavelength.

Figure 1.23: A cartoon of angular differential imaging. The planet (red) appears at different po- sitions in the focal plane at different observing times due to sky rotation. A median frame con- tains the speckle light, but not the planet. This median is subtracted from all the individual data frames, which are then derotated and combined to reveal the planet. This image was taken from www.astrobites.org.

Another highly useful method is called “angular differential imaging” (Marois et al., 2006a) which exploits the fact that while speckles are fixed with respect to the telescope optical system, the sky image can rotate. In a space telescope, this can be accomplished by rolling the telescope; on the

ground, this is achievable in certain telescope configurations, notably the alt-azimuth mounts. In an alt-az system, the field of view rotates with respect to the sky, and usually this is compensated either by rotating the instrument being used or using a K-mirror to rotate the field of view before it enters the instrument. However, if this rotation is not done, then the sky image will rotate with respect to the fixed speckle pattern. This rotation information can be used to discriminate speckles from planets in post-processing.

Both ADI and SSDI are important techniques, but fail to work very well at locations close to the star. In ADI, the amount of rotation (in arc length) is proportional to the separation (s=rθ), so for small separations little rotation is achieved in pixel space. For spectral differential imaging, the amount of motion is proportional to the spatial frequency of the error (x=λ/kx, withxbeing

the position on the detector andkx the spatial frequency of the error in the pupil). Since most of

the errors in optics are at low spatial frequencies, to get most of the speckle positions (x) to change significantly requires a prohibitively large bandwidth.

Another method is based on the fact that speckles are coherent with starlight–that is, speckle wavefronts have a fixed phase relationship with the stellar psf–and thus can be made to interfere with them using some kind of interferometric device. This is called “synchronous interferometric speckle subtraction” (Guyon, 2004). In this case, speckles will modulate with the interferometer position, while planet light will stay fixed. This method has never been implemented due to the complexity. We will have much more to say about interferometric speckle suppression in the final chapter.

1.4.5.2 Data reduction techniques

Spectral differential imaging and angular differential imaging are observing strategies, using either the telescope or an instrument with multiwavelength capabilities to disentangle the image of the planet from bright speckles. Another important strategy is to remove speckles in the image using a different reference star (or stars) and image processing techniques. These are techniques which may be combined with spectral and angular differential imaging when the telescope or instrument allows it, or used independently, as they are of general utility.

The crudest form of this process is classic point-spread function (PSF) subtraction, where an image of a nearby star is multiplied by an appropriate scale factor and subtracted from the target image. If the reference star is chosen nearby the target star, so that the gravity vector and hence optical state of the system is nearly identical, then the speckles between the two should correspond very well. In the subtraction step, the speckles will be preferentially removed, and the image will have an excess of flux at the position of a companion.

An improvement to classic PSF subtraction is called the “locally optimized combination of im- ages” (LOCI) algorithm (Lafreni`ere et al., 2007). In this algorithm, rather than using means or

medians to combine the data frames and subtracting, a linear combination is used. Referring to the target images asTi and the reference images asRi, LOCI minimizes the quantity

σ_i2=X p mp(Ti−Or) 2 (1.53) where Or= X i ciRi (1.54)

where i refers to the image number, p refers to the pixel number, mp is a binary mask to block

out parts of the image not under consideration. In the second line,ciare linear coefficients used to

construct the optimal reference image for a particular maskmi using the the reference images Ri.

In each target image Ti, at locations of the planet, the coefficients will not be able to well-fit the

planet, since it does not exist in the reference images, so an excess of flux will remain. At the last step (not shown), each optimally-subtracted target image is combined with the others for the final result.

Efficiently calculating the coefficientsci such thatσ2i is minimized relies on various matrix inver-

sion schemes, which are beyond the scope of discussion. The main ideas behind LOCI’s success are the use of local segmentation of the image to more precisely capture noise variations, and the building up of linear combinations of basis vectors–in this case, the reference images–to create approximations of the speckles. LOCI and its derivatives, which use slightly different optimization parameters, are some of the most powerful methods of PSF subtraction currently used for high-contrast imaging datasets.

Another approach is using the Karhunen-Loeve eigenimage projection (KLIP) algorithm (Soum- mer et al., 2012). This is more conventionally called principal components analysis, or PCA. Here, the reference images are used to generate “eigenimages,” an orthonormal basis set which the first component captures the most variance in the reference images, the second captures the most vari- ance after the first component has been removed, etc. These components in some sense define an “optimal” low-dimensional approximation of the image, where the first N principal components will capture the most variance in the reference images possible when using N or less orthogonal basis vectors. As such, rather than using the full reference set as in LOCI, the first few principal components form a separate optimal reference set, and each target image can be denoised with

T_i0=Ti− N X j=1 hTi·Zji (1.55) where{Z}=P CA[{R}] (1.56)

whereT_i0 is the denoised image, theZj’s are the principal components generated from the reference

setR, where the firstNare used. N is a free parameter in the reduction, which may be experimented with. As usual, PCA may be performed on the full image or on a subset of an image, where the latter is preferable as PCA works best on images with uniform noise properties, and speckle noise varies as a function of distance from the star. There are many algorithms to calculate the principal components, which we do not delve into. We note that an advantage of the KLIP approach is that it is quite fast compared to LOCI, and can be used to efficiently forward-model any planets in the data or combined with Markov-chain Monte Carlo simulations.

Both of these algorithms have drawbacks. They will reduce the flux of any planetary signal, as the planetary signal will have a nonzero “overlap” with the basis vectors used in LOCI or PCA. This requires careful characterization for understanding the photometry of any detected companions. They also do not use information about the shape of a planet (that is, the size of a PSF), or any spatial structure in the image. For example, PCA will unwrap the image into a long one-dimensional vector, destroying information about proximity of nearby pixels, which will have similar noise properties.

There is much unexplored territory on image post-processing of exoplanetary data sets–the ulti- mate solution will likely involve incorporating all known physics of speckles and instrument telemetry in a full forward-model of the target images.