  We present the results of a study to optimize the principal component
analysis (PCA) algorithm for planet detection, a new algorithm complementing
ADI and LOCI for increasing the contrast achievable next to a bright star. The
stellar PSF is constructed by removing linear combinations of principal
components, allowing the flux from an extrasolar planet to shine through. The
number of principal components used determines how well the stellar PSF is
globally modelled. Using more principal components may decrease the number of
speckles in the final image, but also increases the background noise. We apply
PCA to Fomalhaut VLT NaCo images acquired at 4.05 micron with an apodized phase
plate. We do not detect any companions, with a model dependent upper mass limit
of 13-18 M_Jup from 4-10 AU. PCA achieves greater sensitivity than the LOCI
algorithm for the Fomalhaut coronagraphic data by up to 1 magnitude. We make
several adaptations to the PCA code and determine which of these prove the most
effective at maximizing the signal-to-noise from a planet very close to its
parent star. We demonstrate that optimizing the number of principal components
used in PCA proves most effective for pulling out a planet signal.
