  This paper presents the first application of 3D cosmic shear to a wide-field
weak lensing survey. 3D cosmic shear is a technique that analyses weak lensing
in three dimensions using a spherical harmonic approach, and does not bin data
in the redshift direction. This is applied to CFHTLenS, a 154 square degree
imaging survey with a median redshift of 0.7 and an effective number density of
11 galaxies per square arcminute usable for weak lensing. To account for survey
masks we apply a 3D pseudo-Cl approach on weak lensing data, and to avoid
uncertainties in the highly non-linear regime, we separately analyse radial
wave numbers k<=1.5h/Mpc and k<=5.0h/Mpc, and angular wavenumbers l~400-5000.
We show how one can recover 2D and tomographic power spectra from the full 3D
cosmic shear power spectra and present a measurement of the 2D cosmic shear
power spectrum, and measurements of a set of 2-bin and 6-bin cosmic shear
tomographic power spectra; in doing so we find that using the 3D power in the
calculation of such 2D and tomographic power spectra from data naturally
accounts for a minimum scale in the matter power spectrum. We use 3D cosmic
shear to constrain cosmologies with parameters OmegaM, OmegaB, sigma8, h, ns,
w0, wa. For a non-evolving dark energy equation of state, and assuming a flat
cosmology, lensing combined with WMAP7 results in h=0.78+/-0.12,
OmegaM=0.252+/-0.079, sigma8=0.88+/-0.23 and w=-1.16+/-0.38 using only scales
k<=1.5h/Mpc. We also present results of lensing combined with first year Planck
results, where we find no tension with the results from this analysis, but we
also find no significant improvement over the Planck results alone. We find
evidence of a suppression of power compared to LCDM on small scales 1.5 < k <
5.0 h/Mpc in the lensing data, which is consistent with predictions of the
effect of baryonic feedback on the matter power spectrum.
