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We present a comprehensive full-sky 3-dimensional analysis of the weak lensing fields and their corresponding power spectra. Using the formalism of spin-weight spherical harmonics and spherical Bessel functions, we relate the two-point statistics of the harmonic expansion coefficients of the weak lensing shear and convergence to the power spectrum of the matter density perturbations, and derive small-angle limits. Such a study is relevant in view of the next generation of large-scale weak lensing surveys which will provide distance information about the sources through photometric redshifts. This opens up the possibility of accurate cosmological parameter estimation via weak lensing, with an emphasis on the equation of state of dark energy.
Castro et al. (Mon,) studied this question.