I have a spin-2 field given called shape distortion of galaxies as $$\gamma=\gamma_1+i\gamma_2=|\gamma|e^{-2i\phi}$$ where $\phi$ is the orientation angle.
If this quantity has been measured on the sky coordinate which is a spherical coordinate assuming the centre of the measurement with ($\alpha_0$ ,$\delta_0$) as a zenithal point and the other point that this quantity would be measure with respect to center with ($\alpha$ ,$\delta$) sky coordinate. How can I measure the tangential and cross components of $\gamma$ after gnomonic projection from spherical to Cartesian coordinates?