Zero padding and 2D Fourier transforms: how does zero-padding affect phase?
Symmetric zero-padding (in the center of an image around the N/2,N/2 sample) does not affect the FFT phase result.  Or after an 2d fftshift before the 2DFFT, symmetric zero-padding around the edges (circularly around the 0,0 sample) does not add phase shift.

An FFT phase measure the even to odd ratio around 0,0.  This won't change with any padding that maintains the identical even and odd decomposition of the input.  An fftshift moves the phase reference to the middle of a 2D image, which may make more sense with reference to an odd and even function decomposition of the original input.