Phase spectrum of 2D real function
A phase measurement needs to be referenced to some point. 

The standard FFT computes a circular phase relative to the first sample, or the sample at the 2D origin.  For data that is not exactly integer periodic in the FFT aperture (typically true for any rectangularly windowed data), this is at a circular discontinuity in the data vector.  Thus the result is an alternation of FFT phase results to represent this edge discontinuity. 

An edge discontinuity can be represented by an odd function, and odd functions show up in the imaginary (or sine) components of a DFT of this discontinuity.

You can move this circular or edge discontinuity away from the FFT’s phase zero reference point by doing an fftshift before performing the FFT.  This moves the phase reference point to the center of your data, which hopefully does not have an unintended discontinuity.  This shift most often results in a more continuous phase spectrum across FFT result bins of windowed data.  However a pre-fftshift produces the same result as post flipping the phase of all the odd numbered FFT result bins without the shift, which may be easier to do.