I would like to use Julia to solve the following problem, any suggestions 
are welcome :)

The attached image (obtained in Julia) represents the phase of a 
wavefunction (in radians) on a square lattice, where m and n label the 
lattice sites. Computationally speaking, it is the density plot of a 41x41 
real matrix. 

How can I numerically compute the total change in phase as one goes around 
a closed loop centered on the site $m=n=0$?

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