Phase Unwrapping Function 1D

The unwrapping algorithm in 1-D ensures a more or less continous result, i.e. discontinuities are between π$$ or −π$$ values, if the data or function being unwrapped is well behaved.


function unwrap1D(phase_array)
    Nbins=length(phase_array)
    unwrapped=copy(phase_array)
    for i in 2:Nbins
        while unwrapped[i] - unwrapped[i-1] >= pi
            unwrapped[i] -= 2pi
        end
        while unwrapped[i] - unwrapped[i-1] <= -pi
            unwrapped[i] += 2pi
        end
    end
    return unwrapped
end;



Example of usage:


using PyPlot

plot(phase_data) #raw data









w1d=unwrap1D(phase_data)
plot(w1d);








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Don't think that unwrapping an array always leads to continuous and smooth curves, for it only leads to curves that have at the most discontinuities of 2π. The previous example had great data to work with and therefore the resulting plot was smooth. However, if the raw data happen to be noisy or changing fastly, then the resulting array would rather have notorious discontinuities (still between π and -π) or some wiggles. Check the next example:





using PyPlot

plot(phase_data) #raw data





w1d=unwrap1D(phase_data)
plot(w1d);