Why does the wrapped phase range between (– 𝞹, + 𝞹 ) instead of (0 . 2 𝞹) interval?

I have searched for this particular topic but couldn’t find an answer. According to most papers like (Osmanoğlu et al., 2016), (F Rocca, 2007), (R.F. Hanssen, 2001), (Pepe & Calò, 2017) and more. The relative phase difference value is restricted in (– 𝞹, + 𝞹 ) interval. Even in Snap software, the value is indicated with negative and positive signs. Is it to be convenient with the uplift-subsidence interpretation ?

The (-pi,pi) and (0,2pi) conventions are equivalent, one just needs to know which one is in use.


Some literatures stated an assumption during the phase unwrapping along a particular path, that the wrapped phase differences between adjacent pixels along that path must not exceed a half-cycle ( 𝞹) in order to prevent phase discontinuities, while other literatures stated the same concept but stated that the phase difference must not be equivalent to a whole cycle across the adjacent pixels (2𝞹).

I am confused whether this conflict arise from expressing the wrapped phase differently between the authors either (0, 2𝞹) interval or (- 𝞹 , + 𝞹) interval? or this is a different scenario

What would happen if the path-following phase unwrapping process encountered huge wrapped phase jumps between neighboring pixels other than causing misinterpretation of omitting a number of cycles worth of relative displacement and/or height difference?