  We present a perturbative approach to disordered systems in one spatial
dimension that accesses the full range of phase disorder and clarifies the
connection between localization and phase information. We consider a long chain
of identically disordered scatterers and expand in the reflection strength of
any individual scatterer. We apply this expansion to several examples,
including the Anderson model, a general class of periodic-on-average-random
potentials, and a two-component discrete-time quantum walk, showing
analytically in the latter case that the localization length can depend
non-monotonically on the strength of phase disorder (whereas expanding in weak
disorder yields monotonic decrease). More generally, we obtain to all orders in
the expansion a particular non-separable form for the joint probability
distribution of the transmission coefficient logarithm and reflection phase.
Furthermore, we show that for weak local reflection strength, a version of the
scaling theory of localization holds: the joint distribution is determined by
just three parameters.
