Function split_sheet 

pub(super) fn split_sheet(split: &Split, q2: Complex) -> Sheet

The sheet of v = (q^2 - k^2) / (2 k^2 eta^2) of a diffraction order of squared transverse modulus q2 that continues the Ewald sum from the automatic split to split.

Formula

The argument arg(k_q^2) - pi - arg((k eta)^2) with arg(k_q^2) in [0, 2 pi).

Branch

It takes the root k_q = sqrt(k^2 - q^2) with Im k_q >= 0 of the spectral series (spectral_sw1d). Orders farther off the positive real axis than |arg((k eta)^2)| + SHEET_MARGIN take the principal argument.

Why

The principal ln v misses the sheet where k_q^2 lies between the positive real axis and (k eta)^2 (propagating orders of real k at splits rotated to Im(k eta) > 0). It leaves the side of the cut to rounding where v lies on it (q = 0 for complex k and a real split).