The flux cross-correlation function is a two-point statistic used for description of fluctuations of the transmitted flux in Ly$\alpha$ forest in spectra of distant quasars, which is used for statistical analysis of density fluctuations of neutral intergalactic gas and can be defined as a projection onto the plane perpendicular to the line of sight of more general case — the (2D) flux correlation function. That is why sometimes flux cross-correlation function is called transverse flux correlation function (see e. g. [1]).
The flux cross-correlation function between two lines of sight at angular separation $\theta$ (two spectra of different quasars at separation $\theta$) is defined as where $F(0)$ and $F(\theta )$ denote the pixel flux at the same wavelength (the same redshift) for this two lines of sight. It is assumed, that the mean transmitted flux does not depend on direction, i.e. $\bar {F}(0)=\bar {F}(\theta )=\bar {F}$.
The transverse distance corresponding to angular separation $\theta$ can be written in velocity units as