Three dimensional Doppler tomography

Doppler tomography is a method to compute the emissivity distribution within co-rotating frames of binary stars from observations their emission line profiles at multiple orbital phases. A key assumption as it usually applied that all gas flow parallel plane binary. In this paper I examine possibility lifting allow for motion "$z$" axis well. show problem best considered in Fourier space, and directly constrain 3D transform image velocity but only over 2D surface double-cone centred upon origin, aligned with reciprocal $v_z$ axis. Hence full information needed recovery simply not available. Despite this, an inversion presented tested on number simulated images. While artefacts resulting missing do appear, tests suggest there could be some value applying data real systems, although considerable care when doing so.