Coarse mode atmospheric aerosol particles are abundant in agricultural, desert, and urban environments. Accurate characterisation of these particles' morphology is an important need in scientific and applied contexts, especially to advance our understanding for how such aerosols influence solar radiative forcing of the atmosphere. Elastic light scattering is a standard method to study aerosol particles in a contact-free manner, wherein measured scattering patterns are interpreted to infer particle morphology. Due in part to the absence of wave-phase information in these measurements, the inference is not unique, a difficulty generally known as the inverse problem. An alternative approach is digital holography where wave-phase information is encoded in the measurements. We show that digital holography and spatial filtering can solve the inverse problem for free-flowing aerosol particles in the sense that a measured scattering pattern can be uniquely associated with the particle size, shape, and orientation producing it.