Cirrus are cloud types that are recognized to have a strong impact on the Earth-atmosphere radiation balance. This impact is however still poorly understood, due to the difficulties in describing the large variability of their properties in global climate models. Consequently, numerous airborne and space borne missions have been dedicated to their study in the last decades. The satellite constellation A-Train has proven to be particularly helpful to study cirrus on global scale due to such instruments as the Infrared Imaging Radiometer (IIR), which shows great sensitivity to the radiative and microphysical properties of these clouds. This study presents an algorithm that uses thermal infrared measurements to retrieve the optical thickness of cirrus and the effective size of their ice crystals. This algorithm is based on an optimal estimation scheme, which possesses the advantage of attributing precise uncertainties to the retrieved parameters. Two IIR airborne validation campaigns have been chosen as case studies. It is observed that optical thicknesses could be accurately retrieved but that large uncertainties may occur on the effective diameters. Strong agreements have been found between the products of our algorithm when separately applied to the measurements of IIR and of the airborne radiometer CLIMAT-AV, which comforts the results of previous validations of IIR level-1 measurements. Comparisons with in situ observations and with operational products of IIR also show confidence in our results. However, we have found that the quality of our retrievals can be strongly impacted by uncertainties related to the choice of a pristine crystal model and by poor constraints on the properties of possible liquid cloud layers underneath cirrus. Simultaneous retrievals of liquid clouds radiative and microphysical properties or the use of different ice crystal models should therefore be considered to improve the quality of the results.