X-Ray Reflectometry is a well-established metrology method for thin layer characterization, e.g. for applications to semiconductor industries and astronomy. This technique is based on utilizing the interference of an incident and a reflected X-ray beam on a structure to characterize the optical properties (i.e., layer thickness, layer interface and optical density) of a sample. A common approach for solving this inverse problem is based on variational regularization, fitting the optical parameters to the measured reflectivity data. A key ingredient is the choice of forward model. Traditional approaches assume a pre-defined number of layers, and assume a specific shape on the interfaces connecting the layers [1]. This can lead to fits of bad quality; especially when the real interface shape is significantly different from the shape the model assumed. Recently, a more flexible Free-Form approach to model the optical structure has been proposed [2], which allows for arbitrary piecewise constant profiles. This has the benefit that it does allow a free form of the interface, as well as it allows the number of thin layers present to be varied within the solving of the inverse problem. However, this method is strongly dependent on the discretization of the profile, in particular on the number and width of the bins. This Free-Form discretization substantially increases the number of model parameters compared to traditional approaches. Whilst this allows for a high flexibility in representing the profile, it comes at the cost of increasing the ill-posedness of the optical profile; posing significant challenges for a stable Bayesian reconstruction. In this talk, we study the relation between the discretization of the optical profile and both the quality of fit and the determined uncertainty in the found optical profile. We expect to find a bias-variance trade-off; from which an optimal number of bins can be extracted. To determine the variance in the parameters we make use of Monte Carlo Markov Chain analysis. REFERENCES [1] Nevot, L. and Croce, P. (1980). “Caracterisation des surfaces par reflexion rasante de rayons X. Application a l'etude du polissage de quelques verres silicates,” Rev. Phys. Appl. 15, 761–779 [2] Zameshin, A., Makhotkin, I. A., Yakunin, S. N., van de Kruijs, R. W. E., Yakshin, A. E. & Bijkerk, F. (2016). Reconstruction of interfaces of periodic multilayers from X-ray reflectivity using a free-form approach, J. Appl. Cryst. 49, 1300-1307.