Since the deformation of structures in the optic nerve head (ONH) is associated with glaucoma and other diseases of the optic nerve, measurement of this deformation is of current research interest. This paper considers the computation of cup depth, a measurement of the depth of the internal limiting membrane (ILM). The computation of cup depth requires a reference structure against which to measure the ILM, and the construction of two reference structures is discussed, one based on Bruch's membrane opening (BMO) and the other based on the anterior surface of the peripapillary sclera (AS). A main focus of the paper is the robust computation of mean cup depth, which requires a good sampling of a reconstruction of the ILM surface. To evaluate our algorithm, the construction of synthetic datasets is considered.