We have developed a numerical raytrace model, SHELL3D, which simulates the backlit imaging of cryogenic inertial-confinement fusion (ICF) ignition capsules in three dimensions. We have used this model to investigate the limitations of backlit shadowgraphy as a diagnostic of hydrogen ice surface quality inside the capsules. We impose known modal perturbations upon the simulated inner ice surface, and produce simulated shadowgraphs which are then analyzed as if they were real experimental data. We find that power spectra derived from backlit shadowgraphs appear to be reliable indicators of ice surface power spectra out to Fourier mode numbers as high as 80. We also suggest that some advantages may be obtained by using a collimated backlight, and possibly by utilizing backlit transmission interferometry. These results support the conclusion that backlit shadowgraphy is a valid quantitative diagnostic of lower-mode ice surface imperfections inside transparent spherical ICF shells.