We compare three different methods to co-optimize hybrid optical / digital imaging systems with a commercial lens design software: conventional optimization based on spot diagram minimization, optimization of a surrogate criterion based on a priori equalization of modulation transfer functions (MTFs), and minimization of the mean square error (MSE) between the ideal sharp image and the image restored by a unique deconvolution filter. To implement the latter method, we integrate-for the first time to our knowledge-MSE optimization to the software Synopsys CodeV. Taking as application example the design of a Cooke triplet having good image quality everywhere in the field of view (FoV), we show that it is possible, by leveraging deconvolution during the optimization process, to adapt the spatial distribution of imaging performance to a prescribed goal. We also demonstrate the superiority of MSE co-optimization over the other methods, both in terms of quantitative and visual image quality. This pre-print as been published as: Alice Fontbonne, Hervé Sauer, and François Goudail, "Comparison of methods for end-to-end co-optimization of optical systems and image processing with commercial lens design software," Opt. Express 30, 13556-13571 (2022)