Co-design consists in optimizing an imaging system by taking into account the scene and image formation model, the imaging system and the method of information extraction [Stork and Robinson 2008]. For several years, our team has co-designed phase masks to increase the depth-of-field of optical imaging systems where the end product is a restored image [Diaz et al. 2011, Burcklen et al. 2015, Falcón et al. 2017]. These masks produce a relatively blurred image which quality is independent of the axial position of the object. It is then possible to reconstruct the object at all depths by applying a unique deconvolution process. This co-optimization approach can be formulated by defining the optimization criterion of the phase function of the mask as the mean square difference between an ideal sharp image and the deconvolved image delivered by the system [Mirani et al. 2005, Robinson and Stork 2006, Mirani et al. 2008]. In general, it is preferable to optimize the masks using a closed-form criterion since it considerably accelerates optimization. That is the case if the deconvolution is carried out using a Wiener filter. However, nonlinear deconvolution algorithms are known to have better performance. The question therefore arises as to whether better imaging performance can be obtained by taking into account a nonlinear deconvolution algorithm instead of a linear one in the optimization criterion. To answer this question, we propose to compare the image qualities obtained with these two approaches. We show that the masks obtained by optimizing criteria based on linear and nonlinear algortihms are identical and propose a conjecture to explain this behavior [Lévêque et al. 2021]. This result is important since it justifies a frequent practice in co-design which consists in optimizing a system with a simple analytical criterion based on a linear deconvolution and restoring images with a more efficient nonlinear deconvolution algorithm [Portilla and Barbero 2018].