In this work, we consider how to optimize an optical system, specifically one with diffractive optical elements (DOE). We start by describing optical theory called Fourier optics also known as wave optics. This type of optics is found by making assumptions from the Maxwell equations for magnetic and electrical fields. This leads us to the Rayleigh-Sommerfeld diffraction integral, which we need to propagate light. To optimize an optical system, we introduce the standard optimization methods used when gradients are available and also dive into data-driven methods. Two wellknown algorithms in each category: the Adam optimization method, which is an extension of normal gradient descent methods, and the UNet convolutional neural network. To make the optimization methods work with our physics simulation, we use an automatically differentiable implementation which gives the gradients for the optimization. Combining the two optimization methods with our optics engine, we optimize optical designs such that the resulting intensity on the sample plane resembles some target intensity. We are able to optimize systems with single and multiple DOE and for high and low resolution DOE designs. We find that more lenses makes the optimization better and increases the variability in the created projection. We also find that increasing the resolution severely slows down the optimization with the Adam method. Although, the optimization method Adam is well suited for this optimization task. It becomes computationally very expensive on high resolution due to the physics simulation at every optimization step. Some physical simulations require high resolution to make sure the simulation does not contain to much artefacts. We show that the data-driven approach has potential to solve this issue. We train a network that takes as input a target intensity and outputs the lens that produces that intensity. Combining these results, we conclude that modern optimization methods are well suited for optical system optimization and we find that there is a large untapped potential for data-driven methods in optics.