In this work, we investigate the effects of noise on real-time focal distance control for laser material processing by generating the images of a sample at different focal lengths using Fourier optics and then designing, training, and testing a deep learning model in order to detect the focal distances from the simulated images with varying standard deviations of added noise. We simulate both input noise, such as noise due to surface roughness, and output noise, such as detection camera noise, by adding zero-mean Gaussian noise to the source wave and the simulated image, respectively, for different focal distances. We then train a convolutional neural network combined with a Gaussian process classifier to predict focus distances of noisy images together with confidence ratings for the predictions.