Abstract: Estimating focus error in an image involves a training phase and an application phase. In the training phase, an optical system is represented by a point-spread function. An image sensor array is represented by one or more wavelength sensitivity functions, one or more noise functions, and one or more spatial sampling functions. The point-spread function is applied to image patches for each of multiple defocus levels within a specified range to produce training data. Each of the images for each defocus level (i.e. focus error) is sampled using the wavelength sensitivity and spatial sampling functions. Noise is added using the noise functions. The responses from the sensor array to the training data are used to generate defocus filters for estimating focus error within the specified range. The defocus filters are then applied to the image patches of the training data and joint probability distributions of filter responses to each defocus level are characterized.