Teaching Optical Systems by Example

An optical imaging system generally measures a property of an object as a function of its special coordinates and makes this information available for further use. Conventionally, the design of the system relies on our understanding of the physical properties of the optical system that transfers the light scattered by the object to the detector. For example, since a lens undoes the blurring that occurs when a light field propagates through free space it is used to focus a distant object onto a 2D sensor directly forming an image. In other cases, the situation is more complex and it is not possible to present to the detector directly a clear image of the unknown object. In such cases, the detected signal must be processed further in order to extract the image. In this presentation, we describe how we can perform imaging in such complex systems through the presentation of examples. We describe two cases. First, we consider a multi-mode fiber as an imaging element and we show that we can learn to transmit or interpret arbitrary images sent through the fiber by training the fiber with a set of basis functions. Secondly, we show that we can learn the shape of an object from examples formed by reconfiguring the optical system in a predictable way. We demonstrate this second modality by constructing a neural network that models the optical system and training the network to reproduce the experimentally measured data. The adaptable parameters of the trained network yield the image of the unknown object.