In previous posts, I’ve talked at some length about computed tomography (CT) and optical coherence tomography (OCT). Each of these is a technique for determining information about the internal structure of an object, such as the human body, from exterior measurements of the scattering of electromagnetic waves from the object. In the case of CT, x-rays are used to measure and image a cross-sectional ‘slice’ of the human body, while in OCT, broadband visible light is used to probe a few millimeters into the skin or an internal organ of the human body.
Plenty of other techniques exist for measuring the internal structure of objects, using a variety of different types of waves. Magnetic resonance imaging (MRI) subjects a patient to an intense magnetic field, and makes an image by measuring the radio waves emitted when the field is suddenly switched. Ultrasound imaging uses ultrasonic waves to probe the soft tissues of the human body, and is used in mammography.
Each of these techniques is quite different in its range of application, but all require nontrivial mathematical techniques to reconstruct an image from the raw scattered wave data. These mathematical techniques are broadly grouped into a class of problems known as inverse problems, and I thought it would be worth an optics basics post to discuss inverse problems, their common features, and the challenges in solving them.

