Sometimes I see something in the news that just makes me excited about math. This is the kind of development I would love to explore with a class if I had a few days or weeks to spare! On the other hand, it might form the basis of a great project for a motivated student or group of students.
The company Lytro has introduced the first commercially available light field camera. A traditional camera captures the intensity of light (including relative color intensity) arriving at every point on a film or, in a digital camera, a sensor. A light field camera captures both the intensity and direction of light as it strikes the sensor — it record vectors, rather than scalars (and, in particular, in place of a single scalar it must record multiple vectors, since many different light rays will be striking in the same place). What is the practical upshot? Among other things, you can change the focus after the picture is taken! Follow this link to give it a try (click on the picture to change the focus).
- Learn about focus, and how traditional cameras record a picture. Discuss limitations.
- Learn about vectors and light fields. There is a range of mathematics to explore that could be adapted to different skill levels, from an introduction to vectors up through the algorithms used by the camera.
- Explore the practical and mathematical possibilities of a light field camera. If you can get your hands on one (they’re about $399), take some photos and do a demo!
- How does this “lack of focus on focus” affect the process of photography? Does it affect the way you frame your shots, the kinds of subjects you choose, and so on?
An overview for a general audience can be found on the Lytro “Science Inside” page. For more details, check out Lytro CEO Ren Ng’s surprisingly readable Stanford dissertation on the subject. This is only the latest work to come out of Stanford’s Computer Graphics Laboratory on light fields and related technologies.