Relating transverse ray error and light fields in plenoptic camera images

Plenoptic cameras have emerged in recent years as a technology for capturing light field data in a single snapshot. A conventional digital camera can be modified with the addition of a lenslet array to create a plenoptic camera. The camera image is focused onto the lenslet array. The lenslet array is placed over the camera sensor such that each lenslet forms an image of the exit pupil onto the sensor. The resultant image is an array of circular exit pupil images, each corresponding to the overlying lenslet. The position of the lenslet encodes the spatial information of the scene, whereas as the sensor pixels encode the angular information for light incident on the lenslet. The 4D light field is therefore described by the 2D spatial information and 2D angular information captured by the plenoptic camera. In aberration theory, the transverse ray error relates the pupil coordinates of a given ray to its deviation from the ideal image point in the image plane and is consequently a 4D function as well. We demonstrate a technique for modifying the traditional transverse ray error equations to recover the 4D light field of a general scene. In the case of a well corrected optical system, this light field is easily related to the depth of various objects in the scene. Finally, the effects of sampling with both the lenslet array and the camera sensor on the 4D light field data are analyzed to illustrate the limitations of such systems.