The idea of having a "field" is that a 2d slice of it allows calculating light elsewhere from the field using optical propagation calculations. But this require

The idea of having a "field" is that a 2d slice of it allows calculating light elsewhere from the field using optical propagation calculations. But this requires phase measurements in addition to intensity which is only what conventional cameras capture. It could be easier to understand by looking the parts of a light field camera. Compared to a conventional camera, one type of light field camera has a micro-lens array just before the sensor. So this is like placing a Shack-Hartmann wavefront sensor over the image (apologies for another technical term, but that roughly explains the concept and is easily looked up, implementation details might be different though). An ordinary photograph only stores intensities, so changing the focus given the recorded image is not possible using physical optics calculations (ML/AI algorithms might do the trick, but that's something else). Based on the image formed from each lens in the micro-lens array (i.e. the displacement of the focus from the sensor), it is possible to retrieve the wavefront or lightfield which allows subsequent optics calculations, like post-focusing. The tradeoff is that each micro-lens in the array needs a decent number of pixels for analysis, so the effective 2d resolution is decreased as compared to using all the pixels.