I feel like calling this 5 dimensional is misleading. The "integration" over the pixel area just reflects the fact that the pixel is not infinitesimally small. To say it is a "dimension" of the system does not really convey any extra meaning to the "complexity" of the image. Calling Integration over the 2D lens and 2D pixel "4D" is the same as calling my own image "4D". The 2D pixel plane does not add dimension beyond the lens. The lens does not increase dimension, but instead it adds a transform to the planes of 2D information approaching the pixel plane.
I feel like calling this 5 dimensional is misleading. The "integration" over the pixel area just reflects the fact that the pixel is not infinitesimally small. To say it is a "dimension" of the system does not really convey any extra meaning to the "complexity" of the image. Calling Integration over the 2D lens and 2D pixel "4D" is the same as calling my own image "4D". The 2D pixel plane does not add dimension beyond the lens. The lens does not increase dimension, but instead it adds a transform to the planes of 2D information approaching the pixel plane.