Model Derivation


Unlike conventional cameras, a Standard Plenoptic Camera comes with an array of micro lenses statically placed at the distance of the effective micro lens focal length fs in front of the image sensor.

Derivation of the ray tracing intersection model

Each micro lens projects a micro image on the sensor plane. For simplicity, the animated figure above only depicts 6 micro lenses with rays piercing through their optical centre, a property which defines them to be so-called chief rays. If the main lens is modelled as a thin lens, a special type of chief rays is seen to cross the optical centre of the main lens just as that of a micro lens. Closer inspection reveals that each of these plenoptic chief rays (yellow) impinges on a centre of a respective micro image. Taking this centre as a reference, adjacent micro image positions can be found which are separated by a constant width, commonly known as pixel pitch. Given micro image positions one pixel below the centre, the animation indicates how chief rays (blue) at the respective positions are traced back to object space by the aid of geometrical optics. Similarly, this is applied to chief rays impinging on positions above micro image centres (green).

Thereby, a basic principle of the Standard Plenoptic Ray Tracing Model relies on the property of collimated (i.e. parallel) light rays passing through a convex shaped lens. It is a well known fact in geometrical optics that parallel light rays travelling through a convex lens converge at the focal point on the image side of that lens. This also may be applied the other way around: Light rays that emitted from points along the focal plane diverge before entering the lens material and propagate in a parallel manner after passing through the lens material (See an example).

Taking advantage of the latter statement, it is possible to trace not only chief rays but all kinds of light rays starting from any point at the image sensor. Rays that impinge on an arbitrary position u0 are considered to be parallel in the range between micro lens s and main lens U. Such collimated light beams are refracted when travelling through the main lens and due to the parallel alignment, a light beam focuses at the main lens' focal plane FU. The height of the intersection point with the focal plane FU depends on the light beams' angle and therefore on u. Similar to the micro image position u0, adjacent positions (u1, u2) are traced through the lens system. For the sake of clearness, only chief rays of light beams are depicted in the model.

Since the Standard Plenoptic Ray Tracing Model has been derived, it is time to move on looking at animations describing the Refocusing Synthesis or the Sub-aperture Extraction.



Related Publications



Baseline and triangulation geometry in a standard plenoptic camera   

C. Hahne, A. Aggoun, and V. Velisavljevic, S. Fiebig, and M. Pesch "Baseline and triangulation geometry in a standard plenoptic camera," Int. J. of Comput. Vis. (IJCV), (2017).

[PDF] [BibTeX] [Code]


Refocusing distance of a standard plenoptic camera   

C. Hahne, A. Aggoun, and V. Velisavljevic, S. Fiebig, and M. Pesch "Refocusing distance of a standard plenoptic camera," Opt. Express 24, Issue 19, 21521-21540 (2016).

[PDF] [BibTeX] [Code] [Zemax file] [Image data]


The standard plenoptic camera: applications of a geometrical light field model   

C. Hahne, "The standard plenoptic camera: applications of a geometrical light field model," PhD thesis, Univ. of Bedfordshire, (January, 2016).

[PDF] [BibTeX]



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