Model Derivation


Unlike conventional cameras, a Standard Plenoptic Camera comes with an array of micro lenses attached to the image sensor to acquire depth information. As can be seen from the animation figure below, the lenslet array is 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 example above only depicts 6 micro lenses. If the main lens is modelled as a thin lens, a special type of chief rays can be seen to cross the optical centre of the main lens just as a micro lens' optical centre. Closer inspection reveals that each of these rays (yellow) impinges on a centre of a respective micro image. From that, adjacent micro image positions can be found that are separated by a constant width, commonly known as pixel pitch. Given a position below the micro image centre, the animation indicates how corresponding chief rays (blue) are traced back to object space. The same applies 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 glass 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]


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 refocusing distance of a standard plenoptic photograph   [Invited Paper]

C. Hahne, A. Aggoun, and V. Velisavljevic, "The refocusing distance of a standard plenoptic photograph," in 3D-TV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON), 8-10 July 2015.

[PDF] [BibTex] [Slides]


Light field geometry of a standard plenoptic camera

C. Hahne, A. Aggoun, S. Haxha, V. Velisavljevic, and J. Fernández, "Light field geometry of a standard plenoptic camera," Opt. Express 22, Issue 22, 26659-26673 (2014).

[PDF] [BibTeX]


Baseline of virtual cameras acquired by a standard plenoptic camera setup

C. Hahne, A. Aggoun, S. Haxha, V. Velisavljevic, and J. Fernández, "Baseline of virtual cameras acquired by a standard plenoptic camera setup," in 3D-TV-Conference: The True Vision - Capture, Transmission and Display of 3D Video (3DTV-CON), 2-4 July 2014.

[PDF] [BibTex]


Embedded FIR filter design for real-time refocusing using a standard plenoptic video camera   [Invited paper]

C. Hahne and A. Aggoun, "Embedded FIR filter design for real-time refocusing using a standard plenoptic video camera," Proc. SPIE 9023, in Digital Photography X, 902305 (March 7, 2014).

[PDF] [BibTex]



If you have any questions, feel free to contact:   info [ät] christopherhahne.de