how to find the edges of a transparent dome shaped canopy by using holographic projected images
excerpt taken from Characterising Fulldome Planetarium Projection Systems:
The Limitations Imposed by Physics, and Suggestions on
How to Mitigate
Max R. R¨oßner*
, Lars Lindberg Christensen*
, and Claude Ganter**
*European Southern Observatory
**Sky-Skan, Inc.
June 21, 2016
The Dome as an Optical Component
The largest optical element in a fulldome theatre is the dome itself. The fact that this projection
surface is curved (in contrast to a flat screen in a mainstream movie theatre) causes the dome
to act as an integrating sphere.
Integrating spheres are widely used in optical engineering to smooth out the directional characteristic
of a light source that is to be characterised, averaging over all spatial directions. A
projection dome can be modelled as an integrating sphere cut in half.
When content is projected onto the dome, light is being scattered and reflected not only into
the eyes of the spectators, but is also spread over the entire dome surface. This cross-scattering
compromises contrast as dark areas in the projected image now appear brighter. The image is
said to be “washed out” (refer to figure 1).
2
Figure 1: Simulation-generated images to illustrate the effect of cross-scattering. Left: Original
image; Right: After cross-scattering. The simulation is based on the algorithm presented in [5]
but was exaggerated here for clarity. (Image credit: ESO/S. Brunier)
Therefore, a compromise has to be found between high reflectivity (bright projection with low
contrast) and low reflectivity (dark projection with high contrast). A mathematical foundation,
backed with actual “real world” measurements, can help understand the mechanisms of dome
projection.
3 Model
To further explore the light propagation in a projection dome, a physical model is introduced
here, inspired by the models describing integrating spheres used in optical measurement systems.
The geometry inside an integrating sphere with a surface that is a Lambertian (i.e. diffuse)
scatterer means that light being scattered from one surface element is equally(!) distributed
to all other surface elements of the sphere. As an extreme example, two adjacent pixels of the
projection can exchange the same amount of light as two pixels on opposite sides of the dome. [6]
The fill factor f, suggested in [5], is used to describe the type of content projected in the
planetarium. 0 ≤ f ≤ 1 is the fraction of possible bright content sent to the dome from the
projectors. For example, a fully black frame would be described by f = 0, a fully white frame
by f = 1 and a checkerboard pattern by f = 0.5. Examples for various fill factors can be seen
in figure 2.
Figure 2: Test pattern fulldome frames with increasing fill factors, from f = 0 (left) to f = 1
(right). Note a periodic pattern is not required by the presented theory.