User:Tohline/Appendix/CGH/COLLADAdemonstration
Embracing COLLADA: Demonstration Steps
Here we outline a sequence of steps that likely should be taken in order to build confidence in the Principal Illustration of computer-generated holography that has been laid out in our accompanying discussion.
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Construct a Solid Cube
The desire, here, is to construct a single 2D holographic aperture that will simultaneously generate all six square sides of a cube. We ultimately will furthermore want to break each square side into a pair of triangles, that is, we want to construct a single 2D holographic aperture that will simultaneously generate twelve appropriately aligned triangles. If we learn how to do this effectively, then we will in principle have a tool that can construct 2D holographic apertures that can generate arbitrarily complex "video game" scenes that are composed of a very large number of triangles. Our desire is to be able to construct any already existing video scene by reading in the coordinates of the triplet of points that make up every imaged triangle.
Use Summations
STEP 1: First assume that a square aperture is chopped into 51 × 51 equally spaced points of light, each with a zero phase and uniform brightness. Now, construct a (2D) image plane that is parallel to the aperture and located a distance D from the aperture, and determine the amplitude and phase of the combined light that arrives at each of 51 × 51 locations on the image scene. Given the wavelength of the monochromatic light leaving the aperture, and the chosen distance D, pick widths for the aperture and image screen that make sense. The result should be the generation of a 2D sinc function across the image plane.
STEP 2: Now, flip this construction inside out. Shrink the image plane down to the size of the original aperture and illuminate it such that the phase of the light is zero everywhere, but the amplitude of the light is given by the 2D sinc function. This will be the new aperture. Now construct a new (2D) image plane that is parallel to the new aperture and located the same distance D from the aperture, and determine the amplitude and phase of the combined light that arrives at each of the 51 × 51 locations on this new image screen. The result should be some thing quite close to a uniformly illuminated square. This shows us how to light an aperture — in this case, light it with a 2D sinc function — in order for the resulting holographic image to be one uniformly illuminated face of a cube. Let's label this as "side A" of the cube.
Use Analytic 'Sinc' Functions
See Also
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© 2014 - 2021 by Joel E. Tohline |