I have previously posted an idea about using a Luneburg microlens array to make a 3D display (see link).
The problem is that optical Luneburg lenses had not been been made as of 2011 (see "Hooke's Dream Lens" link), and since then there are very few convincing examples of real optical Luneburg lenses.
An
optical Luneburg lens requires spherical shells of increasing refractive index material. I have previously proposed a method of making a Luneburg lens, but that seems overly complicated (see "hot flocking Luneburg lens").
What is need is a relatively simple way of forming the spherical shell layers in a carefully controlled manner.
I propose a method comprising the following steps:
1. start with a gradient refractive index optic fibre.
Although there are several ways of doing this, my preferred method is using concentric tubes of glass and plastic (I'll explain why later) with different refractive index. For example 100 tubes of 1mm thickness forming a cylinder with diameter of 10cm.The glass tubes are then heated to form a cylinder and then drawn to form a thin fibre.
2. Cut or mill the optic fibre longitudinally so that its shape is a extruded semicircle.
3. Heat and then fold the semicircular fibre on itself so it forms a whole optic fibre again.
4. Cut the folded end of the folded optic fibre. This is a hemisphere.
5. hold two hemispheres together to form a sphere. Heat to form a sphere.
6. the Luneburg lens is formed.
Note that a Luneburg lens in an air medium is impossible, since the outer shells of the Luneburg lens are at (and then progressively higher than) the refractive index of the medium. There are no solids with a refractive index of 1 and slightly above 1.
Instead a Luneburg lens in a medium with a refractive index of say 1.3 could be made. This would require layer with refractive index ranging from 1.3 to 1.85. Plastic layers would be in the range 1.3 to 1.5 and glass layers from 1.5 to 1.85.
Folding the half optic fibre would need to be optimised to result in a perfect hemisphere. For example, the half optic fibre might have a semi-ellipse cross section rather than a semi-circle cross section. The folding could be done into a hemispherical mold to help form the hemisphere perfectly.