Method of producing a reflective or refractive surface

Patent metadata

Field	Value
Publication number	US-9576553-B2
Application number	US-201313974989-A
Country	US
Kind code	B2
Filing date	Aug 23, 2013
Priority date	Sep 13, 2012
Publication date	Feb 21, 2017
Grant date	Feb 21, 2017

Abstract

A method and apparatus for producing a reflective or refractive surface that reflects or refracts light shined thereon and reproduces on a screen a desired greyscale intensity image on which the reflective or refractive surface is based and a corresponding apparatus, wherein the method permits a reproduction of a reference grayscale image with adjustable precision.

First claim

We claim:

1. A method for forming a reflective or refractive surface, comprising:
providing a processor;
discretizing a two-dimensional image formed on a first surface into a first mesh of a plurality of first nodes on the first surface via the processor, wherein a first portion of the plurality of the first nodes on the first surface defines a first cell area A d,1 of the first mesh on which a first beam of light with a first radiant flux Φ 1 is incident, and a second portion of the plurality of the first nodes on the first surface defines a second cell area A d,2 of the first mesh on which a second beam of light with a second radiant flux Φ 2 is incident, and wherein the second cell area A d,2 of the first mesh is adjacent to the first cell area A d,1 of the first mesh and the first cell area A d,1 of the first mesh and the second cell area A d,2 of the first mesh have at least one first one node of the plurality of first nodes in common;
discretizing a reflective or refractive second surface into a second mesh of a plurality of

second nodes on a second surface via the processor, wherein a first portion of the plurality of the second nodes on the second surface defines a first cell area A s,1 of the second mesh on which the first beam of light with the first radiant flux Φ 1 is incident and is deviated towards the first cell area A d,1 of the first mesh, and a second portion of the plurality of the second nodes on the second surface define a second cell area A s,2 of the second mesh on which the second beam of light with the second radiant flux Φ 2 is incident and is deviated towards the second cell area A d,2 of the first mesh, and wherein the first cell area A s,1 of the second mesh is adjacent to the second cell area A s,2 of the second mesh and the first cell area A s,1 of the second mesh and the second cell area A s,2 of the second mesh have at least one second node of the plurality of second nodes in common;
in an iterative optimization process, adjusting positions of one or more second nodes of the first portion of the plurality of second nodes of the first cell area A s,1 of the second mesh on the second surface via the processor, so that the first cell area A s,1 of the second mesh corresponds to a first radiant exitance M 1 of the first beam of light on the first cell area A s,1 of the second mesh on the second surface, wherein the first radiant exitance M 1 corresponds to a brightness of the two-dimensional image in the first cell area A d,1 of the first mesh; and
adjusting positions of one or more second nodes of the second portion of the plurality second nodes of the second cell area A s,2 of the second mesh on the second surface via the processor, so that the second cell area A s,2 of the second mesh corresponds to a second radiant exitance M 2 of the second beam of light on the second cell area A s,2 of the second mesh on the second surface, wherein the second radiant exitance M 2 corresponds to a brightness of the two-dimensional image in the second cell area A d,1 of the first mesh.

2. The method according to claim 1 , further comprising: determining surface normals at each of the one or more second nodes of the first portion of the plurality of second nodes defining the first cell area A s,1 of the second mesh on the second surface with adjusted positions on the second surface via the processor, the surface normals corresponding to rays of the first beam of light that are incident on the second surface and extend between the one or more second nodes of the first portion of the plurality of second nodes defining the first cell area A s,1 of the second mesh with adjusted positions and the first portion of the plurality of first nodes of the first cell area A d,1 of the first mesh on the first surface; and calculating a height field corresponding to the surface normals via the processor, the height field corresponding to the surface normals defining the reflective or refractive second surface.

3. The method according to claim 2 ,
wherein a field of surface normals corresponding to the surface normals is continuous and the height field corresponding to the surface normals is continuously differentiable.

4. The method according to claim 1 ,
wherein the first mesh of the plurality of first nodes and the second mesh of the plurality of second nodes are triangular, or quadrilateral, meshes comprising triangular, or quadrilateral, cell areas, respectively.

5. The method according to claim 1 ,
wherein the first mesh of the plurality of first nodes is a regular fixed mesh.

6. The method according to claim 1 , wherein the first beam of light and the second beam of light comprise the same radiant exitance M i on the second surface.

7. An apparatus for forming a reflective or refractive surface, comprising:
a processor,
wherein the apparatus is configured to perform the method of claim 1 .

8. One or more non-transitory computer readable media having executable programming instructions stored thereon that, when executed by one or more processors of a device cause the one or more processors to perform a method according to claim 1 .

9. A method for forming a reflective or refractive surface, comprising:
providing a processor;
discretizing a two dimensional image formed on a first surface into a first mesh of a plurality of first nodes on the first surface via the processor,
wherein a first portion of the plurality of first nodes on the first surface defines a first cell area A d,1 of the first mesh on which a first beam of light with a first radiant flux Φ 1 is incident, and a second portion of the plurality of first nodes on the first surface defines a second cell area A d,2 of the first mesh on which a second beam of light with a second radiant flux Φ 2 is incident, and
wherein the second cell area A d,2 of the first mesh is adjacent to the first cell area A d,1 of the first mesh and the first cell area A d,1 of the first mesh and the second cell area A d,2 of the first mesh have at least one first node of the plurality of first nodes in common;
discretizing a reflective or refractive second surface into a second mesh of a plurality of second nodes on a second surface via the processor,
wherein a first portion of the plurality of second nodes on the second surface defines a first cell area A s,1 of the second mesh on which the first beam of light with the first radiant flux Φ 1 is incident, and a second portion of the plurality of second nodes on the second surface defines a second cell area A s,2 of the second mesh on which the second beam of light with the second radiant flux Φ 2 is incident, and
wherein the second cell area A s,2 of the second mesh is adjacent to the first cell area A s,1 of the second mesh and the first cell area A s,1 of the second mesh the second cell area A s,2 of the second mesh have at least one second node of the plurality of second nodes in common;
in an iterative optimization process, adjusting positions of one or more first nodes of the first portion of the plurality of the first nodes defining the first cell area A d,1 of the first mesh on the first surface on which the two dimensional image is formed via the processor, so as to correspond to a first radiant exitance M 1 of the first beam of light on the first cell area A d,1 of the first mesh,
wherein the first radiant exitance M 1 corresponds to a brightness of the two-dimensional image in the first cell area A d,1 of the first mesh; and
adjusting positions of one or more first nodes of the second portion of the plurality of the first nodes defining the second cell area A d,2 of the first mesh on the first surface on which the two dimensional image is formed via the pro

Assignees

• Ecole Polytechnique Fed Lausanne Epfl

Inventors

• Pauly Mark
• Kiser Thomas

Classifications

• G02B27/0012 Primary

  Optical design, e.g. procedures, algorithms, optimisation routines · CPC title

• G09G5/02 Primary

  characterised by the way in which colour is displayed {(details of colour display specific for CRTs G09G1/28; specific for flat matrix panels other than liquid crystal displays G09G3/2003; specific for liquid crystal displays G09G3/3607)} · CPC title

• G02B27/0927

  Systems for changing the beam intensity distribution, e.g. Gaussian to top-hat · CPC title

• G06T17/20

  Finite element generation, e.g. wire-frame surface description, {tesselation} · CPC title

• G02B5/10

  with curved faces · CPC title