Apparatus and method for use in fulfilling illumination prescription
The present embodiments provide methods, apparatuses, and assemblies for use in producing a desired output beam that meets a desired intensity prescription. An apparatus can include an input surface, and an optically active output surface that receives a collimated beam, such that the output surface refractively maps an illuminance distribution of the collimated beam into a prescribed intensity pattern. The apparatus can include a collimating lens that collimates an input beam. Additionally, the output surface can be defined according to a cumulative illumination integral for the illuminance distribution and a cumulative illumination integral of the intensity pattern. Some embodiments provide methods that can determine an illumination integral for an illuminance pattern of an input, determine an intensity prescription, establish a spatio-angular correspondence of the input beam with the intensity prescription, derive surface normal vectors, and determine the output surface according to the surface normal vectors.
1. A method for use in defining a lens profile, comprising:
determining an illumination integral for an illuminance pattern of an input beam;
determining a far-field intensity prescription;
establishing a one to one spatio-angular correspondence of transverse location of the input beam with direction in the intensity prescription;
deriving surface normal vectors of an output surface of the transverse locations across the input beam; and
determining the output surface according to the surface normal vectors.
2. The method of claim 1 , further comprising:
determining a normalized cumulative illumination integral for the far-field intensity prescription.
3. The method of claim 2 , wherein the determining the illumination integral further comprises determining a normalized illumination integral for the transverse illuminance pattern.
4. The method of claim 3 , further comprising:
determining modifications for the output surface; and
applying modifications to the output surface to attain the intensity prescription.
5. The method of claim 1 , further comprising:
collimating the input beam generating a collimated input beam; and
the determining the illumination integral for the illuminance pattern of the input beam comprises determining the illumination integral for the illuminance pattern of the collimated input beam.
6. The method of claim 5 , wherein the determining the output surface according to the surface normal vectors comprises determining the output surface so that the intensity prescription is a rectangular pattern.
7. The method of claim 1 , wherein the establishing a one to one spatio-angular correspondence comprises assigning a unique far-field divergence angle to a plurality of spatially related radiuses within the input beam.
8. A method for use in defining a lens profile, comprising:
determining an intensity prescription;
determining an illuminance pattern of an input beam; and
defining an optically active surface of a lens, comprising:
integrating a cumulative flux distribution of the determined illuminance pattern;
integrating a cumulative flux distribution of the determined intensity prescription and obtaining first and second factored profile angles;
sweeping the first profile angle along a space defined by the second profile; and
defining the optically active surface according to the sweep of the first profile angle.
9. The method of claim 8 , further comprising:
modifying the determined optically active surface at perimeters of the determined active surface.
10. The method of claim 9 , further comprising:
determining a subsequent intensity prescription according to the defined optically active surface;
repeating the defining of the optically active surface of the lens; and
determining a subsequent optically active surface according to the subsequent intensity prescription.
11. The method of claim 8 , wherein the integrating the cumulative flux distribution of the determined illuminance pattern comprises calculating a one dimensional integration for a first axis and calculating a one dimensional integration for a second axis; and
wherein the integrating the cumulative flux distribution of the determined intensity prescription comprises calculating a one dimensional integration for the first profile angle and calculating a one dimensional integration for the second profile angle.
12. The method of claim 11 , wherein the integration of the first axis and the integration of the second axis are made equal to a cross-section of the input beam, where the input beam is circularly symmetric.