Microstructures for transforming light having Lambertian distribution into batwing distributions
A light transmissive substrate for transforming a Lambertian light distribution into a batwing light distribution. The light transmissive substrate includes a first surface comprising a plurality of microstructures, and a second surface on a side of the substrate opposite the first surface. The substrate is configured to receive light in a Lambertian distribution from a light source at the first surface and transform the light into a batwing distribution exiting the second surface. The batwing distribution having a peak intensity at about ±30° to about ±60° from X and Y axes, and a minimum intensity at nadir.
1. A light transmissive substrate for transforming a Lambertian light distribution into a batwing light distribution, the light transmissive substrate comprising:
a first surface comprising a plurality of microstructures; and
a second surface on a side of the substrate opposite the first surface, wherein each of the plurality of microstructures has a shape of a pyramid with a roof angle of between about 70° and about 95 and extending in a direction away from the second surface and at least one of the plurality of the microstructures are made from material having a refractive index of about 1.5,
wherein the substrate is configured to receive light in a Lambertian distribution from a light source at the first surface and transform the light into a batwing distribution exiting the second surface, the batwing distribution having a peak intensity at about ±30° to about ±60° from X and Y axes, and a minimum intensity at nadir.
2. The light transmissive substrate according to claim 1 , wherein each pyramid has a base portion and a top portion connected to the base portion, the top portion comprising a tip of the pyramid and having sides disposed at different angles than sides of the base portion.
3. The light transmissive substrate according to claim 2 , wherein at least the microstructures are the made from material having a refractive index of about 1.5, the sides of the base portion are disposed at angles of about 55° relative to a plane substantially parallel to the second surface, and the top portion has a roof angle of between about 85° and about 90°.
4. The light transmissive substrate according to claim 1 , wherein the second surface is substantially planar.
5. The light transmissive substrate according to claim 1 , wherein the second surface comprises a texture.
6. A light transmissive substrate for transforming a Lambertian light distribution into a batwing light distribution, the light transmissive substrate comprising:
a first surface comprising a plurality of microstructures, wherein each of the plurality of microstructures has a shape of a frustum of a pyramid and a recess in a shape of a reverse pyramid; and
a second surface on a side of the substrate opposite the first surface,
wherein the substrate is configured to receive light in a Lambertian distribution from a light source at the first surface and transform the light into a batwing distribution exiting the second surface, the batwing distribution having a peak intensity at about ±30° to about ±60° from X and Y axes, and a minimum intensity at nadir.
7. The light transmissive substrate according to claim 6 , wherein at least the microstructures are made from material having a refractive index of about 1.5, sides of the frustum are disposed at angles of about 55° relative to a plane substantially parallel to the second surface, and the reverse pyramid has a roof angle of between about 85° and about 90°.
8. The light transmissive substrate according to claim 6 , wherein the second surface comprises a texture.
9. The light transmissive substrate according to claim 6 , wherein the second surface is substantially planar.