[CLAIMS] [Claim 1]
An optic to transform incident light emitted by a light source to form an irradiation pattern on a projection surface, wherein the optic has a freeform surface formed by a union of an aspheric lens and a collection of Cartesian ovals, wherein each Cartesian oval is a lens focusing the incident light to a point, and wherein the collection of Cartesian ovals directs the incident light to a collection of points forming a border of the irradiation pattern, and wherein the aspheric lens is a portion of a refractive lens directing the incident light to form an interior of the irradiation pattern, wherein the aspheric lens is combined with the collection of Cartesian ovals to form the union, such that each Cartesian oval shares a radiant focus of the refractive lens and makes a tangential contact with the surface of the aspheric lens at a single point. [Claim 2]
The optic of claim 1, wherein the intensity of the incident light follows Lambert's cosine law, such that the light source is a Lambertian light source, wherein the refractive lens is a Lambertian-uniformizing spot lens reversing the Lambert's cosine law to produce, in response to illumination by the Lambertian light source, a uniform irradiation on the projection surface forming the interior of the irradiation pattern. [Claim 3]
The optic of claim 2, wherein each Cartesian oval shares the radiant focus of the Lambertian-uniformizing lens, wherein each Cartesian oval has a unique focus on the border of the irradiance pattern defined by an optical axis of the Cartesian oval, and wherein each Cartesian oval makes a tangential contact with the surface of the aspheric lens at a unique point. [Claim 4]

The optic of claim 1, wherein at least some Cartesian ovals in the collection of Cartesian ovals have different geometric parameters defined by a focus of the Cartesian ovals on the border of the irradiance pattern and a location of the tangential contact with the refractive lens. [Claim 5]
The optic of claim 1, wherein the freeform surface of the lens formed by the union of the aspheric lens and the collection of Cartesian ovals is a surface of the refractive lens having a divot routing rays of the incident light passing through the divot from an exterior of the irradiation pattern to the border of the irradiation pattern. [Claim 6]
The optic of claim 1, wherein the incident light is collimated, the refractive lens has a flat surface, each the Cartesian oval includes a hyperboloid shape and makes the tangential contact with the surface of the aspheric lens at a hyperboloid vertex. [Claim 7]
The optic of claim 1, wherein the illumination pattern includes a glyph. [Claim 8]
The optic of claim 1, wherein the illumination pattern includes letters forming a word. [Claim 9]
The optic of claim 1, wherein the illumination pattern includes a two-tone image. [Claim 10]
The optic of claim 1, wherein a surface of the optic opposite to the freeform optical surface is frosted, such that the illumination pattern is formed on the frosted surface. [Claim 11]

A luminaire, comprising:
the optic of claim 1; and
the light source arranged in the luminaire to emit the light onto the freeform optical surface to produce the illumination pattern. [Claim 12]
The luminaire of claim 11, wherein the light source includes a light-emitting diode (LED). [Claim 13]
The luminaire of claim 12, wherein the shape of the freeform optical surface is a function of an arrangement of the LED with respect to the freeform optical surface. [Claim 14]
The method for fabricating an optic, comprising:
determining a freeform optical surface transforming incident light emitted by a Lambertian light source into an illumination pattern on a projection surface, wherein the freeform optical surface of the optic is formed by a union of a portion of a Lambertian-uniformizing spot lens producing, in response to illumination by the Lambertian light source, a uniform irradiation on the projection surface forming an interior of the irradiation pattern, and a collection of Cartesian ovals focusing the light from the Lambertian light source along the border of the irradiation pattern; and
fabricating the optic having the freeform optical surface. [Claim 15]
The method of claim 14, further comprising:
determining the Lambertian-uniformizing spot lens transforming the incident light emitted by the Lambertian light source into uniform irradiation of the projection surface;

determining the portion of the Lambertian-uniformizing spot lens contributing to the irradiation of the interior of the irradiation pattern;
determining a volume formed by the collection of Cartesian ovals focusing the light from the Lambertian light source along the border of the irradiation pattern; and
combining the portion of the Lambertian-uniformizing spot lens with the volume to form the freeform optical surface of the optic, such that each Cartesian oval makes a tangential contact with the portion of the Lambertian-uniformizing lens at a single unique point. [Claim 16]
An optic, comprising:
an aspheric lens formed by a portion of a Lambertian-uniformizing spot lens transforming incident light emitted by a Lambertian light source into uniform irradiation; and
a union of Cartesian ovals, wherein each Cartesian oval is a lens focusing incident light to a point, wherein each Cartesian oval shares the radiant focus of the Lambertian-uniformizing lens and makes a tangential contact with the surface of the aspheric lens at a single unique point. [Claim 17]
A luminaire, comprising:
the optic of claim 16; and
the Lambertian light source arranged in the luminaire to emit the light onto the optic, wherein the Lambertian-uniformizing spot lens transforms the incident light emitted by the Lambertian light source into uniform irradiation forming an interior of an irradiation pattern, and wherein each Cartesian oval transforms the incident light emitted by the Lambertian light source onto a corresponding point at a border of irradiation pattern. [Claim 18]

The luminaire of claim 17, wherein the illumination pattern includes a letter, such that the union of Cartesian ovals directs the incident light to form a contour of the letter and the Lambertian-uniformizing spot lens directs the incident light inside the contour.