Abstract: A design method of LED freeform surface illumination system based on XY-polynomial obtains a plurality of data points of a freeform surface, wherein each data point includes a coordinate value Qi and a normal vector Ni. A sum of squares e1(P) of coordinate differences in z direction between the coordinate value Qi and the freeform surface is applied, and by a sum of squares e2(P) between the normal vector Ni of the data points and normal vector ni of the freeform surface a modulus of vector differences is acquired. An evaluation function ƒ(p)=e1(P)+we2(P) is proposed and a plurality of freeform surface shapes obtained by selecting different weightings. The freeform surface shape which has the best imaging quality is achieved as a final shape, and a freeform surface lens based on the final shape is constructed to establish an LED freeform surface illumination system.

Abstract: A construction method of freeform surface shape based on XY-polynomial obtains a plurality of data points of a freeform surface according to an object point and an imaging point in a three-dimensional Cartesian coordinates system Oxyz. Each of the plurality of data points comprises a coordinate value Qi and a normal vector Ni. A first sum of squares e1(P) of coordinate differences in z direction between the coordinate value Qi and the freeform surface is applied, and by a second sum of squares e2(P) between the normal vector Ni of the data points and a normal vector ni of the freeform surface, a modulus of vector differences is acquired. An evaluation function ƒ(p)=e1(P)+we2(P) is proposed and a plurality of freeform surface shapes obtained by selecting and applying different weightings. A final freeform surface shape ?opt is chosen from the plurality of freeform surface shapes.

Abstract: An off-axial three-mirror optical system with freeform surfaces includes an aperture, a primary mirror, a secondary mirror, a tertiary mirror, and a detector. The aperture is located on an incident light path. The primary mirror is located on an aperture transmitted light path. The secondary mirror is located on a primary mirror reflected light path. The tertiary mirror is located on a secondary mirror reflected light path. The detector located on a tertiary mirror reflected light path. A primary mirror surface and a tertiary mirror surface have a same freeform surface equation, and the freeform surface equation is a sixth order x?y? polynomial. A secondary mirror surface is a tenth order aspherical surface.

Abstract: An off-axial three-mirror optical system with freeform surfaces includes a primary mirror, a secondary mirror, a tertiary mirror, and an image sensor. The primary mirror is located on an incident light path. The secondary mirror is located on a primary mirror reflecting light path. The tertiary mirror is located on a secondary mirror reflecting light path. The image sensor is located on a tertiary mirror reflecting light path. A primary mirror surface and a tertiary mirror surface are all xy polynomial freeform surfaces up to a fifth order. A secondary mirror surface is a planar surface.

Abstract: A laser includes a total reflective mirror, an output mirror, a discharge lamp, and an active laser medium. The total reflective mirror, the output mirror, and the discharge lamp define a resonant cavity. The active laser medium is filled in the resonant cavity. The total reflective mirror includes a microstructure. The microstructure is convex ring-shaped structure. The convex ring-shaped structure has a height and a width, and both the height and the width are in a range from about 0.5? to about 2?, while ? is a working wavelength of the laser.

Abstract: A laser includes a total reflective mirror, an output mirror, a discharge lamp, and an active laser medium. The total reflective mirror, the output mirror, and the discharge lamp define a resonant cavity. The active laser medium is filled in the resonant cavity. The total reflective mirror includes a body, a metal film, and at least one microstructure. The at least one microstructure is concaved from a first reflective surface of the total reflective mirror. The at least one microstructure has a depth and a lateral size, and both the depth and the lateral size are in a range from about 0.5? to about 2?, while ? is a working wavelength of the laser.

Abstract: An off-axial three-mirror optical system with freeform surfaces includes a primary mirror, a secondary mirror, a tertiary mirror, and an image sensor. The primary mirror is located on an incident light path. The secondary mirror is located on a primary mirror reflecting light path. The tertiary mirror is located on a secondary mirror reflecting light path. The image sensor is located on a tertiary mirror reflecting light path. The primary mirror, the secondary mirror, and the tertiary mirror are all xy polynomial surfaces up to the sixth order. The off-axial three-mirror optical system with freeform surfaces can achieve push-broom image with small F-number and large field angles.

Abstract: An off-axial three-mirror optical system with freeform surfaces includes a primary mirror, a secondary mirror, a tertiary mirror, and a detector. The primary mirror is located on an incident light path. The secondary mirror is located on a primary mirror reflecting light path. The tertiary mirror is located on a secondary mirror reflecting light path. The detector is located on a tertiary mirror reflecting light path. Each of the primary mirror, the secondary mirror, and the tertiary mirror is an xy polynomial freeform surface up to the fifth order.

Abstract: A method for designing off-axial three-mirror optical system with freeform surfaces is provided. A first initial surface, a second initial surface, and a third initial surface are established. A plurality of feature rays are selected, while the first initial surface and the third initial surface remain unchanged; a plurality of first feature data points are calculated to obtain a third freeform surface equation by surface fitting the plurality of first feature data points. A third freeform surface and the second initial surface are remained unchanged; a plurality of second feature data points are calculated to obtain a first freeform surface equation by surface fitting the plurality of second feature data points. The third freeform surface and a first freeform surface are remained unchanged; a plurality of third feature data points are calculated to obtain a second freeform surface equation by surface fitting the plurality of third feature data points.

Abstract: A method for designing freeform surface is provided. An initial surface is established. A plurality of feature rays are selected. A plurality of intersections of the plurality of feature rays with an unknown freeform surface are calculated based on a given object-image relationship and a vector form of the Snell's law. The plurality of intersections are a plurality of feature data points. An unknown freeform surface equation is obtained by surface fitting the plurality of feature data points.

Abstract: A design method of LED freeform surface illumination system is provided. A light emitting angle of a LED point light source is divided into three regions. Each region can form a rectangular light spot on a light receiving surface. A mapping relationship of each region on the receiving surface is obtained. A light redistribution design for the LED point light source is performed and a system of first order partial differential equations of a freeform surface is achieved. A system of first order quasi linear differential equations of the freeform surface is obtained. A plurality of freeform surface data is obtained by solving the system of first order quasi linear differential equations. The freeform surface is obtained by surface fitting the plurality of freeform surface data.

Abstract: A LED freeform surface illumination system is provided. The LED freeform surface illumination system includes a LED point light source, a freeform surface lens, and a light receiving surface. A light emitting angle ? of the LED point light source is divided into three regions. The freeform surface lens includes a spherical surface and a freeform surface opposite to the spherical surface. The freeform surface comprises three annular regions. Each region of the three regions of the light emitting angle ? of the LED point light source corresponds with one annular region of the freeform surface. Lights of each region of the three regions of the light emitting angle ? of the LED point light source pass the corresponded annular region of the freeform surface to form one rectangular light spot.

Abstract: A light emitting diode includes a first semiconductor layer, an active layer, a second semiconductor layer, a protective layer, and a cermet layer. The active layer is on the first semiconductor layer. The second semiconductor layer is on the active layer. the protective layer is located on the semiconductor layer. The cermet layer is located on the protective layer. A first electrode covers entire surface of the first semiconductor layer away from the active layer. A second electrode is electrically connected to the second semiconductor layer.

Abstract: A light emitting diode includes a substrate, a buffer layer, a first semiconductor layer, an active layer, a second semiconductor layer, and a cermet layer. The active layer is on the first semiconductor layer. The second semiconductor layer is on the active layer. The cermet layer is on the second semiconductor layer. A first electrode is electrically connected to the first semiconductor layer. A second electrode is electrically connected to the second semiconductor layer.

Abstract: A laser includes a total reflective mirror, an output mirror, a discharge lamp, and an active laser medium. The total reflective mirror, the output mirror, and the discharge lamp define a resonant cavity. The active laser medium is filled in the resonant cavity. The total reflective mirror includes a microstructure. The microstructure is concave ring-shaped structure. The concave ring-shaped structure has a depth and a width, and both the depth and the width are in a range from about 0.5? to about 2?, while ? is a working wavelength of the laser.

Abstract: A light emitting diode includes a source layer, a metallic plasma generating layer, a first optical symmetric layer, a first electrode, and a second electrode. The source layer includes a first semiconductor layer, an active layer, and a second semiconductor layer stacked in series. The first semiconductor layer includes a first surface and a second surface opposite to the first surface. The first electrode covers and contacts the first surface. The second electrode is electrically connected with the second semiconductor layer. The metallic plasma generating layer is disposed on a surface of the source layer away from the first semiconductor layer. The first optical symmetric layer is disposed on a surface of the metallic plasma generating layer away from the first semiconductor layer. A refractive index difference between the source layer and the first optical symmetric layer is less than or equal to 0.3.

Abstract: A laser includes a total reflective mirror, an output mirror, a discharge lamp, and an active laser medium. The total reflective mirror, the output mirror, and the discharge lamp define a resonant cavity. The active laser medium is filled in the resonant cavity. The total reflective mirror includes a body, a metal film, and at least one microstructure. Each of the at least one microstructure is a step structure. The step structure includes a plurality of cylinders stacked with each other with respect to their diameters. Both the height and the diameter of the cylinders are in a range from about 0.5? to about 2?, while ? is a working wavelength of the laser.

Abstract: A freeform surface reflective scanning system includes a light source, an aperture, a first freeform surface mirror, and a second freeform surface mirror. The light source is configured to provide a laser. The first freeform surface mirror is located on an aperture side that is away from the light source. The first freeform surface mirror is configured to reflect the laser to form a first reflected light. The second freeform surface mirror is located on a first reflected light path. The second freeform surface mirror is configured to reflect the first reflected light to form a second reflected light. Both the first freeform surface mirror and the second freeform surface mirror are a fourth XY polynomial surface.

Abstract: A light emitting diode includes a first semiconductor layer, an active layer, a second semiconductor layer, and a cermet layer. The active layer is on the first semiconductor layer. The second semiconductor layer is on the active layer. The cermet layer is on the second semiconductor layer. A first electrode covers entire surface of the first semiconductor layer away from the active layer. A second electrode is electrically connected to the second semiconductor layer.

Abstract: A design method of freeform imaging system is provided. An initial freeform imaging system is provided, the initial freeform image system comprising a first initial surface and a second initial surface spaced from each other. A second surface is constructed by calculating a plurality of second data points of the second surface through a plurality of feature rays based on the given object-image relationship. A first surface is constructed by calculating a plurality of first data points of the first surface based on the given object-image relationship and Fermat's principle, wherein the second surface is fixed. The first surface and the second surface substitute for the first initial surface and second initial surface respectively, and repeating steps list above, wherein the plurality of feature rays are intersecting the image plane at the plurality of ideal image points.