Abstract: A method for analyzing distribution of tolerances on a freeform surface in an optical system. Establishes a freeform surface imaging optical system. A plurality of fields is selected, and maximum and minimum margins of wavefront errors in each field are defined. One freeform surface in one field is selected, an isolated point jumping model is established, and an isolated point is placed in different areas of the freeform surface of the one field. A local figure error with extreme values corresponding to each field is resolved, based on the maximum and minimum margins of wavefront errors, and the local surface tolerance distributions of the freeform surface in the plurality of fields are integrated together.

Abstract: A method for designing illumination system with freeform surface, the method comprising: presupposing a plurality of expected light spots; establishing an initial system, wherein the initial system comprises a plurality of collimated light sources, a plane lens and a target plane; designing a sphere lens to replace the plane lens, and obtaining a before-construction-iteration illumination system; selecting a plurality of feature rays and obtaining a plurality of target points; taking the before-construction-iteration illumination system as an initial construction-iteration system, and obtaining an after-construction-iteration illumination system with freeform surface by making multiple construction-iteration, wherein the illumination system with freeform surface is configured to form the plurality of expected light spots.

Abstract: An illumination system with freeform surface comprises a plurality of collimated light sources having same parameters and a freeform surface lens comprising a first freeform surface and a second freeform surface, wherein formula of the first freeform surface and the second freeform surface is expressed as follows: z = c ? ( x 2 + y ? ? 2 ) 1 + 1 - ( 1 + k ) ? c 2 ? ( x 2 + y 2 ) + ? m ? ? n ? A mn ? x m ? y n , in which c is the curvature of the conic surface at the vertex, k is the conic constant, Amn represents the xy polynomials coefficient, m+n?2 and both m and n are even, beams emitted by the plurality of collimated light sources pass through the freeform surface lens to form a plurality of light spots on a target plane.

Abstract: A method for designing off-axial optical system with freeform surfaces is provided. An initial system is established. A freeform surface of the off-axial optical system that needs to be solved is defined as a freeform surface. A number of feature rays are selected. A number of intersections of the feature rays with the freeform surface are calculated point by point based on a given object-image relationship and a vector form of Snell's law. A number of first feature data points are obtained from the intersections and surface fitted to obtain the freeform surface. All the freeform surfaces of the off-axial optical system that need to be solved are obtained by the method above to form a before-iteration off-axial optical system. The before-iteration off-axial optical system is used as the initial system for multiple iterations to obtain an after-iteration off-axial optical system.

Abstract: A method for designing three-dimensional freeform surface is provided. An initial surface and a first three-dimensional rectangular coordinates system are established. A number of feature rays are selected. A number of intersections of the feature rays with a first freeform surface are calculated, wherein the intersections are a number of feature data points. The first freeform surface is obtained by surface fitting the feature data points. An equation of the first freeform surface includes a conic term and a freeform surface term. The first freeform surface is taken as the initial surface for an iteration process.

Abstract: A method for analyzing distribution of tolerances on a freeform surface in an optical system. Establishes a freeform surface imaging optical system. A plurality of fields is selected, and maximum and minimum margins of wavefront errors in each field are defined. One freeform surface in one field is selected, an isolated point jumping model is established, and an isolated point is placed in different areas of the freeform surface of the one field. A local figure error with extreme values corresponding to each field is resolved, based on the maximum and minimum margins of wavefront erroes, and the local surface tolerance distributions of the freeform surface in the plurality of fields are integrated together.

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: An initial system and a constraint condition are established. All freeform surfaces are obtained by surface fitting the feature data points to form a first freeform surface imaging optical system. The first freeform surface imaging optical system is taken as the initial system for multiple iterations to obtain a second freeform surface imaging optical system. The second freeform surface imaging optical system is taken as a first base system. A first surface freedom of the first base system is selected, the values nearby the first surface freedom is selected, and surface positions and tilts of the first base system are changed to obtain a third freeform surface imaging optical system that satisfies the constraint condition. A second base system is selected and the method above is repeated. The freeform surface imaging optical system is obtained until all freedoms for surface positions and tilts have been used.

Abstract: A method for designing illumination system with freeform surface, the method comprising: presupposing a plurality of expected light spots; establishing an initial system, wherein the initial system comprises a plurality of collimated light sources, a plane lens and a target plane; designing a sphere lens to replace the plane lens, and obtaining a before-construction-iteration illumination system; selecting a plurality of feature rays and obtaining a plurality of target points; taking the before-construction-iteration illumination system as an initial construction-iteration system, and obtaining an after-construction-iteration illumination system with freeform surface by making multiple construction-iteration, wherein the illumination system with freeform surface is configured to form the plurality of expected light spots.

Abstract: An illumination system with freeform surface comprises a plurality of collimated light sources having same parameters and a freeform surface lens comprising a first freeform surface and a second freeform surface, wherein formula of the first freeform surface and the second freeform surface is expressed as follows: z = c ? ( x 2 + y ? ? 2 ) 1 + 1 - ( 1 + k ) ? c 2 ? ( x 2 + y 2 ) + ? m ? ? n ? A mn ? x m ? y n , in which c is the curvature of the conic surface at the vertex, k is the conic constant, Amn represents the xy polynomials coefficient, m+n?2 and both m and n are even, beams emitted by the plurality of collimated light sources pass through the freeform surface lens to form a plurality of light spots on a target plane.

Abstract: An initial system and a constraint condition are established. All freeform surfaces are obtained by surface fitting the feature data points to form a first freeform surface imaging optical system. The first freeform surface imaging optical system is taken as the initial system for multiple iterations to obtain a second freeform surface imaging optical system. The second freeform surface imaging optical system is taken as a first base system. A first surface freedom of the first base system is selected, the values nearby the first surface freedom is selected, and surface positions and tilts of the first base system are changed to obtain a third freeform surface imaging optical system that satisfies the constraint condition. A second base system is selected and the method above is repeated. The freeform surface imaging optical system is obtained until all freedoms for surface positions and tilts have been used.

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: A LED optical communication receiving lens includes a first surface and a second surface opposite to the first surface. The first surface includes a first spherical surface and a second spherical surface connected to the first spherical surface. The second surface includes a third spherical surface and a planar surface connected to the third spherical surface. A position of the LED optical communication receiving lens is defined as a three-dimensional Cartesian coordinate system (x, y, z). Sphere centers and symmetric central points of the first spherical surface, the second spherical surface, and the third spherical surface are located on the x axis. The first spherical surface and the planar surface are transmitted surfaces. The second spherical surface and the third spherical surface are reflective surfaces. The present application also relates to a LED optical communication system including the LED optical communication receiving lens.

Abstract: A method for designing three-dimensional freeform surface is provided. An initial surface and a first three-dimensional rectangular coordinates system are established. A number of feature rays are selected. A number of intersections of the feature rays with a first freeform surface are calculated, wherein the intersections are a number of feature data points. The first freeform surface is obtained by surface fitting the feature data points. An equation of the first freeform surface includes a conic term and a freeform surface term. The first freeform surface is taken as the initial surface for an iteration process.

Abstract: A method for designing off-axial optical system with freeform surfaces is provided. An initial system is established. A freeform surface of the off-axial optical system that needs to be solved is defined as a freeform surface. A number of feature rays are selected. A number of intersections of the feature rays with the freeform surface are calculated point by point based on a given object-image relationship and a vector form of Snell's law. A number of first feature data points are obtained from the intersections and surface fitted to obtain the freeform surface. All the freeform surfaces of the off-axial optical system that need to be solved are obtained by the method above to form a before-iteration off-axial optical system. The before-iteration off-axial optical system is used as the initial system for multiple iterations to obtain an after-iteration off-axial optical system.

Abstract: A LED optical communication receiving lens includes a first surface and a second surface opposite to the first surface. The first surface includes a first spherical surface and a second spherical surface connected to the first spherical surface. The second surface includes a third spherical surface and a planar surface connected to the third spherical surface. A position of the LED optical communication receiving lens is defined as a three-dimensional Cartesian coordinate system (x, y, z). Sphere centers and symmetric central points of the first spherical surface, the second spherical surface, and the third spherical surface are located on the x axis. The first spherical surface and the planar surface are transmitted surfaces. The second spherical surface and the third spherical surface are reflective surfaces. The present application also relates to a LED optical communication system including the LED optical communication receiving lens.

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: 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.