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 an off-axis three-mirror imaging system with freeform surfaces is provided. A primary mirror initial structure, a secondary mirror initial structure, and a tertiary mirror initial structure are established. A number of first feature rays are selected, while the primary mirror initial structure and the secondary mirror initial structure unchanged. The first feature rays are forward ray tracked from an object space to an image detector. A number of first feature data points are calculated to obtain a tertiary mirror. A number of fields and a number of second feature rays are selected, while the secondary mirror initial structure and the tertiary mirror unchanged. The second feature rays are reverse ray tracked from the image detector to the object space. A number of second feature data points are calculated to obtain the primary mirror.

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 freeform surface off-axial three-mirror image-side telecentric optical system comprises a primary mirror, a secondary mirror, a tertiary mirror and an image sensor. The secondary mirror is the aperture stop. A reflective surface of the primary mirror is a fourth-order polynomial freeform surface of xy. Each of a reflective surface of the secondary mirror and a reflective surface of the tertiary mirror is a sixth-order polynomial freeform surface of xy.

Abstract: A oblique camera lens includes: a primary mirror configured to reflect a light ray to form a first reflected light; a secondary mirror located on a first path of light reflected from the primary mirror and configured to reflect the first reflected light to form a second reflected light; a tertiary mirror located on a second path of light reflected from the secondary mirror and configured to reflect the second reflected light to form a third reflected light; and an image sensor located on a third path of light reflected from the tertiary mirror and configured to receive the third reflected light; wherein each of the first reflecting surface and the third reflecting surface is a sixth order xy polynomial freeform surface; and a field of view of oblique camera lens in an Y-axis direction is greater or equal to 35° and less than or equal to 65°.

Abstract: A light intensity distribution comprises a carbon nanotube array located on a surface of a substrate, a reflector, an imaging element and a cooling device. The carbon nanotube array absorbs photons from a light source and radiates a visible light. The reflector reflects the visible light and is spaced from the carbon nanotube array. The imaging element images the visible light reflected by the reflector. The cooling device is used to cool the substrate to make a contact surface between the substrate and the carbon nanotube array maintain a constant temperature. The cooling device is located between the substrate and the imaging device. The imaging device is spaced from the cooling device.

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 method of designing a freeform surface optical system with dispersion elements is provided. A nondispersive spherical optical system comprising a nondispersive sphere is constructed. A dispersion element is placed on the nondispersive sphere to construct a dispersive spherical optical system comprising a dispersive sphere. The dispersive spherical optical system is constructed into a dispersive freeform surface optical system comprising a freeform surface. The coordinates of the feature data points on the freeform surface are kept unchanged, and the normal vectors are recalculated. The coordinates and new normal vectors are fitted to obtain a new freeform surface. An iterative algorithm is performed until all freeform surfaces are recalculated to new freeform surfaces.

Abstract: A freeform surface imaging spectrometer system including a primary mirror, a secondary mirror, a tertiary mirror, and a detector is provided. The secondary mirror is a grating having a freeform surface shape, and the grating having the freeform surface shape is obtained by intersecting a set of equally spaced parallel planes with a freeform surface. A plurality of feature rays exiting from a light source is successively reflected by the primary mirror, the secondary mirror and the tertiary mirror to form an image on an image sensor. A reflective surface of each of the primary mirror, the tertiary mirror surface and the tertiary mirror is an xy polynomial freeform surface.

Abstract: An off-axis aspheric three-mirror optical system comprises a primary mirror, a secondary mirror, and a tertiary mirror. Relative to a first three-dimensional rectangular coordinates system in space, a second three-dimensional rectangular coordinates system is defined by a primary mirror location, a third three-dimensional rectangular coordinates system is defined by a secondary mirror location, and a fourth three-dimensional rectangular coordinates system is defined by a tertiary mirror location. The primary mirror in the second three-dimensional rectangular coordinates system, the secondary mirror in the third three-dimensional rectangular coordinates system, and the tertiary mirror in the fourth three-dimensional rectangular coordinates system are all sixth-order polynomial aspheric.

Abstract: A freeform surface off-axial three-mirror imaging system comprising a primary mirror, a secondary mirror, a tertiary mirror, and an image sensor. Each reflective surface of the primary mirror, the secondary mirror, and the tertiary mirror is an xy polynomial freeform surface. A field angle of the freeform surface off-axial three-mirror imaging system is larger than or equal to 60°×1°. An F-number of the freeform surface off-axial three-mirror imaging system is less than or equal to 2.5.

Abstract: The present disclosure relates to a method of designing a freeform surface off-axial imaging system. The method comprises the steps of establishing an initial system and selecting feature fields; gradually enlarging a construction of feature field, and constructing the initial system into a freeform surface system; and expanding a construction area of each freeform surface of the freeform surface system, and reconstructing the freeform surface in an extended construction area.

Abstract: A method for designing freeform surface off-axial three-mirror imaging system with a real exit pupil is related. An initial system is established. A surface located before the real exit pupil is defined as surface M. A number of feature rays are selected. A number of ideal intersections of the feature rays with surface M are calculated. A number of intersections of the feature rays with each surface before surface M are calculated, and each surface before surface M is obtained by surface fitting. A number of intersections of the feature rays with surface M are calculated, and surface M is obtained by surface fitting. Surface M substitute for an initial surface, and repeating steps above, until the intersections of the feature rays with surface M are close to the ideal intersections, and the intersections of the feature rays with an image surface are close to the ideal image points.

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 method for designing a oblique camera lens comprising: step (S1), establishing an initial system, the initial system comprises a primary mirror initial structure, a secondary mirror initial structure, and a tertiary mirror initial structure; step (S2), building a new image relationship; step (S3), keeping the primary mirror initial structure and the secondary mirror initial structure unchanged; selecting a plurality of first feature rays; step (S4), keeping the secondary mirror initial structure and the tertiary mirror unchanged; selecting a plurality of fields and a plurality of second feature rays.

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 system for measuring light intensity distribution is provided and set in a vacuum environment. The system for measuring light intensity distribution comprises a carbon nanotube array located on a surface of a substrate, a reflector, an imaging element and a cooling device. The substrate is cooled by the cooling device to make a contacting surface between the substrate and the carbon nanotube array maintain a constant temperature. The carbon nanotube array is irradiated by a light source to make the carbon nanotube array radiate a visible light, and the substrate is continuously cooled to make the contact surface between the substrate and the carbon nanotube array maintain the constant temperature. The visible light is reflected with the reflector. The visible light reflected by the reflector is imaged with the imaging element to obtain the light intensity distribution of the light source.

Abstract: A light intensity distribution comprises a carbon nanotube array located on a surface of a substrate, a reflector, an imaging element and a cooling device. The carbon nanotube array absorbs photons from a light source and radiates a visible light. The reflector reflects the visible light and is spaced from the carbon nanotube array. The imaging element images the visible light reflected by the reflector. The cooling device is used to cool the substrate to make a contact surface between the substrate and the carbon nanotube array maintain a constant temperature. The cooling device is located between the substrate and the imaging device. The imaging device is spaced from the cooling device.