Abstract: A method for designing an imaging optical system is a point-by-point calculation method based on characteristic light rays (FLR) and characteristic data points (FDP). The basic function of the point-by-point calculation method includes the following steps: according to the given object-image relationship, based on Fermat's principle and the law of retraction and reflection, calculating the propagation path of the FLR passing through a system and the FDP on each optical surface, to obtain a surface shape equation of each optical surface by fitting; and repeating the above process, to solve the surface shape equation of each optical surface one by one, and finally complete the design and solution of the entire imaging optical system.

Abstract: A method for designing a freeform concave grating imaging spectrometer includes selecting a series of light rays incident from different positions of a slit as characteristic light rays. The coordinates and normal directions of characteristic data points at intersections of the characteristic light rays and a surface of a freeform concave grating are calculated. A freeform surface shape of the freeform concave grating is obtained by fitting, so that an initial structure is obtained. Then the initial structure is optimized.

Abstract: An imaging optical system includes a primary reflecting mirror, a secondary reflecting mirror, a tertiary reflecting mirror, and an aperture stop. The imaging optical system has a field of view, a focal length of the field of view that is defined as FFL, and an effective aperture of a field of view entrance pupil that is defined as FEPD. The FFL and the FEPD at a central field of view are greater than that at the edge field of views, and the FFL and the FEPD change continuously.

Abstract: A method for designing a freeform concave grating imaging spectrometer includes selecting a series of light rays incident from different positions of a slit as characteristic light rays. The coordinates and normal directions of characteristic data points at intersections of the characteristic light rays and a surface of a freeform concave grating are calculated. A freeform surface shape of the freeform concave grating is obtained by fitting, so that an initial structure is obtained. Then the initial structure is optimized.

Abstract: A method for designing an imaging optical system is a point-by-point calculation method based on characteristic light rays (FLR) and characteristic data points (FDP). The basic function of the point-by-point calculation method includes the following steps: according to the given object-image relationship, based on Fermat's principle and the law of retraction and reflection, calculating the propagation path of the FLR passing through a system and the FDP on each optical surface, to obtain a surface shape equation of each optical surface by fitting; and repeating the above process, to solve the surface shape equation of each optical surface one by one, and finally complete the design and solution of the entire imaging optical system.

Abstract: An imaging optical system includes a primary reflecting mirror, a secondary reflecting mirror, a tertiary reflecting mirror, and an aperture stop. The imaging optical system has a field of view, a focal length of the field of view that is defined as FFL, and an effective aperture of a field of view entrance pupil that is defined as FEPD. The FFL and the FEPD at a central field of view are greater than that at the edge field of views, and the FFL and the FEPD change continuously.

Abstract: A freeform concave grating imaging spectrometer includes a slit, a freeform concave grating, and an image surface. The lights incident from the slit is irradiated on the freeform concave grating to be dispersed and reflected, to form a reflected light beam. The reflected light beam is irradiated on the image surface, so that the lights of different wavelengths incident from the slit are separated and imaged on the image surface.

Abstract: A method for designing freeform surface imaging system comprises: constructing a series of coaxial spherical systems with different optical power (OP) distributions; tilting all optical elements of each coaxial spherical system by a series of angles to obtain a series of off-axis spherical systems; finding all unobscured off-axis spherical systems; and then specifying a system size or structural constraints, and finding a series of compact unobstructed off-axis spherical systems; constructing a series of freeform surface imaging systems based on the series of compact unobstructed off-axis spherical system, and correcting the OP of entire system; improving an image quality of each freeform surface imaging systems and finding an optimal tilt angle of an image surface; and automatically evaluating an image quality of each freeform surface imaging system based on an evaluation metric, and outputting the freeform surface imaging systems that meet a given requirements.

Abstract: A freeform surface off-axis three-mirror optical system comprises a primary mirror, a secondary mirror, a tertiary mirror, an aperture stop located on the secondary mirror, and an image surface. An incident light beam emitted from an object irradiates and is reflected on the primary mirror to form a first reflected light beam. The first reflected light beam irradiates and is reflected on the secondary mirror to form a second reflected light beam. The second reflected light beam passes through the incident light beam, and then irradiates and is reflected on the tertiary mirror to form a third reflected light beam. The third reflected light beam passes through the incident light beam and does not pass through the secondary mirror, and finally reaches the image surface for imaging. A reflective surface of each of the primary mirror, the secondary mirror, and the tertiary mirror is an xy polynomial freeform surface.

Abstract: A freeform surface off-axis three-mirror optical system comprises a primary mirror, a secondary mirror, a tertiary mirror, an aperture stop located on the secondary mirror, and an image surface. An incident light beam emitted from an object irradiates and is reflected on the primary mirror to form a first reflected light beam. The first reflected light beam irradiates and is reflected on the secondary mirror to form a second reflected light beam. The second reflected light beam passes through the incident light beam, and then irradiates and is reflected on the tertiary mirror to form a third reflected light beam. The third reflected light beam passes through the incident light beam and does not pass through the secondary mirror, and finally reaches the image surface for imaging. A reflective surface of each of the primary mirror, the secondary mirror, and the tertiary mirror is an xy polynomial freeform surface.

Abstract: A method for designing freeform surface imaging system comprises: constructing a series of coaxial spherical systems with different optical power (OP) distributions; tilting all optical elements of each coaxial spherical system by a series of angles to obtain a series of off-axis spherical systems; finding all unobscured off-axis spherical systems; and then specifying a system size or structural constraints, and finding a series of compact unobstructed off-axis spherical systems; constructing a series of freeform surface imaging systems based on the series of compact unobstructed off-axis spherical system, and correcting the OP of entire system; improving an image quality of each freeform surface imaging systems and finding an optimal tilt angle of an image surface; and automatically evaluating an image quality of each freeform surface imaging system based on an evaluation metric, and outputting the freeform surface imaging systems that meet a given requirements.

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 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: 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: 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 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.