US20170285312A1 - Off-axis three-mirror optical system with freeform surfaces - Google Patents

Off-axis three-mirror optical system with freeform surfaces Download PDF

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Publication number
US20170285312A1
US20170285312A1 US15/168,340 US201615168340A US2017285312A1 US 20170285312 A1 US20170285312 A1 US 20170285312A1 US 201615168340 A US201615168340 A US 201615168340A US 2017285312 A1 US2017285312 A1 US 2017285312A1
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United States
Prior art keywords
mirror
reflected light
light path
axis
rectangular coordinates
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Abandoned
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US15/168,340
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English (en)
Inventor
Jun Zhu
Tong Yang
Guo-Fan Jin
Shou-Shan Fan
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Tsinghua University
Hon Hai Precision Industry Co Ltd
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Tsinghua University
Hon Hai Precision Industry Co Ltd
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Assigned to TSINGHUA UNIVERSITY, HON HAI PRECISION INDUSTRY CO., LTD. reassignment TSINGHUA UNIVERSITY ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: FAN, SHOU-SHAN, JIN, GUO-FAN, YANG, TONG, ZHU, JUN
Publication of US20170285312A1 publication Critical patent/US20170285312A1/en
Abandoned legal-status Critical Current

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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B17/00—Systems with reflecting surfaces, with or without refracting elements
    • G02B17/02—Catoptric systems, e.g. image erecting and reversing system
    • G02B17/06—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror
    • G02B17/0626—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror using three curved mirrors
    • G02B17/0642—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror using three curved mirrors off-axis or unobscured systems in which not all of the mirrors share a common axis of rotational symmetry, e.g. at least one of the mirrors is warped, tilted or decentered with respect to the other elements
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B17/00—Systems with reflecting surfaces, with or without refracting elements
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B17/00—Systems with reflecting surfaces, with or without refracting elements
    • G02B17/02—Catoptric systems, e.g. image erecting and reversing system
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B17/00—Systems with reflecting surfaces, with or without refracting elements
    • G02B17/02—Catoptric systems, e.g. image erecting and reversing system
    • G02B17/06—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B17/00—Systems with reflecting surfaces, with or without refracting elements
    • G02B17/02—Catoptric systems, e.g. image erecting and reversing system
    • G02B17/06—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror
    • G02B17/0626—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror using three curved mirrors
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B17/00—Systems with reflecting surfaces, with or without refracting elements
    • G02B17/02—Catoptric systems, e.g. image erecting and reversing system
    • G02B17/06—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror
    • G02B17/0694—Catoptric systems, e.g. image erecting and reversing system using mirrors only, i.e. having only one curved mirror with variable magnification or multiple imaging planes, including multispectral systems
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0025—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for optical correction, e.g. distorsion, aberration

Definitions

  • the present disclosure relates to an off-axis optical system.
  • Off-axis three-mirror imaging system is a kind of off-axis reflective system. If freeform surfaces are used in off-axis three-mirror imaging systems, the aberrations of the system can be significantly reduced, while the system specifications can be greatly improved.
  • the three mirrors are separated in space and they have different freeform surface analytical expressions. If the primary and tertiary mirrors share a same freeform surface expression and are fabricated on a single substrate, the difficulty of system alignment and fabrication as well as the cost for the testing of the system can be reduced.
  • the primary mirror and the tertiary mirror are located generally far away from each other on a single element in this kind of system, a size of the conventional off-axis three-mirror optical system with freeform surfaces is large, and a structure of the conventional off-axis three-mirror optical system with freeform surfaces is not compact.
  • a volume of the single element is large, therefore the surface sag at the edge of the surface is large, which increases the difficulty for fabrication and testing.
  • FIG. 1 is a schematic view of a light path of an off-axis three-mirror optical system with freeform surfaces according to one embodiment.
  • FIG. 2 is a schematic view of a configuration of an off-axis three-mirror optical system with freeform surfaces according to one embodiment.
  • FIG. 3 is a graph showing modulation transfer function curves in long-wave infrared band of partial field angles of an off-axis three-mirror optical system with freeform surfaces according to one embodiment.
  • substantially is defined to be essentially conforming to the particular dimension, shape, or other feature that the term modifies, such that the component need not be exact.
  • substantially cylindrical means that the object resembles a cylinder, but can have one or more deviations from a true cylinder.
  • comprising when utilized, means “including, but not necessarily limited to”; it specifically indicates open-ended inclusion or membership in the so-described combination, group, series and the like.
  • FIGS. 1 and 2 illustrate one embodiment of an off-axis three-mirror optical system with freeform surfaces 100 includes an aperture 102 , a primary mirror 104 , a secondary mirror 106 , a tertiary mirror 108 , and a detector 110 .
  • the aperture 102 is used to control a diameter of incident lights.
  • the primary mirror 104 is located on an aperture side that is away from an object space.
  • the secondary mirror 106 is located on a primary mirror reflected light path.
  • the tertiary mirror 108 is located on a secondary mirror reflected light path.
  • the detector 110 is located on a tertiary mirror reflected light path.
  • a primary mirror reflective surface, a secondary mirror reflective surface and a tertiary mirror reflective surface are all freeform surfaces.
  • a light path of the off-axis three-mirror optical system with freeform surfaces 100 can be depicted as follows. Firstly, incident light transmits through the aperture 102 and reach the primary mirror 104 , and is reflected by the primary mirror 104 to form a first reflected light R 1 . Secondly, the first reflected light R 1 reaches the secondary mirror 106 , and is reflected by the secondary mirror 106 to form a second reflected light R 2 . Thirdly, the second reflected light R 2 reaches the tertiary mirror 108 , and is reflected by the tertiary mirror 108 to form a third reflected light R 3 . Finally, the third reflected light R 3 is received by the detector 110 and imaging.
  • the primary mirror reflected light path, the secondary mirror reflected light path and the tertiary mirror reflected light path overlap with each other. Therefore, a volume of the off-axis three-mirror optical system with freeform surfaces 100 is small, and a structure of the off-axis three-mirror optical system with freeform surfaces 100 is compact.
  • a first three-dimensional rectangular coordinates system (x 1 , y 1 , z 1 ) is defined.
  • a center of the aperture 102 is a first origin of the first three-dimensional rectangular coordinates system (x 1 , y 1 , z 1 ).
  • a horizontal line passing through the center of the aperture 102 is defined as a z 1 -axis, in the z 1 -axis, to the left is negative, and to the right is positive.
  • a y 1 -axis is in a plane shown in FIG. 2 , in the y 1 -axis, in a direction substantially perpendicular to the z 1 -axis, to the upward is positive, and to the downward is negative.
  • An x 1 -axis is perpendicular to a y 1 z 1 plane, in the x 1 -axis, in a direction substantially perpendicular to the y 1 z 1 plane, to the inside is positive, and to the outside is negative.
  • a second three-dimensional rectangular coordinates system (x 2 , y 2 , z 2 ) is defined for a primary mirror location and a tertiary mirror location.
  • a third three-dimensional rectangular coordinates system (x 3 , y 3 , z 3 ) is defined for a secondary mirror location.
  • a fourth three-dimensional rectangular coordinates system (x 4 , y 4 , z 4 ) is defined for a detector location.
  • a second origin of the second three-dimensional rectangular coordinates system (x z , y z , z z ) is in (0, 88.59727, 198.07169) position of the first three-dimensional rectangular coordinates system (x 1 , y 1 , z 1 ), whose unit is millimeter.
  • a z 2 -axis positive direction rotates about 27.84258 degrees along a counterclockwise direction relative to a z 1 -axis positive direction.
  • a third origin of the third three-dimensional rectangular coordinates system (x 3 , y 3 , z 3 ) is in (0, ⁇ 159.26851, ⁇ 22.49695) position of the first three-dimensional rectangular coordinates system (x 1 , y 1 , z 1 ), whose unit is millimeter.
  • a z 3 -axis positive direction rotates about 10.80811 degrees along a clockwise direction relative to the z 1 -axis positive direction.
  • a fourth origin of the fourth three-dimensional rectangular coordinates system (x 3 , y 3 , z 3 ) is in (0, ⁇ 44.59531, ⁇ 47.02867) position of the first three-dimensional rectangular coordinates system (x 1 , y 1 , z 1 ), whose unit is millimeter.
  • a z 4 -axis positive direction rotates about 16.28528 degrees along the counterclockwise direction relative to the z 1 -axis positive direction.
  • each of the primary mirror reflective surface and the tertiary mirror reflective surface is a fifth-order polynomial of x 2 y 2 .
  • the fifth-order polynomial of x 2 y 2 can be expressed as follows:
  • z 2 ⁇ ( x 2 , y 2 ) c ⁇ ( x 2 2 + y 2 2 ) 1 + 1 - ( 1 + k ) ⁇ c 2 ⁇ ( x 2 2 + y 2 2 ) + A 2 ⁇ y 2 + A 3 ⁇ x 2 2 + A 5 ⁇ y 2 2 + A 7 ⁇ x 2 2 ⁇ y 2 + A 9 ⁇ y 2 3 + A 10 ⁇ x 2 4 + A 12 ⁇ x 2 2 ⁇ y 2 2 + A 14 ⁇ y 2 4 + A 16 ⁇ x 2 4 ⁇ y 2 + A 18 ⁇ x 2 2 ⁇ y 2 3 + A 20 ⁇ y 2 5 .
  • z represents surface sag
  • c represents surface curvature
  • k represents conic constant
  • A represents the ith term coefficient. Since the off-axis three-mirror optical system with freeform surfaces 100 is symmetrical about y 2 z 2 plane, even-order terms of x 2 can be only remained.
  • the values of c, k, and A i in the equation of the fifth-order polynomial of x 2 y 2 are listed in TABLE 1. However, the values of c, k, and A i in the fifth-order polynomial of x 2 y 2 are not limited to TABLE 1.
  • the secondary mirror reflective surface is a fifth-order polynomial of x 3 y 3 .
  • the fifth-order polynomial of x 3 y 3 can be expressed as follows:
  • z 3 ⁇ ( x 3 , y 3 ) c ⁇ ( x 3 2 + y 3 2 ) 1 + 1 - ( 1 + k ) ⁇ c 2 ⁇ ( x 3 2 + y 3 2 ) + A 2 ⁇ y 3 + A 3 ⁇ x 3 2 + A 5 ⁇ y 3 2 + A 7 ⁇ x 3 2 ⁇ y 3 + A 9 ⁇ y 3 3 + A 10 ⁇ x 3 4 + A 12 ⁇ x 3 2 ⁇ y 3 2 + A 14 ⁇ y 3 4 + A 16 ⁇ x 3 4 ⁇ y 3 + A 18 ⁇ x 3 2 ⁇ y 3 3 + A 20 ⁇ y 3 5 .
  • z 3 represents surface sag
  • c represents surface curvature
  • k represents conic constant
  • a i represents the ith term coefficient. Since the off-axis three-mirror optical system with freeform surfaces 100 is symmetrical about y 3 z 3 plane, even-order terms of x 3 can be only remained.
  • the values of c, k, and A i in the fifth-order polynomial of x 3 y 3 are listed in TABLE 2. However, the values of c, k, and A, in the fifth-order polynomial of x 3 y 3 are not limited to TABLE 2.
  • a center of the detector 110 is the fourth origin of the fourth three-dimensional rectangular coordinates system (X 3 , Y 3 , Z 3 ).
  • the detector 110 is in a plane of the fourth three-dimensional rectangular coordinates system (X 4 , Y 4 , Z 4 ).
  • the materials of the primary mirror 104 , the secondary mirror 106 and the tertiary mirror 108 can be aluminum, beryllium or other metals.
  • the materials of the primary mirror 104 , the secondary mirror 106 and the tertiary mirror 108 can also be silicon carbide, quartz or other inorganic materials.
  • a reflection enhancing coating can also be coated on the metals or inorganic materials to enhance the reflectivity performance of the three mirrors. In one embodiment, the reflection enhancing coating is a gold film.
  • An effective entrance pupil diameter of the off-axis three-mirror optical system with freeform surfaces is about 40 mm.
  • the off-axis three-mirror optical system with freeform surfaces 100 adopts an off-axis field of view in a vertical direction.
  • a field angle of the off-axis three-mirror optical system with freeform surfaces 100 is about 4° ⁇ 3°, wherein an angle in a horizontal direction is in a range from about ⁇ 2° to about 2°, and an angle in the vertical direction is in a range from about 10.5° to about 13.5°.
  • a wavelength of the off-axis three-mirror optical system with freeform surfaces 100 is not limited, in one embodiment, the wavelength of the off-axis three-mirror optical system with freeform surfaces 100 is in a range from about 8 ⁇ m to about 12 ⁇ m.
  • An effective focal length (EFL) of the off-axis three-mirror optical system with freeform surfaces 100 is about 100 mm.
  • a relative aperture (D/f) of the off-axis three-mirror optical system with freeform surfaces 100 is about 0.4; and a F-number of the off-axis three-mirror optical system with freeform surfaces 100 is a relative aperture(D/f) reciprocal, the F-number is about 2.5.
  • FIG. 3 illustrates off-axis three-mirror optical system with freeform surfaces modulation transfer functions (MTF) in long-wave infrared band of partial field angles are close to the diffraction limit. It shows that an off-axis three-mirror optical system with freeform surfaces imaging quality is high.
  • MTF freeform surfaces modulation transfer functions
  • the off-axis three-mirror optical system with freeform surfaces 100 has advantages as follows:
  • the off-axis three-mirror optical system with freeform surfaces 100 has larger field angle compared with coaxial three-mirror optical systems, the field angle is about 4° ⁇ 3°; thereby enabling the off-axis three-mirror optical system with freeform surfaces 100 has larger rectangular field of view, and larger imaging range.
  • the primary mirror reflective surface, the secondary mirror reflective surface and the tertiary mirror reflective surface are all freeform surfaces, compared with spherical or aspherical system, the off-axis three-mirror optical system with freeform surfaces 100 has more variables, which is beneficial for correcting aberrations, and obtaining better imaging quality.
  • the off-axis three-mirror optical system with freeform surfaces 100 has smaller F-number and larger relative aperture, which allows more lights to enter the off-axis three-mirror optical system with freeform surfaces 100 , and enables the off-axis three-mirror optical system with freeform surfaces 100 has higher input energy and limiting resolution.
  • the primary mirror surface and the tertiary mirror surface use the same freeform surface equation, it is no need to transform coordinate system and surface expressions when fabrication the off-axis three-mirror optical system with freeform surfaces 100 , and the primary mirror and the tertiary mirror can be fabricated on a single element; thereby reducing fabrication difficulty.
  • a space position of the primary mirror is close to a space position of the tertiary mirror, a volume of a primary mirror-tertiary mirror element is small, and thus, the sag at the edge of the is small, which can reduce the fabrication difficulty.
  • Testing of the primary mirror and the tertiary mirror can only use a computer-generated hologram (CGH) component, which can simplify a testing process and reduce costs.
  • CGH computer-generated hologram
  • the primary mirror reflected light path, the secondary mirror reflected light path and the tertiary mirror reflected light path overlap with each other. Therefore, the volume of the off-axis three-mirror optical system with freeform surfaces 100 is small, and the structure of the off-axis three-mirror optical system with freeform surfaces 100 is compact.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Spectroscopy & Molecular Physics (AREA)
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  • Microscoopes, Condenser (AREA)
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US20170370618A1 (en) * 2016-06-24 2017-12-28 Alliance For Sustainable Energy, Llc Secondary reflectors for solar collectors and methods of making the same
CN109143558A (zh) * 2018-10-11 2019-01-04 佛山科学技术学院 一种小型化全天候星敏感器光学系统
CN113075787A (zh) * 2021-03-31 2021-07-06 中国科学院长春光学精密机械与物理研究所 紧凑型光学系统
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US10808965B2 (en) * 2016-06-24 2020-10-20 Alliance For Sustainable Energy, Llc Secondary reflectors for solar collectors and methods of making the same
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CN109143558A (zh) * 2018-10-11 2019-01-04 佛山科学技术学院 一种小型化全天候星敏感器光学系统
CN113741018A (zh) * 2020-05-29 2021-12-03 清华大学 自由曲面离轴三反光学系统
CN113075787A (zh) * 2021-03-31 2021-07-06 中国科学院长春光学精密机械与物理研究所 紧凑型光学系统

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US20170285313A1 (en) 2017-10-05
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US9846298B2 (en) 2017-12-19
CN107290845B (zh) 2019-08-13
TW201736899A (zh) 2017-10-16
CN107290845A (zh) 2017-10-24
TWI616680B (zh) 2018-03-01

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