Small form factor four-mirror based imaging system

Abstract

This application describes a total reflection optical system, comprising: a concave primary mirror having a central hole and a radius, the primary mirror having one of a parabolic surface, a non-parabolic conical surface, or an aspherical surface; a convex secondary mirror facing the primary mirror, the secondary mirror having an aspherical surface, wherein an optical axis extends from the vertex of the primary mirror to the vertex of the secondary mirror; a concave tertiary mirror arranged behind the primary mirror, the tertiary mirror having one of a parabolic surface, a non-parabolic conical surface, or an aspherical surface; a concave quaternary mirror arranged in the central hole of the primary mirror or behind the primary mirror, the quaternary mirror having one of a spherical surface, a parabolic surface, a non-parabolic conical surface, or an aspherical surface; and at least one image plane having one or more focusing sensors, wherein the image plane is positioned at a radial distance from the optical axis not exceeding the radius of the primary mirror.

Description

[0001] Cross - Reference to Related Applications

[0002] This application claims priority to U.S. Provisional Application No. 62,885,296, filed on Aug. 11, 2019, the entire content of which is incorporated herein by reference in its entirety for all purposes and forms part of this specification. Technical Field

[0003] The present disclosure generally relates to optical imaging systems, and more particularly to a small - form - factor four - mirror - based optical imaging system for use in satellites or aircraft. Background Art

[0004] Optical imaging systems are useful in many applications, such as imaging planets or stars. Known optical system designs for satellite imaging include the conventional Three Mirror Anastigmat (TMA) design and the Korsch design. Existing solutions for optical imaging are defective in terms of size and corresponding resolution capabilities. Thus, there is a need for improved optical imaging. Summary of the Invention

[0005] In one aspect, a catadioptric optical system is disclosed. The catadioptric optical system includes: a concave primary mirror having a central aperture and a radius, the primary mirror having one of a parabolic surface, a non - parabolic conical surface, or an aspherical surface; a convex secondary mirror facing the primary mirror, the secondary mirror having an aspherical surface, and the optical axis extending from the vertex of the primary mirror to the vertex of the secondary mirror; a concave tertiary mirror disposed behind the primary mirror, the tertiary mirror having one of a parabolic surface, a non - parabolic conical surface, or an aspherical surface; a concave quaternary mirror disposed in the central aperture of the primary mirror or behind the primary mirror, the quaternary mirror having one of a spherical surface, a parabolic surface, a non - parabolic conical surface, or an aspherical surface; and at least one image plane having one or more focusing sensors. The image plane is positioned at a distance from the optical axis that is no greater than the radius of the primary mirror.

[0006] In some embodiments, the optical system may further include an entrance pupil located near the primary mirror or the secondary mirror, and an exit pupil or a Lyot stop located at one of the following positions: 1) near the quaternary mirror, 2) between the tertiary mirror and the quaternary mirror, and 3) between the quaternary mirror and the image plane.

[0007] In some embodiments, the optical system may further include one or more folding mirrors arranged to deflect light from the four-stage mirror to the image plane, wherein the one or more folding mirrors may be configured to fold the light path. Based on the use of the first folding mirror, the exit pupil may be located between the three-stage mirror and the four-stage mirror, or between the four-stage mirror and the first folding mirror. One of the folding mirrors may be tilted at a specific angle with respect to the optical axis of the system. One of the folding mirrors located in front of the image plane may widen the field of view with reflective and transmissive portions over the same spectral range, where each portion may correspond to a specific sensor among the one or more sensors. One of the folding mirrors located in front of the image plane may enable simultaneous multi-color imaging, where one of the folding mirrors may reflect over a first spectral range and transmit over other spectral ranges, and may reflect over a second spectral range and transmit over other spectral ranges, where one of the aggregation sensors may be dedicated to the first spectral range, and a different sensor among the aggregation sensors may be dedicated to the second spectral range.

[0008] In some embodiments, the shape factor defined as the ratio of the distance between the two-stage mirror and the three-stage mirror to the effective focal length of the optical system may be less than 0.09. The vertices of the primary mirror and the two-stage mirror may form the optical axis, which may be a geometric reference line extending from the vertex of the primary mirror to the vertex of the two-stage mirror. The primary mirror and the two-stage mirror may be symmetric or periodic with respect to the optical axis. The diagonal of the periodic mirror may have an angle of 0 degrees or 45 degrees with the diagonal of the image plane. The optical axis of the three-stage mirror may not coincide with the mechanical axis.

[0009] In some embodiments, the radius of the two-stage mirror may be in the range of 1% to 3% of the effective focal length, and the radius of the two-stage mirror may be in the range of 2% to 3% of the effective focal length. The radius of the four-stage mirror may be in the range of 6% to 22% of the effective focal length.

[0010] In some embodiments, the folding mirror may enable simultaneous multi-color imaging, where each of the folding mirrors may be reflective over a specific spectral range and transmissive over other spectral ranges, and where each additional folding mirror and the corresponding one among the aggregation sensors may be associated with a different spectral range.

[0011] In some embodiments, the distance along the optical axis from the three-stage mirror to the image plane may be in the range of 3% to 9% of the effective focal length, and the distance along the optical axis from the two-stage mirror to the three-stage mirror may be in the range of 4% to 9% of the effective focal length. The system may have an imaging resolution better than 1 m at an altitude of 500 km.

[0012] In some embodiments, the system may be adapted to support simultaneous multi-color imaging, including: 1) panchromatic and RGB and near-infrared, 2) visible and infrared (near-infrared, short-wave infrared, mid-wave infrared, or long-wave infrared), 3) visible and visible, 4) infrared and infrared, 5) UV and visible, or 6) UV and infrared imaging.

[0013] In some embodiments, the diameter of the primary mirror may be in the range of 3% to 8% of the effective focal length. The distance from the focus of the primary mirror may be in the range of 1% to 6% of the effective focal length. The effective focal length may be in the range of 300 mm to 20,000 mm. The optical system may further include a support structure for one or more of the mirrors. The support structure may be manufactured in an additive manner.

[0014] In some embodiments, the image plane may include a charge-coupled device (CCD)-in-CMOS time delay integration (TDI) sensor. The CCD-in-CMOS TDI sensor may be a multi-spectral TDI, back-illuminated imager. The CCD-in-CMOS TDI sensor may include seven CCD arrays, each being 4096×256 pixels. The CCD-in-CMOS TDI sensor may include four panchromatic CCD arrays of 16384×96 pixels and eight multi-spectral CCD arrays of 8192×48 pixels.

[0015] In some embodiments, the primary mirror may have a circular or non-circular shape, the tertiary mirror may have a segmented non-circular shape, and the quaternary mirror has a circular or non-circular shape. The non-circular shape of the primary mirror may enhance the modulation transfer function (MTF) and the signal-to-noise ratio (SNR).

[0016] In some embodiments, the quaternary mirror may face the tertiary mirror and may be positioned to avoid interference with the light rays from the secondary mirror to the tertiary mirror. The optical system may additionally include a support structure for the mirrors, which includes a cylindrical tube or a conical baffle for the primary mirror. The four mirrors may be made of zero-CTE material, low-CTE material, or mid-CTE material, where the four mirrors and the support structure may be made of one material. The system may be adapted to provide imaging in starring, scanning or push-broom, video, stereo, BRDF (bidirectional reflectance distribution function), HDR (high dynamic range), polarization, and low-light modes.

[0017] In some embodiments, the system may be adapted to be mounted on a satellite arranged for non-imaging tasks, including communication satellites, or on an imaging satellite, quasi-imaging satellite, or scientific mission satellite. The system may be adapted to be mounted on an aircraft, a drone, an unmanned aerial vehicle, and a balloon. The back focal length between the quaternary mirror and the at least one image plane may be in the range of 2% to 5% of the effective focal length.

[0018] In another aspect, a total reflection optical system is disclosed, the total reflection optical system comprising: a concave primary mirror having a central hole and a radius, the primary mirror having one of a parabolic surface, a non-parabolic surface, a conical surface or an aspherical surface; a convex secondary mirror facing the primary mirror, the secondary mirror having a hyperbolic surface, wherein the optical axis extends from the vertex of the primary mirror to the vertex of the secondary mirror; a concave tertiary mirror disposed behind the primary mirror, the tertiary mirror having one of a parabolic surface, a non-parabolic surface, a conical surface and an aspherical surface; a concave quaternary mirror disposed in front of the central hole of the primary mirror, the quaternary mirror having one of a spherical surface, a parabolic surface, a non-parabolic surface, a conical surface or an aspherical surface; and at least one image plane having one or more focusing sensors, wherein the image plane is located at a radial distance from the optical axis, the radial distance being not greater than the radius of the primary mirror. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The elements in the drawings are not necessarily drawn to scale so as to enhance their clarity and improve the understanding of these different elements and embodiments described herein. Additionally, in order to provide a clear view of the various embodiments described herein, elements that are common and well understood by those skilled in the art are not shown, and thus the drawings are schematic in form for the sake of clarity and brevity.

[0020] Figure 1A and Figure 1B are schematic diagrams of embodiments of an optical system that can be used for imaging.

[0021] Figure 1C and Figure 1D are schematic diagrams of another embodiment of an optical system that can be used for imaging.

[0022] Figure 1E and Figure 1F are schematic diagrams showing the diagonals of a periodic mirror and an image plane, respectively.

[0023] Figure 1G and Figure 1H show an exemplary embodiment of an optical system having a periodic primary mirror.

[0024] Figure 2A is a block diagram of a schematic diagram showing an embodiment of a payload system for a satellite, the satellite may include various optical systems described herein.

[0025] Figure 2B is a block diagram of a schematic diagram showing an embodiment of an image plane circuit that can be used with various optical systems described herein.

[0026] Figures 3 to 5 is a schematic diagram showing various embodiments of a configuration layout for a mirror and an imaging plane that can be used with various optical systems described herein.

[0027] Figures 6 to 9 FIG. 1 is a schematic diagram showing various embodiments of a mirror configuration layout for a mirror including one or more folding mirrors and an imaging plane, which can be used with various optical systems described herein.

[0028] Figures 10 to 13 FIG. 2 is a schematic diagram showing various embodiments of a mirror configuration layout for a mirror including one or more folding mirrors and two imaging planes, which can be used with various optical systems described herein.

[0029] Figures 14A to 14D FIGS. 3A-3D are respective views of an embodiment of a camera system including the optical system of FIG. 1.

[0030] Figures 15A to 17B FIG. 4 is a graph showing various embodiments of the performance characteristics of the Figure 1A optical system.

[0031] Figures 18A to 20B FIG. 5 is a graph showing various embodiments of the performance characteristics of the Figure 1C optical system.

[0032] Figure 21A And Figure 21B FIGS. 6A and 6B are graphs showing the distortion performance of the Figure 1A and Figure 1C optical systems, respectively. DETAILED DESCRIPTION

[0033] In the following discussion of multiple embodiments and applications, reference is made to the accompanying drawings, which form a part hereof, and in which specific embodiments in which the embodiments described herein can be practiced are shown by way of illustration. It is to be understood that other embodiments can be utilized and changes can be made without departing from the scope of the present disclosure.

[0034] Various inventive features are described below, each of which can be used independently of one another or in combination with another feature or features. However, any single inventive feature may not solve all of the above problems, or may only solve one of the above problems. Additionally, one or more of the above-discussed problems may not be fully solved by the features of each of the embodiments described below.

[0035] Embodiments of small volume, high resolution optical imaging systems and methods that can be used in satellites and other airborne systems are described herein. In Figure 1A FIG. 1, an optical system 100 is shown, and the optical system 100 is one embodiment that can be used to provide high resolution imaging performance in a "micro" or small form factor (volume envelope). The optical system can be "piggybacked" on other missions having existing high bandwidth capabilities.

[0036] Satellite constellations in orbit can work collaboratively to coordinate ground coverage. The orbits of the satellites in the constellation can be synchronized. For example, the orbit can be geosynchronous, where the satellite can have an orbital period equal to the average rotation period of the Earth and in the same direction of rotation as the Earth. Or the orbit can be sun-synchronous, such as a near-polar orbit around the Earth, where the satellite crosses any given point on the Earth's surface at the same local mean solar time, or the orbit makes a complete rotation each year so that the satellite maintains the same relationship with the sun. Synchronization systems introduce complexity due to the need for dedicated platforms and sensors, transmitters, and operating stations. For remote sensing, typical examples of such synchronous constellations include the programs of PLANETSCOPE (also known as DOVE), SkySat, BLACKSKY, and Carbite.

[0037] The systems described herein can be used in systems with synchronous orbits as well as asynchronous orbits. Thus, in some embodiments, the imaging system can be used with an asynchronous constellation of Earth observation camera systems (ACEC). This is especially true for constellations of many small satellites, such as CubeSats, and low Earth orbit (LEO) broadband data relay satellite constellations, such as the SpaceNGSO satellite system, One Web, and Amazon's KUIPER system. Any optical system or its features described herein can include any features of micro-optical and camera systems and other aspects described in "Study on the feasibility of micro camera systems for asynchronous, gigantic satellite constellation", by Youngwan Choi, Proc. SPIE 11127, Earth Observing Systems XXIV, 111270Z (9 September 2019, available at https: / / doi.org / 10.1117 / 12.2529090), the entire content of which is incorporated herein by reference in its entirety.

[0038] An asynchronous constellation may include a camera system on any available platform that has scheduled tasks but can carry additional payloads. The asynchronous constellation may differ from the nominal constellation in that the asynchronous constellation will not be able to operate synchronously and does not provide coordinated ground coverage, with the sole purpose being to provide only an image stream. The most significant benefit of an asynchronous constellation is to avoid or minimize the cost, time, and effort of developing the platform, the need for a specific launch system, and the operation of a dedicated ground control system, which can be a high fixed cost. The advantage of using a LEO broadband data relay satellite for asynchronous constellation imaging is its wide data bandwidth. CUBESATs or other platforms with dedicated imaging or other tasks may suffer from reduced data bandwidth. In the absence of data bandwidth issues, an asynchronous constellation with a LEO data relay satellite can transmit image data as a satellite stream movie or other content stream in a dedicated channel, enabling users to selectively receive, record, and process the image data.

[0039] To achieve this, a much smaller camera system or micro-camera system with size advantages and capable of adapting to any available space is needed. The recent development of smaller cameras has focused only on size advantages, making this development dependent on an optical design that is easier to design, easier to develop, or cheaper to construct. However, while this approach seems reasonable, it may impose limitations or constraints on using such cameras for serious tasks due to a reduction in performance such as optical resolution.

[0040] The optical system 100 and other embodiments of the imaging system described herein can be used for constellation operations and are micro in physical dimensions and advanced in performance. Systems and methods for a 4-mirror telescope for a small form factor are described.

[0041] The embodiments described herein can be for an already planned on-board satellite platform as an auxiliary payload or an additional system. In some embodiments, the imaging system can be the size of a star sensor or tracker. The imaging system can be lightweight. The imaging system can minimize power consumption. The imaging system and its interface with the platform can be simple, enabling easy installation and operation. The imaging system can perform appropriate imaging, which can be described in its specification. The imaging system can have an appropriate MTF value. The imaging system can be designed to operate over a wide spectral range and be equipped with multiple channels over the spectral range, with panchromatic, red, green, blue, and near-infrared as a baseline set. The imaging system can have a large field of view.

[0042] For such a camera system, an important requirement is the distortion characteristic. For higher resolutions, a camera system with a small f-number, a small aperture, and a long effective focal length may require a time delay integration (TDI) sensor to achieve an appropriate signal-to-noise ratio (SNR) for further processing on the ground. The distortion caused by the optical design can cause smear in the camera system. To avoid a significant reduction in the image quality for TDI imaging, the distortion caused by the system should be minimized over the entire field of view (FOV).

[0043] The optical imaging system described herein is based on a reflection or mirror system, which may not be common for small, affordable systems. The usual cameras for CAN- or NANO-SAT are based on a refractive-reflective design to achieve a simple design and cost reduction. Examples are PLANETSCOPE (also known as DOVE), SKYSAT, BLACKSKY, and CARBONITE.

[0044] The SKYSAT camera is designed based on a Ritchey-Cassegrain telescope, which has two mirrors (primary mirror and secondary mirror) and a small number of lenses. The design of the SKYSAT camera is known to be easy to manufacture, cost-effective, and have a simple alignment / assembly logic. Additionally, the design of the SKYSAT camera uses a COTS frame CMOS sensor. The CARBONITE camera is an example of an off-the-shelf astronomical telescope that is modified to adapt to the space environment and is equipped with a commercial CMOS sensor for color video imaging. Using a commercial telescope seems to be a smart move in the sense that development or manufacturing work can be reduced, costs can be significantly lowered, and operational management can be effectively carried out. The entire process is developed to be suitable for implementing a constellation of Earth observation satellites.

[0045] Different from those methods, the optical system implementation for the camera described herein is based on a reflection design, which is a four-mirror system. The optical system described herein may not have a limitation on the spectral range to be covered. The system may be free of chromatic aberration, which is crucial for multispectral imaging. Due to the degrees of freedom of the multi-mirror system, the system may have a high design flexibility. The system may have a mass reduction derived from the light weight of the mirrors. The system may have a small form factor.

[0046] Figure 1A is a schematic perspective view showing the optical layout of the first optical system 100 of the optical path. Figure 1B is a schematic perspective view of the optical system 100 in which the optical path is not shown for clarity. The optical path may indicate multiple spectral bands. Refer to Figure 1C , a perspective view of the optical layout of the second optical system 150 is shown in the figure, and the optical path is shown in the figure. For clarity, Figure 1DAn optical system 150 without an optical path is shown.

[0047] Figure 1A and Figure 1B The first two mirrors of the optical systems 100, 150 in Figure 1C and Figure 1D the primary mirror 104 and the secondary mirror 105, and Figure 1A and Figure 1B the primary mirror 154 and the secondary mirror 155 in Figure 1C and Figure 1D are responsible for the optical power of the system, and thus its effective focal length or resolution can be determined. The "effective focal length" used herein has its ordinary and customary meaning and includes, but is not limited to, the distance from the principal plane of the optical mirror to the imaging planes 118, 168. The entrance pupil 124 of the optical system 100 (shown in

[0048] and

[0049] In some embodiments, the various mirrors and support structures for any of the optical systems described herein may be formed of aluminum, ceramics, engineered composites, other suitable materials, or combinations thereof. In some embodiments, the one or more structures and / or the one or more mirrors may be manufactured by 3D printing techniques, also known as additive manufacturing techniques. For example, both the mirror and the support structure may be additively manufactured as a single piece.

[0050] Figure 1A and Figure 1B the tertiary mirror 113 in Figure 1C and Figure 1D and the tertiary mirror 163 in Figure 1A and Figure 1B help to expand the field of view (FOV) and correct the corresponding residual optical aberrations. The tertiary mirrors 113, 163 may not include the optical axis, for example for simpler manufacturability, and two or more tertiary mirrors may be manufactured from a single substrate piece. Figure 1C and Figure 1DThe four-stage mirror 164 in [system name] can minimize distortion and control the back focal length. As used herein, "back focal length" has its ordinary and customary meaning and includes, but is not limited to, the distance between the last surface of an optical mirror and its image plane. The field of view of the optical systems 100, 150 is designed such that light does not interfere with the central holes of the respective four-stage mirrors and the respective primary mirrors. The four-stage mirrors 114, 164 reflect the respective light along the optical path to the imaging planes 118, 168.

[0051] Figure 1D The second optical system 150 is shown, but the light paths are not shown for clarity. Figure 1B The aperture or central hole 110 in [system name] and Figure 1D the diameter of the central hole 160 in [system name] is minimized to maximize the usable area of the primary mirror, and in some embodiments, is not greater than the respective secondary mirrors 105, 155. Figure 1B The central hole 110 in [system name] and Figure 1D the diameter of the hole 160 in [system name] can be designed large enough so as not to interfere with the light passing through the central holes 110 and 160.

[0052] The primary mirrors 104, 154 and / or the secondary mirrors 105, 155 can be axisymmetric or periodic with respect to their respective optical axes. Figure 1E and Figure 1F are schematic diagrams respectively showing the diagonals of the periodic mirror and the image plane. The diagonal of the periodic mirror can have an angle of 0 degrees or 45 degrees with the diagonal of the image plane. The optical axis of the tertiary mirror may not coincide with the mechanical axis.

[0053] Figure 1G and Figure 1H Exemplary embodiments of optical systems 170, 190 respectively having periodic primary mirrors 174, 194 are shown. The optical systems 170, 190 also respectively include secondary mirrors 175, 195, tertiary mirrors 173, 193, four-stage mirrors 184, 198 and imaging planes 189, 199. The optical systems 170, 190 can have the same or similar features and / or functions as the optical system 100 or 150.

[0054] Optical systems 100, 150 may include any features and / or functions that are the same as or similar to those of other embodiments of the optical systems described herein, and other embodiments of the optical systems described herein may include any features and / or functions that are the same as or similar to those of optical systems 100, 150. For example, optical systems 100, 150 may include any features and / or functions that are the same as or similar to those of optical systems 210, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1430, 1460, and optical systems 210, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1430, 1460 may include any features and / or functions that are the same as or similar to those of optical systems 100, 150. For example, for any of the optical systems described herein, the primary mirror may be concave and have a central aperture.

[0055] The primary mirror may have a parabolic surface, a non-parabolic conical surface, or an aspherical surface. As used herein, "parabolic surface" has its ordinary and conventional meaning and includes, but is not limited to, a reflective surface for collecting light energy and may have a shape that is part of a circular parabolic surface, i.e., a surface generated by rotating a parabola about its axis. As used herein, "non-parabolic conical surface" has its ordinary and conventional meaning and includes, but is not limited to, a curve that rotates about its axis, where the curve is obtained as the intersection of a cone with a plane other than a parabola. For example, a "non-parabolic conical surface" may be hyperbolic, elliptical, or circular. As used herein, "aspherical surface" has its ordinary and conventional meaning and includes, but is not limited to, a surface that is aspherical. In some embodiments, the spherical surface may be slightly modified to reduce spherical aberration.

[0056] The secondary mirror may be convex and face the primary mirror. The secondary mirror may have an aspherical surface. The tertiary mirror may be concave and disposed behind the primary mirror. "Behind" may refer to the side of the primary mirror that is opposite the side of the primary mirror that reflects incident light to the secondary mirror. The tertiary mirror may have a parabolic surface, a non-parabolic conical surface, or an aspherical surface. For example, as Figure 3 shown, the quaternary mirror may be concave and disposed in the central aperture of the primary mirror, either before or after the primary mirror. The quaternary mirror may have one of a spherical surface, a parabolic surface, a non-parabolic conical surface, or an aspherical surface.

[0057] There may be at least one image plane having one or more focusing sensors, where the image plane is located at a specific distance from the optical axis. The optical axis may be defined as a geometric reference line extending between the vertices of the primary mirror and the secondary mirror. The vertex of a given mirror may be the point on the mirror surface where the principal axis intersects the mirror.

[0058] Optical system 100 may have a larger primary mirror 104 and thus have a higher resolution relative to the primary mirror 154 of optical system 150. The resolution of optical system 100 may be better than 1 m at an altitude of 500 km. Optical system 150 may have a resolution better than 2 m at an altitude of 500 km. Optical system 150 may have a larger field of view (FOV) than optical system 100. Optical system 100 may have a narrower field of view (FOV) relative to optical system 150. Optical system 100 may have a volume dimension of 200 mm (W) × 200 mm (H) × 250 mm (L). Optical system 150 may have a volume dimension of 100 mm (W) × 100 mm (H) × 150 mm (L). The weight of optical system 150 may be lighter than that of optical system 100. Both optical systems 100 and 150 may have an appropriate MTF for higher resolution imaging.

[0059] Both optical systems 100 and 150 may have similar mirror types and optical paths. However, the respective purposes and tasks of optical systems 100 and 150 may be different. The purpose of optical system 100 may be to map the Earth's surface and obtain geospatial data. The purpose of optical system 150 may be for remote sensing and environmental monitoring.

[0060] In some embodiments, optical systems 100 and 150 may achieve various parameters for an orbital system and / or an imaging system. Example parameters that can be achieved using optical systems 100 and 150 are described in Table 1. For example, the designed orbit may be arranged at 500 km, the spectral band may be designed to be compatible with imaging of large satellites and scientific satellites other than the panchromatic band, etc. The panchromatic band (PAN band) may be designed to include up to the red edge to improve the modulation transfer function (MTF) in the band, which may be inevitable due to its small aperture size.

[0061]

[0062] Table 1

[0063] Figure 2AIt is a block diagram of an exemplary payload system 200 configuration for an optical system 210 in a satellite. The optical system 210 is shown in a schematic form. The optical system 210 includes a concave primary mirror 204 having a central aperture 212. The primary mirror can have one of a parabolic surface, a non-parabolic conical surface, or an aspherical surface. A smaller convex secondary mirror 205 faces the primary mirror 204 and has an aspherical surface. The secondary mirror can have an aspherical surface. A concave tertiary mirror 213 is disposed behind the primary mirror 204, and the tertiary mirror can have one of a parabolic surface, a non-parabolic conical surface, or an aspherical surface. A concave quadrupole mirror 214 can be disposed slightly behind the central aperture 212 of the primary mirror 204, where the quadrupole mirror can have one of a spherical surface, a parabolic surface, a non-parabolic conical surface, or an aspherical surface. Each of the primary mirror 204, the tertiary mirror 213, and the quadrupole mirror 214 has a positive optical power or focal length, while the secondary mirror 205 has a negative optical power. "Behind" can be defined as described above. Behind can also refer to Figure 2A the direction in Figure 2A , that is, the direction oriented to the right, such that "behind" the primary mirror 204 means the right side of the primary mirror 204, as oriented in the figure.

[0064] An image sensor 216 having up to "n" aggregation sensors that convert light into electrical signals is located behind the primary mirror 204. In some embodiments, the image sensor 216 can transfer the output format of 32 sub-LVDS (low voltage differential signaling) channels of digital data to the control and processing electronics 220 of the satellite through an interface 218. In other embodiments, other output formats are used. The sensor 216 includes a readout integrated circuit (ROIC) for infrared, visible, and other array sensors. Functions supported by the ROIC include the processing and shaping of image signals and can include unit preamplifiers. The interface 218 also includes control signals from the control and processing electronics 220, where, in some embodiments, the control signals can include a serial peripheral interface (SPI) and a clock signal.

[0065] In some embodiments, the data formatting and distribution subsystem 224 receives data through interface 218, and then further sends the data to data processing with the machine learning subsystem 226, and sends it to the data storage and archival subsystem 230 for storage. The stored data from the data storage and archival subsystem 230 can be directly sent to the data processing subsystem 226 for various types of processing. The output of the processed data from the data processing subsystem 226 can be directly sent to the data storage and archival subsystem 230 for storage. The output of the processed data from the data processing subsystem 226 and the data from the data storage and archival subsystem 230 can be sent to the data formatting, encryption, and transmission subsystem 228. Then, the output of the data formatting, encryption, and transmission subsystem 228, such as image data, is sent to the satellite bus for further distribution, and this further distribution can include transmission to an earth station, a relay satellite, or other entities that receive the data. The data processing subsystem 226 can include one or more processors and one or more memories, such as a memory for program instructions and a memory and / or cache for data.

[0066] The payload control electronics subsystem 222 receives remote commands from the satellite bus and provides housekeeping data to the satellite bus. The payload control electronics subsystem 222 provides commands to parts of the payload system 200, including providing commands to the image sensor 216 and / or to the thermal control, temperature data, and optical focus subsystem 234. The thermal control, temperature data, and optical focus subsystem 234 provides control signals, such as thermal control and optical focus, to the optical system 210 through interface 232, and receives temperature data from the optical system 210.

[0067] The power conversion, distribution, and telemetry subsystem 236 receives telemetry commands from the satellite bus and provides telemetry data to the satellite bus. The power conversion, distribution, and telemetry subsystem 236 can also receive power, such as power from the satellite's solar panels or batteries.

[0068] An important issue for imaging systems for smaller satellites such as CUBESATs is calibration, including absolute calibration and inter-sensor calibration. For example, most images from commercial CUBESATs are not calibrated in a standard way on a standard radiance or reflectance scale. Thus, it can be challenging to compare image data with imaging from large commercial satellites or scientific satellites such as MODIS or LANDSAT. Even inter-sensor calibration is uncertain, which may be mainly due to the temporary instability or inconsistent performance of commercial sensors.

[0069] Conversely, sensors for the optical systems described herein, such as the aggregation sensor of sensor 216 in optical system 210, can be developed and customized for space applications, and the consistency and stability of the above sensors can be verified. Importantly, the optical system 210 described herein and all optical systems can be calibrated according to standard procedures and relative to each other such that all image data from the systems are compatible with each other and also with a reference system.

[0070] Reference Figure 2B , an exemplary implementation of a sensor circuit for image sensor 216 is shown in the figure. Image sensor 216 may include a readout integrated circuit (ROIC) 272 and a charge-coupled device (CCD) array 270. Photons incident on the surface of CCD array 270 (the upper surface as oriented in the figure) generate charge, which can be read by electronics and turned into a digital copy of the light pattern falling on the device. In certain implementations, charge-coupled devices from complementary metal-oxide semiconductor (CCD-in-CMOS) time delay integration (TDI) sensors from IMEC International can be used for optical system 210, even with a preferred pixel size of 5 micrometers (μm). In some implementations, a format of 4096 columns and 256 levels for each multi-band CCD array 270 is used, and the back-illuminated sensor combines the TDI CCD array with a CMOS driver and reads out pixels at a pitch of 5.4 μm. On-chip control and sequencer circuits may be included. In certain implementations, a 130 MHz clock 262 may be an input to the image sensor and a serial peripheral interface (SPI) for control. The imager may be connected via an SPI interface and may integrate an on-chip PLL to deliver the output format of 32 sub-LVDS (low-voltage differential signaling) channels that are part of ROIC 272. A seven-band version of the circuit may include seven CCD arrays, each 4096 × 256 pixels.

[0071] In other implementations, other sensor circuits may be used for image sensor 216, which may have arrays 270 of different sizes and different ROICs 272 for outputting data. For example, image sensor 216 may include four panchromatic CCD arrays of 16384 × 96 pixels each and eight multi-spectral CCD arrays of 8192 × 48 pixels each.

[0072] To maximize the area exposed to light, back-illumination technology can be used. This includes bonding the sensor wafer to a carrier wafer and thinning it from the back. This directly exposes the CCD gates to light without obstructing the metal wires. Consequently, the effective fill factor reaches 100%. Back-illuminated CMOS imagers have very high intrinsic light sensitivity and are very effective in detecting (near) ultraviolet and blue light. Several anti-reflection coatings (ARC) can be used to achieve high quantum efficiency in selected regions of the spectrum, such as over 70% in the UV range or over 90% in the visible light range.

[0073] With a TDI sensor, the image quality is sensitive to platform motion, which can be represented by the image smear MTF. The image smear MTF of the optical system 210 can be 0.974, the smear pixel can be 0.2, the TDI step can be 128, and the clock phase can be 4. This can impose requirements on the attitude stability of the platform, which can be 22 micro-radians per second (μrad / sec) or 4.54 arc-seconds per second (arcsec / sec). When the attitude stability requirement is relaxed to a one-pixel smear, the smear MTF becomes 0.75, and the attitude stability can be 23 arcsec / sec.

[0074] Referring Figure 3 , the figure shows a schematic diagram of an embodiment of a total reflection optical system 300. The optical design of the optical system 300 can be different from the traditional three-mirror anastigmat TMA or three-mirror Korsch design. The Korsch design can have an ellipsoidal surface for the primary mirror, a hyperbolic surface for the secondary mirror, and an ellipsoidal surface for the tertiary mirror.

[0075] The optical system 300 includes a concave primary mirror 304 with a central hole 310, where the primary mirror can have a parabolic surface, a non-parabolic conical surface, or an aspherical surface. A smaller convex secondary mirror 305 faces the primary mirror 304 and has an aspherical surface. A concave tertiary mirror 313 is arranged behind the primary mirror 304, where the tertiary mirror can have a parabolic surface, a non-parabolic conical surface, or an aspherical surface. A concave quaternary mirror 314 is arranged in front of the central hole 310 of the primary mirror 304, where the quaternary mirror can have a spherical surface, a parabolic surface, a non-parabolic conical surface, or an aspherical surface. The primary mirror 304, the tertiary mirror 313, and the quaternary mirror 314 each have a positive optical power or focal length, while the secondary mirror 305 has a negative optical power.

[0076] The image plane 316 with one or more concentrating sensors that convert light into an electrical signal is located behind the primary mirror 304. In some embodiments, the image plane 316 is located at a specific distance from the optical axis, which is defined by mechanical symmetry about a line passing through the vertices of the primary mirror and the secondary mirror, and this line may define the "optical axis". This specific distance is within the physical radius of the primary mirror (from the optical axis). Thus, the image plane will not exceed the cylindrical envelope defined by the radius of the optical axis of the primary mirror. The radius of the primary mirror extends perpendicularly from the principal axis of the mirror to the outermost edge of the mirror. The principal axis may be a geometric reference line passing through the center of the mirror and perpendicular to the surface of the mirror.

[0077] The optical system 300 uses a secondary mirror 305 that is symmetric about the optical axis. The tertiary mirror 313 may have a segmented non-circular shape. The quaternary mirror 314 may have a circular or non-circular shape. The primary mirror 304 may have a circular or non-circular shape, with the latter enhancing the modulation transfer function (MTF) and the signal-to-noise ratio (SNR). The circular shape is scribed into a non-circular shape, which may be periodic about the optical axis.

[0078] For the example of a square and its inscribed circle, the inscribed circle may be the shape of the primary mirror for a traditional optical system design. If the radius of the inscribed circle is "r", then the area of the square will be greater than 4 / π. For larger cameras for which a large volume is allocated, this is generally not a problem. However, for small satellites, which are typically cuboid, a primary mirror with a square shape may have a larger area of 4 / π and improve the MTF and SNR.

[0079] Neither the Korsch nor other four-mirror optical designs use a parabolic surface for the primary mirror and / or the tertiary mirror. By using a parabolic surface for the primary mirror and / or the tertiary mirror of the optical system 300, the optical system 300 can provide a unique and affordable solution for missions with budget constraints. For a parabolic surface, a general test setup can be used for manufacturing, or stitching measurements are also possible. Additionally, a commercial production line can be used for manufacturing parabolic mirrors, especially when the mirror is less than 300 mm. In contrast, non-parabolic quadric or aspherical surfaces may require specialized test tools, including computer-generated holograms (CGHs) or null optics.

[0080] For a parabolic surface, a general test setup can be used for manufacturing, or stitching measurements are also possible. Additionally, a commercial production line can be used for manufacturing parabolic mirrors, especially when the mirror is less than 300 mm.

[0081] The primary mirror and the secondary mirrors 304, 305 that form the optical axis are symmetric about this axis or are periodic. The primary mirror and the secondary mirrors face each other. The tertiary mirror 313 faces the back of the primary mirror 304 and can be a segmented mirror. As used herein, "segmented mirror" includes its ordinary and customary meaning and includes, but is not limited to, an array of smaller mirrors designed to act as segments of a single larger curved mirror. The optical axis of the tertiary mirror 313 may not coincide with the mechanical axis. As used herein, "mechanical axis" has its ordinary and customary meaning and may include, but is not limited to, a normal vector at the center or edge of the mirror. In some embodiments, the tertiary mirror 313 is part of a larger mirror. In such embodiments, the optical axis of the tertiary mirror 313 may refer to the optical axis of the larger mirror, and the mechanical axis may refer to the axis of the segmented mirror. The quaternary mirror 314 faces the tertiary mirror 313 and is positioned to avoid interfering with the light rays from the secondary mirror 305 to the tertiary mirror 313.

[0082] The metrology and support structure of the mirror can be a cylindrical tube or a conical baffle of the primary mirror 304, such as those Figures 14A to 14D shown and described for the metrology and support structure of the mirrors. The cylindrical envelope can co - extend with the cylindrical structure to limit the specific distance at which the imaging plane is located with respect to the optical axis between the primary mirror and the secondary mirror. For example, the position of the imaging plane can be radially limited by the radius of the cylindrical structure.

[0083] Light first impinges on the primary mirror 304 and is reflected by the primary mirror 304, then by the secondary mirror 305, third by the tertiary mirror 313, and finally by the quaternary mirror 314, such that the light reaches the image plane 316. The image plane 316 includes one or more sensors, which can be aggregated in an ordered manner. The entrance pupil of the optical system 300 can be located near the primary mirror 304 or the secondary mirror 305. The intermediate foci are formed around the vertex of the primary mirror 304, between the primary mirror 304 and the secondary mirror 305, or between the primary mirror 304 and the tertiary mirror 313. The exit pupil or the Lyot stop can be located near the quaternary mirror 314, between the tertiary and quaternary mirrors 313, 314, or between the quaternary mirror 314 and the image plane 316. As used herein, "Lyot stop" has its ordinary and customary meaning and includes, but is not limited to, an optical stop that reduces the amount of flare that may be caused by diffraction from other stops and baffles in the optical system. The Lyot stop can be located on the image of the entrance pupil of the system and has a diameter slightly smaller than the image of the pupil.

[0084] The optical system 300 has a small form factor. The form factor is defined as the ratio of 1) the distance between the secondary mirror 305 and the tertiary mirror 313 to 2) the effective focal length of the optical system 300. In some embodiments, the optical system 300 has a form factor less than 0.2 and 0.09. The form factor can be from about 0.09 to 0.2, from about 0.04 to less than 0.25. The form factor can be less than 0.25. The form factor can have the following values or approximately the following values: 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.20, 0.21, 0.22, 0.23, 0.24, or 0.25. The form factor can be less than 0.04, less than 0.05, less than 0.06, less than 0.07, less than 0.08, less than 0.09, less than 0.09, less than 010, less than 0.11, less than 0.12, less than 0.13, less than 0.14, less than 0.15, less than 0.16, less than 0.17, less than 0.18, less than 0.19, less than 0.20, less than 0.21, less than 0.22, less than 0.23, less than 0.24, or less than 0.25.

[0085] In addition to the small form factor, the optical system 300 is superior to the prior art in having a much shorter physical distance from the tertiary mirror 313 to the image plane 316. The prior art has a relatively long distance between the tertiary mirror and the image plane and requires one or more folding mirrors to fit within a limited size. Such a configuration may lead to difficulties in optical alignment and thermal instability during operation, which may ultimately result in a degradation of performance. Due to the small form factor and the short distance between the tertiary mirror 313 and the image plane 316, the optical system 300 eliminates unnecessary folding mirrors and simplifies alignment, assembly, and operational stability.

[0086] The optical system can be designed with mirrors of materials having zero coefficient of thermal expansion (CTE) (such as Zerodur, Fused Silica, Suprasil, Astrostiall, etc.), low CTE materials (such as borosilicate glass, such as BOROFLOAT, Pyrex, etc.), and moderate CTE materials (such as Crown glass, such as NBK7).

[0087] For CTE matching, specific combinations of mirror and structural materials are used for the optical system. Super Invar, Invar, or designed composite materials can be used for zero CTE mirror materials. Invar, Kovar, ceramic, or designed composite materials can be used for low CTE mirror materials. Titanium, ceramic, or designed composite materials can be used for moderate CTE mirror materials.

[0088] The monolithic structure can be used as the final solution for an optical system. The mirror and the structure can be made of one material, including aluminum, ceramics, designed composite materials, and is not limited to this list.

[0089] Referring Figure 4 , a schematic diagram of another embodiment of a total internal reflection optical system 400 is shown in the figure. The optical system 400 includes a primary mirror 404, a secondary mirror 405, a tertiary mirror 413, a quaternary mirror 414, and an image plane 416. The primary mirror 404, the secondary mirror 405, the tertiary mirror 413, the quaternary mirror 414, and the image plane 416 may respectively have the same or similar features and / or functions as the primary mirror 304, the secondary mirror 305, the tertiary mirror 313, the quaternary mirror 314, and the image plane 316 of the optical system 300, and the primary mirror 304, the secondary mirror 305, the tertiary mirror 313, the quaternary mirror 314, and the image plane 316 of the optical system 300 may respectively have the same or similar features and / or functions as the primary mirror 404, the secondary mirror 405, the tertiary mirror 413, the quaternary mirror 414, and the image plane 416.

[0090] However, in the optical system 400, the quaternary mirror 414 is located behind the primary mirror 404 but close to the hole 410 in the primary mirror 404. The tertiary mirror 413 is located behind the primary mirror 404 in the optical system 400, further away than in the optical system 300. In some embodiments, the tertiary mirror 413 may be located at a distance behind the primary mirror 404, and the distance is in the range of 20% to 60%, 30% to 50%, or 35% to 45% of the diameter of the primary mirror 404. Figure 3 The primary mirror 404 of the optical system 300 in Figure 4 The optical system 400 of

[0091] Referring Figure 5, a schematic diagram of another embodiment of the total reflection optical system 500 is shown in the figure. The optical system 500 includes a primary mirror 504, a secondary mirror 505, a tertiary mirror 513, a quaternary mirror 514, and an image plane 516. The primary mirror 504, the secondary mirror 505, the tertiary mirror 513, the quaternary mirror 514, and the image plane 516 may respectively have the same or similar features and / or functions as the primary mirror 304, the secondary mirror 305, the tertiary mirror 313, the quaternary mirror 314, and the image plane 316 of the optical system 300, and the primary mirror 304, the secondary mirror 305, the tertiary mirror 313, the quaternary mirror 314, and the image plane 316 of the optical system 300 may respectively have the same or similar features and / or functions as the primary mirror 504, the secondary mirror 505, the tertiary mirror 513, the quaternary mirror 514, and the image plane 516.

[0092] However, in the optical system 500, the quaternary mirror 514 is located at a distance behind the primary mirror 504 that is greater than the distance between the quaternary mirror 414 and the primary mirror 404 of the optical system 400 (see Figure 4 ). Additionally, in the optical system 500, the tertiary mirror 513 is located at a distance behind the primary mirror 504 that is greater than the distances of the respective corresponding mirrors of the optical system 400. In some embodiments, the tertiary mirror 513 may be located at a distance behind the primary mirror 5(0)4 within the range of 45% to 55% of the diameter of the primary mirror 504. The optical system 500 may be designed for much smaller pixel sensors, such as having a pixel size of less than 4 microns in some embodiments. The optical system 500 may differ from the optical system 300 in terms of effective focal length and field of view. In some embodiments, the optical system 500 may have a shorter effective focal length and a wider field of view relative to the optical system 300, which may allow the system 500 to include a sensor with a smaller pixel size. It may be relatively closer to the hole 610 in the primary mirror 613. The tertiary mirror 613 is similarly located behind the primary mirror 604 in the optical system 400. The additional folding mirror 615 receives light from the quaternary mirror 614 and reflects the light to the image plane 616 located above the folding mirror 615. In some embodiments, the image plane 616 is located above and parallel to the optical axis.

[0093] Some embodiments of the optical system may have a longer system optical path length between the image plane 616 using the folding mirror 615 and the four-stage mirror 614. If the image plane 616 is after the three-stage mirror 613, the system optical path length is the distance between the two-stage mirror 605 and the image plane 616. By using the folding mirror 615, the system optical path length is the distance between the two-stage mirror 605 and the two-stage mirror 613. The image plane 616 can be positioned to meet the requirements of the focal length and the field of view. The configuration of the optical system 600 can provide a compact design. Another advantage is that the system 600 can allow for easier installation of the sensor cooler and the heat dissipation plate for the cooler. Additionally, in the optical system 600, the sensor for the image plane can be positioned closer to the main mirror support structure and can hold the sensor in a more stable manner.

[0094] Referring Figure 7 , another embodiment of the catadioptric optical system 700 with a folding mirror 715 is shown in the figure. The optical system 700 may have the same or similar features and / or functions as the optical system 600, and the optical system 600 may have the same or similar features and / or functions as the optical system 700. The optical system 600 includes a primary mirror 704, a two-stage mirror 705, a three-stage mirror 713, a four-stage mirror 714, and an image plane 716. The primary mirror 704, the two-stage mirror 705, the three-stage mirror 713, the four-stage mirror 714, and the image plane 716 may respectively have the same or similar features and / or functions as the primary mirror 604, the two-stage mirror 605, the three-stage mirror 613, the four-stage mirror 614, and the image plane 616 of the optical system 600, and the primary mirror 604, the two-stage mirror 605, the three-stage mirror 613, the four-stage mirror 614, and the image plane 616 of the optical system 600 may respectively have the same or similar features and / or functions as the primary mirror 704, the two-stage mirror 705, the three-stage mirror 713, the four-stage mirror 714, and the image plane 716. As in the optical system 600, the four-stage mirror 714 is located behind the primary mirror 704 but close to the hole 710 in the primary mirror 704. The three-stage mirror 713 is located behind the primary mirror 704 similarly to the optical system 600. The folding mirror 715 receives light from the four-stage mirror 714 and reflects the light to the image plane 716 located below the folding mirror 715. In some embodiments, the image plane 716 is below the optical axis and parallel to the optical axis. The advantage of the configuration of the optical system 700 is that the configuration of the mirrors including the folding mirror 715 results in a more compact design. Another advantage is that the optical system 700 can use sensors for the image plane in larger packages. CMOS sensors or sensors with ROICs tend to have larger packages, such that more circuits or components can be accommodated, and these circuits or components can help minimize readout noise, crosstalk, and blurring.

[0095] Referring Figure 8, another embodiment of a total reflection optical system 800 with a folding mirror 815 is shown in the figure. The optical system 800 may have the same or similar features and / or functions as the optical system 700, and the optical system 700 may have the same or similar features and / or functions as the optical system 800. The optical system 800 includes a primary mirror 804, a secondary mirror 805, a tertiary mirror 813, a quaternary mirror 814, and an image plane 816. The primary mirror 804, the secondary mirror 805, the tertiary mirror 813, the quaternary mirror 814, and the image plane 816 may respectively have the same or similar features and / or functions as the primary mirror 704, the secondary mirror 705, the tertiary mirror 713, the quaternary mirror 714, and the image plane 716 of the optical system 700, and the primary mirror 704, the secondary mirror 705, the tertiary mirror 713, the quaternary mirror 714, and the image plane 716 of the optical system 700 may respectively have the same or similar features and / or functions as the primary mirror 804, the secondary mirror 805, the tertiary mirror 813, the quaternary mirror 814, and the image plane 816. However, the image plane 816 is closer to the optical axis than the image plane 716 near its corresponding optical axis. The quaternary mirror 814 is located behind the primary mirror 804 but further behind than the corresponding component of the optical system 700. The tertiary mirror 813 is further behind the primary mirror 804 than in the optical system 700. The folding mirror 815 receives light rays from the quaternary mirror 814 and reflects the light rays to the image plane 816 located below the folding mirror 815. In some embodiments, the image plane 816 is located below the optical axis and parallel to the optical axis. The optical system 800 is designed for a smaller pixel sensor, which is typically a commercial sensor or a MIL-STD sensor. One advantage of the optical system 800 is that the latest sensors, including commercial sensors or MIL-STD sensors, can be utilized.

[0096] Referring to Figure 9 , another embodiment of a total reflection optical system 900 with a folding mirror 915 is shown in the figure. The optical system 900 may have the same or similar features and / or functions as the optical system 800. The optical system 900 includes a primary mirror 904, a secondary mirror 905, a tertiary mirror 913, a quaternary mirror 914, and an image plane 916. The primary mirror 904, the secondary mirror 905, the tertiary mirror 913, the quaternary mirror 914, and the image plane 916 may respectively have the same or similar features and / or functions as the primary mirror 804, the secondary mirror 805, the tertiary mirror 813, the quaternary mirror 814, and the image plane 816 of the optical system 800, and the primary mirror 804, the secondary mirror 805, the tertiary mirror 813, the quaternary mirror 814, and the image plane 816 of the optical system 800 may respectively have the same or similar features and / or functions as the primary mirror 904, the secondary mirror 905, the tertiary mirror 913, the quaternary mirror 914, and the image plane 916.

[0097] However, in the optical system 900, the image plane 916 is closer to the optical axis than the image plane 816 near its corresponding optical axis. The four-stage mirror 914 is located behind the primary mirror 904 and is at a similar distance from the optical system 800. The three-stage mirror 913 is located behind the primary mirror 904 and is at a similar distance from the optical system 800. The folding mirror 915 receives light from the four-stage mirror 914 and reflects the light to the image plane 916 located above the folding mirror 915. In some embodiments, the image plane 916 is located above and parallel to the optical axis. The advantage of the optical system 900 is that the sensor of the image plane can more stably resist vibration and the cooler with a radiator can be mounted in an easier manner than in other optical system configurations.

[0098] Referring Figure 10 , an embodiment of a catadioptric optical system 1000 with multiple image planes and a folding mirror 1015 is shown in the figure. The optical system 1000 may have the same or similar features and / or functions as the optical system 600. The optical system 1000 includes a primary mirror 1004, a secondary mirror 1005, a three-stage mirror 1013, a four-stage mirror 1014, and a first image plane 1016. The primary mirror 1004, the secondary mirror 1005, the three-stage mirror 1013, the four-stage mirror 1014, and the first image plane 1016 may respectively have the same or similar features and / or functions as the primary mirror 604, the secondary mirror 605, the three-stage mirror 613, the four-stage mirror 614, and the image plane 616 of the optical system 600, and the primary mirror 604, the secondary mirror 605, the three-stage mirror 613, the four-stage mirror 614, and the image plane 616 of the optical system 600 may respectively have the same or similar features and / or functions as the primary mirror 1004, the secondary mirror 1005, the three-stage mirror 1013, the four-stage mirror 1014, and the first image plane 1016. The distance of the first image plane 1016 from the optical axis is similar to the distance of the image plane 616 from its corresponding optical axis. However, the optical system 1000 has a second image plane 1016' similar to the first image plane 1016. The first image plane 1016 may be dedicated to a first spectral range, while the second image plane 1016' may be dedicated to a second spectral range.

[0099] The fourth mirror 1014 is located behind the primary mirror 1004 and is close to the aperture 1010 in the primary mirror 1004 by a distance similar to that in the corresponding component of the optical system 600. The tertiary mirror 1013 is located at a distance behind the primary mirror 1004, and this distance is similar to that in the corresponding component of the optical system 600. The folding mirror 1015 receives light from the fourth mirror 1014 and reflects some light within a certain spectral range to the first image plane 1016 located above the folding mirror 1015. The folding mirror 1015 can transmit light within a second range different from the reflected range. The optical system 1000 achieves simultaneous multi-color imaging by making the folding mirror 1015 reflective in the first spectral range and transmissive in the second spectral range. In some embodiments, the first image plane 1016 is located above the optical axis and parallel to the optical axis, while the second image plane 1016' is located below the optical axis on the opposite side of the optical axis from the first image plane 1016 and perpendicular to the optical axis. One advantage of the optical system 1000 is that due to the characteristics of the folding mirror and multiple imaging planes, multi-color imaging can be performed.

[0100] Referring Figure 11 , another embodiment of a catadioptric optical system 1100 with multiple image planes and a folding mirror 1115 is shown in the figure. The optical system 1100 may have the same or similar features and / or functions as the optical system 1000. The optical system 1100 includes a primary mirror 1104, a secondary mirror 1105, a tertiary mirror 1113, a fourth mirror 1114, a folding mirror 1115, and a first image plane 1116. The primary mirror 1104, the secondary mirror 1105, the tertiary mirror 1113, the fourth mirror 1114, the folding mirror 1115, and the first image plane 1116 may respectively have the same or similar features and / or functions as the primary mirror 1004, the secondary mirror 1005, the tertiary mirror 1013, the fourth mirror 1014, the folding mirror 1015, and the first image plane 1016 of the optical system 1000, and the primary mirror 1004, the secondary mirror 1005, the tertiary mirror 1013, the fourth mirror 1014, the folding mirror 1015, and the first image plane 1016 of the optical system 1000 may respectively have the same or similar features and / or functions as the primary mirror 1104, the secondary mirror 1105, the tertiary mirror 1113, the fourth mirror 1114, the folding mirror 1115, and the first image plane 1116. However, in the optical system 1100, the first image plane 1116 is positioned at a distance from the optical axis greater than the distance of the first image plane 1016 from its corresponding optical axis. The optical system 1100 has a second image plane 1116' similar to the first image plane 1116. The first image plane 1116 may be dedicated to the first spectral range, and the second image plane 1116' may be dedicated to the second spectral range.

[0101] The four - stage mirror 1114 is located behind the primary mirror 1104 and is at a distance from the aperture 1110 in the primary mirror 1104, and this distance is similar to the distance in the corresponding components of the optical system 1000. The three - stage mirror 1113 is located at a distance behind the primary mirror 1104, and this distance is similar to the distance in the respective corresponding components of the optical system 1000. The folding mirror 1115 receives light from the four - stage mirror 1114 and reflects some of this light to the first image plane 1116 located below the folding mirror 1115. The optical system 1100 achieves simultaneous multi - color imaging by making the folding mirror 1115 reflective in a first spectral range and transmissive in a second spectral range. In some embodiments, the first image plane 1116 is located below and parallel to the optical axis, and the second image plane 1116' is located below and perpendicular to the optical axis. An advantage is that the optical system 1100 can use sensors in larger packages for the image plane. CMOS sensors or sensors with ROICs typically have larger packages, allowing for more circuits or components that can help minimize read - out noise, crosstalk, and blurring.

[0102] Referring Figure 12 , another embodiment of a catadioptric optical system 1200 with multiple image planes and a folding mirror 1215 is shown in the figure. The optical system 1200 may have the same or similar features and / or functions as the optical system 1100. The optical system 1200 includes a primary mirror 1204, a secondary mirror 1205, a three - stage mirror 1213, a four - stage mirror 1214, a folding mirror 1215, and a first image plane 1216. The primary mirror 1204, the secondary mirror 1205, the three - stage mirror 1213, the four - stage mirror 1214, the folding mirror 1215, and the first image plane 1216 may respectively have the same or similar features and / or functions as the primary mirror 1104, the secondary mirror 1105, the three - stage mirror 1113, the four - stage mirror 1114, the folding mirror 1115, and the first image plane 1116 of the optical system 1100, and the primary mirror 1104, the secondary mirror 1105, the three - stage mirror 1113, the four - stage mirror 1114, the folding mirror 1115, and the first image plane 1116 of the optical system 1100 may respectively have the same or similar features and / or functions as the primary mirror 1204, the secondary mirror 1205, the three - stage mirror 1213, the four - stage mirror 1214, the folding mirror 1215, and the first image plane 1216. However, in the optical system 1200, the first image plane 1216 is positioned at a shorter distance from the optical axis than the first image plane 1116 is from its corresponding optical axis. The optical system 1200 has a second image plane 1216' similar to the first image plane 1216. The first image plane 1216 may be dedicated to a first spectral range, and the second image plane 1216' may be dedicated to a second spectral range.

[0103] The four - stage mirror 1214 is located at a distance behind the primary mirror 1204, and this distance is greater than the distance in the corresponding components of the optical system 1100. The three - stage mirror 1213 is positioned at a distance behind the primary mirror 1204 that is greater than the distance in the corresponding components of the optical system 1100. The folding mirror 1215 receives light from the four - stage mirror 1214 and reflects the light to the first image plane 1216 located below the folding mirror 1215. The optical system 1200 enables multi - color imaging simultaneously by making the folding mirror 1215 reflective in a first spectral range and transmissive in a second spectral range. In some embodiments, the first image plane 1216 is located below and parallel to the optical axis, and the second image plane 1216' is located below and perpendicular to the optical axis. The second image plane 1216' is positioned closer to the optical axis than the second image plane 1116' near its corresponding optical axis. The optical system 1200 is designed to use a smaller pixel sensor for the image plane. One advantage of the optical system 1200 is that it can utilize the latest sensors, including commercial sensors or MIL - STD sensors.

[0104] Referring Figure 13 , another embodiment of a catadioptric optical system 1300 with multiple image planes and a folding mirror 1315 is shown in the figure. The optical system 1300 may have the same or similar features and / or functions as the optical system 1000. The optical system 1300 includes a primary mirror 1304, a secondary mirror 1305, a three - stage mirror 1313, a four - stage mirror 1314, a folding mirror 1315, and a first image plane 1316. The primary mirror 1304, secondary mirror 1305, three - stage mirror 1313, four - stage mirror 1314, folding mirror 1315, and first image plane 1316 may respectively have the same or similar features and / or functions as the primary mirror 1004, secondary mirror 1005, three - stage mirror 1013, four - stage mirror 1014, folding mirror 1015, and first image plane 1016 of the optical system 1000, and the primary mirror 1004, secondary mirror 1005, three - stage mirror 1013, four - stage mirror 1014, folding mirror 1015, and first image plane 1016 of the optical system 1000 may respectively have the same or similar features and / or functions as the primary mirror 1304, secondary mirror 1305, three - stage mirror 1313, four - stage mirror 1314, folding mirror 1315, and first image plane 1316. However, in the optical system 1300, the first image plane 1316 is positioned at a shorter distance from the optical axis than the first image plane 1016 is from its corresponding optical axis. The optical system 1300 has a second image plane 1316' similar to the first image plane 1316. The first image plane 1316 may be dedicated to a first spectral range, and the second image plane 1316' may be dedicated to a second spectral range.

[0105] The fourth mirror 1314 is located at a distance behind the primary mirror 1304, and this distance is greater than the distances in the respective components of the optical system 1000. The third mirror 1313 is located at a distance behind the primary mirror 1304 that is greater than the distances in the corresponding components of the optical system 1000. The folding mirror 1315 receives light from the fourth mirror 1314 and reflects the light to the first image plane 1316 located above the folding mirror 1315. The optical system 1300 achieves simultaneous multi-color imaging by making the folding mirror 1315 reflective in a first spectral range and transmissive in a second spectral range. In some embodiments, the first image plane 1316 is located above the optical axis and parallel to the optical axis, while the second image plane 1316' is located below the optical axis and perpendicular to the optical axis. The second image plane 1316' is positioned closer to the optical axis than the second image plane 1016' that is closer to its corresponding optical axis. The advantage of the optical system 1300 is that a cooler with a radiator for a sensor can be installed in a way that is easier than other optical system configurations.

[0106] Referring Figure 14A , a perspective cross-sectional view of a camera system 1400 with an optical system is shown in the figure. The box 1410 shows the enclosure of the camera and can be a mechanical interface with the satellite BUS. The metrology structure 1418 shown as a conical structure maintains the distance between the primary mirror 1404 and the secondary mirror 1405. When the temperature changes by 1 °C, the metrology structure 1418 can maintain this distance within 1 micrometer. In Figure 14D The support structure 1408, best shown as a cylindrical tube in

[0107] In some embodiments, the dimensions of the camera are 200 mm × 200 mm × 250 mm. Depending on the focal length of the optical system, these dimensions can vary from 75 mm × 75 mm × 100 mm designed for a 5 m resolution at 500 km to 750 mm × 750 mm × 1000 mm designed for a 0.25 m resolution at 500 km. The overall volume envelope of the camera system can be less than 0.01 m 3 , less than 0.008 m 3 , less than 0.006 m 3 , less than 0.004 m 3 , less than 0.003 m 3 , less than 0.001 m 3 , or from 0.005 m 3 to 0.01 m 3 .

[0108] The shape factor is defined as the ratio of the distance between the secondary mirror and the tertiary mirror to the focal length of the optical system. The distance between the secondary mirror and the tertiary mirror can be measured along the optical path. In some embodiments, the optical system can be implemented with a shape factor having the above values, such as less than 0.2, less than 0.15, or less than 0.1. For the prior art, a shape factor greater than 0.25 is known. With the relatively small shape factor of the optical system described herein, the optical system can provide better imaging resolution at an altitude of 500 km than 1 m, 0.5 m, or 0.25 m. The optical system is also capable of achieving an imaging resolution better than 0.1 m in an elliptical orbit. In other embodiments, the shape factor can be in the range between 0.04 and 0.09. Examples of the focal length of the system, the distance between the secondary mirror and the tertiary mirror for each focal length, and the corresponding shape factor are provided in Table 2.

[0109]

[0110] Table 2

[0111] Referring to Figure 14B , an embodiment of an optical system 1430 for a camera is shown in the figure. When the temperature changes by one degree Celsius, the metrology structure 1448, shown as a conical structure, holds the distance between the primary mirror 1434 and the secondary mirror 1435 within ±1 micron.

[0112] For thermal control of the metrology structure, temperature sensors and heaters (wire or patch type) can be installed on the metrology structure. The payload control electronics reads data from the temperature sensors and controls the heaters to keep the metrology structure 1448 within the specified range so that the focus of the camera system is on the focus sensor.

[0113] The annular structure 1440 is a support structure for the primary mirror 1434 and supports the primary mirror movably to minimize structural deformation that may be caused during assembly. Additionally, the annular structure 1440 can be an interface with the satellite BUS, which can eliminate the need for a box-type housing, such as Figure 14A the housing 1410 shown.

[0114] Referring to Figure 14C, a partially cut-away perspective view of an optical system 1460 for a camera is shown. A metrology structure 1478, shown as conical, maintains the distance between a primary mirror 1464 and a secondary mirror 1465. In some embodiments, when the temperature of the metrology structure 1478 changes by one degree Celsius, the distance between the primary mirror 1464 and the secondary mirror 1465 can be maintained within ±1 micrometer. A support structure 1470, shown as an annular structure for the primary mirror 1464, supports a primary mirror kinematic mounting structure 1472 to minimize structural deformations that may be caused during assembly. Additionally, the support structure 1470 can be an interface to the satellite bus. In certain embodiments, the radius of the support structure 1470 can be defined by the physical radius from the optical axis of the primary mirror 1464. The inner surface of the annular structure 1470 can be a limitation at a specific distance from the optical axis of the above-mentioned image plane 316. The diameter of the primary mirror 1464 is approximately 7% of the focal length of the optical system, and this diameter determines the width and height of the camera system. The length of the camera system is determined by the distance between the secondary mirror 1465 and the tertiary mirror 1465, and the distance between the secondary mirror 1465 and the tertiary mirror 1465 is approximately 4% to 9% of the focal length of the optical system.

[0115] Figure 14D is a partial perspective cut-away view of an optical system 1480, which shows a cylindrical housing 1408 with a radius 1486 equal to the radius of the primary mirror 1404. The imaging plane can be located at a radial distance from the optical axis that is no longer the radius 1486. Thus, to save space, the housing 1408 can also have the same or nearly the same radius as the primary mirror. The optical axis extends between the vertices of the primary mirror and the secondary mirror.

[0116] Performance

[0117] The performance of optical system 100 and optical system 150 is analyzed to evaluate their designed modulation transfer function (MTF), tolerance MTF, and their distortion. Even though MTF and distortion are methods for evaluating the optical performance of a system, they indicate how good the quality of the resulting image is. The MTF in the panchromatic band is lower than that of other large camera systems, and this cannot be avoided due to its smaller aperture size. Despite the lower MTF value, the image quality can be enhanced through ground post-processing, and it can also benefit from having a smaller anti-aliasing effect.

[0118] Reference Figure 15A and Figure 15B , these curves respectively give the optical design MTF and tolerance MTF in the panchromatic band of optical system 100. The Nyquist frequency for estimating the MTF value is 100 mm / cycle for the panchromatic band and 25 mm / cycle for the multispectral band. For tolerance, the sensitivity of each component was studied considering the assembly and alignment logic.

[0119] Reference Figure 16Aand Figure 16B These curves respectively give the optical design MTF and tolerance MTF of the near-infrared (NIR) band of the optical system 100. Refer to Figure 17A and Figure 17B These curves respectively give the optical design MTF and tolerance MTF of the blue band of the optical system 100.

[0120] The estimated MTF values of the optical system 100 are summarized in Table 3. For the panchromatic band, the design MTF is higher than 11%, and the tolerance value is slightly higher than 10%. For the multispectral band, the design value is greater than 57%, and the tolerance value is greater than 51%. Through tolerance, the MTF drop is higher in the multispectral band because these multispectral bands are far from the optical axis and the lower sampling frequency of the multispectral band is reflected.

[0121] Spectral band Design MTF (%) Tolerance MTF (%) PAN (450 - 720 nm) ≥11 ≥10 NIR (770 - 890 nm) ≥57 ≥51 Red (630 - 690 nm) ≥63 ≥55 Green (520 - 590 nm) ≥68 ≥57 Blue (450 - 520 nm) ≥72 ≥59

[0122] Table 3

[0123] Refer to Figure 18A and Figure 18B The analysis results of the optical design MTF and tolerance MTF of the panchromatic band of the optical system 150 are respectively given in the figures. In a similar manner to the optical system 100, the Nyquist frequency of the panchromatic band is 100 mm / cycle, and the Nyquist frequency of the multispectral band is 25 mm / cycle. Considering the assembly and alignment logic, the sensitivity of each component is studied and fed into the analysis.

[0124] Refer to Figure 19A and Figure 19B The optical design MTF and tolerance MTF of the NIR band of the optical system 150 are respectively given in the figures. Refer to [[ID=9J]]Figure 20A and Figure 20B The optical design MTF and tolerance MTF of the blue band of the optical system 150 are respectively given in the figures.

[0125] The estimated MTF values of the optical system 150 are summarized in Table 4. The design MTF of the panchromatic band is greater than 15%, and the tolerance value is greater than 14%. For the multispectral band, the results are different from those of the optical system 100. Due to the wide field of view (FOV) and its position in the FOV, the MTF drop is strange and rougher than that of the optical system 100. The lowest multispectral MTF value is just above 40% at the outer field and unexpectedly at the near-infrared band closer to the optical axis. The tolerance value is managed to be higher than 35%.

[0126] Spectral band Design MTF Tolerance MTF PAN (450 - 720 nm) ≥15 ≥14 NIR (770 - 890 nm) ≥40 ≥35 Red (630 - 690 nm) ≥46 ≥41 Green (520 - 590 nm) ≥49 ≥44 Blue (450 - 520 nm) ≥53 ≥46

[0127] Table 4

[0128] Refer to Figure 21A andFigure 21B , the distortion performance of the optical system 100 and the optical system 150 are respectively shown in the figure. Due to the larger field of view of the optical system 150, the distortion amplitude of the optical system 150 is 0.08 micrometers, which is higher than that of the optical system 100. The distortion amplitude of the optical system 150 is 0.02 micrometers at the edge. However, it should be noted that the distortion amplitudes of both camera systems are still far lower than 1 / 50 pixel, which results in sufficient margin for TDI imaging and indicates a much lower possibility of image quality degradation.

[0129] Despite having a small form factor, the optical system 100 has better performance than other camera systems in constellation operations, as shown in Table 5. The optical system 100 is designed to have a ground sampling distance of 0.9 meters and a swath width of 10.8 kilometers at an altitude of 500 kilometers, which can be comparable to or better than those of SKYSAT. It should also be emphasized that the optical system 100 can simultaneously operate the panchromatic band and the near-infrared band during flight. The panchromatic band and the near-infrared band are optimized to be compatible with other remote sensing tasks and lack other cameras identified in Table 5.

[0130]

[0131] Table 5

[0132] The advantages of the optical system 150 relative to the DOVE camera are better resolution, different spectral bands, and shorter in the axial direction, as shown in Table 6. At an altitude of 500 kilometers, the optical system 150 has a ground sampling distance of 1.85 meters, which is half the resolution of DOVE or PLANETSCOPE. The optical system 150 can be equipped with customized spectral bands that are necessary for extracting meaningful spectral information.

[0133] Parameter Optical system 150 <![CDATA[DOVE or PS2 [2] <!-- 18 -->]]> Orbit altitude (km) 500 475 Ground sample distance (m) ≤1.85 ≤3.7 Spectral band PAN, RGB, NIR Color Swath width (nadir, km) ≤14.8 ≤24.6 Clear aperture (mm) ≤95 ≤90 Length (mm) ≤200 -

[0134] Table 6

[0135] Advantages

[0136] The optical system is based on a 4-mirror all-reflective optical design and has no chromatic aberration and distortion. The absence of chromatic aberration helps the optical system extend beyond the visible spectral range, so the optical system can support imaging in the infrared and UV spectral ranges. The absence of distortion helps the optical system support TDI imaging in orbit and precise measurement in post-processing.

[0137] Some existing technologies, especially the cheaper solutions, still rely heavily on the combination of lenses and mirrors in catadioptric designs, thus limiting their applications, or their optical designs need to be modified from the start to accommodate different spectral ranges. Additionally, catadioptric designs are not easily amenable to TDI imaging, especially for wider field-of-view imaging, because of the inherent or residual aberrations.

[0138] Compared to larger and bulkier systems of existing systems, the form factor is smaller. Compared to the prior art, the optical systems described herein have a much smaller form factor. The optical system is so small that it can be mounted on flying objects with a small form factor, including CUBESATs, small satellites, airplanes, UAVs, drones, or balloons. The optical system can also be an on-board flying object as a second or third payload, which helps to provide various missions or more opportunities for a mission. The optical system is small and light, thus helping to reduce the launch cost and increase the chances of launch compared to the prior art. The benefits are evident when constellation operations are conducted, where the launch cost is a driving factor. The optical system can be developed at a lower cost, making it more affordable than the prior art. When developing the optical system, due to the smaller aperture size, smaller test equipment and facilities can be used. Additionally, the optical system is light and can be transported at a lower logistics cost.

[0139] Compared to the prior art, the development process of the optical system can be automated more effectively. Developing quite a large prior art always requires labor resources, thus leading to an increased budget. For an optical system with a smaller aperture size and light weight, even with affordable equipment, iterative or repetitive processes or procedures can be automated. The process can include optical alignment, optical measurements (such as wavefront error, modulation transfer function, focal length, field of view, instantaneous field of view, distortion, signal-to-noise ratio), and those processes under various conditions. In addition to the economic benefits, due to the shorter physical distance between the mirrors, the optical system can maintain the stability of operation.

[0140] The optical system is based on a four-mirror optical design and provides design flexibility supported by the degrees of freedom of the optical design. With minimal modification of the optical design, it can be adapted to provide imaging in starring, scanning or push-broom, video, stereo, BRDF (Bidirectional Reflectance Distribution Function), HDR (High Dynamic Range), polarization, and low-light modes. The optical system based on the four-mirror optical design can support panchromatic, multispectral, hyperspectral, infrared, and UV imaging with minimal design modification, mainly due to different pixel sizes. The optical system has degrees of freedom in optical design and is capable of supporting super-resolution, high dynamic range, degree of polarization, and other remote sensing or scientific imaging.

[0141] The optical system can support planetary or deep space missions, which require a small form factor for payload selection. Due to capabilities and launch opportunities, the optical system can include various missions, which can include AI-based imaging. The optical system can be used in precision star sensors and stellar sensors.

[0142] The optical system based on a 4-mirror optical design can support simultaneous multi-color imaging. For example, it can include, but is not limited to, panchromatic + RGB + near-infrared imaging, visible + infrared (near-infrared, short-wave infrared, mid-wave infrared, or long-wave infrared) imaging, visible + visible imaging, infrared + infrared imaging, UV + visible, or UV + infrared imaging.

[0143] The optical system with a smaller form factor can be loaded on satellites for non-imaging missions, such as communication satellites (e.g., SpaceX's Starlink). The optical system can also be installed on other imaging satellites, such as quasi-imaging satellites for SAR missions or scientific mission satellites. This functionality potentially enables synchronous or asynchronous constellation operation of the optical system, which improves the temporal resolution of imaging or increases imaging opportunities. Constellation operations in the prior art often require substantial fixed costs for expensive satellites and camera systems, 24 / 7 operation of dedicated control stations, and non-automated image receiving centers. The optical system is capable of synchronous or asynchronous constellation operation, enabling the allocation of resources for control and data reception, thereby significantly reducing fixed costs.

[0144] Although the presently considered exemplary embodiments have been illustrated and described, those skilled in the art will understand that various other modifications can be made without departing from the claimed subject matter and equivalents can be substituted. Additionally, many modifications can be made to adapt a particular situation to the teachings of the claimed subject matter without departing from the central concept described herein. Therefore, the claimed subject matter is not limited to the specific embodiments disclosed, but such claimed subject matter can also include all embodiments falling within the scope of the appended claims and their equivalents.

[0145] It is contemplated that various combinations or sub - combinations of the specific features and aspects of the above - described embodiments can be made, and such combinations or sub - combinations still fall within one or more scopes of the present invention. Additionally, any disclosure herein regarding a particular feature, aspect, method, property, characteristic, quality, trait, element, etc. of an embodiment can be used in all other embodiments set forth herein. Thus, it should be understood that the various features and aspects of the disclosed embodiments can be combined with or substituted for one another to form varying patterns of the disclosed invention. Accordingly, the scope of the present invention disclosed herein should not be limited by the specifically disclosed embodiments above. Additionally, although the present invention is susceptible to various modifications and alternative forms, specific examples thereof have been shown in the drawings and described in detail herein. However, it should be understood that the present invention is not limited to the specific forms or methods disclosed, but rather, the present invention covers all modifications, equivalents, and alternatives falling within the spirit and scope of the described embodiments and the appended claims. Any method disclosed herein need not be performed in the order described.

[0146] The scope disclosed herein also includes any and all overlaps, sub - ranges, and combinations thereof. Language such as "up to", "at least", "greater than", "less than", "between", etc. includes the recited numbers. Numbers preceded by terms such as "about", "approximately", "up to about", and "substantially" as used herein include the recited number and also denote a quantity or feature close to the recited quantity or feature that still performs the desired function or achieves the desired result. For example, the terms "about", "approximately", and "substantially" can refer to a quantity within less than 10%, less than 5%, less than 1%, less than 0.1%, and less than 0.01% of the recited quantity or feature. Features of the embodiments disclosed herein that are preceded by terms such as "about", "approximately", and "substantially" as used herein denote features having some variability that still performs the desired function or achieves the desired result of the feature.

[0147] Regarding the use of substantially any plural and / or singular terms herein, those skilled in the art can translate from plural to singular and / or from singular to plural according to the context and / or application. For clarity, various singular / plural permutations may be set forth herein.

[0148] Those skilled in the art should understand that the terms commonly used herein are generally intended to be "open" terms (e.g., the term "comprising" should be interpreted as "including but not limited to", the term "having" should be interpreted as "having at least", the term "including" should be interpreted as "including but not limited to", etc.). Those skilled in the art should also understand that if a specific number of the introduced embodiments is intended to be enumerated, such intention is clearly enumerated in that embodiment, and in the absence of such enumeration, there is no such intention. For example, for the sake of understanding, the present disclosure may include the use of the introductory phrases "at least one" and "one or more" to introduce the description of embodiments. However, the use of such phrases should not be construed as implying that an embodiment recited by the indefinite article "a" or "an" limits any particular embodiment recited by such a recited embodiment to only one such recited embodiment, even when the same embodiment includes an introductory phrase "one or more" or "at least one" and an indefinite article such as "a" or "an" (e.g., "a" or "an" should often be interpreted as meaning "one or more" or "at least one"); the same is true for the use of the definite article to introduce the description of embodiments. Additionally, even if a specific number of the introduced embodiments is explicitly recited, those skilled in the art should recognize that such a recitation should generally be interpreted as meaning at least the recited number (e.g., the recitation of "two recitations" without any other modifiers generally means at least two recitations, or two or more recitations). Additionally, in those cases where an agreement is made similar to "at least one of A, B, and C, etc.", the use of such a construction is generally meant to be the convention that those skilled in the art will understand (e.g., "a system having at least one of A, B, and C" will include but not be limited to a system having A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, C together, etc.). In those cases where an agreement is made similar to "at least one of A, B, or C, etc.", the use of such a construction is generally meant to be the convention that those skilled in the art will understand (e.g., "a system having at least one of A, B, or C" will include but not be limited to a system having A alone, B alone, C alone, A and B together, A and C together, B and C together, and / or A, B, C together, etc.). Those skilled in the art will further understand that, whether in the specification, embodiments, or drawings, virtually any separate words and / or phrases representing two or more alternative terms should be understood as contemplating the possibility of including one of these terms, any one of these terms, or both of these terms. For example, the phrase "A or B" will be understood to include the possibilities of "A" or "B" or "A and B".

[0149] Although the subject matter has been described herein in terms of certain embodiments and certain exemplary methods, it should be understood that the scope of the subject matter is not limited thereto. On the contrary, the applicant intends to cover variations of the methods and materials disclosed herein that would be obvious to one of ordinary skill in the art and that fall within the scope of the disclosed subject matter.

Claims

1. A total reflection optical system, comprising: A concave primary mirror having a central hole and a radius, the primary mirror having one of a parabolic surface, a non-parabolic conical surface, or an aspherical surface; A convex secondary mirror facing the primary mirror, the secondary mirror having an aspherical surface, wherein the optical axis extends from the vertex of the primary mirror to the vertex of the secondary mirror; A concave tertiary mirror disposed behind the primary mirror, the tertiary mirror having one of a parabolic surface, a non-parabolic conical surface, or an aspherical surface; A concave quaternary mirror disposed in the central hole of the primary mirror or behind the primary mirror, the quaternary mirror having one of a spherical surface, a parabolic surface, a non-parabolic conical surface, or an aspherical surface; and At least one image plane having one or more aggregation sensors, wherein the image plane is positioned at a radial distance from the optical axis not exceeding the radius of the primary mirror, Wherein the shape factor of the total reflection optical system is less than 0.09, the shape factor being defined as the ratio of the distance between the secondary mirror and the tertiary mirror to the effective focal length of the optical system.

2. The optical system according to claim 1 further comprises: An entrance pupil located near the primary mirror or the secondary mirror; And an exit pupil or a Lyot stop located at one of the following positions: 1) near the quaternary mirror, 2) between the tertiary mirror and the quaternary mirror, and 3) between the quaternary mirror and the image plane.

3. The optical system according to claim 1, further comprising one or more folding mirrors arranged to deflect light from the four-stage mirror to the image plane, wherein, The one or more folding mirrors are configured to fold the optical path.

4. The optical system according to claim 3, wherein, Based on the use of a first folding mirror, the exit pupil is located between the tertiary mirror and the quaternary mirror, or between the quaternary mirror and the first folding mirror.

5. The optical system according to claim 3, wherein, One of the folding mirrors is tilted at a specific angle with respect to the optical axis of the optical system.

6. The optical system according to claim 3, wherein, One of the folding mirrors located in front of the image plane widens the field of view using reflection and transmission portions in the same spectral range, wherein each portion corresponds to a specific sensor among the one or more aggregation sensors.

7. The optical system according to claim 3, wherein, One of the folding mirrors located in front of the image plane enables simultaneous multi-color imaging, wherein the one folding mirror is reflective in a first spectral range and transmissive in other spectral ranges, or is reflective in a second spectral range and transmissive in other spectral ranges, wherein one of the aggregation sensors is dedicated to the first spectral range, and a different one of the aggregation sensors is dedicated to the second spectral range.

8. The optical system according to claim 3, wherein, The folding mirrors enable simultaneous multi-color imaging, wherein each of the folding mirrors is reflective in a specific spectral range and transmissive in other spectral ranges, and wherein each additional folding mirror and a corresponding one of the aggregation sensors are associated with different spectral ranges.

9. The optical system according to claim 3, wherein, The optical system is adapted to support simultaneous multi-color imaging, including: 1) panchromatic and RGB and near-infrared imaging, 2) visible and infrared imaging, 3) visible and visible imaging, 4) infrared and infrared imaging, 5) UV and visible imaging, or 6) UV and infrared imaging.

10. The optical system according to claim 1, wherein, The optical system has an imaging resolution better than 1 m at an altitude of 500 km.

11. The optical system according to claim 1, wherein, The vertices of the primary mirror and the secondary mirror form an optical axis, and the primary mirror and the secondary mirror are symmetric about the optical axis or have periodicity.

12. The optical system according to claim 11, wherein, The diagonal of the primary mirror or the secondary mirror with periodicity has an angle of 0 degrees or 45 degrees with the diagonal of the image plane, and wherein the optical axis of the tertiary mirror does not coincide with the mechanical axis.

13. The optical system according to claim 1, wherein, The radius of the secondary mirror is in the range of 1% to 3% of the effective focal length, and the radius of the tertiary mirror is in the range of 2% to 3% of the effective focal length.

14. The optical system according to claim 1, wherein, The radius of the quaternary mirror is in the range of 6% to 22% of the effective focal length.

15. The optical system according to claim 1, wherein, The distance along the optical axis from the tertiary mirror to the image plane is in the range of 3% to 9% of the effective focal length, and the distance along the optical axis from the secondary mirror to the tertiary mirror is in the range of 4% to 9% of the effective focal length.

16. The optical system according to claim 1, wherein, The diameter of the primary mirror is in the range of 3% to 8% of the effective focal length.

17. The optical system according to claim 1, wherein, The distance from the exit pupil or Lyot stop of the primary mirror is ±1% of the effective focal length.

18. The optical system according to claim 1, wherein, The effective focal length is in the range of 300 mm to 20000 mm.

19. The optical system according to claim 1 further includes a support structure for one or more of the mirrors, wherein, The support structure is manufactured in an additive manner.

20. The optical system according to claim 9, wherein, The infrared imaging includes near-infrared imaging, short-wave infrared imaging, mid-wave infrared imaging, or long-wave infrared imaging.

Images