Abstract:
In one embodiment, an optical system includes: a first lens configured to receive incoming light from an object; a first mirror comprising a central aperture, the first mirror configured to refract the light from the first lens, reflect the light, and refract the light reflected from the first mirror; a second mirror configured to receive the light from the first mirror, wherein the light is refracted towards a first surface of the second mirror where the light is reflected back and refracted upon exiting the second mirror; a negative corrector lens configured to refract the light from the second mirror through the central aperture of the first mirror; and a positive corrector lens configured to receive the light through the central aperture of the first mirror and refract the light to an imaging surface.

Description:
BACKGROUND 
       [0001]    Remote sensing of the Earth is promoted by the proliferation of constellations of small satellites in the nanosatellite category. Nanosatellites are composed of 10 cm cubic base units. One 10 cm cubic unit is denoted as 1U, and multiple units can be combined to form larger spacecraft. For example, a spacecraft including three base units will be 10×10×30 cm and is described as being 3U. Remote sensing nanosatellites operate ideally in low Earth orbit, typically in the altitude range of 400 to 700 km. Given their relatively small size, these nanosatellites require compact optical systems to preserve internal volume for the remainder of the support systems necessary to operate a satellite. Typically, when including a compact optical system, optical performance is sacrificed. However, the chief value of the remote sensing satellite is the imagery of the Earth that it produces, and the lower optical performance may not be acceptable. 
       SUMMARY 
       [0002]    In one embodiment, an optical system includes: a first lens configured to receive incoming light from an object; a first mirror comprising a central aperture, the first mirror configured to refract the light from the first lens through a first surface of the first mirror, reflect the light at a second surface of the first mirror, and refract the light reflected from the second surface of the first mirror that is exiting the first mirror at the first surface of the first mirror; a second mirror configured to receive the light from the first mirror, wherein the light is refracted through a second surface of the second mirror towards a first surface of the second mirror where the light is reflected back towards the second surface of the second mirror and refracted by the second surface upon exiting the second mirror; a negative corrector lens configured to refract the light from the second mirror through the central aperture of the first mirror; and a positive corrector lens configured to receive the light through the central aperture of the first mirror and refract the light to an imaging surface, wherein: the first lens, the first mirror, the second mirror, the first negative corrector lens, and the second positive corrector lens are positioned along an axis in a satellite, a first distance between the first lens and the first mirror is less than one third a length of the satellite, and a back focal length of the optical system has a diameter that is no more than half of a largest diameter from the first lens and the first mirror. 
         [0003]    In one embodiment, a satellite includes: a satellite housing comprising: satellite operational components configured to operate the satellite and downlink images captured by the optical system; and an optical system comprising: a forward portion comprising: a first lens configured to receive incoming light from an object; a first mirror comprising a central aperture, the first mirror configured to refract the light from the first lens through a first surface of the first mirror, reflect the light at a second surface of the first mirror, and refract the light reflected from the second surface of the first mirror that is exiting the first mirror at the first surface of mirror; a second mirror configured to receive the light from the first mirror, wherein the light is refracted through a second surface of the second mirror towards a first surface of the second mirror where the light is reflected back towards the second surface of the second mirror and refracted by the second surface upon exiting the second mirror; a negative corrector lens configured to refract the light from the second mirror through the central aperture of the first mirror; and a back portion comprising: a positive corrector lens configured to receive the light through the central aperture of the first mirror and refract the light to an imaging surface to capture images, wherein the optical system is within a length of the satellite housing and the satellite components are located around the back portion. 
         [0004]    In one embodiment, a method includes: receiving, at a first lens, incoming light from an object; refracting, at a first mirror comprising a central aperture, the light from the first lens through a first surface of the first mirror, reflecting the light at a second surface of the first mirror, and refracting the light reflected from the second surface of the first mirror that is exiting the first mirror at the first surface of mirror; receiving, at a second mirror, the light from the first mirror, wherein the light is refracted through a second surface of the second mirror towards a first surface of the second mirror where the light is reflected back towards the second surface of the second mirror and refracted by the second surface upon exiting the second mirror; refracting, at a negative corrector lens, the light from the second mirror through the central aperture of the first mirror; and receiving, at a positive corrector lens, the light through the central aperture of the first mirror and refracting the light to an imaging surface, wherein: the first lens, the first mirror, the second mirror, the negative corrector lens, and the positive corrector lens are positioned along an axis in a satellite, a first distance between the first lens and the first mirror is less than one third a length of the satellite, and a back focal length of the optical device has a diameter that is no more than half of a largest diameter from the first lens and the first mirror. 
         [0005]    The following detailed description and accompanying drawings provide a better understanding of the nature and advantages of particular embodiments. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0006]      FIG. 1  shows an optical system with five elements according to one embodiment. 
           [0007]      FIG. 2  and  FIG. 3  show a relationship of the components of the optical system within a housing according to one embodiment. 
           [0008]      FIG. 4  shows an example of a satellite including the optical system according to one embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0009]    Described herein are techniques for an optical system. In the following description, for purposes of explanation, numerous examples and specific details are set forth in order to provide a thorough understanding of particular embodiments. Particular embodiments as defined by the claims may include some or all of the features in these examples alone or in combination with other features described below, and may further include modifications and equivalents of the features and concepts described herein. 
         [0010]    Particular embodiments provide a five element axially-aligned and axially-compressed optical system, such as a catadioptric cassegrain-type telescope. It will be understood in the art that the catadioptric attribute of the telescope relates the use of a lens and mirror combination and that the cassegrain attribute relates the use a primary concave mirror and secondary convex mirror. In one embodiment, the optical system may conform to the physical requirements of a nanosatellite, such as a 3U remote sensing satellite. A 1U unit is 10×10×10, and a 3U unit includes 3× the 1U size in one dimension, such as the dimensions of 10×10×30 cm. 
         [0011]    To permit sufficient internal volume within the 3U nanosatellite for all components and systems necessary to operate the satellite, such as the satellite&#39;s imaging system, power system, radios, attitude control and determination system, and computer system, the optical system is compact such that the ratio between the optical system&#39;s aperture and the distance between the full aperture elements in the optical system may be the smallest attainable while being diffraction limited across the optical system&#39;s field of view. In one embodiment, the distance between the full aperture elements may be no longer than one-third of the total track length of the optical device when using spherical optical elements and with an overall track length of no more than the elongated length of the housing of the 3U nanosatellite. The back focal length portion, where the back focal length is a distance between the rear-most full aperture element and the image sensor, may have a diameter of no more than half of the full aperture diameter. This narrow back focal length diameter frees substantial volume in the housing of the 3U satellite form factor for the remainder of the satellite&#39;s systems, permitting a viable 3U nanosatellite to be operated. Concurrently, the diameter of the back focal length is large enough to fully illuminate a minimum of a 35 mm image sensor, maintaining focus across the image sensor. In this sense, the optical system (e.g., telescope) is diffraction limited across its field of view, such as across the 400 to 900 nanometer (nm) wavelengths. 
         [0012]    While being compact, the optical system does not sacrifice optical performance. The optical system delivers light to the imaging sensor in sufficient intensity and free of significant aberration such that the satellite can effectively maintain a duty cycle including continuous imaging operations in the presence of sufficient state of charge, onboard storage, and downlink capacity to process and transfer the resulting volume of data. 
         [0013]    To further simplify and reduce volume of the optical system, a nanosatellite may omit a traditional variable focus mechanism to maintain the alignment and focus of the optical system. Without an adjustable focus mechanism, it becomes necessary for the optical system to maintain focus across the thermal gradient present in a space environment. In one embodiment, each element of the optical system is composed of the same material to help maintain focus. When mated to the optical system&#39;s housing material, where the housing material is selected for similarity in coefficient of thermal expansion relative to the optical element material, the optical system expands and contracts uniformly with the housing material in response to thermal gradients. In other embodiments, the optical elements of the optical system may be composed of different materials so long as the coefficient of thermal expansion across the optical system and its mechanical housing are compatible. The optical system is therefore temperature stabilized. 
         [0014]      FIG. 1  shows an optical system  100  with five elements according to one embodiment. System  100  includes a full aperture lens  101 , a primary mirror  102 , a secondary mirror  103 , a corrector lens  104 , and a corrector lens  105 . The five elements converge light onto an image sensor  106 . Not shown are standard light baffles well known in the art to suppress stray light in the optical system. 
         [0015]    In one embodiment, all of these five elements are spherical, and not aspherical. It will be understood in the art that the use of spherical optical elements may be easier to manufacture and lower cost. Use of aspherical optical elements is feasible, but the manufacture of such elements is more complicated, increasing the overall cost and complexity of the overall system. 
         [0016]    Light enters optical system  100  through a full aperture lens  101 . In one embodiment, full aperture lens  101  is a positive meniscus lens that includes a surface that is convex in a direction facing away from a primary mirror  102  and a concave side facing primary mirror  102 . The convex lens focuses light from the object to be imaged onto primary mirror  102 . 
         [0017]    Primary mirror  102  is both a reflector and a lens, which may be referred to as a second surface mirror or a Mangin mirror. In one embodiment, primary mirror  102  is a concave meniscus lens with a central aperture  108 . Light passes through primary mirror  102  twice. For example, light entering through full aperture lens  101  passes through a first surface s 100  of primary mirror  102  until it reaches a second surface s 101  of primary mirror  102 . A second surface s 101  of primary mirror  102  may be reflective, such as the second surface s 101  is covered with a reflective substance, such as aluminum. From the second surface s 101  of primary mirror  102 , the light is reflected back toward second mirror  103 , passing once again through the first surface s 100  of primary mirror  102  prior to reaching second mirror  103 . The effect of light passing through primary mirror  102  twice, once upon entering primary mirror  102  from full aperture lens  101  through first surface s 100  and then again through first surface s 100  after being reflected off the silvered second surface s 101  of primary mirror  102  toward secondary mirror  103 , is to shorten the overall track length of the optical system and to correct for optical aberrations. 
         [0018]    Second mirror  103  may also be a combined reflector and lens. In one embodiment, second mirror  103  is a convex second surface Mangin-type sub-aperture mirror. That is, second mirror  103  is convex on a first surface s 102  facing full aperture primary mirror  102 . Second mirror  103  is separate from full aperture lens  101  and is set in between full aperture lens  101  and primary mirror  102 . 
         [0019]    Light striking second mirror  103  from primary mirror  102  passes through a second surface s 103  of second mirror  103  to the first surface s 102  of second mirror  103 . The first surface s 102  of second mirror  103  is reflective, and can be covered with a reflective substance, such as aluminum. The silvered convex surface s 102  reflects the light, which is refracted toward corrector lens  104  via second surface s 103 . Corrector lens  104  is set in front of central aperture  108  of primary mirror  102  to receive light reflected off the first silvered surface s 102  of second mirror  103 . Light reflected off the first silvered surface s 102  of second mirror  103  passes through second mirror  103  and exits through the second surface s 103  of second mirror  103 . Second mirror  103  thus operates twice on light passing through it, once upon being refracted on entering second mirror  103  from primary mirror  102 , and then again when being reflected off first surface s 102  and being refracted out of the second surface s 103  of second mirror  103 . 
         [0020]    In one embodiment, corrector lens  104  is a sub-aperture negative meniscus lens disposed between second mirror  103  and primary mirror  102 . The sub-aperture lens has a diameter that is less than the full aperture. As corrector lens  104  is a negative lens, light leaving the lens is dispersed outward toward central aperture  108  of primary mirror  102 . Light passes through central aperture  108  to reach corrector lens  105 . The passing of the light is in contrast to the reflection and refraction that was performed by primary mirror  102  when light was passed through lens  101  to the second surface s 101  of primary mirror  102 . 
         [0021]    Sub-aperture corrector lens  105  is set behind the central aperture of primary mirror  102  and before imaging surface  106 . Corrector lens  105  may be a positive plano convex lens. That is, corrector lens  105  has a convex surface that is set away from primary mirror  102 . The surface of corrector lens  105  facing primary mirror  102  is flat, or plano. Although a plano surface is described, surfaces that are not flat may be used. Corrector lens  105  concentrates the light passing through it onto imaging surface  106  at the end of the telescope&#39;s focal length. Corrector lens  104  and corrector lens  105 , when used as a corrector group, operate on the light passing through the optical system to correct lateral color and other aberrations. 
         [0022]    In one embodiment, each optical element described in optical system  100  is spherical in shape and composed of the same material with a refractive index of around n=1.5168 and a coefficient of thermal expansion of around 7.1 ppm/° C. Differing material for the optical elements may be used so long as the refractive index and coefficient of thermal expansion are uniform or balanced. The focal length of this embodiment is 700 mm and its speed is f/7.6. Nanosatellites of 3U configuration equipped with the optical system are intended to operate at an observation distance of between 400 and 700 km above the surface of the Earth with a field of view from 2 to 3 degrees. 
         [0023]      FIG. 2  and  FIG. 3  show a relationship of the components of the optical system within a housing according to one embodiment. The housing of the optical system can be divided into two components: a forward portion  300  and a back focal length portion  301 . The back focal length is the length between the last full aperture optical element to the imaging surface. In this case, the back focal length is from primary mirror  101  to imaging surface  106 . The back focal length portion  301  spans the distance from the end of the forward portion  300  to the image sensor surface shown at  302 . As shown in  FIG. 2 , forward portion  200  of optical system  100  includes the four optical elements of lens  101 , primary mirror  102 , secondary mirror  103 , and corrector lens  104 . Corrector lens  105  is found in a back portion  201 . In other embodiments, corrector lens  105  is closer to primary mirror  2  and may be in the forward portion  200 . In this embodiment, forward portion  200  of optical system  200  is in forward portion  300  and back portion  201  of optical system  100  is in back focal length portion  301 . 
         [0024]    The back focal length portion  301  may be toward the rear of the 3U remote sensing nanosatellite. In one embodiment, the back focal length portion  301  is no greater than half the diameter of the full aperture elements (e.g., lens  101  and primary mirror  102 ) in the optical system. The reduced diameter of the back focal length  301  relative to the diameter of the full aperture forward portion  300  permits sufficient volume in the remainder of the 3U remote sensing nanosatellite for the other systems which comprise a functioning satellite, including power system, auxiliary optical systems, radio hardware, attitude control and determination, computational components, and related circuitry and mechanical implements. By axially compressing the position of four optical elements of lens  101 , primary mirror  102 , secondary mirror  103 , and corrector lens  104 , a longer back focal length portion  301  is achieved, which leaves additional room for the satellite components. 
         [0025]      FIG. 4  shows an example of a satellite  400  including the optical system  100  according to one embodiment. As shown, components  402  of satellite  400  are integrated with optical system  100  in the 3U housing. The 3U housing is 10 cm (Width)×10 cm (Depth)×30 cm (Length). The optical system  100  is set along the 30 cm length of the nanosatellite. The diameter of the full aperture elements of optical system  100  is as large as the 3U housing permits. The reduced diameter of back focal length  301  allows the components  402  of satellite to be included. The forward portion  300  may take up the whole volume of the 3U housing of satellite  400  with small areas of space available due to the fitting of the spherical housing of the optical system in the square housing of satellite  400 . However, by including the full aperture elements as far forward as possible while keeping the entire track length to around 300 mm, more of the interior volume of the 3U satellite is freed for components  402 , which can be positioned around the spherical diameter of back focal length portion  301 . In this sense, given that the distance between the full aperture elements is reduced to no more than one third of the length of the 3U nanosatellite, the resultant optical system is axially-compressed. In one embodiment, at least one sub aperture corrector is placed further back in the back focal length portion  301 . The back portion of focal length portion  301  may be substantially near or flush with the housing of satellite  400 . In some embodiments, components  402  may be located between the back portion of focal length portion  301  and the housing if there is space. 
         [0026]    The forward portion  300  is larger in diameter than the back focal length portion  301 . By compressing the size of forward portion  300 , additional volume is gained in the satellite. The compression of size of forward portion  300  is achieved by including primary mirror  102  as both a reflector and a lens and also second mirror  103  as a combined reflector and lens. Use of aspherical optical elements would permit greater axial compression in the sense that the full aperture optical elements may be placed closer to one another. However, the use of such elements may not be desired as the manufacture of aspherical elements is more difficult and expensive. In the spherical embodiment disclosed, the optical system is compressed as far as spherical elements permit, no greater than one-third the overall track length set in a 3U nanosatellite, while remaining diffraction limited across a field of view of the optical system. 
         [0027]    As used in the description herein and throughout the claims that follow, “a”, “an”, and “the” includes plural references unless the context clearly dictates otherwise. Also, as used in the description herein and throughout the claims that follow, the meaning of “in” includes “in” and “on” unless the context clearly dictates otherwise. 
         [0028]    The above description illustrates various embodiments along with examples of how aspects of particular embodiments may be implemented. The above examples and embodiments should not be deemed to be the only embodiments, and are presented to illustrate the flexibility and advantages of particular embodiments as defined by the following claims. Based on the above disclosure and the following claims, other arrangements, embodiments, implementations and equivalents may be employed without departing from the scope hereof as defined by the claims.