Sliced lens star tracker

A star tracker includes a lens slice, a pixelated image sensor, an ephemeral database and a processor configured to estimate attitude, orientation and/or location of the star tracker based on an image of one or more celestial objects projected by the lens slice onto the pixelated image sensor. The lens slice is smaller and lighter than an optically comparable conventional lens, thereby making the star tracker less voluminous and less massive than conventional star trackers. A lens slice is elongated along one axis. Optical performance along the elongation axis is comparable to that of a conventional circular lens of equal diameter. Although optical performance along a width axis, perpendicular to the elongation axis, of a lens slice can be significantly worse than that of a conventional lens, use of two orthogonal lens slices provides adequate optical performance in both axes, and still saves volume and mass over a conventional lens.

TECHNICAL FIELD

The present invention relates to optics and, more particularly, to lens slices used in star trackers.

BACKGROUND ART

Most artificial satellites, spacecraft and other craft, such as aircraft, ships and ground vehicles (collectively referred to herein as vehicles), require information about their locations and/or attitudes to accomplish their missions. This information may be obtained from one or more sources, such as ground-based radar tracking stations or on-board global positioning system (GPS) receivers, inertial guidance systems (INS) and/or star trackers.

A star tracker is an optical device that measures angles to one or more stars or other sufficiently bright celestial objects with known ephemerides, as viewed from a vehicle. A star tracker typically includes a catalog that lists bright navigational objects and information about their locations in the sky, sufficient to calculate a location of a vehicle in space, given bearings to one or more of the objects. A conventional star tracker includes a lens that projects an image of a celestial object onto a photocell, or that projects an image of one or more celestial objects onto a pixelated light-sensitive sensor array. The lens typically constitutes a large fraction of the volume and the mass of a star tracker. An ideal star tracker would be mechanically and optically simple, small and low in mass.

SUMMARY OF EMBODIMENTS

An embodiment of the present invention provides a star tracker. The star tracker has a field of view. The star tracker includes a database that stores ephemeral data about a plurality of celestial objects. The star tracker includes a pixelated image sensor and a lens slice disposed between the field of view and the pixelated image sensor. A processor is coupled to the pixelated image sensor and to the database. The processor is configured to automatically estimate an attitude of the star tracker, an orientation of the star tracker and/or a location of the star tracker. The processor is configured to base the estimate on: (a) data from the pixelated image sensor generated as a result of an image of at least one celestial object in the field of view being projected onto the pixelated image sensor by the lens slice and (b) data in the database.

The lens slice may define a surface. Light that forms the image of the at least one celestial object in the field of view may pass through the surface. The surface may be a simple curvature surface or a compound curvature surface.

The lens slice may include a first lens slice and a second lens slice. The first lens slice may have a first optical axis and a first longitudinal axis. The second lens slice may have a second optical axis and a second longitudinal axis. The first optical axis may be spaced apart from the second optical axis, and the first longitudinal axis may be perpendicular to the second longitudinal axis.

The first lens slice may include a first cylindrical lens, and the second lens slice may include a second cylindrical lens.

The first lens slice may define a first surface. At least some light that forms the image of the at least one celestial object in the field of view may pass through the first surface. The first surface may be a first simple curvature surface. The second lens slice may define a second surface. At least some light that forms the image of the at least one celestial object in the field of view may pass through the second surface. The second surface may be a second simple curvature surface.

The first lens slice may define a first surface. At least some light that forms the image of the at least one celestial object in the field of view may pass through the first surface. The first surface may be a first compound curvature surface. The second lens slice may define a second surface. At least some light that forms the image of the at least one celestial object in the field of view may pass through the second surface. The second surface may be a second compound curvature surface.

The first lens slice may be elongated along the first longitudinal axis, and the second lens slice may be elongated along the second longitudinal axis.

The first lens slice may have a first focal distance, and the second lens slice may have a second focal distance. The pixelated image sensor may include a first pixelated image sensor array and a second pixelated image sensor array. The first pixelated image sensor array may be disposed the first focal distance from the center of the first lens slice. The second pixelated image sensor array may be disposed the second focal distance from the center of the second lens slice.

The processor may be disposed in a volume. The volume may be bounded on a first side by a first imaginary plane that intersects one end of the first lens slice and extends perpendicular to the pixelated image sensor. The volume may be bounded on a second side by a second imaginary plane that intersects the other end of the first lens slice and extends perpendicular to the pixelated image sensor. The volume may be bounded on a third side by a third imaginary plane that intersects one end of the second lens slice and extends perpendicular to the pixelated image sensor. The volume may be bounded on a fourth side by a fourth imaginary plane that intersects the other end of the second lens slice and extends perpendicular to the pixelated image sensor.

The lens slice may include a cross-shaped spherical lens slice.

The lens slice may include a cross-shaped monocentric lens slice.

The lens slice may have a focal length. The pixelated image sensor may include a plurality of image sensor arrays. Each image sensor array of the plurality of image sensor arrays may be disposed the focal length from the center of the monocentric lens slice.

Another embodiment of the present invention provides a navigation system. The navigation system includes a database storing ephemeral data about a plurality of celestial objects. The navigation system also includes first, second and third star cameras. Each star camera of the first, second and third star cameras has a respective field of view. Each star camera of the first, second and third star cameras includes a respective pixelated image sensor and a respective lens slice disposed between the respective field of view and the respective pixelated image sensor. The navigation system also includes a processor coupled to the pixelated image sensor of each of the first, second and third star cameras and to the database. The processor is configured to automatically estimate an attitude of the navigation system, an orientation of the navigation system and/or a location of the navigation system. The processor is configured to base the estimate on: (a) data from the respective pixelated image sensors of the first, second and third star cameras generated as a result of an image of at least one celestial object in the field of view of at least one of the first, second and third star cameras being projected onto the respective pixelated image sensor by the respective lens slice and (b) data in the database.

Each star camera of the first, second and third star cameras may have a respective optical axis. The optical axes of the first, second and third star cameras may be mutually orthogonal.

For each star camera of the first, second and third star cameras, the respective lens slice may include a respective first lens slice and a respective second lens slice. The respective first lens slice may have a respective first optical axis and a respective first longitudinal axis. The respective second lens slice may have a respective second optical axis and a respective second longitudinal axis. The respective first optical axis may be spaced apart from the respective second optical axis. The respective first longitudinal axis may be perpendicular to the respective second longitudinal axis.

For each star camera of the first, second and third star cameras, the respective first lens slice may be elongated along the respective first longitudinal axis, and the respective second lens slice may be elongated along the respective second longitudinal axis.

The processor may be configured to provide separate estimates of the attitude of the navigation system, the orientation of the navigation system and/or the location of the navigation system, for each of the first, second and third star cameras. The navigation system may also include a navigation filter. The navigation filter may be configured to estimate an improved attitude of the navigation system, an improved orientation of the navigation system and/or an improved location of the navigation system. The navigation filter may base the improved estimate on the separate estimates of the attitude of the navigation system, orientation of the navigation system and/or location of the navigation system.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

In accordance with embodiments of the present invention, a star tracker having a sliced lens is disclosed, as well as methods for making lens slices. Several shapes of lens slices are disclosed, including a wide-angle cross-shaped monocentric lens slice. A lens slice is smaller and lighter than an optically comparable conventional circular lens, thereby making the star tracker less voluminous and less massive than conventional star trackers. A lens slice is elongated along one axis. Optical performance along the elongation axis is comparable to that of a conventional circular lens of equal diameter. Although optical performance along a width axis, perpendicular to the elongation axis, of a lens slice can be worse than that of a conventional lens, use of two orthogonal lens slices provides adequate optical performance in both axes, and still saves volume and mass over a conventional comparable circular lens.

Lenses

A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. An example of a simple conventional lens100is shown in perspective inFIG. 1and in top view inFIG. 2. The simple lens100includes a single piece of transparent material, whereas a compound lens (not shown) includes several adjacent or spaced apart simple lenses (elements), usually arranged along a common axis, and sometimes cemented together. Unless otherwise indicated, as used herein, including in the claims, the term lens includes simple and compound lenses.

Lenses are made from materials that are transparent, at wavelengths of interest, such as glass or plastic. Lenses are typically molded to (at least approximate) desired shapes and sometimes ground and/or polished.

The degree to which a lens, mirror, or other optical system converges or diverges light is referred to as the optical system's optical power. Converging lenses have positive optical powers, while diverging lenses have negative optical powers. An optical system that neither converges nor diverges light has a power of 0. As used herein, including in the claims, a powered optical system or element is one that has a power greater than 0 or less than 0. An optical system or element that has a power of 0 is not powered and is not, therefore, considered herein to be a lens.

Returning toFIG. 1, the lens100has two light-transmitting surfaces (“faces”), as exemplified by surfaces102and104. One or both of the faces can be convex or concave, and one of the faces may be flat. For example, face102of the lens100is convex. Both faces need not, however, have the same sense of curvature (concave or convex), and the two faces need not be symmetrically curved with respect to each other. In some lenses (not shown), one face is planar. In top view, as inFIG. 2, most lens faces are circular in shape. As used herein, including in the claims, a top view of a lens is a view along the optical axis106of the lens, looking at a light-transmission face of the lens.

Most lenses are spherical lenses, i.e., the two faces are parts of respective spherical surfaces. A line joining the centers of the spheres making up the lens faces is called an optical axis of the lens. Typically, the lens axis passes through the physical center of a lens, because of the way the lens is manufactured. An aspheric lens is a lens with at least one face profile that is not a portion of a sphere or cylinder. A spherical or aspherical lens focuses light into a point, exemplified by point108, at least in ideal cases. A lens may focus different wavelengths of light at different locations. However, for simplicity of explanation, wavelength-induced differences in focal lengths are ignored.

A cylindrical lens, an example of which is shown at300inFIG. 3, is a lens that focuses light into a line instead of a point, as contrasted with a spherical or aspherical lens. The curved face or faces, exemplified by faces302and304, of a cylindrical lens are sections of respective cylinders, and they focus an image passing through the cylindrical lens into a line, exemplified by line306, parallel to the intersection of a face302or304of the lens300and a plane tangent to the face302or304. A cylindrical lens300therefore compresses a projected image in a direction308perpendicular to this line306, but the lens leaves the image unaltered in a direction310parallel to the line306. A cylindrical lens300has a longitudinal axis312extending through the cross-section of the lens and parallel to a direction310in which the lens is elongated. As used herein, including in the claims, the term longitudinal axis means an axis extending in a direction that corresponds to a largest dimension of an object.

A developable surface is a surface with zero Gaussian curvature, i.e., a surface that can be flattened onto a plane without distortion (stretching or compressing). Conversely, a developable surface can be made by transforming a plane, i.e., by folding, bending, rolling, cutting and/or gluing the plane. Thus, a cylindrical lens surface302or304is a developable surface, because the cylindrical lens surface can be formed by rolling a plane. A developable surface is also referred to as a simple curvature surface or a simple curve surface.

A non-developable surface, also referred to as a compound curvature surface or a compound curve surface, is a surface with non-zero Gaussian curvature. For example, a sphere is a non-developable surface. Thus, a spherical or aspherical lens face102or104(FIG. 1) is a compound curvature surface, whereas a cylindrical lens face is not a compound curvature surface.

Acylindrical lenses are cylindrical counterparts to aspherical lenses, i.e., elongated lenses with developable surfaces that are not portions of cylinders. Acylindrical lenses are designed to combine aberration-reducing benefits of an aspheric surface with one-dimensional focusing of standard cylindrical lenses. For simplicity, as used herein, including in the claims, the term cylindrical lens includes cylindrical and acylindrical lenses, and the term spherical lens includes spherical and aspherical lenses. Suitable cylindrical, acylindrical, spherical and aspherical lenses are readily available, such as from Thorlabs Inc., Newton, N.J.

Lens Slice

Disclosed is a novel lens, referred herein to as a lens slice. One exemplary embodiment of a lens slice400and its optical axis402are shown in perspective inFIG. 4and in top view inFIG. 5. A lens slice is a transmissive optical device that focuses or disperses a light beam by means of refraction. A lens slice has at least one curved (cylindrical, acylindrical, spherical or aspherical) surface (face), exemplified by faces404and406, through which the light beam passes. Thus, a lens slice is a powered optical element, like conventional lenses. However, a lens slice includes at least one elongated (in top view) portion. Each elongated portion has a respective elongation axis, exemplified by elongation axis408, which is perpendicular to an optical axis402of the lens slice. Conceptually, as shown schematically inFIG. 6, some embodiments of a lens slice may be thought of as a diametric portion400sliced from a conventional spherical or aspherical lens600. Optical performance along the elongation axis408of a lens slice400is comparable to that of a conventional lens, such as lens600, of equal diameter410. However, optical performance along a width axis412(perpendicular to the elongation axis) of a lens slice400can be significantly worse than that of a conventional lens. Aspects of a lens slice may be, but are not necessarily, rotationally symmetric about the optical axis402. Some embodiments of lens slices400have fields of view on the order of about 30°.

In other embodiments, a lens slice is, or includes, a cylindrical or acylindrical lens. Thus, as used herein, including in the claims, the term lens slice includes cylindrical and acylindrical lenses.

A conceptual conventional spherical or aspherical lens600, from which the lens slice400may be thought of as being sliced, is shown inFIG. 6. InFIG. 6, the lens slice400is indicated by dashed lines602and604. Thus, the lens slice400includes only a portion606of the conceptual lens600. Whereas conventional spherical and aspherical lenses100(FIG. 2) are generally circular, in top view, a lens slice400(FIGS. 4-6), according to this embodiment, can be described as an elongated diametric slice of a spherical or aspherical lens, i.e., a slice that extends across a diameter, indicated by dashed line608(FIG. 6), i.e., from edge to edge, of the conceptual conventional lens600from which it is sliced and that includes all portions of the conceptual lens through which the optical axis610extends. Elongated herein means the light admitting surface (face)404(FIG. 5), as seen in top view, is longer along one dimension500than along an orthogonal dimension502, where both dimensions500and502are perpendicular to the optical axis402. Length of the lens slice400refers to the longer dimension500, and width of the lens slice400refers to the shorter dimension502. According to some embodiments, a lens slice has a length-to-width ratio of at least about 3:1, 5:1, 8:1 or 10:1.

FIG. 7is a perspective schematic illustration showing light rays traced from several point light sources700,702,704and706, such as stars in a field of view, through the exemplary lens slice400, to create respective images708,710,712and714on a focal plane716. As noted, optical performance along the elongation axis718of a lens slice400is comparable to that of a conventional lens of equal diameter, such as the conceptual conventional spherical or aspherical lens600, but optical performance along the width axis720of a lens slice400can be worse than that of a conventional lens600. Consequently, the images708-714are elongated blobs, rather than circles or points. For example, the length722of the image714is the same as would be projected by the conceptual conventional spherical or aspherical lens600. However, the width724of the image714is larger than would be projected by the conceptual conventional spherical or aspherical lens600. The same is true for the other images708-712.

Essentially, the lens slice400spreads the images708-714in a direction parallel to the width axis720, compared to the conceptual conventional spherical or aspherical lens600. Nevertheless, centroids, represented by a crosshair715, of the images708-714are not modified. Consequently, processors, such as those used in star trackers, can use the images708-714to ascertain locations of the centroids on an image sensor and, therefore, a location or attitude of a star tracker, as the processors would do with circular or point images, assuming the images708-714do not overlap sufficiently to confuse centroid-determining logic in the processors.

Star Tracker

FIG. 8is a perspective schematic illustration of a star tracker800that includes two lens slices802and804to image celestial objects, exemplified by stars806,808and810, in a field of view812onto respective pixelated image sensors814and816, according to an embodiment of the present invention. The lens slices802and804are disposed between the field of view812and the pixelated image sensors814and816. Centers of each lens slice802and804may be disposed distances from the respective image sensor814and816equal to respective focal lengths of the lens slice802and804. The two focal lengths may, but need not, be equal. The lens slices802and804and the pixelated image sensors814and816collectively form a star camera. Of course, the two image sensors814and816may be replaced by a single large image sensor (not shown) or more than two small image sensors (not shown).

Each lens slice802and804has a respective optical axis818and820and a respective longitudinal (elongation) axis822and824. Each lens slide802and804is elongated along its respective elongation axis822or824. The lens slices802and804are disposed such that the optical axes818and820are spaced apart from each other, and the longitudinal axes822and824are perpendicular to each other. Consequently, the two lens slices802and804spread their respective image blobs in orthogonal directions.

Each lens slice802and804projects respective images of the celestial objects806-810onto its respective pixelated image sensor814and816. For example, celestial object810is projected by lens slice802onto pixelated image sensor814as image826, and the same celestial object810is projected by the other lens slice804onto the other pixelated image sensor816as image828. Thus, even if images of more than one celestial object806-810overlap on one of the two pixelated image sensors814or816, the images of these celestial objects are not likely to overlap on the other one of the pixelated image sensors814or816.

A database830stores ephemeral data, such as a star catalog containing information about a plurality of celestial objects, such as some or all of the celestial objects806-810. A processor832is coupled to the pixelated image sensors814and816. The processor832is configured to automatically estimate an attitude of the star tracker800, an orientation of the star tracker800and/or a location of the star tracker800. The processor832performs the estimation based on data in the database830and image, location, separation or angle data from the pixelated image sensors814and816. The data from the image sensors814and816is generated as a result of one or more images, for example image826, of at least one celestial object, for example star810, in the field of view812being projected onto the pixelated image sensor814or816by the lens slice802or804.

The data from the pixelated image sensors814and816may be compressed or uncompressed. The image data may include pixel value (brightness) data, or binary data simply indicating whether a given pixel receives more than a predetermined threshold amount of light, i.e., with respect to pixels on which images826-836of the celestial objects806-810are projected. Location data from the image sensors814and816may include pixel number or pixel coordinate information about pixels that receive more than a predetermined threshold amount of light or where a centroid is detected. Separation data from the image sensors814and816may include numbers of pixels, or distances in some other unit, between pixels that receive more than a predetermined threshold amount of light or where centroids are detected. Angle data from the image sensors814and816may include angles, taking into account focal length of the lens802or804, between pairs of the celestial objects804-810, or their centroids, that are projected onto the image sensors814and816.

The estimate from the processor832may be referred to as a navigation solution838. The processor832may be configured to perform the functions described herein by executing instructions stored in a memory (not shown). As used herein, including in the claims, the term estimate (as a verb) means to estimate or to calculate.

In a conventional star tracker, x-y positions of celestial object images on a single pixelated image sensor are used to ascertain positions of the celestial objects, angles between pairs of celestial objects or the like. Because the lens slices802and804are orthogonal, each pixelated image sensor814and816essentially provides position information along a respective orthogonal axis, as suggested by axes X and Y. The processor832may use the x position of a centroid of a given image, for example image826, on one image sensor814, and the processor832may use the y position of the centroid of the corresponding image828, i.e., the image cast by the same celestial object810, on the other image sensor816. Optionally, the processor832may obtain the x and y coordinates of the centroids of both images826and828from both image sensors814and816, and the processor832may estimate an improved x and y coordinates from the coordinates of the two centroids, such as by averaging. In calculating the average, the processor832may weight the x and y coordinates from the two image sensors814and816differently, based on which image sensor814or816experiences less image spread by the respective lens slice802or804. For example, the image826is spread less in the X direction on the image sensor814than on the image sensor816. Thus, the processor may weight the x coordinate of the centroid of the image826from the sensor814more heavily than the x coordinate of the centroid of the image828from the sensor816.

Thus, using two orthogonally, or otherwise differently, oriented lens slices802and804compensates for the elongation of each image blob and possible consequential loss of resolution or introduction of beam spread or ambiguity due to blob overlap. Thus, the star tracker800should perform at least as well as a comparable conventional star tracker, yet the star tracker800is smaller and less massive than a comparable conventional star tracker, because the lens slices802and804collectively are less voluminous and less massive than a conventional lens in the conventional star tracker. As noted, the lens of a conventional star tracker typically constitutes a large fraction of the mass and volume of the star tracker. Thus, the savings in volume and mass described herein can be considerable.

The two lens slices802and804inFIG. 8form an L shape840. The lens slices802and804project light onto the two image sensors814and816. At least some of the projected light may travel between the lens slices802and804and the image sensors814and816through a volume bounded on two sides by the L shape840. However, other volume bounded by the L shape840is available to house electronics, such as the processor832, memory storing the database830, a power supply (not shown), etc.

FIG. 9is a perspective schematic illustration of the star tracker800ofFIG. 8showing the volume900bounded by the two sides of the L shape840. The volume900may be bounded on a first side by a first imaginary plane902that intersects one end of the first lens slice802and extends perpendicular to the pixelated image sensors814and816. The volume900may be bounded on a second side by a second imaginary plane904that intersects the other end of the first lens slice802and extends perpendicular to the pixelated image sensors814and816. The volume900may be bounded on a third side by a third imaginary plane906that intersects one end of the second lens slice804and extends perpendicular to the pixelated image sensors814and816. The volume may be bounded on a fourth side by a fourth imaginary plane908that intersects the other end of the second lens slice804and extends perpendicular to the pixelated image sensors814and816. As noted, the processor832, the memory storing the database830and other electronics may be disposed within the volume900, thereby making a compact star tracker800.

Other Lens Slice Shapes

In the lens slices400,802and804shown inFIGS. 4-6, 8 and 9, left and right sides414and504, respectively, (best seen inFIGS. 4 and 5) of the lens slices are parallel to each other and to the optical axes402,818and820. However, the left and right sides of a lens slice need not be parallel to each other or to the optical axis of the lens slice.FIG. 10is a perspective view of a lens slice1000having left and right sides1002and1004, respectively, that are parallel to the optical axis1006, according to an embodiment of the present invention. However, the left and right sides1002and1004are not parallel to each other. As a result of the left and right sides1002and1004being not parallel to each other, lengths1008and1010are not equal to each other.

FIG. 11is a perspective schematic illustration of a lens slice1100having left and right sides1102and1104, respectively, that are not parallel to the optical axis1106and not parallel to each other, according to another embodiment of the present invention. As a result of the left and right sides1102and1104being not parallel to the optical axis1106, lengths1108and1110are not equal to each other.

Each surface of each lens slice802and804shown inFIGS. 8 and 9may have a simple curvature surface or a compound curvature surface. Each lens slice802and804shown inFIGS. 8 and 9may be a cylindrical or an acylindrical lens. In the case of simple curvature surfaces, such as cylindrical or acylindrical lenses, the image blobs, such as image blobs826and828, may be lines, possible lines that extend the full width of the respective image sensor814or816. Nevertheless, the combination of two orthogonally, or otherwise differently, oriented lens slices802and804enable the processor832to disambiguate images that overlap on only one of the two image sensors814or816. For example, if images834and836overlap on image sensor816, but images830and832from the corresponding stars808and806, respectively, do not overlap on the other image sensor814, the processor832can measure the x coordinates of the stars808and806using the image sensor814. If the two images overlap indistinguishably on the other image sensor816, the y coordinate of the two images may be treated as equal to each other.

FIG. 12is a perspective schematic illustration of a lens slice1200, similar to the lens slices400,802and804shown inFIGS. 4-6, 8 and 9. However, the lens slice1200includes two elongated portions1202and1204that intersect at the optical axis1206and are mutually orthogonal, thereby forming a cross-shaped lens slice. The cross-shaped lens slice1200may have simple curvature surfaces or compound curvature surfaces. The surfaces may be, for example, spherical or aspherical surfaces.

FIG. 13is a perspective view of a cross-shaped lens slice1300, similar to the lens slice1200, except with non-parallel left and right sides1302and1304, as described with respect to the lens slice1000shown inFIG. 10. The cross-shaped lens slice1300has an optical axis1306and may have simple curvature surfaces or compound curvature surfaces. The surfaces may be, for example, spherical or aspherical surfaces.

FIG. 14is a perspective schematic illustration of another cross-shaped lens slice1400. The lens slice1400has an optical axis1401. As suggested by dashed equator line1402, the lens slice1400is conceptually a slice of a monocentric lens (“ball lens”). Being a monocentric lens slice1400, the lens provides a wide field of view. Some embodiments of monocentric lens slices have fields of view on the order of about 180°. To capture the wide field of view, or a portion thereof, several image sensor arrays, exemplified by image sensor arrays1404,1406,1408and1410, may be disposed on the opposite side of the lens slice1400from the field of view1412. Each image sensor array1404-1410may be disposed a distance from the center of the lens slice1400equal to the focal length of the lens slice1400. Optionally, the lens slice1400may be optically coupled to the image sensor arrays1404-1410by respective bundles of optical fibers (not shown). The lens slice1400and the image sensor arrays1404-1410may replace the two lens slices802and804and the two image sensors814and816in the star tracker800(FIG. 8), such as to produce a wide-field-of-view star tracker.

Functionally, the lens slice1400acts as two of the lens slices400described with respect toFIGS. 4, 5 and 7, where the two lens slices have a common optical axis and the two lens slices are arranged such that their elongation axes408are perpendicular to each other and to the common optical axis. The cross-shaped monocentric lens slice1400produces cross-shaped blob images of point light sources. However, centers of the cross-shaped images are bright, relative to arms of the cross-shape, which facilitates finding centroids of the images.

One important characteristic of any lens is its angular resolution, i.e., the smallest angle between two distinguishable points imaged by the lens. The angular resolution can be calculated according to well-known equation (1),

θ=1.22⁢λD(1)
where:
θ is the angular resolution,
λ is the wavelength of light and
D is the diameter of the lens aperture.
Thus, other things being equal, a large diameter lens or aperture (i.e., a small numerical aperture value) provides better (smaller) angular resolution than a small diameter lens or aperture.

As noted, optical performance along the elongation axis of a lens slice is comparable to that of a conventional lens of equal diameter, but optical performance along the width axis of a lens slice can be worse than that of a conventional lens. Consequently, in an optical system that includes a lens slice, the lens slice should be oriented such that the elongation axis, for example the long dimension500(FIG. 5), aligns with an axis along which the greatest angular resolution is required. Once the required angular resolution of a lens slice is determined, the long dimension500may be calculated, using equation (1). After the long dimension500is determined, the orthogonal dimension502may be determined, based on the size (area) of the lens or aperture required to admit the amount of light needed.

Making Lens Slices

As noted, in some embodiments, a lens slice400(FIGS. 4, 5 and 6) includes only a portion606of the conceptual lens600remaining after the conceptual lens600has been partitioned (cut) through lines602and604. Lens slices can, but need not, be manufactured by conventional machining processes. For example, material may be cut to remove the material from conventional circular lenses, as suggested inFIG. 6. Alternatively, lens slices may, for example, be manufactured by casting or injection molding suitable transparent material in desired shapes, such as shapes similar to the lens slice400ofFIGS. 4 and 5, or other shapes, examples of which are described herein, such as with respect toFIGS. 10-14. Injection molding may be appropriate for relatively small lens slices.

For relatively large lens slices, as schematically illustrated inFIG. 15, the lens slices may be made by cutting pieces, exemplified by piece1500, from a cylindrical or acylindrical lens1502. The cylindrical or acylindrical lens1502may be made by conventional techniques to have the desired or nearly desired final simple curvature profile(s) of the lens slice. Optionally, after the piece1500has been cut from the cylindrical or acylindrical lens1502, one or both surfaces1504and/or1506of the piece1500may be ground and/or polished to add a respective second dimension of curvature (to create a compound curved surface), as shown inFIG. 16. Additional pieces may be cut from the cylindrical or acylindrical lens1502, as suggested by dashed line1508.

Regardless of manufacturing technique, optical surfaces (faces) of lens slices may be polished to smooth the surfaces and/or to more precisely shape the surfaces. Lens slices used for imaging should have compound curved surfaces. However, lens slices used in situations where only one dimension of measurement is necessary, such as in each of the two star cameras in the star tracker discussed with respect toFIG. 8, may be sufficient with only simple curved surfaces.

Multi-Directional Star Camera-Based Navigation System

FIG. 17is a perspective schematic view of a navigation system1700, according to an embodiment of the present invention. The navigation system1700includes three star cameras1702,1704and1706. Optical axes1708,1710and1712of the three star cameras1702-1706may be mutually orthogonally, or otherwise differently, oriented. Each star camera1702-1706may be constructed as described herein, such as with respect toFIGS. 7-14. Thus, each star camera1702-1706has a respective field of view1714,1716and1718and a respective pixelated image sensor1720,1722and1724and a respective lens slice1726,1728and1730disposed between the respective field of view1714-1718and the respective pixelated image sensor1720-1724.

The lens slices1726-1730are shown inFIG. 17as single-elongation-axis lens slices. However, in each star camera1702-1706, any type of lens slice may be used, including multiple-elongation axes lens slices, such as the lens slices discussed with respect toFIGS. 12-14, as well as groups of differently-oriented lens slices, as discussed with respect toFIGS. 8 and 9. For example, each lens slice1726-1730may include a respective first lens slice and a respective second lens slice, analogous to the two lens slices802and804discussed with respect toFIGS. 8 and 9. Each first lens slice may have a respective first optical axis and a respective first longitudinal axis, analogous to the optical axis818and the longitudinal axis822. Each second lens slice may have a respective second optical axis and a respective second longitudinal axis, analogous to the optical axis820and the longitudinal axis824.

Within each star camera1702-1706, the respective first optical axis may be spaced apart from the respective second optical axis, and the respective first longitudinal axis may be perpendicular to the respective second longitudinal axis, as discussed with respect toFIG. 8. Each first lens slice may be elongated along the respective first longitudinal axis, and each respective second lens slice may be elongated along the respective second longitudinal axis, as discussed with respect toFIG. 8.

The navigation system1700also includes a database1732storing ephemeral data about a plurality of celestial objects and a processor1734coupled to the pixelated image sensors1720-1724and to the database1732. The processor1734is configured to automatically estimate an attitude of the navigation system1700, an orientation of the navigation system1700and/or a location of the navigation system1700, shown inFIG. 17as a navigation solution1736. The processor1734is configured to base the estimate on: (a) data from the respective pixelated image sensors1720-1724generated as a result of an image of at least one celestial object, such as a star1730,1732,1734or1736, in the respective field of view1714-1718being projected onto the respective pixelated image sensor1720-1724by the respective lens slice1726-1730and (b) data in the database1732.

The processor1734may be configured to provide separate estimates of the attitude of the navigation system1700, the orientation of the navigation system1700and/or the location of the navigation system1700, for each of the three star cameras1702-1706. The navigation system1700may also include a navigation filter1746. The navigation filter1746may be configured to estimate an improved attitude of the navigation system1700, an improved orientation of the navigation system1700and/or an improved location of the navigation system1700. The navigation filter1746may base the improved estimate on the separate estimates of the attitude of the navigation system1700, orientation of the navigation system1700and/or location of the navigation system1700. The navigation filter1746may be implemented by the processor1734. Alternatively, a separate navigation filter1746may be coupled to the processor1734.

The processor1734may be configured to perform the functions described herein by executing instructions stored in a memory (not shown). Similarly, the navigation filter1746may be implemented by the processor1734or by a separate processor (not shown), and that processor may be configured to perform the functions described herein by executing instructions stored in a memory (not shown).

Compound Lens Slice

As noted, a simple lens includes a single piece of transparent material, whereas a compound lens includes several adjacent or spaced apart simple lenses (elements), usually arranged along a common axis, and sometimes cemented together. A lens slice can include several such elements, where each element can itself be a lens slice. An exemplary compound lens slice1800is shown schematically in top view and in perspective cut-away view inFIGS. 18 and 19, respectively. As shown inFIG. 19, the exemplary compound lens slice1800includes four separate elements1900,1902,1904and1906. Of course, a compound lens slice may include any number of separate elements.

While the invention is described through the above-described exemplary embodiments, modifications to, and variations of, the illustrated embodiments may be made without departing from the inventive concepts disclosed herein. For example, although specific parameter values, such as dimensions and materials, may be recited in relation to disclosed embodiments, within the scope of the invention, the values of all parameters may vary over wide ranges to suit different applications. Unless otherwise indicated in context, or would be understood by one of ordinary skill in the art, terms such as “about” mean within ±20%.

As used herein, including in the claims, the term “and/or,” used in connection with a list of items, means one or more of the items in the list, i.e., at least one of the items in the list, but not necessarily all the items in the list. As used herein, including in the claims, the term “or,” used in connection with a list of items, means one or more of the items in the list, i.e., at least one of the items in the list, but not necessarily all the items in the list. “Or” does not mean “exclusive or.”

Although aspects of embodiments may be described with reference to flowcharts and/or block diagrams, functions, operations, decisions, etc. of all or a portion of each block, or a combination of blocks, may be combined, separated into separate operations or performed in other orders. References to a “module” are for convenience and not intended to limit its implementation. All or a portion of each block, module or combination thereof may be implemented as computer program instructions (such as software), hardware (such as combinatorial logic, Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), processor or other hardware), firmware or combinations thereof.

Embodiments, or portions thereof, may be implemented by one or more processors executing, or controlled by, instructions stored in a memory and/or accessing data stored in the memory or another memory. Each processor may be a general purpose processor, such as a central processing unit (CPU), a graphic processing unit (GPU), digital signal processor (DSP), a special purpose processor, etc., as appropriate, or combination thereof.

The memory may be random access memory (RAM), read-only memory (ROM), flash memory or any other memory, or combination thereof, suitable for storing control software or other instructions and data. Instructions defining the functions of the present invention may be delivered to a processor in many forms, including, but not limited to, information permanently stored on tangible non-writable storage media (e.g., read-only memory devices within a computer, such as ROM, or devices readable by a computer I/O attachment, such as CD-ROM or DVD disks), information alterably stored on tangible writable storage media (e.g., floppy disks, removable flash memory and hard drives) or information conveyed to a computer through a communication medium, including wired or wireless computer networks. Moreover, while embodiments may be described in connection with various illustrative data structures, systems may be embodied using a variety of data structures.

Disclosed aspects, or portions thereof, may be combined in ways not listed above and/or not explicitly claimed. In addition, embodiments disclosed herein may be suitably practiced, absent any element that is not specifically disclosed herein. Accordingly, the invention should not be viewed as being limited to the disclosed embodiments.