Solid catadioptric lens with two viewpoints

This application is a continuation-in-part of U.S. patent application Ser. No. 10/721,194, filed Nov. 24, 2003 now U.S. Pat. No. 7,038,846. This application also claims priority from U.S. Prov. Pat. Appl. No. 60/716,890, filed Sep. 14, 2005. Both applications are incorporated herein by reference.

The present invention relates generally to optical lenses, and more particularly to solid catadioptric lenses with two viewpoints.

Catadioptric lenses are well-known in computer vision and imaging systems, robotic sensors, and various other applications. Each imaging application typically has specific design requirements, resulting in many different types of catadioptric lenses. Unfortunately, many wide-angle lenses and optical systems are complex and expensive.

For example, U.S. Pat. No. 6,449,103 discloses a variety of complicated wide-angle lens systems. U.S. Pat. No. 5,473,474 to Powell discloses a panoramic imaging system that is comparatively simple. One embodiment has two spherical refractive surfaces and a single elliptical reflective surface. It is not evident, however, that this system would be useful in certain machine vision applications since the design does not produce the important feature of a single view-point (SVP). The SVP feature can only be produced by a special class of catadioptric lenses and is important in machine vision applications, i.e., performing optical measurements of a scene, because it permits the distortion-free reconstruction of the image. U.S. Pat. No. 6,611,282 to Trubko et al. discloses a folded-type catadioptric lens having an SVP feature. This system would be useful for many machine vision applications, but would be limited in its use for optical ranging applications involving absolute measurement of distances unless two or more such lenses are used in stereo-vision or multiple-view systems that are well known in the art. It would be desirable to have a single, simple, compact, inexpensive lens with a wide field of view that is suitable for optical ranging and similar applications.

According to one aspect of the invention, a dual viewpoint solid catadioptric lens having the feature of two SVP's is provided. The lens has a first spherical refractive surface whose center is located on an optical axis of the lens. The lens also has a second, smaller spherical refractive surface whose center is also located on the optical axis of the lens. The lens has a first ellipsoidal reflective surface whose foci are on the optical axis of the lens and a second ellipsoidal partially reflective surface whose foci are also on the optical axis of the lens. Moreover, a focus of the first ellipoidal reflective surface is conicident with the center of the first spherical refractive surface. Similarly, a focus of the second ellipoidal reflective surface is conicident with the center of the second spherical refractive surface. In addition, the other foci of the two ellipses are coincident with each other. Specific embodiments of the invention include variations of design parameters such as the field of view, eccentricities and sizes of the ellipsoidal surfaces, radii of curvature of the spherical refractive surfaces, additional light shaping surfaces, and so on.

FIG. 1 is a cross-sectional view of a dual-viewpoint solid catadioptric lens according to an embodiment of the invention.

FIG. 2 is a cross-sectional view of an embodiment of the invention used with a relay lens and aperture.

FIG. 3 is a cross-sectional view of an embodiment of the invention used with a wavelength selective beam splitter and two detectors.

FIG. 4 is a cross-sectional view of an embodiment of the invention having less than maximal view angles.

FIG. 1 is a cross-sectional view of a dual-viewpoint solid catadioptric lens according to an embodiment of the invention. The lens has a first spherical refractive surface S 1 whose center C 1 is located on an optical axis 100 of the lens. Surface S 1 has a radius of curvature r 1 which is the radius of dashed circle 102 , which is shown in the figure to aid in the understanding of the lens geometry. The lens also has a second, smaller spherical refractive surface S 2 whose center C 2 is also located on the optical axis 100 of the lens. Surface S 2 has a radius of curvature r 2 which is the radius of circle 104 . In this particular embodiment, the center C 2 of the smaller circle 104 lies within the larger circle 102 . In other words, the distance between centers C 1 and C 2 is less than radius r 1 . In other embodiments, the center C 2 may lie outside the larger circle 102 , i.e., the distance between C 1 and C 2 is greater than r 1 .

The lens has a first ellipsoidal reflective surface E 1 whose foci F 1 and F 1 ′ are both on the optical axis 100 . In other embodiments, focus F 1 ′ lies on optical axis 100 , but focus F 1 does not lie on axis 100 . The cross-section of surface E 1 is a portion of dashed ellipse 106 . Focus F 1 is coincident with center C 1 . Consequently, rays passing through surface S 1 at normal incidence will pass through C 1 =F 1 and reflect from surface E 1 directed toward focus F 1 ′. The lens also has an ellipsoidal partially reflective surface E 2 whose foci F 2 and F 2 ′ are on the optical axis 100 of the lens. The cross-section of surface E 2 is a portion of dashed ellipse 108 . Focus F 2 is coincident with center C 2 and focus F 2 ′ is coincident with focus F 1 ′. Consequently, rays passing through surface S 2 at normal incidence will pass through C 2 =F 2 and partially reflect from surface E 2 directed toward focus F 2 ′=F 1 ′. Thus, C 1 and C 2 provide two viewpoints, denoted SPV 1 and SPV 2 , for the lens.

Circle 102 intersects with ellipse 106 at point I 1 . In this particular embodiment, point I 1 is directly above focus F 1 . Similarly, circle 104 intersects with ellipse 108 at point I 2 directly above focus F 2 . Consequently, this embodiment provides a maximum view angle σ 1 max =π/2 for SVP 1 and σ 2 max =π/2 for SVP 2 , where σ 1 max is the angle between the optical axis and the point of intersection of S 1 and E 1 as measured from C 1 , and σ 2 max is the angle between the optical axis and the point of intersection of S 2 and E 2 as measured from C 2 . Point I 2 also is the point of intersection of circles 102 and 104 and thus defines the minimum view angle σ 1 min of SVP 1 defined by r 2 =r 1 sin(σ 1 min ), i.e., (σ 1 min is the angle between the optical axis and the point of intersection of S 2 and E 2 as measured from C 1 . Circle 104 also intersects with surface S 3 at point I 3 , which defines the minimum view angle σ 2 min of SVP 2 given by r 3 =r 2 sin(σ 2 min ), i.e., σ 2 min is the angle between the optical axis and the point of intersection of S 2 and S 3 as measured from C 2 . Moreover, in this embodiment points I 1 , I 2 and I 3 are collinear with focus F 1 ′=F 2 ′.

This particular embodiment of the lens is a solid body of revolution about optic axis 100 and may be constructed from two or more solid sections to provide partially reflective surface E 2 within the lens interior. It is also preferable for the sections to be made of materials that allow matching of the refractive index across surface E 2 to prevent refraction of rays crossing this surface. In preferred embodiments, the interior of the lens has a uniform index of refraction. The lens sections can be molded using standard moldable optical materials such as Acrylic, polystyrene, or moldable glass. The surfaces are preferably coated with appropriate optical coatings to provide required reflective or transmission properties. For example, the ellisoidal surfaces can be coated with aluminum or other metal to provide proper reflectivity. Also, multilayer dielectric coatings can be used on surfaces E 1 , E 2 , S 1 , or S 2 to provide reflectivities at certain wavelengths to provide different wavelengths to pass through SPV 1 and SPV 2 to the image detector 114 . Methods for creating selective beamsplitting properties of the surfaces are well known in the art. Since surface E 2 is located in the interior of the fully assembled lens, and since it must have some partially reflective properties to allow rays to pass from SVP 1 to the image detector, then this surface can also serve as the mating surface between two solid molded lens sections that are properly coated. The lens sections can be attached using standard optical adhesives. It is also preferable that the lens sections have the same index of refraction to avoid any rays from being refracted at the interface between the sections. Other methods for fabricating the required optical surfaces and lens sections from various optical materials may include injection molding, diamond point turning, CNC polishing, Sol-Gel techniques, precision etching, lithography, or any other standard optical fabrication methods that are well known in the art.

In this embodiment a non-optical cylindrical surface S 3 having a radius r 3 extends the lens body from point I 3 on surface S 2 and is terminated by a light shaping surface L having a focal length f. Surface L could be, for example, a convex surface passing through F 1 ′=F 2 ′ thereby causing a focused image of object point P to be projected onto image detector 114 . In general, light shaping surface L may be curved or flat and is preferably designed to refract the pencil of rays for imaging purposes. It is also preferable to have an aperture stop 111 with fixed or variable dimensions positioned at F 1 ′=F 2 ′ to control the numerical aperture and insure that the chief imaging rays pass through F 1 ′=F 2 ′ thereby enforcing the condition that all chief imaging rays pass through SPV 1 or SPV 2 . This is a result of the elliptical surfaces E 1 and E 2 , which forms an image of the aperture stop 111 at both points F 1 and F 2 . For example, in the present embodiment, rays are refracted at surface L so that they are directed to image detector 114 .

In an alternate embodiment, shown in FIG. 2 , light shaping surface L is flat and is positioned at point F along the optical axis 100 . The lens in FIG. 2 is otherwise identical to that of FIG. 1 . In addition, a relay lens 113 is provided to focus the rays upon the detector 114 . Those skilled in the art will appreciate that many other optical configurations may be used to provide desired imaging of the rays exiting the lens.

In operation, consider an object point P which radiates light rays in all directions. However, from point P only two rays, 112 and 110 , are normal to surfaces S 1 and S 2 , respectively. Rays 112 and 110 therefore pass through focal points C 1 and C 2 , respectively, and are then reflected from ellipsoidal surfaces E 1 and E 2 , respectively, toward common focal point F 1 ′=F 2 ′. Light shaping surface L refracts the rays 110 and 112 before passing through an image relay lens 113 , which has a focal length f and is placed between surface L and a detector 114 for forming images on detector 114 as points P′ and P″, respectively. It is to be noted, however, that surface E 2 is only partially reflective and may be constructed to divide a beam of light into a reflective component and a transmissive component using many well-known techniques for forming optical surfaces having beam-splitting functions, i.e., thin dielectric films for wavelength separation, or a thin metal coating for amplitude separation. Other methods for providing this partially reflective surface could include a thin air gap between two solid sections of lens body. Consequently, when ray 112 is transmitted through surface E 2 toward common focal point F 1 ′=F 2 ′ a portion 116 may be reflected from surface E 2 , thereby reducing the intensity of ray 112 that is imaged at point P″. Similarly, when ray 110 is reflected from surface E 2 toward common focal point F 1 ′=F 2 ′ a portion 118 may be transmitted through surface E 2 , thereby reducing the intensity of ray 110 that is imaged at point P′. The beam-splitting properties (i.e., partial reflectivity and partial transmissivity) of surface E 2 is preferably selected to insure that the intensities of points P′ and P″ are of the same order of magnitude.

The angle Δσ between the two rays 110 and 112 originating from the object point P is related to the distance Δd between the two points P′ and P″ in the image. In particular, ray 112 makes an angle σ 1 with optical axis 100 as measured from point C 1 , while ray 110 makes an angle σ 2 with optical axis 100 as measured from point C 2 . The difference Δσ=σ 2 −σ 1 is transformed by light shaping surface L and relay lens 113 into distance Δd between points P′ and P″. Thus, a measurement of the distance Δd provides information about the angle Δσ. Moreover, the displacement of points P′ and P″ from the optical axis 100 provides information about the values of angles σ 1 and σ 2 . This information can then be used in optical ranging applications to determine position information of point P. For example, knowledge of angles σ 1 , σ 2 , and the distance between C 1 and C 2 allows the location of point P to be determined by triangulation. Moreover, if some information about point P is already known, that information can be used together with knowledge of angles σ 1 and σ 2 to more accurately determine location information about point P. For example, in some applications it may be known a priori that P lies in an object plane located at a predetermined distance from the lens along the optical axis. This constraint can be used to provide more accurate estimation of location information for P using knowledge of angles σ 1 and σ 2 . If, in addition, the angle between the optical axis and the object plane is known, this information provides even more information which can be used to determine the location of point P with high accuracy. Conversely, location information of point P can be used to estimate the angle between the optical axis and the object plane.

In an alternate embodiment, the surfaces S 1 and S 2 are provided with different coatings which perform wavelength filtering. For example, the transmission spectra of the coatings on S 1 and S 2 could be centered at different wavelengths. Consequently, the detected wavelengths of image points P′ and P″ can be used to determine which viewpoint the corresponding ray passed through. Additionally, partially reflective surface E 2 may have properties such that only certain wavelengths (or a band of wavelengths) may be selected to pass through both S 1 and E 2 , and whereby a different set of wavelengths can pass through S 2 and also be reflected by E 2 . These wavelength selective properties of S 1 , S 2 , and E 2 may be chosen to allow images P′ and P″ to be identified by a two distinctive sets of wavelengths. This would be useful when detector 114 can distiguish between the SVP-identifying wavelengths, such as a CCD array with a color filter mask (i.e., as used in typical color digital cameras). In another embodiment, illustrated in FIG. 3 , detector 114 is a position sensitive detector (PSD) that can only track the position of a single point image. In this case, a wavelength selective beam splitter 117 may be used in the space between relay lens 113 and detector 114 . Beam splitter 117 is designed to pass the image of P″ onto detector (PSD) 114 while reflecting the image of P′ onto a second detector (PSD) 115 . Thus, if light emanating from object point P comprises a set of wavelengths such that some may pass through SVP 2 and some through SVP 1 to form respective point images P′ and P″ on detectors 114 and 115 , then PSD detector 114 can independently track the movement of image point P″ as viewed from SVP 1 , and PSD detector 115 can independently track the movement of image point P′ as viewed through SVP 2 . This type of optical ranging system can thus perform continuous distance ranging by triangulation as the object point P moves relative to the optical system.

Other embodiments of the invention can employ certain variations of design parameters for the lens while still operating on the same fundamental principles of the invention. For example, FIG. 4 shows a variant of the embodiments shown in FIG. 1-3 . As in the previous embodiments, this embodiment includes two spherical surfaces S 1 and S 2 with centers C 1 and C 2 on optical axis 100 and two ellipsoidal surfaces E 1 and E 2 with foci F 1 , F 1 ′ and F 2 , F 2 ′, respectively, all on the optical axis, where F 1 =C 1 , F 2 =C 2 , and F 1 ′=F 2 ′. In contrast with the previously described embodiments, however, the spherical surface S 1 has a smaller radius so that intersection point I 1 is not directly above center C 1 . Consequently, σ 1 min is increased and σ 1 max is decreased, resulting in a smaller field of view as compared to the lenses described in FIGS. 1-3 . Despite these differences, this embodiment can be used in much the same manner as the embodiments described above in relation to FIGS. 1-3 . Although the field of view is reduced, this embodiment has the advantage of a smaller size. Another technique for reducing the size of the lens is to form the spherical surface S 1 as two or more concentric spherical segments.

In this particular embodiment, ellipsoidal surfaces E 1 and E 2 can be characterized by their respective radius of curvatures (semi-latus rectums) R 1 and R 2 and their respective conic constants K 1 and K 2 . In some cases it may be preferrable for surfaces E 1 and E 2 to have the same eccentricity (i.e., K 1 =K 2 ) and their respective radius of curvatures R 1 and R 2 are in the proportion r 1 :r 2 . In particular, in some embodiments R 1 =r 1 and R 2 =r 2 . FIG. 4 also shows the geometrical parameters L 1 , L 2 , L 3 , L 4 , L 5 , and L 6 , which are given below in terms of R 1 , R 2 , K 1 , and K 2 . These parameters represent the distance between foci, or between one focus and a vertex for the ellipsoids of revolution E 1 and E 2 . These geometric distances are useful for constructing the dual viewpoint lens assembly in terms of the radii of curvatures R 1 , R 2 , and the conic constants K 1 , K 2 that define the ellipsoidal surfaces E 1 and E 2 respectively and which also enforces the confocal condition: F 1 ′=F 2 ′.

L 1 =R 2[1 −srt (− K 2)]/[1 +K 2]=Distance: Vertex of E 2 to F 2

L 2=2 *R 2 [srt (− K 2)]/[1 +K 2]=Distance: F 2 to F 2′

L 3 =R 2[1 +srt (− K 2)]/[1 +K 2]=Distance: Vertex of E 2 to F 2′

L 4 =R 1[1 −srt (− K 1)]/[1+ K 1]=Distance: Vertex of E 1 to F 1

L 5=2 *R 1 [srt (− K 1)]/[1 +K 1]=Distance: F 1 to F 1′

L 6 =R 1[1 +srt (− K 1)]/[1 +K 1]=Distance: Vertex of E 1 to F 1′

Those skilled in the art will appreciate that various other design parameters may be altered as well, including sizes of the ellipsoidal surfaces, radii of curvature of the spherical refractive surfaces, additional light shaping surfaces, and so on. It will also be noted that points I 1 and I 2 are not necessarily collinear with focus F 1 ′=F 2 ′, nor is the maximum field of view angle for both viewpoints the same. It should also be appreciated that the object points (i.e., such as point P in FIG. 1 ) may be light sources such as LEDs, illuminated pixels on a computer display, retroreflectors, or any illuminated or luminous objects, which may further be grouped to produce illuminated patterns of point objects, lines, or areas either in a plane or in three dimensional space.

It will also be appreciated that the lenses of the present invention can be used in an inverse manner, exchanging image and object, to project beams from a light source located at the position P′ or P″, thereby projecting a point image out into the environment to the position P. In such a case it is then possible to project a point light source located at position P′ out into the environment to provide a point image at point P through SVP 2 and also allow the reflected light at point P to be imaged through SVP 1 to point P″ on a detector. This would allow triangulation ranging to a non-luminous or non-illuminated object.

It will also be appreciated that the confocal condition F 1 ′=F 2 ′ can be satified for dual viewpoint imaging even if the the three points F 1 , F 2 , and F 1 ′=F 2 ′ are not colinear. In this case F 1 may not lie on the axis defined by the two points F 1 ′=F 2 ′ and F 2 . Such an asymmetric lens assembly would operate in the same manner as in the embodiments described above, but would not have a symmetric field of view about the optical axis defined by F 1 ′ and F 2 ′. This asymmetric design may be advantageous in usage cases where a larger field of view is desired for a preferred viewing direction (i.e., a selected azimuthal viewing angle where a maximum field of view is desired) at the expense of having a smaller field of view at 180 degrees azimuthally opposed from such a preferred viewing direction.