Imaging system, method, and application

Abstract

To provide a multi-camera panoramic imaging system having no parallax, a method, and an application.SOLUTION: In a method for forming an image of an object having no parallax, a multi-camera panoramic imaging system includes a plurality of discrete imaging systems arranged in a side-by-side array. A field of view of each discrete imaging system is conjoined with a field of view of each adjacent discrete imaging system, and a stencil of chief rays at the edge of the field of view of any one imaging system of the discrete imaging systems is substantially parallel to a stencil of chief rays at the edge of the field of view of any adjacent imaging systems of the discrete imaging systems such that all of the substantially parallel stencils of chief rays appear to converge to a common point when viewed from object space.SELECTED DRAWING: Figure 12

Description

Technical Field

[0001] Cross - Reference to Related Applications This application claims the benefit of priority of U.S. Provisional Application No. 61 / 989,136, filed May 6, 2014, the subject matter of which is incorporated herein by reference in its entirety.

[0002] Aspects and embodiments of the present invention relate most generally to optical imaging systems, related methods, and uses thereof, more specifically to panoramic optical imaging systems, related methods, and uses thereof, and most specifically to panoramic optical imaging systems with zero or near - zero parallax, related methods, and uses thereof.

Background Art

[0003] Current 360 - degree systems without parallax use the placement of mirrors to scan the image and are limited by an imaging speed of 10 frames per second (fps). Google uses a 360 - degree camera with refractive lenses developed by Immersive Media to take pictures for its Street View software. The pictures have to be post - processed and corrected for parallax, which is time - consuming and reduces Google's ability to push the boundaries of its Street View concept. A fisheye lens provides wide - angle imaging but at the cost of high distortion. Distortion is a physical result of mapping a large sphere onto a small flat image plane.

[0004] Several companies have developed optical systems to simplify the process of taking panoramic images. Instead of rotating a camera to obtain multiple shots, all of the photos are captured simultaneously using multiple cameras that image different parts of the scene. Immersive Media and Greypoint Imaging have developed one-shot 360-degree cameras that are available at prices ranging from $10,000 to $100,000. Both companies develop software to automatically correct the artifacts (parallax) generated in the images and provide a solution superior to panoramas taken by a single camera, such as an iPhone® camera. However, the software is not perfect, and many artifacts still exist in the images. As an anecdote, Google had to hire a programmer to correct the images frame by frame for artifacts caused by parallax by sending a person with a Dodeca360 camera (provided by Immersive Media) all over the Grand Canyon.

[0005] Parallax and Chief Ray of the Optical System Parallax is defined as "the effect by which the position or direction of an object appears different when viewed from various positions, e.g., through the camera finder and lens." Parallax is generated as a result of stitching together images from multiple cameras, each with its own unique view of the world.

[0006] Referring to FIG. 1, the chief ray of the optical system is the meridional ray that starts at the edge of the object, crosses the center of the optical axis at the aperture stop, and ends at the edge of the image at the detector. Thus, the chief ray defines the size of the image.

[0007] The chief ray plays a significant role in the disparity generated by stitching together multiple images. Figure 2 shows two aligned optical systems (cameras). For the upper lens unit, the square, triangle, and rectangle are mapped to the same point in the image, while for the lower lens unit, they are mapped to three separate points as shown. In the upper imaging system, they are imaged by the same chief ray, whereas for the lower imaging system, they are imaged by three separate chief rays. When the two images are combined in Figure 3, a disparity will occur, resulting in an image as shown in Figure 4.

[0008] The pursuit of an algorithm capable of correcting disparity has continued for many years. Although many solutions have been developed, artifacts still remain in the panoramic image, even when using the most sophisticated algorithms to date. For some people, this may not be a problem as they can hire software engineers to correct the images frame by frame. However, for the general consumer, this option of correcting each image is not feasible. A better solution for effectively correcting disparity is needed before such a system can be made available in the consumer market. It is desirable to solve the problem of optically reducing disparity in the image rather than computationally.

[0009] Current designs created for one-shot panoramic imaging suffer from disparity as they are created from imaging systems with overlapping fields of view. Figure 5 is taken from U.S. Patent No. 2,696,758. This figure shows how disparity is generated in a 360-degree imaging system available today. The fields of view overlap, and the triangle that appears at the edge of the FOV for the lower lens system appears at approximately 0.707×FOV in the upper imaging system. Thus, the triangle is mapped to different image points for each camera. In the lower part, it is mapped to the full FOV (the edge of the image). SUMMARY OF THE INVENTION MEANS FOR SOLVING THE PROBLEM

[0010] Accordingly, the inventor recognized the advantages and benefits of a panoramic imaging system and related methods in which there is no parallax and the parallax is removed optically rather than by post-processing software. Such a system would provide a scalable way to map the streets of the earth, enable the creation of virtual tours for both cities and civilian institutions, provide high frame rate video surveillance, have military applications including unmanned aerial vehicles and tank technology, and provide an alternative to fisheye lenses for wide-angle imaging that pays the price of high distortion. BRIEF DESCRIPTION OF THE DRAWINGS

[0011]

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DETAILED DESCRIPTION OF THE INVENTION

[0012] Aspects of the present invention are multi-camera panoramic imaging systems without parallax. According to non-limiting embodiments, a multi-camera panoramic imaging system includes a plurality of distinct imaging systems arranged in an array, the field of view of each distinct imaging system is combined with the field of view of each adjacent distinct imaging system, and further, the stencil of the chief ray at the edge of the field of view of any one imaging system in a distinct imaging system is such that all stencils of the chief ray that are substantially parallel appear to converge to a common point when viewed from the object space, and at the edge of the field of view of any adjacent imaging system in a distinct imaging system, it is substantially parallel to the stencil of the chief ray. In various non-limiting embodiments, the multi-camera panoramic imaging system may include, or be further characterized by, the following mechanisms, limitations, features, either alone or in various combinations thereof. - It includes a plurality of identical and separate imaging systems. - At least 50% of the stencil of the chief ray deviates from parallel by 20 degrees or less. - Each of the separate imaging systems includes an image sensor, and further, an apparent focus point is located behind the image sensor in each of the separate imaging systems. - None of the separate imaging systems physically overlap. - The system has an icosahedral geometry, and further the system is characterized by a 360-degree FOV. - The front lens in each of the separate imaging systems is part of a single adjacent free-form optical device. - Each image sensor is a wavefront sensor. - Each of the separate imaging systems has a curved image plane to accommodate the distortion and Petzval curvature of the imaging system.

[0013] Aspects of the present invention are methods for forming an image of an object without parallax. According to non-limiting embodiments, the method is to provide a panoramic imaging system, the panoramic imaging system including a plurality of separate imaging systems each characterized by a field of view, and all of the parallel stencils of the chief rays appear to converge to a common point when viewed from the object space, so that the stencil of the chief ray at the edge of the field of view of the imaging system immediately adjacent to a separate imaging system is made substantially parallel to the stencil of the chief ray at the edge of the field of view of the separate imaging system, including constraining the stencil of the chief ray at the edge of the field of view of any imaging system in the separate imaging system, and the imaging system is parallax-free. In various non-limiting embodiments, the panoramic imaging method may include, or be further characterized by, alone or in various combinations of the following mechanisms, limitations, features, steps. - Further including constraining at least 50% of the stencil of the chief ray to deviate from parallel by 20 degrees or less. - Further including using an algorithm to correct the distortion aberration in the 360-degree image formed by the imaging system.

[0014] Aspects of the present invention are methods for designing a panoramic imaging system with (substantially) no parallax. According to non-limiting embodiments, the method is to determine the overall panoramic imaging system geometry, wherein the overall panoramic imaging system includes a plurality of separate imaging systems whose respective fields of view are arranged in an array side by side such that the fields of view of adjacent imaging systems are combined, and to design the separate imaging systems such that the stencils of the chief rays at the edge of the field of view of one imaging system in a separate imaging system are substantially parallel to the stencils of the chief rays at the edge of the field of view of an adjacent imaging system in the separate imaging system, so that the stencils of the chief rays that are substantially parallel appear to converge at a common point when viewed from the object space. In various non-limiting embodiments, the panoramic imaging method may include, or may be further characterized by, the following mechanisms, limitations, features, steps, either alone or in various combinations thereof. - The overall panoramic imaging system includes a plurality of identical and separate imaging systems. - When designing the separate imaging systems, ensure that there is no physical overlap between any of the plurality of separate imaging systems. - When designing the separate imaging systems, ensure that an apparent focus point is located behind each respective image sensor of each separate imaging system.

[0015] To achieve the minimum parallax in a panoramic camera, the fields of view (FOV) of the imaging systems must not overlap. Therefore, the chief rays at the edge of the FOV must approach the optical system parallel to the chief rays at the edge of the adjacent optical system.

[0016] Figure 6 shows two aligned imaging systems without parallax. The chief rays at the edges of each system are constrained to be parallel to each other. Thus, an object located along this line is imaged at the same point in the image plane. This is an approach that can be utilized for designing individual lens elements. The fields of view do not overlap with each other. This is because the chief rays at the mixing angles are constrained to be parallel to each other and converge at a common point. The common point depends on the geometry in which the lenses are placed. In other words, the chief rays are constrained to be parallel such that when looking at the lens system from the object space, they appear to cross the optical axis at the same point. In reality, they cross the optical axis at the image sensor located in front of the virtual point, but when looking through the lens system from the object space, they appear to cross at the same point.

[0017] NP point (non-parallax point) To aid in the understanding of the previous concept, we define a term called the non-parallax point (NP point). The NP point is an abstract concept used to understand how the chief rays at the edges of the FOV can be physically made to be parallel to each other and what rules they should follow. The NP point is the point at which the chief rays at the edges of adjacent optical systems cross the optical axis when looking at the system from the object space for a panoramic imaging system without parallax.

[0018] According to the embodied invention, the NP points of each imaging system must be at the same position. That is, the light rays of adjacent optical systems must be parallel. FIG. 9 shows an imaging system where the NP point is located in front of the imaging sensor. FIG. 10 shows two imaging systems aligned such that the chief rays at the edges of the FOV of each imaging system are parallel to the other. This constraint means that the NP point must be at the same position for both systems. When the NP point is in front of the image sensor, it is impossible to align the NP points without overlapping lens elements. This system would have no parallax, but it is physically impossible to achieve. This indicates that in designing the optical system, the NP point should be behind all the elements in the imaging system so that the elements do not physically overlap each other.

[0019] FIG. 11 shows a system where the NP point is located behind the image plane. In this case, as shown in FIG. 12, it is possible to arrange a number of imaging systems so that their fields of view do not overlap. The exact position of the NP point is determined by the geometry of the lens arrangement. By arbitrarily choosing a position, that is, by arbitrarily selecting the ray height and the angle of incidence so that the chief ray appears to cross the optical axis behind the image plane, the geometry of the lens system may require hundreds of lens units to capture a complete 360-degree image. The position of the NP point must be determined after considering the geometry one wishes to use for the lenses.

[0020] Embodiments of the present invention relate to a multi-camera panoramic imaging system, in which the fields of view of adjacent imaging units are combined to form the combined field of view of the entire imaging system, as shown in the schematic of FIG. 7. Conventional panoramic imaging systems assemble the imaging units in such a way that their respective fields of view overlap, as shown in the schematic of FIG. 8, which results in parallax in the resulting image and requires correction software to stitch the images together to remove the parallax.

[0021] In this exemplary embodiment, the light rays that hit the edge of one imaging unit are constrained to be parallel to the incident light rays of the adjacent imaging unit so that both imaging systems share the same set of edge light rays. As seen in the 3D model of FIG. 13, the light rays at the edge of one imaging unit are the same as the light rays at the edge of the adjacent imaging unit. The light rays are gray lines constrained to be located along the surface of the dodecahedron edge. The gray light rays at the edge of each pentagonal lens coincide with the light rays entering the adjacent surface. All the light rays at the radius below the edge rays are located at a smaller angle of incidence so that these rays do not overlap with the rays from the adjacent system.

[0022] The embodied panoramic imaging system utilizes the aforementioned technique of designing an imaging system where the NP point is behind the image sensor and combines a number of lens systems in a dodecahedron geometry to create a 360-degree FOV camera with minimal or no parallax.

[0023] The first lens element is shaped on a regular pentagonal surface. The complete system is composed of 12 individual imaging units, each having a common NP point for light rays that are constrained to have an angle of incidence that follows the pentagon edge and satisfies the geometry specified by the dodecahedron geometry.

[0024] A dodecahedron is a polyhedron with 12 surfaces. A polyhedron is a three-dimensional solid consisting of a collection of polygons connected at the edges. Each face of the dodecahedron is a regular pentagon (a pentagon with equal-length sides). The dodecahedron has several important geometric properties that must be understood in order to design lens systems using the geometry. The properties will be discussed in turn next, after briefly discussing why the first lens must be shaped on a pentagonal surface.

[0025] By using a lens bounded by a circle as the first element in an icosahedron geometry, it is impossible to capture all the information in a 360-degree field of view using current techniques for aligning edge rays. The missing area (the shaded area in Figure 14) when the first lens is inscribed in a pentagon creates a blind spot. Since the fields of view never overlap, this information is never captured. It can be calculated that the ratio between the circular area and the pentagonal area in which the circular area is inscribed is equal to π / 5 or 62.83%. This is the maximum amount of information we can record for a 360-degree field of view around us. The blind spot created between the lens and the pentagon removes approximately 40% of the information in the 360-degree image.

[0026] The following description is intended to show the icosahedron geometry and is necessary when generating a lens system using the aforementioned NP technology and icosahedron geometry, but is not essential for generating a panoramic imaging system without parallax as embodied herein.

[0027] Characteristic 1: Diameter of the circle circumscribing a regular pentagon For each of the 12 individual lens systems, the first lens is designed to circumscribe each of the regular pentagons of the icosahedron as shown in Figure 15. The diameter of the circle circumscribing a regular pentagon is as follows. D = a / sin(36°) = 1.7013a

[0028] In the above formula, "a" is the side length of the regular pentagon. The first lens element of each system completely circumscribes each pentagon, and thus the diameter of the first lens element for each system is given as 1.7013a as shown in Figure 16.

[0029] Characteristic 2: Inscribed sphere tangent to the center of each pentagon The radius of the inscribed sphere (the tangent to each face of the icosahedron) is as follows.

Equation

[0030] Characteristic 3: Intermediate radius of the dodecahedron The intermediate radius is the point connecting the center of the dodecahedron and the midpoint of each edge. This length is given as follows.

Equation

[0031] Constraints The geometric characteristics of the dodecahedron constrain the design of the 12 lenses that embody the dodecahedron. In particular, we have the following four parameters based on the descriptions given above. 1. Diameter of the first lens element: 1.7013a 2. Distance from the first lens element to the center of the dodecahedron: 1.1135a 3. Distance from the upper end of the first lens element to the center of the dodecahedron: 1.31a 4. FOV = 37.3777 degrees Given any two of the first three constraints, it follows that the angle between the optical axis of the lens and the upper end of the first lens element is 37.3777 degrees (see FIG. 19). tan -1 ((1.7013 / 2) / 1.1135) - 37.377° We desire that this angle of 37.37 degrees be the field of view of the lens. This ensures that the NP point, i.e., the point at which the chief ray of the mix (the mix angle being the full FOV) intersects the optical axis in object space, is located at the center of the dodecahedron. All other constraints ensure that the lens element is located in front of the NP point and that the element lies within the 31.717-degree half-angle cone of light.

[0032] Diameter of other lens elements and sensors Given the four constraints provided above, we can determine what the size of each lens element after the first lens element must be in order to fit within the dodecahedron geometry. For any lens or sensor element to fit within the dodecahedron, it must lie within the 31.717-degree cone of light that starts at the center of the dodecahedron and touches the diameter of the first lens element. As the distance from the first lens element increases, the diameter of the preceding lens element decreases proportionally (see Figure 20).

[0033] The maximum overall diameter of any lens element or sensor preceding the first lens element must geometrically be less than or equal to (1.1135a - D) / tan(31.716 degrees). In this formula, D is the distance of that element from the first lens element. *

[0034] Therefore, here we have five constraints that ensure this lens system conforms to the dodecahedron geometry and enables 360-degree imaging. 1. Diameter of the first lens element: 1.3763a. 2. Distance from the first lens element to the center of the dodecahedron: 1.1135a. 3. Distance from the top of the first lens element to the center of the dodecahedron: 1.31a. 4. FOV = 37.377 degrees 5. φ Li < (1.1135a - D LI、Li ) tan(31.717°) In this formula, φ Li is the distance D LI、Li ​Any which is separated from the first lens element by the diameter of the lens element. Assuming that all lenses are given the five constraints described above so that they fall within a 31.717-degree cone of light emerging from the center of the dodecahedron, it is possible to construct a lens system without parallax.

[0035] System design The geometry for the lenses was selected. Platonic solids have the property that they are composed of many solids of equal geometry and volume. For a system that images 360 degrees, this allows a composite imaging system to be made from the same replicated lens design. The dodecahedron geometry was selected because it is approximately spherical in its geometry.

[0036] In order for the edge rays of one imaging unit to be positioned parallel to the edge rays of an adjacent unit, they must be incident at the same angle. The angle shared by both imaging units is the angle of the dodecahedron edge face. At the center of the edge face, the angle with respect to the center of the dodecahedron center is 31.717 degrees, as shown in FIG. 21. At the corner of the edge face, the angle with respect to the center of the dodecahedron center is 37.377 degrees, as shown in FIG. 22.

[0037] To match the rays along adjacent imaging units, the first lens of the imaging unit is cut into a pentagon that coincides with the surface of the dodecahedron. At the center of the edge, the rays hitting the surface are incident at an angle of incidence of 31.717 degrees. At the corner of the edge, the angle of incidence of the incident rays is 37.377 degrees. At all points along the edge of the lens, the angle of incidence of the incident rays is made to coincide with the geometry of the dodecahedron surface.

[0038] The incident angles for 37 rays along the edge of the pentagonal lens were calculated using trigonometry, knowing the distance from the center of the dodecahedron to the center of the pentagonal face and the distance from the center of the dodecahedron to the edge points of the problem as shown in FIGS. 21 and 22. The height of each ray was constrained to be located along the pentagonal edge. For example, using a radius of 120 mm showing the circumcircle of surface 1, the ray at point 1 has a height of 48.54 mm and an incident angle of 31.717 degrees. The ray at point 37 has a height of 60 mm and an incident angle of 37.377 degrees. Table I shows the ray height and incident angle values for 37 points from point 1 to point 36 in FIG. 23.

[0039] [Table 1]

[0040] A diagram showing the ray constraints is shown in FIG. 24. Ray 1 has a height of 48.54 mm and an incident angle of 31.717 degrees. Ray 1 is the ray passing through point 1 in FIG. 24. Ray 2 has a height of 60 mm and an incident angle of 37.377 degrees and is the ray passing through point 37 in FIG. 24. All 37 rays are constrained by the ray heights and angles specified in the above table. Constrained in this way, all rays enter the lens at the same angle as the surface of the dodecahedron. Looking at those same rays in another way, we can see that the rays are properly constrained to the pentagonal geometry at the correct incident angles as shown in FIGS. 25 and 26.

[0041] [Appendix 1] A method for forming a panoramic image, providing a panoramic imaging system arranged in an array of a plurality of separate imaging systems arranged side by side, each of said separate imaging systems being characterized by a field of view, Constraining a plurality of principal rays that strike along an edge of the field of view of each of the separate imaging systems so that all of the principal rays appear to converge to a common point when viewed from the object space, and so that the fields of view in each of the plurality of separate imaging systems are combined but do not overlap with the field of view of the immediately adjacent imaging system in the separate imaging systems, to be substantially parallel to another plurality of principal rays that strike along an adjacent edge of the field of view of the immediately adjacent imaging system in the separate imaging systems; A method comprising. [Appendix 2] Further comprising constraining at least 50% of the principal rays that strike along an adjacent edge of the field of view of the adjacent separate imaging systems so as to deviate from parallel by 20 degrees or less. The method according to Appendix 1. [Appendix 3] Each of the separate imaging systems shares the same set of principal rays as the immediately adjacent imaging system in the separate imaging systems. The method according to Appendix 1. [Appendix 4] Each of the plurality of separate imaging systems is identical. The method according to Appendix 1. [Appendix 5] The step of providing the panoramic imaging system comprises Configuring the array arranged in a three-dimensional geometric shape having a center; Configuring each of the plurality of separate imaging systems with a front lens having a plurality of edges, the plurality of edges defining a plurality of edge surface angles at points along the edges with respect to the center of the three-dimensional geometric shape and an intermediate point of the front lens; Configuring each edge in the plurality of edges so as to be adjacent to an adjacent edge in an adjacent front lens; Including The step of constraining the plurality of chief rays that strike along the field of view includes the step of making the angle of incidence at each of the plurality of chief rays along the edge coincide with the edge plane angle along the adjacent edge. The method according to appendix 1. [Appendix 6] The three-dimensional shape is a dodecahedron, the front lens in each of the separate imaging systems is configured to have a pentagonal shape, the edge of the pentagonal shape has a length a, the diameter of the circle circumscribing the pentagonal shape is equal to a / sin(36°)=1.7013a, and the radius of the sphere inscribed within the dodecahedron is [Number] equal to, and the distance from the center of the dodecahedron to the midpoint at the edge of the front lens is [Number] equal to The method according to appendix 5. [Appendix 7] A multi-camera panoramic imaging system, a plurality of separate imaging systems characterized by a field of view and arranged in an array, wherein the fields of view in each of the separate imaging systems are combined but do not overlap with the fields of view of each adjacent separate imaging system, and all of the chief rays appear to converge to a common point when viewed from the object space. Each of the separate imaging systems including a front lens is configured to constrain the plurality of chief rays that strike along the edge of the field of view of any imaging system in the separate imaging system to be substantially parallel to another plurality of chief rays that strike along the adjacent edge of the field of view of the imaging system immediately adjacent to the separate imaging system. A multi-camera panoramic imaging system. [Appendix 8] At least 50% of the chief rays that strike along adjacent edges of the fields of view of adjacent separate imaging systems deviate from parallel by 20 degrees or less. The multi-camera panoramic imaging system according to appendix 7. [Appendix 9] Each of the separate imaging systems includes an image sensor, and further, the common point is located behind the image sensor. The multi-camera panoramic imaging system according to appendix 7. [Appendix 10] The arranged array forms a three-dimensional geometric shape having a center, and each of the front lenses in the separate imaging systems has a plurality of edges that define a plurality of edge surface angles at points along the edge with respect to the center of the three-dimensional geometric shape and an intermediate point of the front lens, and each of the edges in the plurality of edges is configured to be adjacent to an adjacent edge in an adjacent front lens, and the plurality of edge surface angles along the edge in each of the plurality of edges coincide with the incident angles in each of the plurality of chief rays along the adjacent edge in the adjacent front lens. The multi-camera panoramic imaging system according to appendix 7. [Appendix 11] The three-dimensional shape is a dodecahedron, and each of the front lenses in the separate imaging systems is configured to have a pentagonal shape, the edge of the pentagonal shape has a length a, the diameter of the circle circumscribing the pentagonal shape is equal to a / sin(36°)=1.7013a, and the radius of the sphere inscribed in the dodecahedron is

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Claims

Claim 1 A method for generating polygonal and conical fields of view in an imaging system, comprising the following steps: Providing an outer lens element having a polygonal shape with a plurality of edges, each of the edges having a plurality of edge surface angles with respect to the optical axis of the imaging system; Configuring the imaging system to provide polygonal and conical fields of view that match the plurality of edge surface angles along the edges of the outer lens element, and to limit a plurality of chief rays to form the polygonal and conical fields of view, and corresponding to the polygonal shape and the plurality of edge surface angles of the outer lens element; A method characterized by comprising the above. Claim 2 The method according to claim 1, further comprising the step of cutting the outer lens element into the polygonal shape. Claim 3 The step of configuring the imaging system includes applying a plurality of constraint conditions for both the height and the ray angle of the rays along the plurality of edges in order to match the field of view of the imaging system with the polygonal shape of the outer lens element and the plurality of edge surface angles along the edges of the outer lens element. The method according to claim 1. Claim 4 The method according to claim 1, wherein the polygonal shape is a pentagon. Claim 5 The method according to claim 1, wherein the angular half-width of the polygonal field of view is from about 31 degrees to about 37 degrees. Claim 6 The method according to claim 1, further comprising the step of forming an image having a polygonal shape on the image plane using the polygonal and conical fields of view. Claim 7 An imaging system, comprising an outer lens element having a polygonal shape with a plurality of edges, each of the edges having a plurality of edge surface angles with respect to the optical axis of the imaging system, the imaging system being configured to provide polygonal and conical fields of view that match the plurality of edge surface angles, the imaging system forming polygonal and conical fields of view and being constrained to have a plurality of chief rays corresponding to the polygonal shape and the plurality of edge surface angles of the outer lens element. An imaging system characterized by the above. Claim 8 The imaging system according to claim 7, wherein the imaging system is configured to match the field of view of the imaging system with the polygonal shape of the outer lens element and the plurality of edge surface angles along the edges of the outer lens element. Claim 9 The imaging system according to claim 7, configured to apply a plurality of constraint conditions for both the ray height and the ray angle along the plurality of edges in order to match the field of view of the imaging system to the polygonal shape of the outer lens element and the plurality of edge surface angles along the edge of the outer lens element.

10. The imaging system according to claim 7, wherein the angular half-width of the field of view is from about 31 degrees to about 37 degrees.

11. The imaging system according to claim 7, wherein the polygonal shape is a pentagon.

12. The imaging system according to claim 7, wherein the field of view is projected toward an NP point located behind the focal plane of the imaging system.

13. A multi-camera imaging system comprising a first imaging system and a second imaging system arranged adjacent to each other, wherein each of the first and second imaging systems includes an outer lens element having a polygonal shape with a plurality of sides, each side having a plurality of edge surface angles with respect to the optical axes of the first and second imaging systems, and is configured to provide a polygonal and conical field of view, and the polygonal and conical field of view of the first imaging system merges with the polygonal and conical field of view of the second imaging system along one side to form a composite image with minimal or no parallax. A multi-camera imaging system characterized by this.

14. Each of the first imaging system and the second imaging system applies a plurality of constraints for both the height and the angle of the light rays along a plurality of sides, and is configured to match the field of view of the first imaging system and the field of view of the second imaging system to the polygonal shape of the outer lens element and the plurality of edge surface angles along the sides of the outer lens element. The multi-camera imaging system according to claim 13.

15. Each of the first imaging system and the second imaging system is configured to form the polygonal and conical field of view and is constrained to have a plurality of chief rays corresponding to the polygonal shape and the plurality of edge surface angles of the outer lens element. The multi-camera imaging system according to claim 13.

16. The plurality of chief rays from the first imaging system and the second imaging system appear to converge toward a common NP point when viewed from the object space. The multi-camera imaging system according to claim 13.

17. The multi-camera imaging system according to claim 13, wherein the polygonal shape of the outer lens element is a pentagon. **Claim 18** The multi-camera imaging system according to claim 13, wherein the angular half-width of the polygonal field of view is from about 31 degrees to about 37 degrees.

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