HK1234932B - Imaging system and method - Google Patents

Description

Imaging systems and methods

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to 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.

Technical Field

Various embodiments and aspects of the present invention generally relate generally to optical imaging systems, methods related thereto, and applications thereof; more specifically, to panoramic optical imaging systems, methods related thereto, and applications thereof; and most specifically, to panoramic optical imaging systems with zero parallax or substantially no parallax, methods related thereto, and applications thereof.

Background Art

Current parallax-free 360-degree systems use an arrangement of mirrors to scan images and are limited to an imaging speed of 10 frames per second (fps). Google uses a 360-degree camera with a refractive lens developed by Immersive Media to capture photos for its Street View software. These photos must be post-processed and corrected for parallax, which is time-consuming and reduces Google's ability to expand its Street View initiative. Fisheye lenses provide wide-angle imaging, but at the cost of high distortion. Distortion is a physical result of mapping a large spherical object onto a small, flat image plane.

Several companies have developed optical systems to simplify the process of capturing panoramic images. Instead of rotating the camera to take multiple shots, multiple cameras are used to image different parts of the scene, capturing all of them simultaneously. Immersive Media and Greypoint Imaging have developed single-shot 360-degree cameras, available at price points ranging from $10,000 to $100,000. Both companies have developed software to automatically correct for artifacts (parallax) in the images and provide better resolution than a panorama captured by a single camera (e.g., an iPhone camera). However, the software isn't perfect, and many artifacts still exist in the images. For example, Google had a person carry a Dodeca 360 camera (provided by Immersive Media) around the Grand Canyon and had to hire programmers to correct the images frame by frame for artifacts caused by parallax.

Parallax and chief rays in optical systems

Parallax is defined as “the effect whereby the position or orientation of an object appears different when viewed from different positions (such as through a viewfinder and a camera’s lens).” Parallax results from stitching together images from multiple cameras, each with its own unique perspective of the outside world.

1 , the chief ray of an optical system is a meridional ray that starts at the edge of the object, intersects 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.

Chief rays play a key role in the parallax produced by stitching together multiple images. Figure 2 illustrates two optical systems (cameras) side by side. For the lens unit on the top, the square, triangle, and rectangle are mapped to the same point in the image, while for the lens unit on the bottom, they are mapped to three different points, as shown. In the top imaging system, they are imaged by the same chief ray, while for the bottom imaging system, they are imaged by three different chief rays. When the two images in Figure 3 are combined, parallax will occur, resulting in the image shown in Figure 4.

The search for an algorithm that can correct for parallax has been ongoing for many years. Numerous approaches have been proposed, but even with the most sophisticated algorithms to date, artifacts remain in panoramic images. Sometimes, this isn't a problem, as software engineers can be hired to repair the images frame by frame; however, for the average consumer, this option of correcting each image is not feasible. A better approach to effectively correcting parallax is needed before such a system can be made available to the consumer market. It would be preferable to address the problem of reducing parallax in images optically, rather than computationally.

Current designs created for single-shot panoramic imaging suffer from parallax because they are created from imaging systems with overlapping fields of view. Figure 5 is taken from U.S. Patent 2,696,758. This figure illustrates how parallax arises in currently available 360-degree imaging systems. The fields of view overlap, and a triangle appearing at the edge of the FOV of the bottom lens system will appear at approximately 0.707 times the FOV in the top imaging system. Thus, the triangle is mapped to a different image point for each camera. At the bottom, it is mapped to the full FOV (the edge of the image).

Thus, the inventors have recognized the advantages and benefits of a panoramic imaging system and associated methods that are parallax-free and eliminate parallax optically rather than through post-processing software. Such a system would have various applications, including: providing a scalable way to map planetary streets; allowing the creation of virtual tours of both cities and private institutions; high frame rate video surveillance; military applications including drones and tank technology; and an alternative to fish-eye lenses that provide wide-angle imaging at the expense of high distortion.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 illustrates the chief ray of an optical system. The chief ray defines the height of the object and the height of the image.

Figure 2 illustrates why parallax occurs when using multiple refractive imaging systems to capture images of a scene. In the top lens unit, three objects are mapped to the same image point; in the bottom lens unit, they are mapped to three separate image points.

FIG3 (left) illustrates the image formed by the top lens unit in FIG2, while the image on the right is formed by the bottom lens unit.

FIG. 4 shows the image that would result from combining the two images in FIG. 3 .

Figure 5 illustrates how parallax occurs in currently designed cameras. The fields of view overlap, and a triangle appearing at the edge of the FOV in the bottom lens system will appear at approximately 0.707 times the FOV in the top imaging system. Consequently, this triangle is mapped to a different image point for each camera. In the bottom camera, it is mapped to the full FOV (the edge of the image).

Figure 6 illustrates two side-by-side imaging systems with no parallax. The principal rays at the edge of each system are constrained to be parallel to each other. Thus, objects located along this line are imaged to the same point in the image plane.

FIG. 7 illustrates the location of the no-parallax (NP) point (as defined below) for the two imaging systems shown.

Figure 8 shows that the principal rays at the edge of the FOV are not parallel, so the NP points are located at different positions.

FIG9 illustrates an imaging system with an NP point located in front of the image sensor.

FIG10 illustrates two imaging systems aligned so that the chief rays at the edge of each FOV are parallel to each other.

FIG11 shows an imaging system with an NP point behind the image plane.

FIG12 shows a multi-unit imaging system with co-located NP dots.

FIG13 shows a 3-dimensional representation of a 360 degree lens system with edge rays constrained to be along each dodecahedron face.

Figure 14 shows a circle inscribed in a pentagon, illustrating the blind spot that would result if the lens were round rather than pentagonal.

Figure 15 shows the first lens element of each system, initially designed as a circumscribed regular pentagon.

Figure 16: The diameter of the first lens element is limited to 1.7013a, where a is the side length of a regular pentagon.

Figure 17: The distance from the center of the first lens element to the center of the dodecahedron (NP point) is 1.1135a, where a is the side length of the pentagon.

Figure 18: The distance from the top of a pentagonal face to the NP is limited to 1.31a, where a is the side length of a regular pentagon. Here, the NP is the center of the dodecahedron.

Figure 19: A simplified diagram illustrating the constraints imposed on the first lens element relative to the center of a dodecahedron. "a" is the side length of each regular pentagon in the dodecahedron.

Figure 20: A simplified diagram illustrating that the maximum length of any element is constrained to fit within the 31.717 degree half-angle cone of light emanating from the center of the dodecahedron.

Figure 21: A three-dimensional representation of 1/12 of a dodecahedron and the angle between the center of the dodecahedron and the center of the pentagonal edge.

Figure 22: A three-dimensional representation of 1/12 of a dodecahedron and the angles between the center of the dodecahedron and the edges of the pentagonal sides.

Figure 23: Pentagonal shaped lens element showing the height to Ray 1 and Ray 37.

Figure 24: Zemax plot of the current lens design, showing ray 1 and ray 37 in the model.

Figure 25: 3D Zemax plot of the current lens design from the rear view.

Figure 26: 3D Zemax plot from the side view.

Summary of the Invention

One aspect of the present invention is a multi-camera panoramic imaging system with no parallax. According to a non-limiting embodiment, the multi-camera panoramic imaging system includes a plurality of discrete imaging systems arranged in a side-by-side array, wherein the field of view of each discrete imaging system is connected to the field of view of each adjacent discrete imaging system, and further wherein the chief ray template at the edge of the field of view of any discrete imaging system in the discrete imaging systems will be substantially parallel to the chief ray template at the edge of the field of view of any adjacent discrete imaging system in the discrete imaging systems, such that all substantially parallel chief ray templates appear to converge to a common point when viewed from object space. In various non-limiting embodiments, the multi-camera panoramic imaging system may include or be further characterized by the following features, limitations, characteristics, either alone or in various combinations thereof:

-comprising multiple identical discrete imaging systems;

- wherein at least 50% of the main ray template deviates from parallel by 20 degrees or less;

- wherein each of the separate imaging systems comprises an image sensor, further wherein the apparent convergence point is located behind the image sensor of each of the separate imaging systems; - wherein none of the separate imaging systems physically overlap;

- wherein the system has a dodecahedral geometry, further wherein the system is characterized by a 360 degree FOV;

- wherein the front lens of each of the discrete imaging systems is part of a single continuous freeform optical device;

- wherein each image sensor is a wavefront sensor;

- wherein each of the separate imaging systems has a curved image plane so as to match the distortion and Petzval curvature of the imaging system.

One aspect of the invention is a method for forming an image of an object without parallax. According to a non-limiting embodiment, the method includes: providing a panoramic imaging system, wherein the panoramic imaging system includes a plurality of discrete imaging systems, each discrete imaging system being characterized by a field of view; and constraining a chief ray template at an edge of the field of view of each of the discrete imaging systems to be substantially parallel to a chief ray template at an edge of the field of view of an immediately adjacent one of the discrete imaging systems, such that all parallel chief ray templates appear to converge to a common point when viewed from object space, wherein the imaging system is parallax-free. In various non-limiting embodiments, the panoramic imaging method may include or be further characterized by the following features, limitations, characteristics, steps, either alone or in various combinations thereof:

- further comprising constraining at least 50% of the main ray template to deviate from parallel by 20 degrees or less;

- Further comprising: using an algorithm to correct distortion aberrations in the continuous 360-degree images formed by the imaging system.

One aspect of the invention is a method for designing a (substantially) parallax-free panoramic imaging system. According to a non-limiting embodiment, the method includes: determining an overall panoramic imaging system geometry, wherein the overall panoramic imaging system includes a plurality of discrete imaging systems with corresponding fields of view, the discrete imaging systems being arranged in a side-by-side array such that the fields of view of adjacent imaging systems are connected; designing the discrete imaging systems such that a chief ray template at an edge of the field of view of each of the discrete imaging systems will be substantially parallel to a chief ray template at an edge of the field of view of an adjacent one of the discrete imaging systems, such that the substantially parallel chief ray templates appear to converge to a common point when viewed from object space. In various non-limiting embodiments, the panoramic imaging method may include or be further characterized by the following features, limitations, characteristics, steps, either individually or in various combinations thereof:

- wherein the overall panoramic imaging system comprises a plurality of identical discrete imaging systems;

- wherein, when designing the discrete imaging systems, it is ensured that there is no physical overlap between any discrete imaging systems in the plurality of discrete imaging systems;

- wherein, when designing these separate imaging systems, it is ensured that the apparent convergence point is located behind the corresponding image sensor of each separate imaging system.

DETAILED DESCRIPTION

For panoramic cameras to achieve minimal parallax, the fields of view (FOVs) of the imaging systems must not overlap. Thus, the chief rays at the edges of the FOVs must be close to the optical system parallel to the chief rays at the edges of the adjacent optical system.

Figure 6 illustrates two side-by-side imaging systems without parallax. The chief rays at the edge of each system are constrained to be parallel to each other. Thus, objects located along this line are imaged to the same point in the image plane. This is an approach that can be used to design individual lens elements. The fields of view do not overlap because the chief rays at the blend angle are constrained to be parallel to each other and converge to a common point. This common point will depend on the geometry of the lens package. In other words, the chief rays are constrained to be parallel so that they appear to intersect the optical axis at the same point when the lens system is viewed from object space. In reality, they intersect the optical axis at the image sensor, which is located in front of this imaginary point, but from object space looking towards the lens system, they appear to intersect at the same point.

NP point (no parallax point)

To help understand the aforementioned concepts, we define the term "parallax-free point" (NP point). The NP point is an abstraction used to understand how the principal rays at the edge of the FOV can be physically made parallel to each other and what rules they should obey. The NP point is the point where, for a parallax-free panoramic imaging system, the principal rays at the edge of the adjacent optical system intersect the optical axis when the system is viewed from object space.

According to the embodied invention, the NP point of each imaging system must be located at the same position. That is, the light rays of adjacent optical systems must be parallel. Figure 9 shows an imaging system with an NP point located in front of the imaging sensor. Figure 10 illustrates two imaging systems that are aligned so that the main rays at the edge of the FOV of each are parallel to each other. This restriction means that for both systems, the NP point must be at the same position. When the NP point is in front of the image sensor, it is impossible to align the NP point without overlapping the lens elements. This system will not have any parallax, but it is physically impossible to achieve. This shows that when designing the optical system, the NP point should be located behind all elements in the imaging system so that no elements physically overlap with each other.

Figure 11 illustrates a system in which the NP is located behind the image plane. When this is the case, multiple imaging systems can be arranged so that the fields of view do not overlap, as shown in Figure 12. The exact location of the NP will be determined by the geometry of the lens arrangement. By arbitrarily selecting the position—that is, arbitrarily choosing the ray height and angle of incidence so that the chief ray appears to intersect the optical axis behind the image plane—the geometry of the lens system may require hundreds of lens elements to capture a full 360-degree image. The NP location must be determined after considering the desired lens geometry.

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 a composite field of view of the entire imaging system, as illustrated in the schematic diagram of FIG7 . Conventional panoramic imaging systems place imaging units together in such a way that their corresponding fields of view coincide, as illustrated in the schematic diagram of FIG8 , which results in parallax in the resulting images and requires correction software to stitch the images together to eliminate the parallax.

In this exemplary embodiment, light rays incident along the edge of one imaging unit are constrained to be parallel to the incident rays of the adjacent imaging unit, allowing both imaging systems to share the same set of edge rays. As shown in the 3D model in Figure 13, the light rays at the edge of one imaging unit are identical to those at the edge of the adjacent imaging unit. These rays are the gray lines confined to the surface along the edges of the dodecahedron. The gray lines at the edge of each pentagonal lens correspond to the light rays entering its adjacent surface. All light rays at radii below the edge rays have smaller angles of incidence, preventing them from overlapping with light rays from the adjacent system.

The embodied panoramic imaging system utilizes the aforementioned technology of designing the imaging system with an NP point located behind the image sensor, and combines multiple lens systems in a dodecahedron geometry to create a 360-degree FOV with minimal or no parallax.

The first lens element will be shaped as the surface of a regular pentagon. The complete system will consist of 12 discrete imaging units, each with a common NP for light rays along the edges of the pentagon and constrained to have angles of incidence that satisfy the geometry specified by the geometry of the dodecahedron.

The dodecahedron is a polyhedron with 12 faces. A polyhedron is a three-dimensional cube composed of a collection of polygons joined at its edges. Each side 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 that utilize this geometry. After briefly discussing why the first lens must be formed with pentagonal faces, these properties will be discussed in turn.

By using a circularly edged lens as the first element in the dodecahedron geometry, it's impossible to capture all the information within the 360-degree field of view using current edge-ray alignment techniques. The missing area created by the first lens inscribed within the pentagon (the shaded area in Figure 14) creates a blind spot. Since the fields of view never overlap, this information is never captured. It can be calculated that the ratio of the area of the circle to the area of the pentagon it inscribes is equal to π/5, or 62.83%. This is the maximum amount of information we can record for the 360-degree field of view around us. The blind spot created between the lens and the pentagon removes nearly 40% of the information in the 360-degree image.

The following description is intended to illustrate the geometry of the dodecahedron and is necessary when creating a lens system utilizing the aforementioned NP technology and the dodecahedron geometry, but is not necessary for the purpose of creating the parallax-free panoramic imaging system embodied herein.

Property 1: The diameter of the circle circumscribing a regular pentagon

For each of these 12 individual lens systems, the first lens will be designed so that it circumscribes each of the regular pentagons of the dodecahedron shown in Figure 15. The diameter of the circle circumscribing the regular pentagon is:

D＝a/sin(36°)＝1.7013a

In the above equation, "a" is the side length of a regular pentagon. The first lens element of each system will completely circumscribe each pentagon, and therefore the diameter of the first lens element of each system is given as 1.7013a, as illustrated in Figure 16.

Property 2: An inscribed sphere touching the center of each pentagon

The radius of the inscribed sphere (tangent to each of the faces of the dodecahedron) is:

This radius is the distance from the center of the dodecahedron (which will be the NP point for each lens in this design) and the center of the pentagonal face (coinciding with the center (optical axis) of the first lens element in the system occupying this pentagon). This point is located at the center of each pentagonal face. The length between the NP point and the dodecahedron center is limited to 1.1135a, where a is the length of one of the pentagonal sides, as illustrated in Figure 17.

Property 3: Median radius of a dodecahedron

The median radius is the point connecting the center of the dodecahedron to the middle of each edge. This length is given by:

This equation limits the distance between the top of the pentagonal face and the NP point, as shown in Figure 18. Limit

The geometric properties of the dodecahedron constrain the design of the 12 lenses that will materialize the dodecahedron. Specifically, based on the description given above, we have the following four parameters:

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 top 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, we get the angle between the optical axis of the lens and the top of the first lens element to be 37.3777 degrees (see Figure 19):

tan ^-1 ((1.7013/2)/1.1135)-37.377°.

We want this 37.37 degree angle to be the field of view of the lens. This will ensure that the NP point is at the center of the dodecahedron, which is the point where the chief rays of the blend (the blend angle is the full FOV) intersect the optical axis in object space. All other restrictions will ensure that the lens elements are located in front of the NP point and that the elements fall within the 31.717 degree half-angle light cone.

Diameters of other lens elements and sensors

Using the four constraints given above, we know what size each lens element after the first must be in order to fit within the dodecahedron geometry. In order for the lens elements to fit, any lens and sensor element must fit within a 31.717-degree cone of light that begins at the center of the dodecahedron and is tangent to the diameter of the first lens element. As the distance from the first lens element increases, the diameter of the lens elements decreases proportionally (see Figure 20).

It can be found that the maximum diameter of any lens element or sensor before the first lens element is geometrically less than or equal to (1.1135a-D)*tan(31.716 degrees), where D is the distance of this element from the first lens element.

Thus, we now have five constraints that will allow this lens system to fit into the geometry of the dodecahedron and allow 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.

Where is the diameter of any lens element separated from the first lens element by a distance DL1 _,Li . Given the above five constraints, a parallax-free lens system can be constructed if all lenses are designed so that they fall within a 31.717 degree light cone emanating from the center of the dodecahedron.

System Design

The geometry of these lenses was chosen. Ideal cubes have the property that they are constructed from many cubes of equal geometry and volume. For 360-degree imaging systems, this allows for the creation of a composite imaging system with identical, repeating lens designs. The dodecahedron geometry was chosen because it approximates a sphere in its geometry.

In order for the edge rays of one imaging element to be parallel to those of the adjacent element, they must enter at the same angle. The angle shared by these two imaging elements is the angle of the edge surface of the dodecahedron. At the center of the edge surface, the angle relative to the center of the dodecahedron is 31.717 degrees, as illustrated in Figure 21. At the corners of the edge surface, the angle relative to the center of the dodecahedron is 37.377 degrees, as illustrated in Figure 22.

To align light rays along adjacent imaging units, the first lens of each imaging unit is cut into a pentagonal shape to match the surface of a dodecahedron. At the center of the edge, light rays incident along the surface enter at an angle of incidence of 31.717 degrees. At the corners of the edge, the angle of incidence of the incoming light rays is 37.377 degrees. At all points along the lens edge, the angle of incidence of the incoming light rays matches the geometry of the dodecahedron surface.

Knowing the distance from the center of the dodecahedron to the center of the pentagonal face, and knowing the distance from the center of the dodecahedron to the edge points discussed as shown in Figures 21 and 22, trigonometric functions are used to calculate the angles of incidence of the 37 light rays along the edge of the pentagonal lens. The height of each ray is constrained to be along the pentagonal side. For example, using a radius of 120 mm for the circumscribed circle describing surface 1, the ray at point 1 has a height of 48.54 mm and an angle of incidence of 31.717 degrees. The ray at point 37 has a height of 60 mm and an angle of incidence of 37.377 degrees. Table 1 describes the ray heights and angles of incidence for the 37 points between points 1 and 36 in Figure 23.

Table I

(The data shows a limit of 37 rays along the edge of the first lens)

A simplified diagram illustrating these ray constraints is shown in Figure 24. Ray 1 has a height of 48.54 mm and an angle of incidence of 31.717 degrees. Ray 1 is the ray that passes through point 1 in Figure 24. Ray 2 has a height of 60 mm and an angle of incidence of 37.377 degrees and is the ray that passes through point 37 in Figure 24. All 37 rays are constrained by the ray heights and angles specified in the table above. Constrained in this way, all rays enter the lens at the same angle as the surfaces of the dodecahedron. Looking at those same rays another way, we can see that the rays are properly confined to the pentagonal geometry at the correct angles of incidence, as illustrated in Figures 25 and 26.

Claims (14)

1. A method for forming a panoramic image, the method comprising: A panoramic imaging system is provided, the panoramic imaging system having multiple discrete imaging systems arranged in a side-by-side array, each of the discrete imaging systems being characterized by a field of view; and Multiple principal rays illuminating along the field of view edge of each of the discrete imaging systems are restricted to be substantially parallel to additional principal rays illuminating along the adjacent edge of the field of view of the next adjacent discrete imaging system. This makes all principal rays illuminating along the field of view edge of the discrete imaging systems appear to converge to a common point when viewed from object space, and the field of view of each of the multiple discrete imaging systems is connected to but does not overlap with the field of view of the next adjacent discrete imaging system. 2. The method of claim 1, further comprising: limiting at least 50% of the principal rays illuminating along adjacent edges of the field of view of adjacent discrete imaging systems to a deviation from parallelism by 20 degrees or less. 3. The method of claim 1, wherein each of the discrete imaging systems shares the same set of principal rays illuminating along the edge of the field of view with the discrete imaging system immediately adjacent to it. 4. The method of claim 1, wherein each of the plurality of discrete imaging systems is identical. 5. The method of claim 1, wherein the step of providing the panoramic imaging system comprises: The side-by-side array is configured into a three-dimensional geometry with a center. Each of the plurality of discrete imaging systems is configured 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 relative to the center of the three-dimensional geometry and the midpoint of the front lens. Each of the plurality of edges is configured to be adjacent to an adjacent edge in the adjacent front lens, and The step of limiting the plurality of principal rays illuminating along the edge of the field of view includes matching the angle of incidence of each of the plurality of principal rays along the edge to the edge surface angle along the adjacent edge. 6. The method of claim 5, wherein the three-dimensional shape is a dodecahedron, and the front lens in each of the discrete imaging systems is configured to have a pentagonal shape, wherein the edge of the pentagonal shape has a length a, the diameter of the circle circumscribed in the pentagonal shape is equal to a/sin(36°) = 1.7013a, and the diameter of the sphere inscribed in the dodecahedron is equal to: And the distance from the center of the dodecahedron to the midpoint of the edge of the front lens is equal to 7. A multi-camera panoramic imaging system, comprising: Multiple discrete imaging systems, characterized by their fields of view and arranged in a side-by-side array, wherein the field of view of each discrete imaging system is connected to but does not overlap with the field of view of each adjacent discrete imaging system, and each discrete imaging system includes a front lens configured to limit multiple principal rays illuminating along the edge of the field of view of any one of the discrete imaging systems to be substantially parallel to additional principal rays illuminating along the adjacent edge of the field of view of an adjacent discrete imaging system, such that when viewed from object space, all principal rays illuminating along the edge of the field of view of each of the discrete imaging systems appear to converge to a common point. 8. The multi-camera panoramic imaging system of claim 7, wherein at least 50% of the principal rays irradiated along adjacent edges of the field of view of adjacent discrete imaging systems deviate from parallel by 20 degrees or less. 9. The multi-camera panoramic imaging system of claim 7, wherein the side-by-side array forms a three-dimensional geometry with a center, the front lens in each of the discrete imaging systems has a plurality of edges, the plurality of edges defining a plurality of edge surface angles at points along the edges relative to the center of the three-dimensional geometry and the midpoint of the front lens, each of the plurality of edges being configured to be adjacent to an adjacent edge in an adjacent front lens, and the plurality of edge surface angles along the edges of each of the plurality of edges matching the incident angle of each of the plurality of principal rays along the adjacent edge in the adjacent front lens. 10. The multi-camera panoramic imaging system as described in claim 9, Wherein, the three-dimensional shape is a dodecahedron, and the front lens in each of the discrete imaging systems is configured to have a pentagonal shape, wherein the edge of the pentagonal shape has a length 'a', the diameter of the circle circumscribed in the pentagonal shape is equal to a/sin(36°) = 1.7013a, and the diameter of the sphere inscribed in the dodecahedron is equal to: And the distance from the center of the dodecahedron to the midpoint of the edge of the front lens is equal to 11. The multi-camera panoramic imaging system of claim 7, wherein the front lens of each discrete imaging system in the discrete imaging system is part of a single continuous freeform optical device. 12. The multi-camera panoramic imaging system of claim 7, wherein each of the discrete imaging systems has a curved image plane to match the distortion and petzvar curvature of the imaging system. 13. The multi-camera panoramic imaging system of claim 7, wherein each of the discrete imaging systems includes an image sensor, and further wherein the common point is located behind the image sensor. 14. The multi-camera panoramic imaging system of claim 13, wherein the image sensor is a wavefront sensor.