Wednesday, July 31, 2019
Looking At The Term Omnidirectional Imaging Film Studies Essay
First, allow ââ¬Ës specify the term ââ¬â ââ¬Å" omnidirectional â⬠. The term ââ¬Å" omnidirectional â⬠is derives from a prefix ââ¬Å" omni â⬠which forms the significance ââ¬Å" all â⬠or ââ¬Å" every â⬠while ââ¬Å" directional â⬠is bespeaking a way in infinite. Hence, this term ââ¬Å" omnidirectional â⬠implies an equal sensitiveness in all directional. Normally, this term is widely used in the telecommunications field such as omnidirectional mike which is a device that can pick up sound from all around it. Other than this, an omnidirectional aerial can direct or have signals every bit good in all waies and a VHF omnidirectional scope ( VOR ) is used as a wireless pilotage system for aircraft. Due to the advancing of the engineering, the use has been expanded to other field of designs. For illustration, an omnidirectional treadmill is used as a treadmill that allows a individual to walk in any way without traveling. Besides this, there is a specially design wheel that allows motion in any way and normally use into automatons which is called Mecanum Wheel. In picture taking, an omnidirectional camera is a camera that can see all 360 grades around it. All of these executions have referred to the impression of bing in every way. Omnidirectional imagination shows a 360 grades ocular position which has a similar construct with an omnidirectional camera. This sort of imagination is of import in several countries such as security force. The security force applies this construct as a ocular surveillance which can cut down the offense rates and increase the safety of the populace as shown in Figure 1. This is due to the omnidirectional vision shows a broad angle of position which has the ability to see around 360 grades. Figure 1: The camera with hemispherical FOV for big country surveillance application The omnidirectional image is round form and must be unwrapped to obtain a bird's-eye image as depicted in Figure 2. ( a ) ( B ) Figure 2: Image taken by an omnidirectional camera with a inflated mirror. Figure ( a ) indicates the omnidirectional image. Figure ( B ) indicates the corresponding bird's-eye image. Although omnidirectional images allow increasing the field of position ( FOV ) , some jobs arise. Anamorphosis in omnidirectional images introduces complexness in image processing and reading such as optical flow calculation. Optical flow is computed from images spatio-temporal derived functions in order to gauge the evident gesture in a digital image sequence. Using appropriate gesture theoretical accounts, the pels evident gesture can be related to the camera gesture. Refering omnidirectional images, a simple camera interlingual rendition implies a complex evident gesture. Indeed, a camera interlingual rendition does non bring forth an evident interlingual rendition of all the pels in the image. Figure 3 has depicted both status explained above. Figure: Pixels gesture for a classical camera interlingual rendition ( a ) and for an omnidirectional camera ( B ) Ordinary cameras used in machine vision either have a narrow field of position ( FOV ) or have a broad FOV but suffer from complex deformation. It can be hard to undo a broad FOV image to obtain perspective projection positions accurately. Based strictly on the ideal perspective projection imaging theoretical account, it has been shown that surfaces of revolution of conelike subdivision curves are the lone mirror forms that can be paired with a individual convergence projection camera to make single-viewpoint ( SVP ) , catadioptric omnidirectional position systems whose omniview image can be unwrapped to perspective projection positions without systematic deformations. By utilizing multiple normal cameras positioned decently in relation to a plane mirror pyramid, a high declaration, SVP, broad FOV system can be built. The trade-offs, though, are the high monetary value and complexnesss involved with multiple cameras. Bulky size, weight, standardization, synchronism, and addition differences are jobs associated with multi-camera systems that single-camera systems are free of. An SVP system is worthwhile if the benefits outweigh the drawbacks for a peculiar application. The advantages of the single-camera, SVP, catodioptric household of omnidirectional imaging systems come with a monetary value. The most important tradeoff is a much lower image spacial declaration compared with normal cameras, multi-camera omniview systems, or revolving normal camera scanning system because single-camera, SVP, catadioptric systems have an enlarged FOV without a corresponding addition in the figure of physical feeling units ( e.g. , pels ) .Omnidirectional Image Scree ning SystemAn omnidirectional imagination system consisting a brooding mirror for sing object within a hemisphere field of position form a individual practical position point at the local centre of said brooding mirror, a projector for projecting a light beam toward said brooding mirror, and a variable wavelength filter optically positioned between said projector and said brooding mirror for bring forthing a form holding a spatially distributed wavelength spectrum of said brooding mirror, where a generator responsive to the hemispherical image informations for bring forthing 3-dimensional image.Field of InventionThe innovation presents a set of methods and setup for omnidirectional stereo imagination. By ââ¬Å" omnidirectional imagination system â⬠, we mean a system that is able to get images with a field-of-view ( FOV ) covering full hemisphere ( 180 solid infinite angle ) , at the same time without any mechanical moving portion. The FOV of a conventional camera or a light p rojector can be dramatically increased by using a brooding mirror decently placed in forepart of the camera or the projector. A brace of omnidirectional cameras is able to organize a alone stereo imagination of environing scene with 360 degree position angle. A combination of an omnidirectional camera and an omnidirectional structured visible radiation projector can besides supply a agencies to obtain quantitative three dimensional measurings of the objects around the camera system. The omnidirectional three dimentional imaging methods and setup presented herein may offer alone solutions to many practical systems that need coincident 360 grade sing angle and three dimensional measuring capableness. A figure of attacks had been proposed in the yesteryear for imaging systems to accomplish broad FOV. None of them nevertheless is able to bring forth 3D omnidirectional images. In the undermentioned paragraphs, we give a briefly study on the stake-of-the-art of current imaging systems that seek to accomplish broad FOV. Before the innovation of omnidirectional camera, a camera with revolving parts is used to capture image in all way. Although it produce high declaration of image, but it takes some clip in capturing it. Hence, some attack has been proposed in the yesteryear for imaging system to accomplish a broad field-of-view ( FOV ) . However, none of them is able to bring forth 3D omnidirectional images. Presently, there are some imaging systems are produced to seek for a broad FOV: Conventional Cameras Most bing imaging systems employ electronic detector french friess or photographic movie to enter optical image collected by its optical lens system. The image projection for most camera lenses is modeled as a ââ¬Å" pin-hole â⬠with a individual centre of projection. Since sizes of camera lens and the imagination detector have their practical restrictions, the light beams that can be collected by a camera lens and received by the imagination device typically organize a maize with really little gap angle. Therefore, angular FOV for conventional camera is within a scope of 5 to 50 grades. For illustration, an 8.5 millimeter F/1.3 camera lens for 1/2 â⬠CCD ( Charge Coupled Device ) bit merely has an angular FOV of 41.2 grade. Fish-Eye Lenss Optical applied scientists had designed several versions of wide-viewing-angle lens system, called the fish-eye lens. The fish-eye lens features a really short focal length which, when used in topographic point of conventional camera lens, enables the camera to see object for much wider angle ( about 180 grade of hemisphere ) . In general, the wider FOV, the more complicated design the fish-eye lens has. To obtain a hemispherical FOV, the fish-eye lens must be rather big in dimension, complex in optical design, and therefore expensive. Besides, it is really hard to plan a fish-eye lens that ensures individual position point restraint, i.e. , all incoming chief visible radiation beams intersect at a individual point to organize a fixed point of view. This is so a job with commercial fish-eye lenses, including Nikon ââ¬Ës Fisheye-Nikkor 8-mm f/2.8 lens. Although the acquired image by fish-eye lenses may turn out to be good plenty for some visual image applications, the deformation c ompensation issue has non been resolved, and the high unit-cost remain to be major hurdlings for its wide-spread applications. The fish-eye lens technique has the advantage of following a statically positioned camera to get a broad angle of position. However the nonlinear belongings resulted from the semi-spherical optical lens mapping make the declaration along the round boundary of the image really hapless, while the FOV corresponding to the round boundary of the image normally represents a land or floor where a high declaration of image is required. Multi-Camera System or Revolving Imaging Systems Large FOV of objects may be obtained by utilizing multiple cameras in the same system, each point towards a different way. However, issues on seamless integrating of multiple images is farther complicated by the fact that image produced by each camera has different centres of projection. The cost for such a system is normally high. The image processing required by multiple cameras or revolving camera method to obtain precise information on place and AZ of an object takes a long clip, which is non suited for real-time conflict field mold and reconnaissance applications. Another straightforward solution to increasing the FOV of an imagination system is to revolve the full imagination system about its centre of projection An image sequence acquired by the camera at different places are ââ¬Å" sewed â⬠together to obtain a bird's-eye position of the scene. Such an attack has been late proposed by several research workers. A really interesting attack developed by employs a camera with a non-frontal image sensor to scan the universe. The first disadvantage of any revolving image system is that it requires the usage of traveling parts, and preciseness placement devices. A more serious drawback is that such systems lack the capableness of at the same time an geting image with broad FOV. Although such system can get precise azimuth information in omnidirectional position, the imagination procedure is time-consuming and the method is non applicable to real-time jobs such as avoiding hit against traveling obstructions or supervising scene with nomadic objects. This restricts the usage of revolving systems to inactive and non-real-time applications. In contrast, the innovation presented herein, called the omnidirectional camera, is capable of capturing real-time omnidirectional images without utilizing any traveling parts. By ââ¬Å" omnidirectional images â⬠, we mean images with a FOV covering full hemisphere ( 180 solid infinite angle ) , at the same time. As one can see, a bird's-eye camera is still non omnidirectional, since it can merely supply a wide-angle of FOV at certain clip case, non in all waies. Figure: Comparison between our Omnidirectional Camera, bird's-eye camera and conventional camerasBrooding MaterialWhen visible radiation radiation passes from one medium into another holding a different index of refraction, some of the visible radiation is scattered at the interface between the two media even if both are transparent. The coefficient of reflection represents the fraction of the incident visible radiation that is reflected at the interface. In general it must be treated as a directional belongings that is a map of the reflected way, the incident way and the incident wavelength. Mirrors surely have a distinguishable brooding quality most other stuffs do non. This is due to the alone colour, composing and smoothness the mirror has. Polished, glistening metals make good mirrors because metal behaviors electricity good. Since the electronic field inside the metal is zero, negatrons at that place will ever call off out a field that is non zero ( even if the field originates outside the metal ) . Since light travels in electromagnetic moving ridges, when it hits a mirror ( most frequently made with sprayed Ag and glass ) , the lone manner to call off out the field and put it to zero is to reflect those moving ridges back out, hence a contemplation. This procedure is similar to singing a long rope attached on one terminal. If you give a hanging rope with one loose terminal one, large shingle, the rope will beckon to the top, and so back down. This is what happens when light hits a mirror. Some molecules hold light and convert some of it to heat. These stuffs are normally black. White stuffs have molecules that about instantly let go of visible radiation after absorbing it. There is an full scope of soaking up in different colourss. Metal works good for mirrors because it reflects seeable visible radiation on all parts of the surface at the same clip. While unsmooth surfaces do reflect visible radiation ( depending on colour and composing ) , they typically reflect visible radiation in all waies. You can see this in concrete, for illustration. It seems to scintillate because it reflects light, but non in one way or ordered manner. Mirrors, nevertheless, do reflect in one way. Because metal ( including metal pigment ) is smooth, it ââ¬Ës the best stuff for mirrors.Visible Spectrum WavelengthElectromagnetic Radiation Electromagnetic radiation is considered to be wave-like, dwelling of electric and magnetic field constituents that are perpendicular to each other and besides to the way of extension. Electromagnetic radiation consists of visible radiation, heat or beaming energy, radio detection and ranging, moving ridges, and X raies. Each of it has a specific scope of wavelengths. Figure: An electromagnetic moving ridge demoing electric field, magnetic field constituents and the wavelength. Figure: The spectrum of electromagnetic radiation. Visible visible radiation prevarications within a really narrow part of the spectrum with wavelengths runing between about 0.4 micron and 0.7 micron. The sensed colour is determined by the wavelength ; for illustration, radiation holding wavelength of about 0.4 micron appears to be violet, whereas green and ruddy colour occur at about 0.5 and 0.65 micron severally.CoatingMetallic elements are opaque and extremely brooding. The sensed colour is determined by the wavelength distribution of the radiation that is reflected and non absorbed. A bright silvery visual aspect when exposed to white light indicates that the metal is extremely brooding over the full scope of the seeable spectrum. Aluminum and Ag are two metals that exhibit this brooding behaviour. Copper and gilded appear red-orange and yellow severally because of the energy associated with white light photons holding short wavelength is non reemitted as seeable visible radiation. The huge bulk of optical constituents are made of assorted types of glass, and the bulk of those objects are coated with thin beds of particular stuffs. The intent of these coatings is to modify the contemplation and transmittal belongingss of the constituents ââ¬Ë surfaces. High-reflection coatings can be applied to the exterior of an object. For illustration, a level piece of glass is used to bring forth a first-surface mirror. Alternately, they can be applied to an internal surface to bring forth a second-surface mirror, which is used to build certain prisms. High-reflection coatings can be classified as either insulator or metallic coatings. Metallic coatings are used chiefly for mirrors. They do non trust on the rules of optical intervention but instead on the physical and optical belongingss of the surfacing stuff. However, metallic coatings are frequently over-coated with thin dielectric movies to increase the coefficient of reflection over a coveted scope of wavelengths or scope of incidence angles. Over-coating metallic coatings with a difficult, individual, dielectric bed of half-wave optical thickness improves scratch and tarnish opposition but merely marginally affects optical belongingss. Depending on the insulator used, such over-coated metals are referred to as lasting, protected or hard-coated metallic reflectors. The chief advantages of metallic coatings are broadband spectral public presentation, insensitiveness to angle of incidence and polarisation, and low cost. Their primary disadvantages include lower lastingness, lower coefficient of reflection and lower harm threshold. Today ââ¬Ës multilayer dielectric coatings are unusually difficult and lasting. With proper attention and handling, they can hold long life lastingness. Quarter-wave thicknesses of alternately high- and low-refractive index stuffs are applied to the substrate to organize a dielectric multilayer stack, as shown in figure. By taking stuffs of appropriate refractile indexes, the assorted reflected wave-fronts can be made to interfere constructively to bring forth a extremely efficient reflector. The extremum coefficient of reflection value is dependent upon the ration of the refractile indices of the two stuffs, every bit good as the figure of layer braces. Increasing either increases the coefficient of reflection. Over limited wavelength intervals, the coefficient of reflection of a dielectric surfacing easy can be made to transcend the highest coefficient of reflection of a metallic coating. Furthermore, the coatings are effectual for both s- and p-polarization constituents, and can be designed for a broad angle of incident scope. However, at angles that are significantly distant from the design angle, coefficient of reflection is markedly reduced. CVI Melles Griot is a taking provider of preciseness optical constituents and multielement optical system. CVI Melles Griot shows that: Our protected gold, Ag, and aluminum coatings exhibit exceeding broadband coefficient of reflection and are practical for many applications. Typical utilizations for these mirrors include single-use applications where the experiment itself amendss the mirror. A assortment of diameters and square sizes are offered, including an 8 â⬠ten 8 â⬠protected aluminium version.CoatingProtected GoldProtected SilverProtected AluminumSubstrate Float Glass Thickness 3.2 Aà ± 0.25 millimeter Coefficient of reflection Ravg & gt ; 96 % from 800 nm ââ¬â 20 Aà µm Ravg & gt ; 97.5 % from 450 ââ¬â 2 Aà µm Ravg & gt ; 96 % from 2 ââ¬â 20 Aà µm Ravg & gt ; 90 % from 450 nm ââ¬â 2 Aà µm Ravg & gt ; 95 % from 2 ââ¬â 20 Aà µm Damage Threshold 2 J/cm2 1064 nanometer, 10 N, 10 Hertz 3 J/cm2 1064 nanometer, 10 N, 10 Hertz 0.3 J/cm2 1064 nanometer, 10 N, 10 Hertz Front Surface Flatness & lt ; 5Ià »/inch @ 633 nanometer Diameter Tolerance +0.0/-0.25 millimeter Clear Aperture & gt ; 90 % of Surface Surface Quality 60-40 Scratch-DigALoadingâ⬠¦ Materials those are capable of conveying visible radiation with comparatively small soaking up and contemplation is transparent-one can see through them. Translucent stuffs are those through which visible radiation is transmitted diffusely ; that is, visible radiation is scattered within the inside, to the grade that objects are non clearly distinguishable when viewed through a specimen of the stuff. Materials that are imperviable to the transmittal of seeable visible radiation are termed opaque. When light returns from one medium into another, several things happen. Some of the light radiation may be transmitted through the medium, some will be absorbed and some will be reflected at the interface between the two media. Most of the captive radiation is reemitted from the surface in the signifier of seeable visible radiation of the same wavelength which appears as reflected visible radiation. The coefficient of reflection for most metals is between 0.9 ââ¬â 0.95 and some little fraction of energy from electron decay procedure is dissipated as heat. Metallic elements are opaque and extremely brooding. The sensed colour is determined by the wavelength distribution of the radiation that is reflected and non absorbed. A bright silvery visual aspect when exposed to white light indicates that the metal is extremely brooding over the full scope of the seeable spectrum. Aluminum and Ag are two metals that exhibit this brooding behaviour. Copper and gilded appear red-orange and yellow severally because of the energy associated with white light photons holding short wavelength is non reemitted as seeable visible radiation. When visible radiation radiation passes from one medium into another holding a different index of refraction, some of the visible radiation is scattered at the interface between the two media even if both are transparent. The coefficient of reflection represents the fraction of the incident visible radiation that is reflected at the interface. If the visible radiation is normal or perpendicular to the interface, so Where and are the indices of refraction of the two media. If the incident visible radiation is non normal to the interface, R will depend on the angle of incidence. Since the index of refraction of air is really close to 1. Thus the higher the index of refraction of the solid, the greater is the coefficient of reflection. For typical silicate spectacless, the coefficient of reflection is about 0.05. Merely as the index of refraction of a solid depends on the wavelength of the incident visible radiation. This means that the coefficient of reflection vary with wavelength. Contemplation losingss for lenses and other optical instruments are minimized significantly by surfacing the reflecting surface with really thin beds of dielectric stuffs such as Mg fluoride. Mirror Manufacturing In modern times the mirror substrate is shaped, polished and cleaned, and is so coated. Glass mirrors are most frequently coated with non-toxic Ag or aluminum, implemented by a series of coatings: Tin ( II ) Chloride Silver Chemical activator Copper Paint The Tin ( II ) Chloride is applied because Ag will non bond with the glass. The activator causes the tin/silver to indurate. Copper is added for long-run lastingness. The pigment protects the coating on the dorsum of the mirror from abrasions and other inadvertent harm. In some applications, by and large those that are cost-sensitive or that require great lastingness, mirrors are made from a individual, bulk stuff such as polished metal. Technical mirrors may utilize Ag, aluminum or gold coating and achieve coefficient of reflection of 90 % ââ¬â 95 % when new. A protective transparent greatcoat may be applied to forestall oxidization of the brooding bed. Applications necessitating higher coefficient of reflection or greater lastingness where broad bandwidth is non indispensable usage dielectric coatings, can accomplish coefficient of reflection every bit high as 99.99 % over a narrow scope of wavelength. Mirror Manufacturing Base Glass, which is a major mirror constituent, is really non a really good stuff for contemplation. In fact, it is merely able to reflect four per centum of the visible radiation it comes in contact with. What it has is a uniformity belongings that allows it to hold really few bumps, peculiarly when it is polished. The smoothness of glass makes it a good campaigner for a base of a brooding metal. Coating The base stuff, in order to go brooding, needs to be coated with a substance that reacts good to visible radiation. The most normally used stuffs are metal coatings such as Ag, gold or chrome. Mercury was used by mirror makers until it was finally abandoned in the fortiess due to jobs with toxicity. Modern mirrors now make usage of aluminium as the metallic coating. Mirrors that are used under high temperatures are frequently coated with Si oxides and Si nitrates which tend to be a protective coating applied to forestall scrape. Design Mirrors need to integrate surface regularity in their designs in order to go effectual. The glass sheets that are used demand to be level and lasting. For family usage, the thickness of the mirror is taken into consideration, with its strength increasing proportionally to its thickness. For heavy-duty mirrors, such as those used in scientific research, the surface has to be specially designed to retain uniformity while adding a curvature. This gives the mirror the ability to concentrate every bit good as reflect visible radiation. The design of the mirror besides specifies the sort of surfacing to be used. The features that are of import in the pick of the surfacing include lastingness and coefficient of reflection. Procedure To do a mirror, the first measure is to cut and determine the glass harmonizing to the formulated design. Diamond-tipped proverbs are normally used to make a all right coating. After this, the panels, called spaces, are placed in an optical grinding machine. This machine uses an scratchy liquid and a grinding home base to make a smooth texture on the glass. Finally, the brooding stuff is placed on the glass utilizing an evaporator, which has the ability to heat the metal used for surfacing until it evaporates onto the spaces ââ¬Ë surface. Integrity The quality control of mirrors is an of import portion of the fabrication procedure. The mirror ââ¬Ës surface is by and large inspected utilizing the bare oculus or a microscope in order to look into if there are any abrasions or variability. An infrared photographic procedure may besides be used to see if there is a deficiency of uniformity in the thickness of the metal. In some instances, the mirror may besides be placed under environmental proving wherein it is subjected to heat or cold to see how good it can defy assorted temperatures. Possibly you ââ¬Ëve been in a state of affairs where you have n't had a mirror on manus and have resorted to utilizing the most brooding surface around you. Depending on the colour, form and texture of the surface, it may hold sufficed, but mirrors surely have a distinguishable brooding quality most other stuffs do non. This stems from the alone colour, composing and smoothness a mirror has. Get downing With Metal Polished, glistening metals make good mirrors because metal behaviors electricity good. Since the electronic field inside the metal must be zero, negatrons at that place will ever call off out a field that is non zero ( even if the field originates outside the metal ) . Since light travels in electromagnetic moving ridges, when it hits a mirror ( most frequently made with sprayed Ag and glass ) , the lone manner to call off out the field and put it to zero is to reflect those moving ridges back out, hence a contemplation. This procedure is similar to singing a long rope attached on one terminal. If you give a hanging rope with one loose terminal one, large shingle, the rope will beckon to the top, so back down. This is what happens when light hits a mirror. How Color Affects Reflection Some molecules hold light and convert some of it to heat. These stuffs are normally black. White stuffs have molecules that about instantly let go of visible radiation after absorbing it. There is an full scope of soaking up in different colourss. Metal works good for mirrors because it reflects seeable visible radiation on all parts of the surface at the same clip. Silver works good in peculiar because it ââ¬Ës the closest to white and reflects a assortment of colourss better ( Cu and gold would non reflect blue good, for illustration ) . How Smoothness Affects Contemplation While unsmooth surfaces do reflect visible radiation ( depending on colour and composing ) , they typically reflect visible radiation in all waies. You can see this in concrete, for illustration. It seems to scintillate because it reflects light, but non in one way or ordered manner. Mirrors, nevertheless, do reflect in one way. Because metal ( including metal pigment ) is smooth, it ââ¬Ës the best stuff for mirrors. Mirrors that are warped or non wholly smooth give distorted images. Obtaining Omnidirectional View Using Reflective Mirror. To dramatically increase the FOV of an imagination system, there is an unusual attack: utilizing a brooding surface. The FOV of a picture camera can be greatly increased by utilizing brooding surface with properly designed surface forms. The rear-view mirror in a auto is a day-to-day illustration of utilizing brooding mirror to increase the FOV of a driver. There are a figure of surface profiles that can be used to bring forth omnidirectional FOV. Figure list three illustrations: conelike mirror, spherical mirror, and parabolic mirror. The optical geometry of these bulging mirrors provides a simple and effectual agencies to change over picture camera ââ¬Ës two-dimensional position into an omnidirectional position around the perpendicular axis of these mirrors, without utilizing any traveling portion. At the first glimpse, it appears that the omnidirectional imagination undertaking can be accomplished by utilizing any bulging mirror. Unfortunately, this is non the instance. In reexamining some BASIC of image formation, we know that an image is two dimensional form of brightness ( or colourss ) . A satisfactory imagination system must continue two indispensable features: Geometric correspondence: there must be a one-to-one correspondence between pels in an image and point in the scene. Single point of view restraint: each pels in the image corresponds to a peculiar sing way defined by a beam from that pel on image plane through a ââ¬Å" pinhole â⬠( individual sing point ) . Notice that although the convex mirrors listed in Figure can greatly increase the FOV, and may turn out adequate for certain omnidirectional scene monitoring applications, they are non satisfactory imaging devices. These reflecting surfaces do non continue the individual point of view restraint ( SVC ) . For a high quality omnidirectional imagination system, all the light beams coming in the omni imager caput should hold a individual ( practical ) sing point. Design of the omni-mirror that meets the SVC In this subdivision, we will discourse a desirable convex mirror surface profile that satisfies the individual point of view restraint: all the ( extensions of ) visible radiation beams reflected by the mirror must go through through a individual ( practical ) point of view. We call such a brooding mirror the omni-mirror. Let us first define necessary symbols and nomenclature. As shown in the Figure, we use an off-shelf picture camera with a regular lens whose FOV covers full surface of the omni-mirror. Since the optical design of camera and lens is rotationally symmetric, all we need to find is the cross-section map zAà ® that defines the mirror surface cross-section profile. The mirror is so the solid of revolution obtained by brushing the cross-section about the optical axis. The map of the omni-mirror is to reflect all viewing beams coming from picture camera ââ¬Ës screening centre ( focal point, labeled as C ) to the surface of physical objects in the FOV. The cardinal characteristic of this contemplation is that all such reflected beams must hold a projection towards a individual practical screening point at mirror ââ¬Ës focal centre, labled as O. In other words, the mirror should efficaciously maneuver sing beams such that the camera equivalently sees the objects in the universe from a i ndividual point of view O. We choose hyperboloid as the desirable form of the omni-mirrors. A well-known characteristic of a inflated curve is that: the extension of any beam reflected by the inflated curve originated from one of its focal points passes through its another focal point. If we choose the hyperbolic profile for the omni-mirror, and topographic point a picture camera at its focal point C, as shown in Figure, the imagination system will hold a individual point of view at its another focal point O, as if the picture camera were placed at the practical screening location O. The alone characteristic of the omni-mirror is that the extension of the entrance light beam sensed by the CCD camera is ever go throughing through a individual practical point of view O regardless of the location of the projection point M on the mirror surface.
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