NON-PROVISIONAL
`UTILITY PATENT APPLICATION
`TRANSMITTAL- 37 CFR 1.53(b)
`
`Duplicate
`{]
`(check,if applicable)
`
`MAIL STOP PATENT APPLICATION
`Commissionerfor Patents
`P.O. Box 1450
`Alexandria, VA 22313-1450
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`-O =
`=
`. Gin ==
`Attorney Docket No.: 10000-25US (100137/US/WO)
`First Named Inventor: Jean-Claude ARTONNE etal. 2S =
`Express Mail Label No.:EV312205282US
`=> ;
`Total Pages of Transmittal Form: 3
`= 2
`IN
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`Transmitted herewith for filing is the non-provisionalutility patent application entitled:
`
`METHOD FOR CAPTURING AND DISPLAYING A VARIABLE RESOLUTION
`DIGITAL PANORAMIC IMAGE
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`whichis:
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`an
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`a
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`[]
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`Original; or
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`[X] Continuation,
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`[
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`] Divisional, or
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`[
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`] Continuation-in-part (CIP)
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`of prior International Application No. PCT/FR02/01588 filed May 10, 2002.
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`Anticipated Group/Art Unit: or Class , Subclass .
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`[
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`]
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`This non-provisional patent application is based on Provisional Patent Application No.,
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`filed .
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`Enclosed are:
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`[X]
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`(X]
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`C
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`Specification (including Abstract) and claims: 31 pages.
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`11 sheets of drawings (formal).
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`Application Data Sheet.
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`Newly executed/unexecuted Declaration (original/copy).
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`Copyof Declaration from prior application.
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`Separate Power of Attorney (including 37 CFR 3.73(b) statement,if applicable).
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`Microfiche computer program (Appendix).
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`Nucleotide and/or Amino Acid Sequence Submission, including:
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`Computer readable copy
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`[ ] Paper Copy
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`[ ] Verified Statement.
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`Under PTO-1595 Cover Sheet, an assignment of the invention
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`Nameof Assignee: 6115187 CANADAINC.
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`Certified copy(ies) of Application No(s). filed is/are filed:
`[
`] herewith
`or
`[] inprior application .
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`7085870 v1
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`1
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`APPLE 1002
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`APPLE 1002
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` Applicant(s), by its/their undersigned attorney, claim(s) Small Entity Status under
`37 C.F.R. §1.27 as [
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`or[{ ] a Non-Profit Organization.
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`Preliminary Amendment.
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`Information Disclosure Statement, PTO/SB/08A,andcited references.
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`Request for Nonpublication of Application Under 35 U.S.C. §122(b)
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`Other:
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`Thefiling fee is calculated as follows:
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`SMALL ENTITY |
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`CLAIMS NO. FILED|NO. EXTRA Pe|BASIC FEE:BASIC FEE:
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`PTotal|26-20=[|XD
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`3aae|OR|X86__|
`] Multiple Dependent Claims Present[ $145 |$[|ORT $290 [$|
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`|$290_|
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`The Commissioneris not authorized to chargethe filing fee at this time as we
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`

`CORRESPONDENCE ADDRESS
`
`
`©
`NovemberIl,2002By:
`
`
`(Date)
`
`OHN D. SIMMONS
`Registration No. 52,225
`AKIN GUMP STRAUSS HAUER & FELD LLP
`One Commerce Square
`2005 MarketStreet, Suite 2200
`Philadelphia, PA 19103-7013
`Telephone: 215-965-1200
`Direct Dial: 215-965-1268
`Facsimile: 215-965-1210
`E-Mail: jsimmons @akingump.com
`
`[X] Customer Numberor Bar Code Label: 000570
`
`JDS:sm
`Enclosures
`
`3
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`

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`‘Express Mailing Label No.: EV312205282US
`
`Attorney Docket No. 10000-25US
`(100137/US/WO)
`
`TITLE OF THE INVENTION
`
`(0001)
`
`Method For Capturing And Displaying A Variable Resolution Digital Panoramic Image
`
`CROSS-REFERENCE TO RELATED APPLICATIONS
`
`[0002]
`
`This application is a continuation of International Application No. PCT/FR02/01588,
`
`filed May 10, 2002 the disclosure of which is incorporated herein by reference.
`
`BACKGROUND OF THE INVENTION
`
`[0003]=Thepresent invention relates to obtaining digital panoramic images and displaying
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`panoramic images on computerscreens.
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`[0004]
`
`Fig. 1 represents a classical device allowing a digital panoramic image to be produced
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`10
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`and presented on a computer screen. The device comprises a digital camera 1 equipped with a
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`panoramic objective lens 2 of the "fish-eye" type, having an angular aperture on the order of 180°.
`The camera 1 is connected to a computer 5, such as a microcomputer for example, equipped with a
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`screen 6. The connection to the microcomputer 5 may be permanent, when, for example, the camera
`1 is a digital video camera, or temporary, when, for example, the camera1isastill digital camera
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`15
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`equipped with an image memory,the connection then being carried outat the time the imagefiles
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`are to be transferred into the microcomputer.
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`[0005]
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`Fig. 2 schematically represents the appearance of a panoramic image 3 obtained by
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`meansof the panoramic objective lens 2. The round appearance of the image is characteristic of the
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`axial symmetry of panoramic objective lenses and the image has dark edges4 that will subsequently
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`20
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`be removed. This digital panoramic imageis delivered by the camera 1 in the form of a computer
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`file containing image points coded RGBA arrangedin a two-dimensional table, "R" being the red
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`pixel of an image point, "G"the green pixel, "B"the blue pixel, and "A" the Alpha parameter or
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`transparency. The parameters R,G, B, A are generally being coded on8 bits.
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`[0006]
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`The imagefile is transferred into the microcomputer 5 which transformstheinitial image
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`25
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`into a three-dimensionaldigital image, then presents the user with a sector of the three-dimensional
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`image in a display window 7 occupyingall or part of the screen 6.
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`[0007]
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`Fig. 3 schematically showsclassical steps of transforming the two-dimensional
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`panoramic imageinto a panoramic imageoffering a realistic perspective effect. After removing the
`black edges ofthe image, the microcomputerhasa set of image points forming an image disk 10 of
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`30
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`center O and axes OX and OY. The imagepoints of the image disk are transferredinto a three-
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`dimensional space defined by an orthogonal coordinate system of axes O'X'Y'Z,the axis O'Z being
`7078397 v1
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`perpendicular to the plane of the image disk. The transfer is performed by a mathematical function
`implemented by an algorithm executed by the microcomputer, and leads to obtaining a set of image
`points referenced in the coordinate system O'X'Y'Z. These image points are for example codedin
`spherical coordinates RGBA(@,9), @ being the latitude and @ the longitude of an image point. The
`angles @ and @ are codedin 4 to 8 bytes (IEEE standard). These image points form a hemisphere 11
`when the panoramic objective lens used has an aperture of 180°, otherwise a portion of a
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`hemisphere. The microcomputerthushas a virtual image in the shape of a hemisphere one sector 12
`of which, correspondingto the display window7,is presented on the screen (Fig. 1) considering
`that the observer is on the central point O'of the system of axes O'X'Y'Z, which defines with the
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`10
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`center O" of the image sector 12, a direction O'O"called "viewing direction”.
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`[0008]
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`_—_In order to avoid the imagesector displayed 12 having geometrical distortions unpleasant
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`for the observer, the classical panoramic objective lenses must havea distribution function of the
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`imagepoints accordingto the field angle of the object points of a panoramathatis as linear as
`possible. Therefore, if two points A’, B', situated on the same meridian of the hemisphere 11, and
`the corresponding points A, B on the image disk 10 are considered, the ratio between the angles
`(A'O'Z) and (B'O'Z) mustbe equal to the ratio between the distances OA and OB onthe imagedisk.
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`15
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`20
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`[0009]
`Dueto this property of linearity of a classical panoramic objective lens, image points
`correspondingto object points having an identical field angle form concentric circles C10, C20...
`C90 on the imagedisk 10, as represented in Fig. 4A. Classically, “field angle of an object point"
`means the angle of an incidentlight ray passing through the object point considered and throughthe
`center of the panorama photographed,relative to the optical axis of the objective lens. Thefield
`angle of an object point can be between 0 and 90° for an objective lens having an aperture of 180°.
`Therefore, the circle C10 is formed bythe image points corresponding to object points havingafield
`angle of 10°, the circle C20 is formed by image points corresponding to object points havinga field
`angle of 20°, etc., the circle C90 being formed by the imagepoints havinga field angle of 90°.
`[0010]_Fig. 4B representsthe shape ofthe distribution function Fdcof a classical panoramic
`objective lens, which determines the relative distance dr of an image pointin relation to the center
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`25
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`of the image disk according to the field angle o of the corresponding object point. The relative
`distance dr is between 0 and 1 andis equalto the distance of the image pointin relation to the center
`of the image divided bythe radius of the image disk. The ideal form of the function Fdcis a straight
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`30
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`line of gradient K:
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`7078397 vi
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`dr=Fdc (a) =K a
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`in which the constant K is equal to 0.111 degree” (1/90°).
`[0011]
`This technique of displaying a digital panoramic image sector on a computerscreen has
`various advantages,particularly the possibility of "exploring" the panoramic imagebysliding the
`image sector presentedon the screento the left, the right, upwards or downwards, until the limits of
`the panoramic image are reached. This techniquealso allows complete rotationsof the image to be
`carried out when two complementary digital images have been taken and suppliedto the
`microcomputer, the latter thus reconstituting a complete panoramic sphere by assembling two
`hemispheres. Another advantage provided by presenting a panoramic image on screenis to enable
`the observer to make enlargements or zoomson parts of the image. The zoomsare performed
`digitally, by shrinking the image sector displayed and expanding the distribution of the image points
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`on the pixels of the screen.
`(0012)
`Various examples ofinteractive panoramic images can be found on the Web. Reference
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`could be madein particular to the centralsite “http://;www.panoguide.com"("The Guide to
`Panoramas and Panoramic Photography") whichgivesa full overview ofall the products available
`to the public to produce these images. Software programsallowing digital panoramic photographs
`to be transformedinto interactive panoramic images are offered to the public in the form of
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`downloadable programs or CD-ROMsavailablein stores.
`[0013]
`Despite the various advantagesthat this technique for displaying digital images offers,
`the digital enlargements have the disadvantage of being limited bythe resolution of the image sensor
`used whentaking the initial image and the resolution of an image sensor is generally much lower
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`than that of a classical photograph. Therefore, when the enlargementincreases, the granulosity of
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`the image appears asthelimits of the resolution of the image sensor are being reached.
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`[0014]
`To overcomethis disadvantage, it is well known to proceed with pixel interpolations so
`as to delay the apparition of the blocks of color which betray the limits of the resolution of the
`sensor. However, this method only improves the appearance of the enlarged image sector and does
`not in any wayincreasethe definition. Another obvious solution is to provide an image sensor with
`a high resolution, higher than the resolution required to present an image sector without
`enlargement, so that there is a remaining margin of definition for zooms, However,this solution is
`expensive as the cost price of an imagesensor rapidly rises with the numberofpixels per unit of
`area.
`
`[0015]
`Someattempts have been madeto improve the quality of the enlargements, by changing
`the optical properties of the panoramic objective lenses themselves. Thus, U.S. Patent No.
`5,710,661 teaches capturing a panoramic image with two overlocking objective lenses using a set of
`7078397 v1
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`mitrors. A first set of mirrors provides an overall view, and a mobile central mirror provides a
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`detailed view on a determined zone of the panorama. However,this solution does not offer the same
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`flexibility as digital zooms, particularly when the imageis not displayed in real time, as the observer
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`no longerhasthe possibility of choosing the image portion that he wants to enlarge once the
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`photograph has been taken.
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`BRIEF SUMMARYOF THE INVENTION
`
`[0016]
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`Therefore, the present invention comprises a method allowing the physical limits of
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`image sensors to be circumventedandthe definition offered by digital enlargements concerning
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`certain parts of a digital panoramic imageto be improved, without the need to increase the number
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`10
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`of pixels per unit of area of an image sensoror to provide an overlocking optical enlargement
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`system in a panoramic objective lens.
`
`[0017]
`
`Thepresent invention is based on the observation that, in several applications, only
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`certain zones of a panoramic imageare ofa practical interest and are likely to be expanded by the
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`observer by meansof a digital zoom. Thus, in applications such as video surveillance,
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`15
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`videoconferencing, visio-conferencing, a panoramic camera canbe installed against a wall or on the
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`ceiling and there is generally no reason to make enlargements on the zones of the panoramic image
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`correspondingto the wall or the ceiling. Similarly, as part of a videoconference performed by
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`meansof a panoramic camera, the most interesting zone is generally situated at a specific place
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`situated towards the center of the image (in the case of individual use) or on the edgesof the image
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`20
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`(in the case of collective use or visio-conferencing). Furthermore, when usedfor recreation and
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`leisure, most panoramic images comprise parts that are less interesting than others, such as the parts
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`representing the sky or a ceiling for example, the most useful part generally being in the vicinity of
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`the center of the image.
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`[0018]
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`Therefore, the present invention is based on the premise that a panoramic image has
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`25
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`some zonesthat are not very useful and that can tolerate a reasonable definition to the benefit of
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`other zones of the image.
`[0019}
`Onthebasis ofthis premise,the idea of the present invention is to produce panoramic
`photographs by meansof a panoramic objective lens that is not linear, which expandscertain zones
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`of the image and compresses other zones of the image. The technical effect obtainedis that the
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`30
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`expandedzonesof the image cover a numberofpixels of the image sensorthatis higher than if they
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`were not expanded, and thus benefit from a better definition. By choosing an objective lens that
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`7078397 vi
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`expands the most useful zones of an image (which depend onthe intended application), the
`definition is excellent in these zones and thedefinition is mediocre in the zonesof lesser importance.
`
`Thus, the present invention proposes a method for capturing a digital panoramic image,
`[0020]
`by projecting a panoramaonto an image sensor by meansof a panoramic objective lens, in which
`the panoramic objective lens has an image pointdistribution function that is not linear relative to the
`field angle of object points of the panorama,the distribution function having a maximum divergence
`of at least 410% comparedto a linear distribution function, such that the panoramic image obtained
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`hasat least one substantially expanded zoneandat least one substantially compressed zone.
`[0021]
`According to one embodiment,the objective lens has a non-linear distribution function
`that is symmetricalrelative to the optical axis of the objective lens, the position of an imagepoint
`relative to the center of the image varying accordingtothe field angle of the corresponding object
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`10
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`point.
`(0022)
`
`According to one embodiment, the objective lens expandsthe center of the image and
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`compressesthe edges of the image.
`(0023)
`According to one embodiment,the objective lens expands the edges of the image and
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`15
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`compressesthe center of the image.
`[0024]
`According to one embodiment, the objective lens compresses the center of the image and
`the edges of the image, and expands an intermediate zone of the image located betweenthe center
`
`and the edges of the image.
`(0025)
`According to one embodiment, the objective lens comprises a set of lenses forming an
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`20
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`apodizer.
`[0026]
`
`According to one embodiment, the set of lenses forming an apodizer comprisesatleast
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`one asphericallens.
`[0027]
`According to one embodiment,the set of lenses forming an apodizer comprisesatleast
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`25
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`one diffractive lens.
`
`[0028]
`
`According to one embodiment, the objective lens comprises a set of mirrors comprising
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`at least one distorting mirror.
`[0029]
`The presentinvention also relates to a methodfor displaying an initial panoramic image
`obtained in accordance with the method described above, comprising a step of correcting the non-
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`30
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`linearity of the initial image, performed by meansof a reciprocal function of the non-linear
`distribution function of the objective lens or by meansof the non-linear distribution function.
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`According to one embodiment, the step of correcting comprises a step of transforming
`[0030]
`the initial imageinto a corrected digital image comprising a numberof imagepoints higherthan the
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`numberofpixels that the image sensor comprises.
`[0031]
`According to one embodiment, the method comprisesa step ofcalculating the size of the
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`corrected image, by meansofthe reciprocal function of the distribution function,so that the
`resolution of the corrected image is equivalent to the most expanded zoneofthe initial image, and a
`step of scanning each imagepointof the corrected image, searchingfor the position of a twin point
`of the image point on the initial image and allocating the color of the twin pointto the image point
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`of the corrected image.
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`10
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`[0032]
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`According to one embodiment, the initial image and the corrected image comprise an
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`image disk.
`
`[0033]
`According to one embodiment, the method comprisesa step oftransferring the image
`points of the corrected image into a three-dimensional space anda step of presenting one sector of
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`15
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`the three-dimensional image obtained on a display means.
`[0034]
`According to one embodiment, the method comprises a step of determining the color of
`image points of a display window,by projecting the imagepoints of the display window onto the
`initial image by meansof the non-linear distribution function, and allocating to each imagepoint of
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`the display windowthecolorof an image pointthat is the closest on the initial image.
`[0035]
`According to one embodiment, the projection of the image points of the display window
`onto the initial image comprisesastep ofprojecting the image points of the display window onto a
`20
`sphere or a sphereportion, a step of determiningthe anglein relation to the center of the sphere or
`the sphere portion of each projected imagepoint, and a step of projecting onto the initial image each
`image pointprojected onto the sphereor the sphere portion, the projection being performed by
`meansofthe non-linear distribution function consideringthe field angle that each point to be
`projected has in relation to the centerof the sphere or the sphere portion.
`[0036]
`Thepresentinventionalso relates to a panoramic objective lens comprising optical
`meansfor projecting a panoramainto an image plane of the objective lens, the panoramic objective
`lens having an imagepointdistribution function that is not linear relative to the field angle of object
`points of the panorama,the distribution function having a maximum divergenceofat least 10%
`comparedto a linear distribution function, such that a panoramic image obtained by meansofthe
`objective lens comprises at least one substantially expandedzone andatleast one substantially
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`30
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`25
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`compressed zone.
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`7078397 v1
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`According to one embodiment,the panoramic objective lens has a non-linear distribution
`[0037]
`function that is symmetrical relative to the optical axis of the objective lens, the position of an image
`pointrelative to the center of an image obtained varying according to the field angle of the
`
`corresponding object point.
`[0038]
`According to one embodiment, the panoramic objective lens expands the center of an
`
`image and compressesthe edgesof the image.
`[0039]
`According to one embodiment, the panoramic objective lens expands the edges of an
`
`image and compressesthe center of the image.
`[0040]
`According to one embodiment, the panoramic objective lens compresses the center of an
`image andthe edgesof the image, and expands an intermediate zone of the image located between
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`10
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`the center and the edges of the image.
`[0041]
`According to one embodiment, the panoramic objective lens comprisesa set of lenses
`
`forming an apodizer.
`[0042]
`According to one embodiment, the set of lenses forming an apodizer comprisesat least
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`15
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`one asphericallens.
`[0043]
`According to one embodiment,the set of lenses forming an apodizer comprises atleast
`
`one diffractive lens.
`
`[0044]
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`lenses.
`
`[0045]
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`20
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`According to one embodiment, the panoramic objective lens comprises polymethacrylate
`
`According to one embodiment, the panoramic objective lens comprises a set of mirrors
`
`comprisingat least one distorting mirror.
`
`BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
`
`[0046]
`
`The foregoing summary,as well as the following detailed description of preferred
`
`embodimentsofthe invention, will be better understood whenread in conjunction with the
`
`25
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`appended drawings. For the purpose ofillustrating the invention, there are shownin the drawings
`embodiments whichare presently preferred.
`It should be understood, however,that the invention is
`
`notlimited to the precise arrangements and instrumentalities shown.
`
`[0047]
`
`[0048]
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`30
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`a screen;
`
`In the drawings:
`
`Fig.
`
`1 described above represents a system for displaying a digital panoramic image on
`
`[0049]_Fig. 2 described aboverepresents a panoramic imagebeforeit is processed by a
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`computer,
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`7078397 v1
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`Fig. 3 described above shows a classical method for transforming a two-dimensional
`[0050]
`panoramic imageinto a three-dimensional digital panoramic image;
`[0051]
`Fig. 4A and 4B described above showthelinearity of a classical panoramic objective
`
`lens;
`
`Figs. 5 and 6 show oneaspect ofthe method accordingto the present invention and
`[0052]
`respectively representa distribution of image points obtained with a classical panoramic objective
`lens and a distribution of image points obtained with a non-linear panoramic objective lens
`
`according to the present invention;
`[0053]
`Figs. 7A and 7B showa first example of non-linearity of a panoramic objective lens
`
`10
`
`according to the present invention;
`[0054]
`Fig. 8 shows a second exampleof non-linearity of a panoramic objective lens according
`
`to the present invention;
`
`[0055] Fig. 9 showsathird exampleof non-linearity of a panoramic objective lens according to
`
`15
`
`the present invention;
`[0056]
`Fig. 10 represents a system for displaying a digital panoramic image by meansof which
`a methodfor correcting the panoramic image according to the present invention is implemented;
`[0057]
`Fig. 11 schematically showsa first embodimentof the correction method according to
`
`the present invention;
`
`[0058]
`
`Fig. 12 is a flow chart describing a methodfor displaying a panoramic image
`
`20
`
`incorporating the first correction method accordingto the present invention,
`[0059]
`Fig. 13 schematically shows a second embodimentof the correction method according
`
`to the present invention;
`
`[0060]
`
`‘Fig. 14 is a flow chart describing a methodfor displaying a panoramic image
`
`incorporating the second correction method according to the present invention;
`[0061]
`Fig. 15 is a cross-sectionof a first embodimentof a non-linear panoramic objective lens
`
`25
`
`according to the present invention;
`[0062]
`Fig. 16 is an exploded cross-section of a system of lenses present in the panoramic
`
`objective lens in Fig. 15;
`[0063]
`Fig. 17 is a side view of a lens present in the panoramic objective lens in Fig. 15; and
`[0064]
`Fig.
`18 is the diagram of a second embodimentof a non-linear panoramic objective lens
`
`30
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`according to the present invention.
`
`DETAILED DESCRIPTION OF THE INVENTION
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`7078397 v1
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`A - Compression/expansionofaninitial image
`[0065]
`Fig. 5 schematically represents a classical system for taking panoramic shots, comprising
`[0066]
`a panoramic objective lens 15 of optical axis OZ anda digital image sensor 17 arrangedin the image
`plane of the objective lens 15. Here, four object points a, b, c, d will be consideredthat belong to a
`panorama PM located opposite the objective lens and respectively having angles of incidence a1,
`02, -02, -a.1. As explained in the preamble,the field angle of an object pointis the angle that an
`incidentlight ray passing through the object point considered and throughthe centerof the
`panorama PM,marked bya point "p" on Fig.5, hasrelative to the optical axis OZ of the objective
`lens. In this example,the angle 1 is equal to two times the angle 02. On the imagesensor 17,
`imagepointsa’, b’, c', d' corresponding to the objectpoints a, b, c, d are located at distances from the
`center of the image respectively equal to d1, d2, -d2, -dl. As the distribution of the image points
`accordingto the field angle of the object points is linear with a classical panoramic objective lens,
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`the distances d1 and d2 are linked by the followingrelation:
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`di/al = d2/a2
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`Asthe angle a1 is here equal to 202,it follows that:
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`dl = 2d2
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`[0067]
`Asis well knownby thoseskilled in the art, the term "linearity" here refers to a ratio of
`proportionality between the distance of an image point measuredrelative to the center of the image
`andthe field angle of the corresponding object point. The notion of “linearity” in the field of
`panoramicobjective lenses is therefore different from that prevailing in the field of paraxial optics
`(in the vicinity of the optical axis) when the conditions of Gauss are met.
`[0068]
`Fig. 6 represents a system for taking shots of the same type as above,but in which the
`classical panoramic objective lens 15 is replaced by an objective lens 18 accordingto the present
`invention, the image sensor 17 being arranged in the imageplane ofthe objective lens 15. The
`projection onto the image sensor17 of the object points a, b, c, d having angles of incidence al, a2,
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`-a2 and -c11 relative to the axis OZ of the objective lens and to the center "p" of the panorama are
`considered again. On the image sensor 17, the corresponding image points a", b", c", d" are located
`at distances from the center of the image respectively equal to dl’, d2’, -d2', -dl'’.
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`[0069]
`Accordingto the present invention, the objective lens 18 hasa distribution function of
`the image points that is not linear. Theratio of the distances d1', d2', -d2', -d1' are not equal to the
`ratio of the anglesof incidence a1, «2, -02, -a1. In the example represented, the distance d2'is
`clearly greater than d1'/2, such thatthe central part of the panoramic imageprojected onto the image
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`sensor 17, which correspondsto a solid angle 22 centered on the optical axis OZ, occupies a
`greater area on the imagesensor 17 than the area it occupies in Fig. 5 with the classical panoramic
`objective lens (hatched zone). This central part of the panoramic image is therefore projected onto
`the image sensor with expansionofits area, in relation to the area the central part would occupyif
`the objective lens were linear. The result is that the numberof pixels of the image sensor covered
`bythis part of the imageis greater than in previous practices and that the definition obtainedis
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`improved. Onthe other hand, the part of the image delimited by twocircles respectively passing
`through the points a", d" and through the points b", c" is compressedrelative to the corresponding
`part in Fig. 5, and the definition on the edges ofthe image is less than that obtained with a classical
`linear objective lens, to the benefit of the central part of the image.
`[0070]
`Byapplyingthe principle accordingto the present invention, which involves expanding
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`one part of the image and compressing anotherpart of the image, the part to be expandedandthe
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`part to be compressed can be chosen according to the intended application, by producing several
`types of non-linear objective lenses and by choosing an objective lens suited to the intended
`application. Depending on the intended application, the mostuseful part of a panoramic image may
`be located in the center of the image,on the edge of the image, in an intermediate zone situated
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`betweenthe center and the edge of the image, etc.
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`[0071]
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`Figs. 7A-7B, 8 and 9 show three examples of non-linear distribution functions according
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`to the present invention.
`[0072]
`Thedistribution function shownin Figs. 7A and 7B correspondsto the example in Fig. 6,
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`that is a panoramic objective lens that expands the imagein the center. Fig. 7A represents
`equidistant concentric circles C10, C20,..., C90 present on an imagedisk, eachcircle being formed
`by imagepoints corresponding to object points having the samefield angle. Thecircle C10 is
`formed by the image points corresponding to object points having a field angle of 10°, the circle C20
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`is formed by imagepoints corresponding to object points havingafield angle of 20°, etc. By
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`comparing Fig. 7A with Fig. 4A described in the preamble,it appears that the circles C10 and C20
`are further from the center of the image and further from each other than the circles C10 and C20
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`obtained with a classical objective lens, while the circles C30 to C90 are closer to each other. This
`panoramic image thus has an expanded zonein the center and a compressed zone on the edgeof the
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`image disk.
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`[0073]
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`Fig. 4B represents the curve of the corresponding distribution function Fdl. The
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`classical linear distribution function, expressed by Fdc = Ka andin the form ofa straight line of
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`gradientK,is also represented as a guide mark (the constant K being equal to 1/90 for an objective
`lens having an aperture of 180°,i.e., a gradient of 0.111 per degree). The field angle o of the object
`points is represented on the X-axis and is between 0 and 90°. Therelative distance dr of an image
`pointin relation to the center of the image disk is represented on the Y-axis and is between 0 and1.
`The curveof the function Fdl hasa higher gradient than the straight line Fde for angles o of
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`between 0 and 20°, then a lesser gradient after 20° and up to 90°. A high gradient means an
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`expansion of the image and a low gradient means a compressionofthe image.
`[0074]
`As demonstrated in this example, the curve Fdl has a point of maximum divergence Pd
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`at the angle & = 20°. “Point of maximum divergence"refers to the image point Pd(«) at which the
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`greatest gap in relative distance dr in relation to a corresponding point Pdl(c) on the linear
`distribution straight line Ka can be observed.
`In this example, the point Pd(a=20°) hasa relative
`distance dr equal to 0.5 relative to the center of the image while the corresponding point Pdl(a=20°)
`on the linear curve Fdc hasa relative distance dr of 0.222. The maximum divergence DIVmax of
`the distribution function Fd1 accordingto the present invention can be calculated by a formula of
`the type:
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`DIVmax% = [[dr(Pd) - dr(Pdl)]/[dr(Pdl)]]*100
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`1.€.:
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`DIVmax% = [[dr(Pd) - K*a(Pd)]/[K*a(Pd)]]*100
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`In which dr(Pd)is the relative distance in relation to the center of the point of maximum divergence
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`Pd, dr(Pdl) is the relative distance in relation to the center of the corresponding pointon the linear
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`distribution straight line Fdc, a(Pd) being the abscissa of the pointPd,i.e., the field angle of the
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`corresponding object point.
`[0075]
`In the example considered here, the maximum divergence is therefore equal to +125%.
`This value of maximum divergence accordingto the present invention is clearly higher than that due
`to the possible design errors or manufacturing errors of a classical panoramic objective lens, which
`is of a few percent. Generally speaking, a non-linear objective lens accordingto the present
`invention has a maximum divergence onthe order of 10% at least, to obtain an expansion ofthe
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`useful parts of the image whichres