United States Patent
`
`[191
`
`[11]
`
`3,953,111
`
`Fisher et al.
`[451 Apr. 27, 1976
`
`[54] NON-LINEAR LENS
`
`[75]
`
`Inventors: Ralph W. Fisher, St. Charles;
`George Licis, Manchester; Wayne
`W. Schurter, Bridgeton, all of Mo.
`
`[73] Assignee: McDonnell Douglas Corporation, St.
`Louis, Mo.
`
`[22]
`
`Filed:
`
`Nov. 4, 1974
`
`[21] Appl. No.: 520,487
`
`[52] US. Cl.................................. 350/189; 350/181
`[51]
`Int. Cl.2 .................... 829D 13/18; GOZB 13/08
`[58] Field of Search ........... 350/189, 192, 198, 175,
`350/ 181
`
`[56]
`
`References Cited
`UNITED STATES PATENTS
`
`6/1962 Hughues ............................. 350/192
`3,037,426
`FOREIGN PATENTS OR APPLICATIONS
`
`1,105,632
`
`4/1961 Germany ......................... 350/175 R
`OTHER PUBLICATIONS
`
`Rigler; A. K. and Vogt; T. P., “Spline Functions: an
`Alternative Representation of Aspheric Surfaces,”
`Applied Optics, Vol. 10, No. 7, pp. 1648—1651, July,
`1971.
`
`Primary Examiner—John K. Corbin
`Assistant Examiner—Conrad Clark
`
`Attorney, Agent, or Firm—Graveley, Lieder &
`Woodruff
`
`[57]
`
`ABSTRACT
`
`A non-linear lens possesses distortion characteristics
`which are such that objects along the optical axis of
`the lens occupy disproportionately large areas of the
`image cast by the lens, whereas objects near the pe—
`riphery of the field of view occupy a disproportion-
`ately small area of the image. The distortion charac—
`teristics approximate the formula Hqin"3 9 where H
`is height measured from the optical axis and 0 is the
`angle measured from the optical axis. The image cast
`by the lens falls on the vidicon of a television camera
`where it
`is scanned and transmitted to a projector.
`Since the lens enlarges objects in the vicinity of the
`optical axis, those objects are transmitted with much
`greater detail than objects in the peripheral region of
`the view. The transmitted image is reproduced at a
`projector and the reproduced image is
`rectified
`through another lens having identical distortion char-
`acteristics. This lens casts the rectified image on a
`spherical screen. The final image which appears on
`the screen possesses a high degree of acuity in the re-
`gion of the optical axis and substantially less acuity in
`peripheral regions. The resolution throughout the en-
`tire field of the reproduced image corresponds quite
`closely to the resolution characteristics of the human
`eye.
`
`10 Claims, 7 Drawing Figures
`
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`Panasonic Exhibit 1004 Page 1 of 9
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`

`

`U.S. Patent
`
`April 27, 1976
`
`Sheet 10f3
`
`3,953,111
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`30 H2. FRAME RATE
`
`I 000
`
`I00
`
`6
`
`BANDWIDTHINMEGAHERTZ
`
`
`
`
`
`
`
`
`ANGULAR
`RESOLUTION
`MINUTES
`ARC
`
`80
`I20
`FIELD OF VIEW - DEG
`
`FIG.I
`
`RELATIVE
`
`ACUITY
`
`RESOLUTION MIN OF ARC
`
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`
`4o
`0
`40
`DEGREES FROM FOVEA
`
`FIG. 2
`
`,
`
`80
`
`M
` NON - LINEAR LENS
`H = Sufi/39
`
`FISHEYE LENS
`H=K®
`
`
`
`
`
`
`CONVENTIONAL
`
`CAMERA LENS
`
`
`ov
`IO
`20 30 40
`50
`6O 7O
`80
`90
`
`H = K tan 9
`
`(H)
`
`
`
`NORMALIZEDIMAGEHEIGHT
`
`9.0.0.0:-whomo
`
`O
`
`FIG. 3
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`Panasonic Exhibit 1004 Page 2 of 9
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`

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`U.S. Patent
`
`April 27, 1976
`
`Sheet 2 of 3
`
`3,953,111
`
`ERROR SIGNALS
`
`
`
`
`
`VIDEO +CAMERA
`ELEVATION AND
`AZl MUTH
`
`COMMANDS
`
`PROJECTION
`SCREEN
`
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`NON-LINEAR
`
`LENS
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`Panasonic Exhibit 1004 Page 3 of 9
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`

`

`US. Patent
`
`April 27, 1976
`
`Sheet 3 of 3
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`3,953,111
`
`Inmlfi
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`Panasonic Exhibit 1004 Page 4 of 9
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`

`

`1
`
`NON-LINEAR LENS
`
`3,953,111
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`2
`eye is immediately moved to bring the foveal axis to the
`thing of interest and thereby provide a clearer image of
`it.
`
`The Government has rights in this invention pursuant
`to Contract Number N00014-73-C-0154 awarded by
`the Department of the Navy.
`BACKGROUND OF THE INVENTION
`
`The present invention relates in general to lenses and
`more particularly to a lens having non-linear distortion
`characteristics.
`‘
`.
`‘
`The typical remote viewing system utilizes a televi-
`sion camera at the remote location, some type of pro—
`jector at the observer location, and a television trans-
`mitting system linking the two. These viewing systems
`fall far short of duplicating the visuai characteristis of
`the human eye in that they have extremely limited
`fields of ,view or else poor resolution in a large field of
`View.
`
`In particular, for any fixed angular resolution (mea-
`sured in minutes of arc) and frame rate (usually 30 Hz
`or frames/sec.) a definite relationship exists between
`field of View and bandwidth for transmitting that field
`of view. For example, commercial television, which
`utilizes a 525 line raster traced 30 times per second,
`operates on a bandwidth of 3.93 MHZ. To match the
`resolution of the human eye, which is one minute of arc
`along its foveal or optical axis, the field of view for
`commercial television must be restricted to less than
`10° (see FIG. 1). On the other hand, if the field of view
`is increased to about 180°, which is the field of view for
`the human eye, the bandwidth must be increased to
`1000 Mhz to maintain one minute of arc resolution
`over the entire field. This demands a raster of 10,000
`lines and is far in excess of the capabilities of current
`television systems.
`'
`Indeed, the most advanced television currently avail-
`able utilizes an 875 line system and requires a band-
`width of 10.9 Mhz.» This provides a field of view of
`about 20° with one ‘minute arc resolution throughout
`the entire field, which is far less than the 180° field of
`view possessed by the human eye.
`From the foregoing, it is clear that present television
`viewing systems present a dilemma. If the field of view
`is sufficient to encompass all possible locations of inter-
`est, resolution is so low that detection or clear observa-
`, tion is impossible. On the other hand, if the resolution
`is adequate to insure that the objects will be seen
`clearly, the field of view is quite limited and many
`objects of interest are located outside of the field of
`view.
`
`In a sense the human eye provides a solution for the
`foregoing dilemma. The human eye possesses high
`optical acuity along and in the vicinity of its foveal or
`optical axis, ,but the acuity diminishes outwardly there—
`from. In other words, the eye distinguishes fine detail
`directlyjin front of it, but not to the sides. This charac-
`teristic is not derived from the shape of the eye lens,
`but instead results from the fact that most of the optical
`fibers for the eye are concentrated in the vicinity of the
`optical axis. Hence, only along the optical axis does the
`eye possess one minute of arc resolution. .The resolu-
`tion becomes progressively less toward the periphery of
`the field of vision (see FIG. 2). Nevertheless, the reso-
`lution in the peripheral area is sufficient to detect the
`presence of many objects in that area as well as much
`movement in that area. Of course, when the eye detects
`anything of interest in the peripheral areas, the head or
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`SUMMARY OF THE INVENTION
`
`One‘of the principal objects of the present invention
`is to provide a lens having non-linear distortion charac-
`teristics which are such that objects located along and
`near theoptical axis of the lens occupy a disproportion—
`ately large area of the image produced by the lens.
`Another object is to provide a lens of the type stated
`which closely approximates the resolution characteris-
`tics of the human eye over a wide field of view. A fur-
`ther object is to provide a lens of the type stated which
`is ideally suited for use in remote viewing systems in
`that it provides a wide field of view with maximum
`acuity along the optical axis. These and other objects
`and advantages will become apparent hereinafter.
`The present invention is embodied in a lens which
`distorts a field of view such that objects in the vicinity
`of the optical axis occupy a disproportionately large
`area of the image cast by the lens and objects in the
`peripheral region of the field of view occupy a dispro-
`portionately small area of the image. The invention also
`consists in the parts and in the arrangements and com—
`binations of parts hereinafter described and claimed.
`DESCRIPTION OF THE DRAWINGS
`
`In the accompanying drawings which form part of the
`specification and wherein like numerals and letters
`refer to like parts wherever they occur:
`FIG. 1 is a graph showing the relationship between
`field of view, angular resolution, and bandwidth for
`transmitting a picture of a remote location by televi-
`sron;
`FIG. 2 is a graph showing relative acuity of the
`human eye throughout the field of view for the eye;
`FIG. 3 is a graph showing the distortion characteris-
`tics of the lens of the present invention in terms of
`normalized image height and field of view and compar-
`ing such distortion characteristics with the distortion
`characteristics of a fisheye lens and a conventional
`camera lens;
`FIG. 4 is a graphic representation of the non—linear
`distortion characteristics and showing how equal incre-
`ments on the image plane correspond to unequal incre—
`ments in the field of view;
`FIG. 5 is a schematic perspective view of the remote
`viewing system in which the non-linear lens may be
`utilized;
`FIG. 6 is a sectional view of the non-linear lens; and
`FIG. 7 is an enlarged sectional view of the second and
`third lens groupings for the non-linear lens.
`DETAILED DESCRIPTION
`
`The lens of the present invention (FIGS. 6 and 7)
`provides non-linear image distortion characteristics
`over an extremely wide field of view which approaches
`160°. This is in contrast to so-called fisheye lenses
`which provide linear distortion characteristics.
`In
`paticular, with a linear or fisheye lens the image height
`is directly proportional to the field angle (FIG. 3). The
`relationship is defined by the formula H=K 0 where H
`is the image height from the optical axis, K is a con-
`stant, and 0 is the angle measured from the optical axis.
`Thus, with a linear lens an object occupying twice the
`angle as another object, when measured from the opti-
`cal axis, will cast an image twice as high as the other
`
`Panasonic Exhibit 1004 Page 5 of 9
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`

`

`3
`object. On the other hand, with a non—linear lens of the
`present invention the image height is equal to a variable
`function of the field angle (FIG. 3). The relationship is
`approximated by the formula H=sin“a 0. Thus, objects
`centered along the optical axis of the non-linear lens L
`cast a much larger image than objects located near the
`periphery of the field of view with the size diminishing
`as the angle from the Optical axis increases. The result
`of the distortion is that objects along the optical axis
`occupy a disproportionately large share of the image
`cast by the lens when compared with other objects
`closer to the periphery of the field of view for the lens.
`In effect, the center of the non-linear lens is a telephoto
`lens, while the periphery of the lens amounts to a wide
`angle lens with the annular region between the center
`and periphery varying from telephoto to wide angle.
`Naturally, the image produced is quite distorted. The
`typical camera lens is represented by the formula H=K
`tan 0 (FIG. 3) and is non-linear, but in a sense opposite
`from that of the lens of the present invention.
`The non-linear transfer characteristics of the lens
`may be illustrated by breaking the image into equal
`angular
`increments (FIG. 4) and comparing each
`image increment with the correSponding increment it
`represents in the actual field of view. Clearly, equal
`angular increments on the image side of the lens repre-
`sent unequal increments on the object side of the lens.
`More specifically, near the optical axis relatively small
`arcs on the object side are converted to large arcs on
`the image side, thus enlarging the image. At about 25°
`from the optical axis arcs on the object side equal the
`arcs on the image side and this portion of the lens may
`be considered linear. Objects from about 25° to 80°
`(lens periphery) occupy arcs much larger than they
`cast on the image side with the variance in arcs becom-
`ing greater as the object approaches the periphery of
`the field. Hence, objects within 25° of the optical axis
`for the lens are magnified with the magnification being
`substantial along the lens axis, whereas objects in the
`annular region located beyond 25° are reduced in size,
`with the reduction becoming progressively greater as
`the maximum field angle for the lens is approached.
`To appreciate the lens requires an understanding of
`the remote viewing system in which it is utilized. That
`viewing system basically comprises (FIG. 5) a televi~
`sion camera at the remote location, a projector at the
`observer location, and a transmission system linking
`the camera and projector in both directions. Both the
`camera and projector are fitted with non-linear lenses
`having identical distortion characteristics. However,
`the projector lens is mounted just the reverse of the
`camera lens so that it rectifies the distortion created by
`the camera lens. The camera is supported on a gim-
`balled mount and is therefore capable of swinging both
`vertical and horizontal angles with respect to fixed
`coordinates at the remote location. A suitable servo
`mechanism bridges the gimballed mount to control the
`position of the camera. The projector is likewise sup-
`ported on a gimballed mount which permits it to swing
`both vertical and horizontal angles with respect to fixed
`coordinates at the observer location. Another servo
`- mechanism bridges the gimballed mount of the projec-
`tor, and this servo is slaved to the camera through the
`transmission system such that a change in elevation or
`azimuth of the camera with respect to its fixed coordi-
`nates results in a corresponding change in elevation
`and azimuth of the projector with respect to its fixed
`coordinates.
`
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`3,953,111
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`4
`The projector projects the transmitted image through
`its non-linear lens which casts the image upon a spheri‘
`cal screen surrounding the projector. The observer
`views the screen from the position of the projector.
`Positioned on the projector is an oculometer which
`views the observer’s eye through a transparent beam-
`splitter, and in effect tracks the observer’s eye, produc-
`ing error signals whenever the foveal axis of the eye
`deviates from the optical axis of the projector lens. In
`other words, error signals are produced when the fo-
`veal axis of the eye and the optical axis of the projector
`lens intersect the screen at different locations. These
`signals are converted into elevation and azimuth com-
`mands which are transmitted to the servo system for
`the camera through the transmission system. The com-
`mands cause the camera to change elevation and azi—
`muth, and the movement is such that the corresponding
`movement of the projector reduces the error and brings
`the foveal axis of the camera back toward coincidence
`with the optical axis of the lens, at least at the screen.
`Thus, the oculometer controls the position of the cam-
`era and the camera controls the position of the projec-
`tor, so in effect the camera and projector are both
`slaved to the observer’s eye through the oculometer.
`The oculometer and s‘ervo mechanisms for the camera
`and projector should all respond fast enough to bring
`the optical axis of the projector lens into coincidence
`with, or at least within 2 percent of, the foveal axis for
`the eye within 0.2 seconds. This is about as rapidly as
`the eye can fixate and perceive when changing from
`one object of interest to another, so the lag in the pro—
`jector is barely discernible, if at all. A suitable oculom-
`eter is marketed by Honeywell Inc., Radiation Center,
`Boston, Mass.
`Referring again to the television camera at the re-
`mote location,
`the camera lens casts the distorted
`image of all objects in the field of view on the vidicon
`of the camera, and this vidicon is scanned in the usual
`manner, that is with a beam which traces a raster pat-
`tern at uniform velocity. The conventional commercial
`television system of 525 lines per scan and 30 scans per
`second may be employed. This requires a bandwidth of
`3.93 MHz (FIG. 1). The beam in effect picks the image
`off of the camera vidicon.- Since the objects along the
`optical axis are magnified and occupy a disproportion-
`ately large area of the vidicon, they are picked off the
`vidicon in great detail. On the other hand, objects in
`the peripheral region of the field of view are reduced in
`size and occupy relatively little area on the vidicon.
`Hence, they are picked off of the vidicon with substan-
`tially less detail. The picture is transmitted accordingly.
`The magnification along and near the optical axis is
`great enough to enable the beam to extract one minute
`of arc detail, which is all an eye with 20—20 vision can
`perceive along its foveal axis. The beam extracts .
`greater angles of arc detail away from the optical axis
`and hence poorer resolution is available in this area. In
`this regard, it will be recalled that to extract one minute
`arc detail over a full 180° requires a 10,000 line vidicon
`or in other words a bandwidth of 1000 MHz which is
`far in excess of present television capabilities.
`The distorted image cast upon the vidicon of the
`camera is reproduced by the light valve of the projector
`and this image likewise has at least one minute of arc
`resolution along the optical axis with the resolution
`diminishing toward the periphery of the image so that
`only much larger angles of are are discernible beyond
`the optical axis. The image so produced is rectified by
`
`
`
`Panasonic Exhibit 1004 Page 6 of 9
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`

`

`3,953,111
`
`6
`ment 6. The inside element c also has a spherical sur-
`face R, which faces the tapered interior of the housing
`2 andIS presented toward the second lens grouping B.
`Along the optical axis Z for the lens, the element a has
`a thickness t1, the element b a thickness t2, and the
`element c a thickness t3. Index matching oil couples the
`matching surfaces R2 of the lens elements a and b and
`the matching surfaces R3 of the lens elements b and c.
`The outside and inside lens elements a and c are formed
`from type SK16 glass, whereas the intermediate lens
`element is formed from type F2 glass. The index of
`refractiOn for SK16 glass is 1. 62041 and for F2 glass is
`1.62004. The Abbe number for SK16IS 60. 27 and for
`F2 is 36. 25.
`
`5
`the projector lens which casts it upon the spherical
`screen. The resulting screen image constitutes a faithful
`reproduCtion of the scene which lies within the field of
`view for the camera lens. The projector lens in no way
`affects the resolution of the image it transmits and as a
`result the image appearing on the screen shows detail
`as close as one minute of are at the optical axis for the
`lens and the area immediately surrounding it, but in the
`remaining area such detail is not available. In other
`words, the resolution in the other areas is somewhat
`less. Hence, the projected image is very sharp and clear
`on the screen at the Optical axis, that is directly in front
`of the projector, and then turns somewhat fuzzy or
`blurred in the surrounding area particularly at the max-
`imum angle of 80° from the optical axis.
`The variance in clarity or in resolution of the final
`image cast upon the screen closely resembles the opti-
`cal characteristics of the eye (FIG. 2). In this connec-
`tion, it will be recalled that most of the optical sensing
`elements for the human eye are concentrated along the
`foveal axis.
`
`As previously mentioned, the oculometer tracks the
`eye position and causes the camera to change position
`in response to eye movement while the projector un—
`dergoes corresponding movement as a result of being
`slaved to the camera Consequently, the foveal or opti—
`cal axis of the eye is always directed at the center of the
`projected image, that is the portion along the optical
`axis for the projector lens. This is the portion having
`the one minute of arc resolution. Since the resolution
`
`of the eye falls off with the angle from the foveal axis,
`little is lost by having'the resolution of the projected
`image diminish with the angle from the optical axis.
`The resolution in the surrounding area of the picture is
`still good enough to permit the eye, as a result of the
`built-in peripheral vision, to detect movement and ob-
`jects of interest, and if 'whatever is detected appears
`interesting enough, the viewer will turn his eye toward
`it. This, of course, causes the camera and projector to
`change position so that the formerly blurred area of the
`image to which the eye is turned lies along the optical
`axis of the camera and projector lenses and is projected
`with high resolution.
`The non--1inear lens (FIGS. 6 and 7) has three lens
`sets or groupings A, B and C. Its aperture ratio is 5. 6
`and it forms a 0.358 F diameterimage where Fis the
`focal length along the optical axis Z. The first lens
`grouping Ais considerably larger than the other group-
`ing B and C andis contained in the large end of a ta—
`pered lens housing. The other lens groupings B and C
`are contained within a subhousing which fits into the
`small end of the tapered main housing. The first lens
`grouping is a triplet and provides the mapping function,
`that is the unique distortion which is essentially defined
`by the formula H=sin"3 0.‘ Thesecond grouping B,
`which has four elements, contains the aperture stop
`and forms an image of the scene as distorted by the first
`grouping A The third grouping C is a single element
`which functions as a field flatener, that is it makes the
`image cast by the second grouping B planar.
`The first lens' grouping A (FIG. 6') consists of three
`lens elements a, b, and 'c with no air gaps between adja-
`cent elements. The outside lens element a has a non-
`spherical surface R1 exposed outwardly and a spherical
`surface R2 presented inwardly against a matching sur-
`face R2 on the intermediate element b. The opposite
`surface R3 of the intermediate element 17 is non-spheri-
`cal and abuts a matching surface R3 on the inside ele-
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`Turning now to the second lens grouping B, it con—
`sists of four lens elements, namely, a convex-concave
`lens element d, a double convex lens element 2, a dou-
`ble concave lens element f, and a double convex lens
`element g, all arranged in that order from the first lens
`grouping A. The innermost lens element d has spherical
`surfaces R5 and R6 and a thickness t5, along the optical
`axis Z. The next lens element e has spherical surfaces
`R7 and R8 and a thickness :7 along the optical axis Z.
`Next,
`is the double concave lens element f having
`spherical surfaces R9 and R10 and a thickness t“, along
`the optical axis ._2. The surface R10 of the element f
`corresponds to and is against a matching surface Rm on
`the lens element g which has another spherical surface
`Ru presented toward the third lens grouping C. The,
`surfaces R6 and R7 of the lens elements d and e, respec-_
`tively, are separated by an air gap t6 measured along the
`axis Z of the lens, while the surfaces R6 and R9 of the
`lens elements e and f, respectively, are separated by an
`air gap t8 measured along the Optical axis 2. The match-
`ing surfaces R10 of the lens element f and g are ce-
`mented. The lens elements d and f are formed from
`type F2 glass, while the lens elements e and g are
`formed from type SK16 glass.
`The third lens grouping C contains a single lens ele-
`ment h having a non-spherical and non-planar surface
`R12 which is presented toward the second lens group B
`and a spherical surface R13 exposed outwardly. The
`lens element h has a thickness t12 along the optical axis
`Z and is made from the .type SK16 glass.
`The first and second lens groupings A and B are
`separated by an air gap t, which1s measured from the
`surface R4 to the surface R5 along the axis 2 ofthe lens.
`The second and third lens groupings B and C are sepa-
`rated by an air gap t11 which is the distance between the
`surfaces R11 and R12 measured along 'the'optical axis Z.
`The distorted image formed by the non-linear lens
`exists in an image plane p located beyond the third lens
`grouping 'C. The vidicon of the’ television camera
`should be at'this plane p.
`The surfaces R2, R4, R5, R6, R7, R3, R9, R10, R11 and
`R13 are all spherical and have their centers of curvature
`along the optical axis Z of the lens. The surfaces R1, R3,
`and R12, while being curved, are not spherical. The
`radii of curvature forthe surfaces Rl through R13 fol-
`low:
`
`‘
`
`1.4F
`
`1.09IF
`0.2373F
`0.272F
`0.3936F
`0.334F
`0.2268F
`
`R,
`< R2
`R:
`< R,
`<—R5
`<—Ra
`< R,
`<—R,,
`<—R9
`
`1.37F
`:
`< 1.5 F
`:
`0. 729F
`< 1.092F
`< 0. 2376F
`< 0. 273F
`.< 0. 3940F
`< 0.335F
`< 0.2271F
`
`(at optical axis only)
`
`(at optical axis only)
`
`Panasonic Exhibit 1004 Page 7 of 9
`
`

`

`7
`
`1 1 1
`
`3 ,9 5 3,
`
`0.2801=
`0.57IF
`
`0.4]68F
`
`< R“,
`<—R,,
`—Ru
`<—R,a
`
`-continued
`< 0.285F
`< 0.572F
`:
`0.314F
`< 0.4173F
`
`(at optical axis only)
`
`5
`
`10
`
`15
`
`20
`
`25
`
`where F is the focal length of the lens along its optical
`axis Z. Note, that since the surfaces R1, R3 and R13 are
`not spherical, the radii of curvature listed above for
`those surfaces represents only radii along the optical
`axis Z of the lens.
`The thicknesses of the various lens elements mea-
`sured along the optical axis 2 follow:
`0.199F <t,<0.202F
`0.399F<t2<0.402F
`O.399F<t3<0.402F
`O.047F<t5<0.049F
`0.186F<t7<0.189F
`0.019F<t9<0.022F
`0.06F<tm<0.07F
`0.08F<t12<0.09F
`The thicknesses of the air gaps measured along the
`optical axis Z follow:
`3.248F<t4<3.251F
`O.0004F<t6<0.0014F
`. 0.266F<tn<0.267F
`0.037F<ts<0.041F
`As previously noted, the surfaces R1, R3, and R“, are
`neither spherical nor planar. Furthermore, not one of 30
`them fits any single known mathematical formula. They
`are defined in terms of splines, that is each surface is
`broken up into increments or intervals which are de-
`fined’separately. The surfaces R1, R3 and R13 are con-
`sidered spline surfaces and are defined by the following
`cubic spline equation:
`
`35
`
`S(p)=Ml-l
`
`(pr—10)3
`6 hi
`
`+M,
`
`(P—Pi-l)5
`‘6 h,
`
`,
`
`M_ h,
`+ XH— —“-'—6
`
`(
`
`h.
`
`+ (Xi_
`
`Mihf
`
`6
`
`)(rm—Q-
`
`40
`
`where
`
`Surface
`R1
`0.0000000
`0.2108668
`0.8554116
`1.7838662
`1.9775600
`—
`—
`0.0000000
`1.0780200
`2.1560400
`3.2340801
`3.6360801
`—
`—
`0.3644990
`0.3596961
`. 0.4358774
`~0.6375478
`-—2.1376087
`—
`—
`
`X(0)
`X( 1)
`X(2)
`X(3)
`X(4)
`X(5)
`X(6)
`p(O)
`p( 1)
`p( 2)
`p(3)
`p(4)
`p(S)
`p(6)
`M(O)
`M(l)
`M(2)
`M(3)
`M(4)
`M(5)
`M(6)
`
`8
`
`Surface
`R3
`0.0000000
`0.1795877
`0.7202623
`1.4361922
`1.6027882
`-—
`—
`0.0000000
`0.7222734
`1.4444546
`2.1668202
`2.4760010
`—
`—
`0.6859612
`0.6935749
`0.6937277
`—1.4543979
`—0.6921574
`—
`—
`
`Surface
`R12
`0.0000000
`-0.0029324
`—0.004l 130
`—0.000476l
`0.0065340
`0.0100000
`0.0100000
`0.0000000
`0.0825000
`0.1650000
`0.2475000
`0.3300000
`0.4010000
`0.5000000
`—1 .5916510
`0.5983017
`0.7436587
`0.6856855
`-0.5200549
`0.0000000
`0.0000000
`
`What is claimed is:
`
`l. A non-linear lens comprising first lens means for
`distorting a scene in the field of view for the lens such
`that objects in the vicinity of the optical axis are given
`substantially greater prominence than objects in the
`peripheral region of the field of view, and second lens
`means for forming a real image of the scene as distorted
`by the first lens means, whereby objects in the vicinity
`of the optical axis will occupy a disproportionately
`large area of the real image and objects in peripheral
`regions of the scene will occupy a disproportionately
`small area of the real image.
`2. A lens according to claim 1 wherein the field of
`view is at least approximately 160°.
`3. A non-linear lens according to claim 1 and further
`characterized by third lens means for causing the real
`image formed by the second lens means to lie in a
`plane.
`4. A non-linear lens according to claim 1 wherein the
`distortion in the real image approximates the formula
`H=sin ”39
`
`pH = The value of the spline surface height at the 45
`start of the ith interval.
`
`p,- = The value of the spline surface height at the end
`of the ith interval.
`
`X“ = The value of the spline surface sag at the start
`of the ith interval.
`
`50
`
`X, = The value of the spline surface sag at the end of
`the ith interval.
`
`h, = p, - p1.) = The length of the ith interval.
`M“ = The value of the slope derivative at the start of
`the ith interval.
`
`.
`
`55
`
`M, = The value of the slope derivative at the end of
`the ith interval.
`
`p = The spline surface height (independent variable)
`S(p) = The spline surface sag as a function of height
`(dependent variable)
`The slope of a spline surface element at a particular
`height (p) is given by
`
`Slope = d S(P)/dp
`
`60
`
`65
`
`The values of spline surface sag (X), spline surface
`height (p), and slope derivative (M) for various spline
`intervals 0, l, 2, etc. follow:
`
`where H is the distance in the image measured from the
`optical axis and 0 is the angle measured from the opti-
`cal axis.
`
`5. A non—linear lens according to claim 1 wherein the
`first lens means comprises a plurality of individual lens
`elements and the second lens means includes a plurality
`of different lens elements.
`
`6. A non—linear lens comprising a first lens grouping
`for distorting a scene in the field of view for the lens
`such that, objects in the vicinity of the optical axis are
`given greater prominence than objects in the peripheral
`region of the field of view, the first lens grouping in-
`cluding first, second, and third lens elements, the first
`lens element having surfaces R1 and R2, the second lens
`element having surfaces R2 and R3, and the third lens
`element having surfaces R3 and R4, the surface R2 of
`the first lens element matching the surface R2 of the
`second lens element and being substantially in contact
`therewith, the surface R3 of the second lens element
`matching the surface R3 of the third lens element and
`being substantially in contact therewith, the surfaces R1
`and R3 being curved at the optical axis and being non-
`spherical beyond the optical axis, the surfaces R2 and
`R4 being spherical substantially throughout, the radii of
`
`Panasonic Exhibit 1004 Page 8 of 9
`
`

`

`9
`the surfaces along the optical axis being substantially as
`follows:
`
`10
`wherein the value for p at spline intervals 0, 1, 2, etc. is
`
`3,953,111
`
`1.41:
`
`1.091F
`
`R.:
`<112
`R3:
`<11,
`
`1.37
`1.5
`0.729
`1.092
`
`<
`
`<
`
`F
`F
`F
`F
`
`p(O)
`p( 1)
`p(2)
`p(3)
`p(4)
`
`0.0000000
`1.0780200
`2.1560400
`3.2340801
`3.6360801
`
`0.0000000
`0.7222734
`1.4444546
`2.1668202
`2.4760010;
`
`10
`
`and wherein the value for M at spline intervals 0, 1, 2,
`etc. is
`
`M(O)
`M( 1)
`M(2)
`M(3)
`M(4)
`
`0.3644990
`0.3596961
`0.4358774
`—0.6375478
`—2.l376087
`
`0.6859612
`0.6935749
`0.6937277
`-l.4543979
`—0.6921574.
`
`9. A non‘linear lens according to claim 6 wherein the
`second lens grouping comprises a convex-concave first
`lens element, a double convex second lens element, a
`double concave third lens element, and a double con-
`vex fourth lens element, arranged in that order from
`the first lens grouping, the first lens element having a
`thickness t5 along the optical axis and spherical sur-
`faces R5 and R6, the second lens element having a
`thickness t7 and spherical surfaces R1 and R8, the third
`lens element having a thickness t9 and spherical sur—
`faces R9 and R10, and the fourth lens element having a
`thickness tm and spherical surfaces Rm and R“, the
`surface R10 of the third lens element matching the sur-
`face Rm of the fourth lens element and being substan-
`tially in contact therewith, the surfaces R6 and R7 being
`separated by a distance t6 along the optical axis and the
`surfaces R3 and R9 being separated by a distance t8
`along the optical axis; wherein the radii of curvature for
`the surfaces are:
`1.091F<R4<1.092F
`. 0.2373F<R5<0.2376F
`0.272F<R6<O.273F
`0.3936F<R.,<0.3940F
`0.334F<R8<0.335F
`0.2268 F<R9<O.2271F
`0.280F<R10<0.285F
`0.571F<R11<0.572F;
`wherein the thicknesses of the lens elements along the
`optical axis are
`»
`O.047F<t5<0.049F
`0.186F<t7<0.189F
`0.019F<t9<0.022F
`0.06F<tlo<0.07F
`0.08F<t12<0.09F;
`and wherein the spaces separating the lens elements
`are:
`
`0.0004F < t6 < 0.0014F
`0.037F < ts < 0.041F
`10. A non-linear lens according to claim 9 wherein
`the surface R4111 the first lens grouping and the surface
`R5 in the second lens grouping are separated by a dis-
`tance L; which is greater than 3.248F and less than
`3.251F.
`*
`*
`*
`*
`*
`
`Panasonic Exhibit 1004 Page 9 of 9
`
`where F is the focal length of the lens along the optical
`axis of the lens; and a second lens grouping for forming
`a real image of the scene as distorted by the first group-
`ing, whereby objects in the vicinity of the optical axis
`will occupy a disproportionately large area of the real
`image and objects in peripheral regions of the scene
`will occupy a disproportionately small area of the real
`image.
`7. A lens according to claim 6 wherein the first, sec—
`ond, and third