the invention will now be described in detail by way of two specific examples which are in no way intended to be limiting of the invention as hereinafter claimed . the principles of the present invention apply equally well to indirect ophthalmoscopy lenses of the contact and non - contact type and as utilized with an indirect ophthalmoscope , slit lamp biomicroscope , operating microscope , or other instrument , as well as for use in photographic and video monitoring and recording applications . as such , a variety of lenses of different design , power and configuration may be utilized within the scope of the invention . referring to fig1 there is shown a single element aspheric , indirect ophthalmoscopy lens 10 constructed in accordance with the present invention and positioned anterior of a cornea 12 of a patient &# 39 ; s eye 14 which includes a crystalline lens 16 , a pupil 17 and a retina 18 . indirect ophthalmoscopy lens 10 includes a posterior surface 20 and an anterior surface 22 and may be held in a retaining fixture 24 in a conventional manner with a threaded retaining insert 26 . other types of fixtures may be used to secure lens 10 . for example , when used with an operating microscope ( not shown ), lens 10 may be fixed in a known microscope adapter assembly ( also not shown ). indirect ophthalmoscopy lens 10 is used in the usual manner to form a real , aerial image of the retina when placed an appropriate distance from cornea 12 . thus , as illustrated , bundles of light rays 30 , 32 and 34 originating at and diverging from points 36 , 38 and 40 , respectively , on retina 18 , pass through crystalline lens 16 , exit the eye through pupil 17 and cornea 12 . the light ray bundles then pass through lens 10 which focuses the light rays to form a real , aerial image 44 . however , as contrasted with known prior art indirect ophthalmoscopy lenses , the image produced by the lens constructed according to the invention as described below , while in actuality being substantially planar , if not slightly over corrected , will appear to the observer to have a three dimensional concave curvature , giving a sense of the curvature of the actual retina due to the specific distortion introduced into the image as hereinafter described . each surface of lens 10 is characterized by the following polynomial formula : where y is the semi - diameter value ; r is the apical radius of curvature ; e is the apical eccentricity ; x is the distance from the apex of the surface along its axis of revolution ; a , b and c are constant coefficients ; and f , g and h are constant exponents . for both the posterior and anterior surfaces of the lens , r can range from about 0 . 003 m to about 0 . 221 m ; e from about 0 to about 6 . 0 ; a , b , and c from about - 80 to about + 160 ; and f , g and h from about 0 . 5 to about 3 . 0 . thickness of lens 10 may range from about 0 . 001 m to about 0 . 020 m while diameter may range from about 0 . 005 m to about 0 . 070 m . lens 10 can be made from any suitable optical material such as glass or plastic , including pmma or cr - 39 ( allyl diglycol carbonate ). additionally , the index of refraction of the material selected may range from about 1 . 4 to about 2 . 1 , covering the range of conventionally available clear optical materials . in a preferred embodiment of the invention , one of the two lens surfaces , preferably the flatter of the two , may be defined simply as a conic , with the higher order terms of the equation omitted or set to zero , while the opposing surface will have active coefficients of substantial magnitude to achieve the stated optical characteristics of the present invention . in a specific example of this preferred embodiment , applicant made a lens wherein lens surface 20 was designed as a conoid with r = 0 . 01589 m and e = 3 . 0 ; and lens surface 22 was designed according to the following polynomial values : r = 0 . 00935 m ; e = 2 . 0 ; a = 1 . 1 ; b =- 45 . 66 ; c = 35 . 0 ; f = 1 . 2 ; g = 1 . 8 ; h = 2 . 4 . the lens was designed with a diameter of 0 . 019 m , a center thickness of 0 . 00535 m and the glass material had an index of refraction of 1 . 883 . turning now to fig2 there is shown on the right - hand side of the graph a distortion curve of the single element non - contact lens of fig1 constructed according to the above formula and polynomial values . the horizontal axis indicates percentage of distortion , which corresponds to relative magnification as previously discussed . thus , an increasing percentage of distortion indicates an increasing magnification and a decreasing percentage of distortion indicates a decreasing magnification . the vertical axis represents the normalized field of the lens in air . generally speaking , indirect ophthalmoscopy lenses corrected for field curvature and astigmatism exhibit insufficient correction of distortion and as such , the aerial image produced may appear flat , as opposed to having a curved appearance corresponding to the curvature of the retina itself . a distortion plot of such a lens will show only negative distortion or insufficient distortion correction . if fully corrected for distortion , the indirect ophthalmoscopy lens exhibits poor field characteristics and excess magnification in the periphery of the image . the distortion plot of fig2 represents not only a desirable compromise of distortion , defining a lens generally well corrected , if not slightly over corrected for field curvature , but additionally one that presents a three dimensional concave appearance that imparts to the observer a sense of the curvature of the actual retinal . progressively increasing magnification peripheralward in the central region of the aerial image initially provides the sense of the visualized retina approaching the observer . proceeding toward the periphery of the aerial image , magnification shifts direction , reducing image size and lateral magnification , thus providing a visual sense that an equatorial region of the retina is being approached . it is this unique character of continuously and progressively increasing , then decreasing magnification that promotes the visual sense of the three dimensional concave curvature of the retina according to the present invention . furthermore , the reduced field of view normally resulting from excess peripheral magnification has been avoided by designing the indirect ophthalmoscopy lens according to the distortion characteristics shown . table i below lists in the first two columns the x values and corresponding y values calculated at 0 . 0005 m increments ( i . e . increments of the semi - diameter of the lens ) using the foregoing polynomial formula with the polynomial values listed above for the lens of fig1 . the third column is the instantaneous eccentricity calculated at the corresponding x and y points shown in the first two columns . as can be seen , the eccentricity progressively and continuously decreases from the center of the lens toward the periphery , attesting to the aspheric , non - conoidal shape of the lens according to the invention . table i______________________________________y x ecc______________________________________ . 000500000 . 000013262 2 . 932212 . 001000000 . 000052280 2 . 559429 . 001500000 . 000115470 2 . 363625 . 002000000 . 000201007 2 . 227660 . 002500000 . 000307063 2 . 119918 . 003000000 . 000431951 2 . 027539003500000 . 000574190 1 . 944101 . 004000000 . 000732534 1 . 865957 . 004500000 . 000905972 1 . 790843 . 005000000 . 001093717 1 . 717243 . 005500000 . 001295195 1 . 644070 . 006000000 . 001510026 1 . 570484 . 006500000 . 001738018 1 . 495785 . 007000000 . 001979154 1 . 419333 . 007500000 . 002233593 1 . 340484 . 008000000 . 002501674 1 . 258536 . 008500000 . 002783926 1 . 172652 . 009000000 . 003081088 1 . 081761 . 009500000 . 003394142 . 984386______________________________________ referring to fig3 there is shown a multiple element , indirect ophthalmoscopy contact lens 50 including a cone shaped lens holder 52 securing and interconnecting a contact lens element 54 and an anterior lens element 56 . contact lens element 54 is mounted in the small end of cone shaped lens holder 52 and extends outwardly therefrom to enable contacting with a cornea 58 of a patient &# 39 ; s eye 59 . contact lens element 54 may be secured in place with an optical glue , by means of interlocking threads or by other conventional means . anterior lens element 56 is mounted slightly inwardly of the larger diameter end of cone shaped lens holder 52 to protect its outer ( anterior ) lens surface . anterior lens element 56 is maintained in a fixed position by a conventional threaded retaining ring 64 against a compressible o - ring 66 , which itself abuts against a shoulder 68 of cone shaped holder 52 . lens holder 52 allows manipulation of the ophthalmoscopy lens 50 when operatively disposed with contact lens element 54 in place against the eye 58 of a patient . both contact lens element 54 and anterior element 56 may be made of homogenous transparent optical material , such as glass or plastic , the index of refraction of the material ranging from about 1 . 4 to about 2 . 1 . contact lens element 54 has posterior and anterior surfaces 55 and 57 , respectively , and anterior lens element 56 has posterior and anterior surfaces 60 and 62 , respectively , each of which surfaces can be characterized by the foregoing polynomial formula . one or both surfaces of anterior lens 56 or of a plurality of lens elements anterior to the contact lens element may incorporate the aspheric , non - conoidal surface contributing to the variable magnification characteristics of the present invention . for simplicity in design and ease of manufacturing , it is preferable to limit this aspheric , non - conoidal shape to the anterior or steeper lens surface of the most anterior lens element ( i . e . surface 62 in fig3 ). each of the lens surfaces of the contact lens element may have the profile of a conoid , meaning that the higher order terms of the polynomial formula are set to zero . preferably , for the posterior contact lens surface 55 , r can range from about 0 . 007 m to about 0 . 0084 m , and e from about 0 . 0 to about 0 . 9 . for the anterior contact lens surface r can range from about 0 . 004 m to about 0 . 100 m and e from about 0 . 0 to about 3 . 0 . thickness of the contact lens may range from about 0 . 0005 m to about 0 . 015 m while the diameter of its useable optical portion may range from about 0 . 004 m to about 0 . 020 m . for both the posterior and anterior surfaces 60 , 62 of anterior lens 56 , r can range from about 0 . 003 m to about 0 . 221 m ; e from about 0 to about 6 . 0 ; a , b , and c from about - 80 to about + 160 ; and f , g and h from about 0 . 5 to about 3 . 0 . thickness of the anterior lens 56 may range from about 0 . 001 m to about 0 . 020 m while diameter may range from about 0 . 005 m to about 0 . 050 m . spacing between contact lens element 54 and anterior lens element 56 may range from about 0 . 00005 m to 0 . 025 m . the optical material may be treated to include light filtering properties for absorbing specific wavelengths of light . it is preferred that contact lens element 54 be made of polymethylmethacrylate and anterior element 56 of optical glass , such as schott lakn16 with an index refraction of 1 . 734 . both surfaces of anterior element 56 and the anterior surface of contact lens element 54 may be coated with an anti - reflective coating to minimize reflections and increase light transmission . as shown in fig3 light ray bundles 70 , 72 and 74 originating at and diverging from points 76 , 78 and 80 , respectively , of retina 82 , exit eye 59 through pupil 84 and cornea 58 and are refracted by contact element 54 towards anterior lens element 56 which focuses the converging light ray bundles at aerial image 88 . a contact indirect ophthalmoscopy lens constructed according to the invention may be used with the slit lamp biomicroscope , operating microscope or other instrument . because a variety of lenses of different power are utilized with each instrument , a variety of lenses of different design , power and configuration may be utilized in combination with the principles of the present invention which employ variable magnification to produce the three dimensional effect of the retinal image . the lens of fig3 as an example , may be constructed for use with an operating microscope in vitreoretinal surgery , and used with a suture down scleral ring ( not shown ). in a specific example of a contact indirect ophthalmoscopy lens illustrated in fig3 posterior and anterior surfaces 55 , 57 of contact lens element 54 each have a conoidal shape , wherein for the posterior surface 55 , r = 0 . 0077 m and e = 0 . 425 ; and for the anterior surface 57 , r = 0 . 00695 m and e = 0 . 425 . contact lens element 54 is made of polymethylmethacrylate with an index of refraction of 1 . 491 and has a diameter of 0 . 0105 m and center thickness of 0 . 0024 m . spacing between the contact lens element and the anterior lens element is 0 . 0005 m . the posterior surface 60 of anterior lens 56 is also designed as a conoid with r = 0 . 01248 m and e = 2 . 64 . the anterior surface 62 of anterior lens 56 is designed according to the above polynomial formula wherein r = 0 . 00805 m ; e = 1 . 43 ; a = 1 . 1 ; b =- 27 . 35 ; c = 35 ; f = 1 . 2 ; g = 1 . 8 ; and h = 2 . 4 . anterior lens element 56 is produced from an optical quality glass with an index of refraction of 1 . 734 , has a diameter of 0 . 01626 m and a center thickness of 0 . 006 m . referring again to fig2 there is shown on the left - hand side of the graph a distortion curve for the foregoing example of the multi - element , contact , indirect ophthalmoscopy lens illustrated in fig3 . as with the distortion curve of the single , non - contact , indirect ophthalmoscopy lens illustrated on the right - hand side of fig2 the distortion characteristics shown represent not only a desirable compromise of distortion , defining a lens generally well corrected , if not slightly over corrected for field curvature , but additionally one that represents a concave fundus appearance , thus imparting a sense of the actual curvature of the retina being imaged . progressively increasing magnification peripheralward in the central region of the aerial image initially provides the sense of the visualized retina approaching the observer . proceeding toward the periphery of the image , the distortion curve indicates that magnification shifts direction , reducing image size and lateral magnification , thus providing a visual sense that an equatorial region of the retina is being approached . preferably , the variable distortion according to the invention is positive in the central region by no more than about 10 % and is negative in the peripheral region by no more than 15 %. it is additionally preferable that the total distortion for any one lens system vary by no more than an absolute value of 15 % over the extent of the real , aerial image . table ii below lists in the first two columns the x values and corresponding y values at 0 . 0005 m increments of the semi - diameter , describing the anterior lens surface 62 of anterior lens 56 of the multiple element indirect ophthalmoscopy lens according to the polynomial parameter values of the foregoing example . the third column shows the calculated instantaneous eccentricity values for the corresponding values of x and y . as with the lens of fig1 the anterior lens surface 62 of lens 56 demonstrates continuously and progressively decreasing eccentricity toward the periphery of the lens surface , attesting to the aspheric , non - conoidal shape of the lens surface . table ii______________________________________y x ecc______________________________________ . 0005 . 0000154 2 . 513254 . 0010 . 0000608 2 . 143257 . 0015 . 0001345 1 . 952909 . 0020 . 0002349 1 . 824425 . 0025 . 0003602 1 . 725957 . 0030 . 0005088 1 . 644595 . 0035 . 0006795 1 . 573918 . 0040 . 0008710 1 . 510303 . 0045 . 0010826 1 . 451518 . 0050 . 0013134 1 . 396095 . 0055 . 0015630 1 . 343020 . 0060 . 0018310 1 . 291556 . 0065 . 0021174 1 . 241149 . 0070 . 0024223 1 . 191366 . 0075 . 0027460 1 . 141849 . 0080 . 0030888 1 . 092296 . 0085 . 0034517 1 . 042437 . 0090 . 0038354 . 992014 . 0095 . 0042413 . 940777______________________________________ in summary , the present invention provides a variety of lens types in an improved indirect ophthalmoscopy lens system , producing a clear and focused aerial image of the fundus and vitreoretinal structures of the eye with unique optical properties aiding the practitioner in various diagnostic , treatment and surgical procedures where an appreciation of the curvature of the retinal image is desirable or required . although preferred embodiments of the invention have been described , it is to be understood that various modifications would be obvious to those skilled in the art and are embodied within the present invention as defined by the appended claims .
an ophthalmoscopy lens system is provided for collecting light rays emanating from a patient &# 39 ; s eye and focussing the collected light rays to produce a real , aerial image of the fundus of the patient &# 39 ; s eye . the ophthalmoscopy lens system includes a plurality of lens surfaces at least one of which is shaped to provide in conjunction with the other lens surfaces variable image distortion such that the aerial image , as viewed by an observer from a position anterior of the ophthalmoscopy lens system , has an apparent three dimensional concave curvature that imparts to the observer a sense of the actual concave curvature of the fundus being imaged .