CA2137151A1 - Checkered placido apparatus and method - Google Patents

Abstract

A Multi-Functional Corneal Analysis System for ascertaining the shape of the corneal surface of the eye comprises a CCD camera, frame grabber board and digital image processing algorithm with associated processing circuitry. The CCD camera receives a reflection of a target such as Placido's disc from the surface of the cornea. The CCD image of the reflection of the Placido disc from the corneal surface is captured by the frame grabber board and subjected to digital analysis after treatment in an edge detector. The edge detector reduces the number of data points that must be processed to define the radius of each ring in the reflected Placido disc image. The resultant data are processed to derive surface contour and to provide a display in tabular, graphic or pictorial form of the contour data so generated. The system can be used to design custom contact lens.

Description

wo 93/2404g 2 1 3 7 1 ~i ~ PC~/US93/05293 , --l :

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CHECKERED PLACIDO APPARATUS AND METHOD

This specification incolporates by reference, an appendix from U.S. Patent AppliG~tion No. 07/891,961 filed June 2, 19~2, entit'ed "Checkered Placido Apparatus and Method." The appendix is a source code listing for the CORNEAL
ANALYSIS SYSTEM software, contained on 11 micro~1che, having 997 frames.
The source code is also submitted on diskette, as part of Ihis application.

A number of forrns of eye surgery including larnellar cornea1 surgery, keratomileusis, epikeralophakia. cataract surgery. penetra~in$ keratoplasty, corneal Iransplantation radia} keratotomy as well as laser refractive keratectomy involve a consideration of corneal surface topo~raphy. In radial keratotorny, for example. a number of cuts are made into the cornea in order tO chan~e its curvature ard correct refractive power so that images focus closer to the retina, if not upon it for best visual acuity. It has been reported that after radial keratotomy 'labout 55 ~ ~`
percent of the patients function without glasses and the remaining 45 percent have some degree of improvement.'l Origination of ~he technique of radial keratotomy and other techniques in refraetive surgery are generally credited to Dr. ~~
Svyatasklav Fyodoro~ of the Soviet IJnion who is reputed to have performed thousands of such operations. i `

While ophthalmic surgery is often successfully perforrned, the results oblained have been subject ~o varia~ion occasioned by the particular operaung wo 93/24049 2 ~ 3 7 1 S ~ -2- PCr/uss3/0s293 "style" of the individual sur~eon which dictates the number, location and depth of incision. Elements of subjective judgment are pararnount. It would be useful to provide a device ~hat could assist the surgeon in rnore quantitatively assessing pre-operative and post-operative corneal contours.

The present system relates tO improvements in the art of photokeratometry and more particularly to ~he use of digital image processing techniques to ascertain the radius of curvature. refractive power and contour of the cornea. A
keratometer is an instrument for detennining the curvature shape of the corneal ~0 surface which generally uses a Placido or other illuminated target that is centered :-around the patient's line of si~ht. The reflection of a Placido or other illuminated tar~get by the patient's cornea or by the tear film on the anterior surface of the cornea is subsequently analyzed to deterrnine the surface contour of the eye.

The technique in modern forrn dates from the early thirties when the Zeiss optical company of Germany introduced a "Photo Keratoscope" In general, the arl has required the ima,~e reflected by the eye to be photo~raphed and the image on the film measured in a second step to derive ~e quan~itative data from which the contour rnap is ~enerated.
~0 Recent improvements have been in the area of automa~ing this photogrammetric analysis by re-imaging the photograph with a television apparatus and digital signal conversion. After digiti;zation, computer analysis ~f the resultant information is pefformed with conven~ional image analysis al~orithms. This type of data analysis is computer intensive and the image formed by the television ~ ;
system contains a large amount of redundant and extraneous information. For --adequate resolution the sampling rate must exceed the data frequency by at leastthree to one, thus generating a huge number of data points for mathematical analysis. Consequently ~he systems are costly, complex, slow and often lack realresolution in the image analysis. Other means have been used for clinical measurements such as direct casting of the eye surface in plastic or wax and ;

W0 93/24049 . ; Pcr/us93/05293 coating the cornea with talcum powder and projecting a ~rid on this surface f~r photogrammetric analysis.
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The initi.al development in.keratometry came from Gullstrand ~n 1896.
S Gullstrand disclosed the foundation for the current technology but his apparatus had no provision tO compensate for aberrations in the optical system other than limiting the photo~raphic coverage of the cornea to a 4mm area. As a result, multiple exposures and calculations were necessary to map the corneal surface.

Much of the modern technique was developed by Amsler in 1930 and embodied in his "Photo-Keraeoscope" which also required measurement and calculation as a separate step to derive the corneal shape data.
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At present, the clir~ical standard is the Bausch and Lom~ Keratometer, which is sold commercially. The Bausch and Lomb Keratometer only measures the average of the corneal~ radius in two mendians of the central 3mm "cap" of the cornea. The st~ndard technology does not provide tot~l surface topo~raphy of thecornea and thus is inadequate for many diacnosdcally significant abnormalities, ~ ;`
contact lens fit~ing, or the needs of ophthalmic sur~ic.~l procedures. In addition, the prior art technique is cumbersome and involves great potential for error.

The standard ins~rument which is in most common use for central optical zone shape measurement is the Bausch .and Lomb Keratometer. Several companies '~
offer similar devices with similar principles of operation. In these devices a sin~gle Mire image is projected on a small central portion of the anterior surface of the cornea usually 3mm in diameter. The user is required to operate se~reral controls 7, to bring the op~ic. lly split Mire images reflected from the cornea simultaneously into focus and alignment. In addition, the operator manually records the data obtained at two per~endicular axes. Other instruments are also a~ailable, such as the Haag-Streit Javal Schiotz device which measures only one .~xis a~ a t~me, but is :-slightly easier to use and tends to be rnore accurate in practice than the Bausch and k~
WO 93/~4049 2 1 3 7 1 S 1 PCl /US93/05293 Lomb system. In addition there e~cists a photographic system made by International Diagnostic Instrument Limited under the trademark `-~
"CORNEASCOPE" (and a simi}ar system made by Nidek in Japan), as well as autokeratomeiers by several manufacturers. The CORNEASCOPE produces 5 ins~nt photographs of the reflection of a Placido disc and requires a second instrument separate from the camera assembly to analyze the data. This system isfairly accurate, but expensive and tedious to use. The autokeratometers all are limlted to a single zone of approximately 3mm diameter and, in cases where the magnitude of the astigmatism is low, are inaccurate in their assessment of axes of 10 astigmatism. Also available are three computer-direct systems which use conventional image analysis algorithms in conjlmction with a mini-computer.
These are the C orneal Modeling System (CMS) introduce in 1987 by Computed Anatomy, Inc. of New York, New York and the ECT-100, introduced into the market by Visioptic of Houston, Texas and a system using }ight emit~ing diodes 15 disposed in concentric rings built by Zeiss of Germany. The Placido disc-photo technique is superior to the Bausch and Lomb Keratometer because of the much greater arnount of comeal surface analyzed from the Placido reflection as opposed to the mires of the Keratometer.

A number of patents have been issued that relate to keratorneters. U.S.
Patent No. 3,797,921 proposes the use of a camera to record the Placido reflec~ion from a patients eye. From this photograph, the radius of surface cuNature of the .
cornea is determined at several points and calculated using a complex computer --system. The use of a ~round glass focusing screen with the small aperture of the ~ ~ -optical system and large linear magnification makes use difficult and requires ada~ened room for opera~ion.

U.S. Patent No. 4,440,477 proposes a method and device for measuring the corneal surface, comprising a slit larnp for illumina~ing the corneal surface, a camera for recording the reflection from the corneal surface, and a processor to '~ .

~: -s:

W093/24049 213 71;t~ l Pcr/us93/o5~93 calculate the image distance and ~he radius of curvature of the eye. Il~e operation of the processor is not detailed in IJ.S. Patent No. 4,440,477.

A more recent entry into the market is the "Corneal Modeling System"
manufactured by Computed Anatomy Incorporated of New York which uses a light cone Placido target in conjuncuon with a "frame ~rabber" to digitize and store for conventional ima~e analysis the pictorial data. The Placido is in cylindrical forrn and illurninated from one e~d. This cylindrical Placido maintains a small aperture op~ical system creatin~ a large depth of field of focus for theimaging system and. consequently, requires a sophisticated focus deterrnining ,-apparatus to assure accurate and reproducible image evaluation. lllis system is said tO produce corneal thickness data using a scanning laser, as well as the surface contour but is very expensive and does not lend itself to clinical applications which are increasingly cost driven.
~-The prior art systems discussed above tend to be both expensive and difficult to use. Many of the~prior art devices have a significant potential forerror, due to complexity of the calculation, the imagin~ of the corneal surface and the difficulty in operatlng these syslems.
Since even a normal human cornea will not be perfectly spherical, the illuminated rings will generally be reflected from the corneal sllrface as a pattern of shapes variously distorted irom the circular. The data per~aining to ~e coordinates of points in the two-dimensional video image is processed to define a .-2~ three-dimensional corneal su~face yielding ~he equivalenL spherical radius of curvature (or dioptric power~ for each of the acquired points. f Accordingly, there is provided herein a new technique for image analysis that provides ~ull topographical mapping of the cornea, with almost instant display 30 of the corDeal radius of curvature at enough points to permit accurate assessmen~
of the surface shape. The improved photo keratorneter includes a transilluminate WO 93/24049 2 1 3 7 1 ~ 1 Pcr/US93/05293 -6-target or "Placido", which is reflected by the surface of the eye to be examined.
A CCD carnera and lens system is mounted behind the Placido so that the optical axis is coincident with ~.e visual axis of the eye being examined ~rld is generally centered in the target member to provide an image of the reflection of the target by the eye. ~he image information of multiple "rings" on the cornea from the CCD carnera is then captured by a frame grabber board and processed by an edge detection algorithm to derive the locus of image bri~htness discontinuities which are assoclated with the target reflection from the eye. These image points are, in turn, transferred to storage in the internal memory as di~gital representations of the x, y locus of the ima~e brigh~/dark transitions represen~ing the Placido ring edges.

The stored data associated with the CCD image of the target reflection are then treated by an image processing algorithm in a conventional electronic computer to derive the surface contour of the eye and to generate the display ofthe derived shape information for use by the operator. The Multi-Functional Corneal Analysis Sys~em described herein can serve as a sensitive method to detennine proper contact lens ~lt by measuring the shape of both front and back surfaces of the contact lenses and comparing these shape measurements with the shape of the eye to which the said lens is to be applied.
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An Illustrative system in accordance with the invention the Eyesys Multi- ;~
functional Corneal Analysis System which combines the ~ea~ures of an automatic -~
keratometer, photokeratoscope and corneal topography device into a sin~le , ............................................................................................. ~. . .
instrument. Comprehensive keratometric results and quantitative corneal surface : ~;
measurements provide multi-functional corneal evaluation capabilities. Multiple . j2 ,.. ''-'.'' analysis routines offer information from basic kera~ometric readings to :
intermediate zone values and graphics to full surface topography color mappLng.
An easy ~o use joy-s~ick and positior~ing aid provides precise patient alignment and .:
image focus. User-friendly menus guide users to quick and reproducible exams.
An on-line operators manual provides rapid assistance. For most examst processing time is under 10 seconds for 360 meridians. Corneal information is 21~71~ -.
WO 93/~4049 1 PCrJuss3/05293 I

reported as numerical values with graphic presentations for the 3mm, Smm and 7mrn zones~ corneal contour profille graphics of any two meridians and ,~-topographical c~lor surface maps according to either dioptric power Gr millimeter radius of curvature. IJp to four surface maps can be displayed for comparative S analysis. Patient exams can be archived to hard disc or floppy disc and recalled at any time. Permanent records may be produced Yia optional Polaroid carnera or color graphics printer.
, An illustrative system in accordance with the invention u~ilizes a unique data-acquisition design to perforrn rapid~ cost-effeclive ~uantitative photokeratoscopy. The system obtains a complete 360 degree measurement (approximate corneal zone diameter .9 - 9.5 mm) with only a single da~a-acquisi~ion "shot," eliminating the need for camer2 rotation. ~he system ha~ a more precise and user reco~nizable focusing target and improved op~ics over other systems known in the art, which further enhances the accuracy and reproducibility of corneal topographic profiles. The interval between electronic data capture and complete display for all meridians is less than lû seconds. The system is packaged either as a single tabletop unit wi;h a base dirnension of rou~hly 18" X
23" which includes an integrated IBM-compatible computer and a photographic port so that standard photokeratoscopic photo~raphs on Polaroid or 35-mm film -can easily be ob~ained or as a modular unit on a mobile pedestal with dimensionsof 32" x 24" with computer housin~ separate from photokeratoscope. Yideo output is available for video image storage if desired. In addition to standard numerical displays, new color graphics for corneal profiles and for isodioptric color-coded contour maps can be selected. The system in acsordance with the ,.-invention is easy to use and ~herefore suitable for use in a standard clinical setting.
Its data-acquisi~ion desigrl provides rapid data capture and display and offers distinct advantages for clinical and research applications.

Figure 1 is an overview of the system.

WO 93t24049 2 1 3 7 1 5 1 -8 Pcr/lJS~3/052~3 Figure 2 is a cross section of the system.
, Figure 3 is a detail of ~he system menus and graphic presenta~ions.

Figure 4 is a diag~arn of OphCal principles.

Figure 4A ~nd 4B are a graphic presentation of the operation of the focusing aid.

Fi~ure S is a detail of the construction of the focusing aid.

Figure 6 is an operational sketch of the focusing aid.

Figure 7 is operational depiction of the op~ical assembly and patient 15 positionin~ assembly.
...

Figure 8 is a mechanical drawing of the optical assembly housin~. ;

. . .
Figure 9 is a schematic of the power supply. ~ -~
- -Figure 10 is a blocl~ diagram and schematic and PAL equations for the frame grabber board.

Fi~ure 11 is the op~ical path layout and design methodolo~y.

Figure 12 is the system menus and hi8h level descrip~ion of the sof~ware.

Figure 13 is a cross section of the eye. `-, Figure 14 is a f~ont view of the eye. - -~

1","
213~1Sl `
WO 93/24049 Pcrtuss3/os293 Figure 15 is a graphical representation of the checkered Placido apparatus in operation. i Figure 15A is a front view of a checkered Placido apparatus.

Figure 17 is a reanriew of a checkered~ Placido apparatus.

Figure 18 is a diagonal view of a checkered Placido apparatus.

I. SYSTEM OVERVIEW
Figures 13 and 14 illustrate the more impor$an~ features of the eye as they relate to keratometry. T pupil of the eye is defined by the central area surrounded by the iris. The iris opening size is controlled by the autonomic nerve 15 system in rela~ion to ~he brightness of illumlnation as well as other factors and may be as small as one millirneter ~n diarneter in bright light to five millirneters in -~
diameter in dim light. The constriction of the iris in bri~ht light also provides an increase in depth of focus such as is observed in conventional photo~raphy. The reflection of the one or more concentric rings of Ihe Placido off of the anterior 20 ~ corneal surface will appear as more or less circular bright rings superimposed on the pupil and iris when viewed by the television camera. The interior of the eye is shown as a horizontal cross-section to show the more important s~ructures. The globe is eRclosed in a semi-ri~id white membrane called the sclera. The transparent membrane a~ the front is called the cornea. The cornea is a thin 25 membrane which is supported in shape by the pressure of the fluid behind ~he membrane and in f~ont of the crystalline lens. The lens is supported by a systemof filaments and muscle t;issue which cooperate to change its thickness and, in consequence, the focal length of the lens.

The primary focusing power of the optical system of the eye is provided by the light refraction curvature of the cornea and the fluid ~llling the anterior WO 93/~4049 ~ 1 3 7 1 ~ o- Pcr/US93/0~293 charnber, while the lens serves to permit the change of plane of focus from nearobjects to distant scenes. The light entering the eye through the iris opening is brought to focus on the surface of the retina which lines a large portion of theinner globe and contains the photo-receptor cells. These cells are of two general types, rods and cones. The rods predominate in the areas peripheral to central image and are highly sensitive to light but devoid of color sensitivity. The rods provide "scotopic" or night vision. The cones predominate in the central retina and in the "fovea", where cri~ical central vision takes place. The enter of vision is located in the foYea which is displaced frorn the optical axis of the eye by some five to seven de&rees. ~ecause the surface of the cornea is nol a perfect spherical section the curvature of the surface is asymmetrical around the center of vision or -~
visual axis and must be taken into consideration in keratornetry. - -....

As noted in U.S. Patent Nos. 3,542,458 and 4,440,477 the reflec~ion of an object in a convex mirror will produce an irnage which is "virtual" (cannot be formed on a screen, but can be viewed directly) erect, and reduced in size by an -amount which is a function of the radius of curvature of the mirror. In this system, the tear filrn and/or the surface of the cornea acts as such a mirror. The forrnula often used to define the light reflected from a transparent surface is -~
dependent upon the index of refraction of the op~ical medias involved.

The commonly used values of the indices of refraction, n, for the three - ~ ~
media of transrnission in this case, air to tear film and cornea are 1.000 for air, ~ ` -1.333 for the tear film and 1.3375 for the cornea. There exists appro~cimately atwo percPnt reflection a~ both of these optical inteffaces, i.e. the air/tear film and , .
tear film/anterior corneal surface. The small thickness of the tear film places both reflections in close proximity so tha~ they are indistinguishable from each other for instrumental purposes. As a result these reflec~ions are lumped toge~her for clinical applications. However, the small amount of light in the reflected pattern influences the system design, as discussed below.

21371~
WO 93/24049 - Pcr/~s93/0~293 1. .

The anterior surface of the normal cornea is not quite spherical, as it~
appears to have been assumed in the construction of many of the prior art devices such as the Bausch and I~omb Keratometer, but is more nçarly an ellipsoid. The central two or three millimeters of the normal cornea does conform reasonably toS the spherical form so the simplistic model will serve to illustrate the optics of the system for rays at or near the common op~cal axis.

The user is most often interested in data presenta~ion in terms of diopters of focusing power of the cornea. The radius inforrnation can then be converted to 10 this form in the commonly use formula as follows:

d = (n-1)/r where the index of refraction of the cornea n is assumed to be 1.33~5 and the 15 radius of curvature of the corneal surface r is expressed in meters. It should be noted that there is not an a~reement on the actual value of the effective index of refrac~ion of ~he comea to be employed in keratometrv and that the calculation of corneal curvature in dioptnc form also involves optical correCLion factors to compensate for the effectively negative "lens" formed by the rear surface of the20 comea. In practice the value of index of refraction used by several systems for this conversion range from 1.332 (Zeiss) 1.336 ~Arnerican Optical) to 1.3375 (Haag-Streit and Bausch & Lomb). The "normal" range of curvature in the central zone ranges from 7.2 ~o 8.3mm with a mean value of 7.8mm. Some representative values for the Bausch & Lomb instruments converting the readings 25 into diop~ers are shown in the following table:

-... ~..... .
~ ,. .... .- , WO ~3/24049 213 71 ~ L PCr/USs3/0529~

Dioptral curvature Surface radius in mm ~ ;
61.0 5.53 60.0 5.63 ' -47.0 7.1~
45.0 7.50 44.0 7.67 ;
42.0 8.04 ~1.0 8.23 ` -From the foregoing it foLlows ~hat the con~ersion of the data into dioptric form is not dif~lcult and involves the use of a selected constant but that the data so expressed is subject to variable error inherent in the technique. The cornmon keratometer has been used for many years with data in dioptric form, even though -the magnitudes are not precisely accurate. The choice of display form either in diopters or milhmeter radius of curvature is selectable in this system to perrnit the `-user to choose between the more accurate and the more common form. The display of the derived data may be in graph forrn for ease of assimilation and -. .. -appliGa~ion by the user. ~-~
, .,'";
llle dala of interest to the user is generated from the pixel radii of each - - -chord of Placido rin~ reflection in the aequired image in any of the possible directions from center. The millimeter radius of curvature and dioptric cunra~ure of the su~face at eaeh of these points is then provided to the user for his evaluation. The keratometer known in the art and in common use measures two ~ ~
perpendicular meridians at each selected angle and produces da~a in the from of - -"Kl, K2", cylinder and~axis. These terms refer to the average dioptric curvatllre ~ -from both sides of visual axis in each of the two meridians which have the greatest and least curvature, assumed to be 90 degrees apart in "regular" as~igmatism the ~`
m~gnitude of the di~ference be~ween the two, and the angle rela~ive to the ~-horizontal of the la~ger of the two. The terms are commonly used and are recognized by the user as definitive of these descrip~ive elements as derived byconvention~l keratometry. The axis can either be measured or assumed to be regular (90 degrees apart), however, in today's applications more comprehensive 2 1 3 7 1 ~ 1 I
W0 93/24049 Pcr/us93/05293 data is necessary. K values are obtained for a full 360 degrees by a process~of repeated measurement and recordation. t To reduce the amount of data required to define the ring image size in 5 radial terms, only those pixel loci which define a change of bri~htness greater ~.an a threshold value are stored. Each nng reflection produces one data point at each reflection edge. These points can be used to determined the actual locus of the center of the rin~ reflections. The optical system is preferably provided with an :
optical fiber which de~mes the optical center of the system and provides a bright point of light for the patient to fixate upon. The reflection of this small point from the cornea provides a true center form which all measurements are rnade.
Furthermore the numerical scatter of the data points is a function of the focus and overall image quality which perrnits the evaluation of each measurement for minimum acceptable quality. The decision to reject any measurement which does not fulfill the quality standard is set into the software. This is due to the re~uirement that the objecl distance be known and fixed for accurate data analysis.
Small erro}s in focus can de~rade the measurement and so an optical system with a small depth of field of focus and a software scatter determina~ion are used toinsure accuracy. The eerltral fixation target reflectlon from the optical fiber is also examined for relationship to the true center of the picture and if the ima~e is decentered in either axis by a predetermined amount the measurement is invalidated. The shadow cast by the nose, brow, lashes, etc. as well as the lid margin which may lie within the camera field will cause some data points to be missing from the ~heoretical maximum number. The lash shadows will not completely obscure the area to be measured and so some minimum number of valid points may be selected which will permit the areas thus partially masked to be def~ed with a large degree of con~ldence. The entire picture is examined Ior brightness transitions in this manner and the axis determined by mathema~ical algorithms in the computer. Given that, for examplet the image resolution of thesystem provides a pi~el size, Placido image referred. of .014mm ~750 pixels--,~.. ,. ., - - ~

2 1 3 7 1 ~
WO 93/~4049 Pcr/us93/05293 .

- , ,, lOmm so one pixel = 1/75mm or .0133mm) then an estimate of the minimum curvature difference and radial interval detectable by the system can be derived. ' -For best accuracy, each instrument should be calibrated periodically to S compensate for minor differences in system magnification and linearity to obtain - -maximum accuracy of the derived data. Fo~ this reason calibration means - -preferably are provided as a pan of the computer software and the user may checkthe calibration and reset the table values at any time.

Referring now to Figure 4, the optical theory dia~ram shows some of the relationships which are of interest in the present system.

An object (the comea of the eye to be mear.ured) with a size h is imaged by reflection at plane d with asl image size h'. The ma~nification is derived by the -usual formula:

rn = h'/h -...
The focal len~th of a convex mirror is negative and e~ual tO one-half of the radius of curvalure~ The sum of the reciprocals of the object and image distances is equal to the reciprocal of the focal length. These two can then be combined tv the form:

, 1/o + 1/i = l/-f = -2tr -or . '~
i = or I [2(or)-r]
, ~ .
It follows that the remainder of the image is formed in a similar fashion and that the same figure applies in any meridian. (These fonnulae are only true 30 for rays which are very close to the optical a~is). From the size of the object, .... . . . ~ ., .. , . ~ . ... . . , ~ .. . . . . . . . . ..

1,.
2 13 7 1 tj l :
W~ 93/~4049 P~r/us93/05293 size of the image, the distance and the optical magnification, the radius of cuna~urecanbecalculated ~follows:

R = M (2U/O) I

Where:
M is the magnification constant of camera and optics;
U is the distance from object to cornea;
I is the observed size of image; and (:) is the actual size of object.

The objects ima~ed are the several nngs of the tar~et which yield the curvature of the eye at sever~ distances from the center of ~he co~nea. For the i~ -lS ring, all ~he constants are lumped into one, Ki, thus:

Rj = Kj Ii ~ ~

Rj is the radius of curvature of cornea of the i~ ring;
20 Ij is the observed size of i~ ring; and Kj is the i~ ring conversion const~nts.

.
Thus, all ~hat is needed for computa~ion of curvatures are the ~ constants.
The Kj's can be calculated bu~ it is much easier. and more aecurate, to measure 25 them by calibra~ing the instrument wi~h balls of known, precise diameter Ro ~d setting all ~ = 1. The values of Vj are measured which provides a measurement of I, since V; = 1 x Ij. Thus, the collstants are determined by: I

~ = Ro/Vj Where:

WO93/Z4049 21371 S I PCr/~Ss3/05293 -16- ; ~

': '., :' ,. ..

~ is the known radius of calibration ball; and Vj is the measured radius of calibrahon ball with ~ set to 1. -.~
Accordin~ to conventional techniques a table is constructed to provide a look up system for conversion of measured reflex diameters, representing a range -of known surface curvature values. In this manner the necessary de~ree of ;
precision may be achieved to assure accurale output data accuracy for the intended ~-application. Interpolation between table entries is quite practical and reduces the number of table entries needed to assure accurate measuremen~s.
' ,'',.''. -' A more exact surface shape characterization could. in theory, be obtained ~-by the method iterated by Wittenberg and Ludlam in a paper published in the -Journal of the Optical Society of Arnerica Vol. 56 No. 11, November 1966 but thesimpler form provides adequate accuracy for clinical use. The ma~nification ~ ~ -factor and the effective nurnerical aperture are chosen as a compromise between the most desirable small relative aperlure and acceptably small depth of ~leld to facilita~e the setup and focusing step. This provides an acceplable error from subject positioning resulung from inability to judge srnall differences in subject distance due to` the depth of focus of the optical system as well as adequate image bri~htness for noise reduction. In most, if not all cases, the exact sw~ace contour - -is of less interest to the clinician than the relative contour. For exarnple, in a ~`
surgical application, the object is to arrive at a smoo~h, regular corneal surface, which has a similar shape in two perpendicular axes. That is to say that the corneal astigmatism is minimal. The errors of measurement are least at, or near,the center of ~e cornea which is the main image forming su face of the eye.
Therefore small error accumulation in the periphery of the cornea are tolerable.In surgical procedures where the cornea is cut, su~ure tension and loca~ion can - L
alter the surface shape. The peripheral curvature must be rnaintained as closely as possible to the same value in all axes if there is to be no induced pos~-operative astigmatisrn. The keratometer carl provide inforrnation for post-operative adjustment of sulures to better achieve this result. The shape derivation for ..... ... .. .. . . .

2 1 3 ~
WO 93/24049 -17- Pcr/VS93/05293 contact lens fit~ing is also a comparative process in that the lenses may also-be measured by the instrument and so small errors from true surface derivation cancel and the resulting data are usable m a clinical context.
-S Because the eye is centered in the picture by adjustment of the instrument and headrest at the time of setup and because the subject is fLxating on a target which is coaxial with the system's optical alcis, the center of the reflected image and thus, the cornea can be located exactly by a rather simple software technique.
The largest difference between the two central image points from the f1~ation lamp reflection collstitutes a measurernent that is equivalent to a diarneter of th~ inner Placido ring reflection (in pixel terms). One-half of that measured value is thecenter of the figure. lhe remainder of the analysis is based upon similar technique and is much less software intensive than ~he classical image analysis algorithms which make more complex decisions about a much larger number of lS pictorial elements each of which may have one of many numerical values which may represent intensity, saturation and hue. Thus it can be seen that this system substitu~es novel me~s and me~hod for the conventional image analysis lechnique to permit the construction of a very inexpensive system which can be used to produce cLinically useful data when operated by unsophisticated users within theeconomic constraints imposed by current clinical fee structures.

Ihe computer program controls measurements, data analysis and display '~
format. Each sin~le measurement consists of measuring the edges of the Placido reflec~iorl in view. Subsequent to the data ~athering step, the curvatures are 3 computed from the available edges. Any values ~alling outside of a window of selectable size are considered "bad". Ihen the half chord measurements for each ring from the selected data points are derived. I~e values of cur~ature are t similarly computed for each ring image on each side of center at enough angles to pennit accurate assessment of major and minor a7cis angles.
The formula used for compu~ing the curvatures is:

, . - - . . . . . . .

Wo g3/24049 2 1 3 7 ~ Pcr/US93/0~293 '' '" - ,' Where~
~ is the radius of corneal surface curvature of i~ ring; , '' ~ is the lumped constant of i~ ring: and -",,' ~ is the measured radius of i~ ring. ,',, (The lumped constant depends on magnification. rin,g size. local rate of curvature etc.) The constants ~ are determined by calibrating the instrument by measuring '~
objects of known radius. These data are stored on a disk, in an ~PROM (Erasable ' '-, Pro~rammable Read'Only Memory). Eor some similar means for use by the main program. The provision of a vanable focal length camera lens would permit ' adjustment to compensate the maPnification errors which will result from the ,~
tolerance of focal len~th of commercial lenses if desired but the calibration table method is the preferred embodirnent.
:, II. PROCESSING CIRCUITRY AND OPERATIOI~
Referring now to Flgure 2, the lceratomèter of the preferred embodiment comprises a Placido or similar targel, a lens system. a CCD (Charge Coupled De~dce) camera 50 for receiving the reflection of the Placido 2 from the eye andan image processing sub-system 48.
~ ~' The,eye to be exammed is posi~ioned according to conventional techniques preferably a~ a distance of 3 inches from the Placido and centered on the optical ' system. Referring to Figure 15 for more detail the Placido is in the form of a -trans-illuminated surface of translucent material 220 with ~he CCI) camera lens cen~ered in the Pl~cido. and with the lens, in ~urn, surrounded by concentric circles of opaque material 221. The Placido is illuminated by one or more lamps ` ' -222 placed behind the disc surface so the translucent areas are bright circles as viewed by the subject. By this technique an image is provided in a plane 223 posterior to the normal corneal surface of the eye 224. Refernng back to Figure 2, the reflec~on of this image is received by a CCD camera after passing through ~ '~

213~
~ WO 93/24049 Pcr/uss3/05~93 the lens. The lens preferably includes an objective lens 53 located at or near its focal length from the eye. A beam splitter or mirror 15 may be included along with a second lens 52 whereby a portion of the image formed by the objec~ive lens may be diverted to a carnera port for photographic recordation of the eye and the S Placido reflection. Otherwise the remainin~ imae portion is brou~ht into focus at the photo-sensitive surface of the C(: D camera 51.

The subject is placed in front of the instrument with the chin supported in a rest (24) which may be adjusted for subject size in terms of chin to eye dimension.
This adjustment (25) is typically a screw operated device. The optical assembly (58) is mouneed in suitable "slides" or rollers ~45. 46) which permit motion in two perpendicular planes without rotation so that either eye may be aligned on the optical axis and ~he ima~e brought into cri~ical focus by the motions. The Placido (2) is illuminated from behind by a lamp (27) which mav be a circular fluorescent 1~ tube or other type as desired. The assembly is also moveable in the vertical axis which could be by a means of a slide (32, 33) under control of a screw (31). Therotation of the screw may be by a knob or a motor dnve comprising a motor (40).
pulleys (37, 39~ and a cooperatin~ belt (38) or other suitable means to permit the eleva~ion of the op~ical axis to be under operalor control for alignrnent of theoptical axis of the instrument with the eye to be measured. The action of a "joy-stick" (42) mounted in a ball and socket system (43) under operator control via a cam or fric~ion member (44) preferably propels the instrument on the slides, rollers or wheels (45, 46) to facilitate the positioning and focus steps. The present system in accordance with the invention utilizes a positioner assembly from SCO,Scandicci, Florence, I~ly. A brow rest (26) may be mounted on the head support system (49) to insure the fixed position of the eye to the instrument while the adjustrnent and measurement are made. The patient is requested to focus his eye ', on the fixation target (79) to assure the coincidence of the optica~ axes of the t instrument with the eye (1). After ~he positioning and focus step, the operator 30 presses the switch (41) or a foot operated switch, at which ~ime the por~ions of the .
; -W093/24049 ~1 37I~ Pcr/uss3/o~293 --20~
'~

image rela~ing to the measurement to be made are captured by the electronic~ ~
assembly (48) and suitable power supply (47) operatively associated therewith. .~ :-An object (tne Placido) is reflected from the surface of the cornea and th~
si~e of the reflection is measured. The focal length of a convex mirror is one-half ~-of the radius of curvature and tne image and object sizes can be related to the focal length. The object in this case is preferably a Placido or Placido's disc.

The data points which are recorded in memoly comprise pixel numbers which denote the locus in X, Y tenns of each brightness transi~ion in the picture which are over tnreshold magnitude. These poin s are contaminated to some : ~.
extent by random noise and so must be treated to remove Ihe noise. establish center~ng and focus accuracy and general quality prior to being converted into final form for use in standard display algorithms. As the data points are stored in memory at the time of recordauon, the points which define line numbers can be identihed by addition of a flag bit in the position commonly occupied by the si~n bit. This is possible because the data points all bear a common posi~ive sign and makes sortin~ simpler by making use of a si~n compare ins~ruction available in most cornputers. The line numbers are stored as a paired table with the data `~
points provided by ~he pixel numbers in the measurement and the process -continues until all data points are so sor~ed. The end of data in storage is indicated by either a line number or a pixel number being equal to æro which is caused by clearing the entire data memory to zeros prior to each measuremen~
This technique reduces the number of data points to be treated in the ensuing calculations. A numerical mask is set into the software to defime a small area at the center of the picture which defined the location in which the fixation tar~et reflection will be found if the instrument is properly aligned with the eye (1). The reflection of the ~lxation targe~ should be inside this mask for best accuracy. The data points within a slightly larger area are averaged to define the optical center of the data ~o be treated.

WO 93/24~)49 PCT/U~i93/0~29 1, !

If the average data point is wi~hin the mask area, it is stored as the cerrter point for polar data form conversion; if outside the mask the measurement is aborted. The operator may be notified of the error or an automatic repeat measurement for some given number of tries, commonly (3) can be done prior to S the notification as desired.

After the data forrnat conversion from cartesian to polar forrn the angle ccunt is set to zero and the points in radial sequence are stored in a table. 1 his is repeated for as many angles as are desired. The increase in the nurnber of an~les 10 enhances later display use but increases the calculaLion ~ime so the number of angles is user selected.

After all desired angles have been converted, the da~ points are exarnined by distance from center as groups. It should be noted that this is in sequence 15 terms as opposed to discrete distance terrns in that the reflection will be closed, nested curves, but not circles or other re~ular f1~ures in most cases.

.
The radially selected groups are subjected to a smoothing process such as least squa}es or moving avera~e window to define the shape of Lhe reflection of 20 the Placido. To provide the common form of central K1. K2, Cylinder and Axis,the innermost smooth curve may be presumed to be an ellipse and the calculationsproduce the "best fit" ellipse from the smoothed data. From this ~e Kl an~ K2 are determined by look up and inlerpolation from the calibration data ~able and the numerical difference becomes "Cylinder" or astigma~ism. The ~ixis is, of course,25 the major axis angle of the deterrnined ellipse in anti-clockwise form from zero degrees in the horizontal plane extendin,~ to the ri~ht of the o~igin.

The remainin~ steps ~ake each set of points for successive concentric reflections and smooth them in like fashion. Any data point which fails to ~lt the 30 smooth curve by more than two standard deviations or other like threshold parameter is ~hen deleted and the data resmoothed. The smoothed dala are then ,. .. ~. .

~ ;

WO93/24049 .~ 71 j I Pcr/us93/os293 l -..

converted to X, Y and millimeter radius of surface curvature form by table look up for use in any desired display format.
' The area of comeal coverage is 0.9mm -9.Omm (@42.5D). The axis range S is 0-360 degrees (1 degree Increments). The diopter ran~e is 9D - 99D. The resolution is +l-0.25 diopters. The dimensions of an inte~rated system .t embodiment are 23"D x 18"W x~24"H, 80 pounds, otherwise, the system components can be modulanzed and provided on a compact mobile pedestal table.

SYSTEM COMPONENTS

The system in accordance with the invention is cornprised of a .
photokeratoscope, a Placido 2, a patient focusing assembly 202, a computer 203, a high resolution CCD video carnera, a 14" VGA color moni~or 200 and an image -~ -processin,~ subsystem. The system is mounted-on a table top which is at~ached to `
a moveable pedestaI 205.

The illus~rative system in accordance with the invention includes the --~following components: ;
,:
Photokeratoscope, case, C~D camera, Placido, light chamber, opucs assembly, patient focusin~ assembly, positioning base/chinrest, IBM AT : `-compatible computer or 80386 based computer, 101 Key Enhanced Keyboard, 40 Megabyte Hard Disc Drive, 1.44 Megabyte Floppy disc Drive, High Resolution r~ - -CCD Video Camera, 14" VGA Color Monitor, Ima~e Processing Sub-System, Ima~e processin~ algorithms, frame grabber board, power supply board, pedestal, '~
tabletop. -`

i ?~,:
WO 93/240492 ~ 3 7 1 ~ ~ Pcr/usg3/o5293 IMAGE PROCESSING

The image processing software and all other software used in the system in accordance with the invention is set out in the appendix. The software is adapted 5 for speed and perforrnance in numerous ways. The software uses integer mathematics in lieu of floating point mathematics to obtain a substantial increase in speed on the family of processors used by the system. the Intel X~6 family of processors, available frorn Inte} Corporation, Santa Clara Califomia. These techniques improve perforrnance on any processor. however. Integer math is even 10 faster than using a co-processor for floating point operations. lhe math uses a ~ced point operator. For instance, to use the number 3.279 the proxy number 3,279 is manipulated instead using integer math; the decimal point is later placed in the result as necessary. This is much faster than floating point math. The systern in aceordance with the invention also uses integer math for sines and 15 cosines, simply scaled by 1000 to ~ive a significant increase in perforrnance.
Because only three significant digits are necessary, this scale by 1000 operation works adequately to ~ive three signi~lcant digits.

Numerous performance enhancements are detailed in Ihe source listin~. An 20 important factor in performance enhancement is the archilectural desi~n of the software as well as the selee~ion of steps and sequence used ~o perform the image processing and other function. Additionally the technologies of ima~e processing, parallel processing and expert systems are incorporated in~o the software design.

The software design is par~llel. It can be executed on a parallel processor such as a super computer and would not be forced to be sequential. Therefore thearchitecture has been designed so that it can be executed in a parallel implementation . .

.~,!
W~g3,24~49 21371 j I P~/ll:,'S93/052~3 ; ~

EDGE DETECTION
.

Ihe system in accordance wit.h the invent.ion uses an edge detection algorithm implemented in software. Each Placido ring that is reflected in the S cornea is seen as two edges by the edge detector. Other known systems use peakamplitude ta detect Plac}do ring loc,ations which is less accurate ,and generates fewer da~a points for post ima~Je capture analysis. The system in accordance with the invention uses the edge detection software to sense the interior and exterior ed,ge of each ring (see Figure 12K). The image processing software then counts -:
the number of pixels to each ~dge of a Placido ring, and then rotates 1 degree and - -repeats the process of counting pixels.

For example, if nine Placido rings were used and reflected off of the cornea they would generate ei,ghteen ring ed,ges; this imp}ies 363 degrees x 18 edges--S760 points of corneal topographic informa~ion. Older style keratometers ~:
only utilized four data points, the radius to a sing}e mire or ring measured 90 degrees apart and then photographed the mire reflected in ~he cornea to quantify a :
spher~cal characteris~ics of the cornea. The total analysis alone took oYer 20 -minutes to complete. The system in accordance with the in~en~ion performs a full360 degree analysis in under 15 seconds.
, The number of pixels counted to the edge of a Placido ring corresponds to a particular radius of curvature when compared to the calibration curve for the system. The edge detector which resides as software in the computer looks at thepattern of rings reflected from the cornea oa the CCD camera and captured by the . ¦
frame grabber board and counts the number of pixels to the edge of each concentric ~ . The num,ber of pixels counted to each ring e~,~e is proportional to -the radius of curvanlre of the corneal surface of the eye at that point.

The image processing software resides in the in~egrated computer performing edge detec~ion to find the edge of each Placido ring reflecled on the 2 1 3 71 ~ 1 Wo g3/24~49 Pcr/us93/05293 i comeal surface, tùen in a~e processing al~onthm sof~ware creates a table of pL~cel dls~ances to each Placido ring edge thus generating a pixel count or distance to a 1:
rLng edge that is proportional to the cornea! radius of curY~ lre. The system inaccordance with the invention uses sub-pixels 1/10 resolution to determine position 5 of edges and diopter measurements. These calculated pixel distances are cornpared to the calibration curve IO generate the topographic curvature for the-object cornea.

Software also includes function for patient history, data base management.
10 displays, drivin~ the video board, writing pixels to ~he display board buffer, site speci~lc profiles for communications pararneters, doctor preferences for number of colors on the screen, file manipulation code, menus and numerous other functionsevident upon examination of the software source listings in the appendi~.

CALIBRATION CURVE

The illustrative system in accordance with the invention ~enerates a calibration curve by ima~ging objects with a known radius of curvature. The calibra~ion routine calculates and stores a look up table (essen~ially a calibra~ion 20 curve) for each of four calibra~ion spheres in the current design. each tablecorresponding to the number of pixels counted for this known radius of cuIvature.
The number of calibration spheres can easily be increased or decreased. Presently these four tables are used to ~enerate an interpolated calibration curve (pi~el versus diopter or radius of curvature). This best-fil curve, presently calibrated to 25 four known radius-of-curvature calibration objects, gives the radius of curva~ure for a given pixel count when imaging an object with an unknown radius of curvature. Il~e software source code is listed fully in the appendi~.

wo 93,24049 2 ~ 3 ~ Pcr/us93/os293 DATA PRESENTATION AND DISPLAY

Corneal information can ~be repo.~ed as a set of nurner.cal values or may be displayed in a color-graphic presentation. The system in accordance with the S invention is capable of graphical presentation of the 3mm, jmm and 7mm zones, ;
or as a corneal contour profile graphic of any meridian. The system in accordance with the inveniion can also generate topographic color coded surface maps in either diopter or millin:leter radius of curvature scales. Up to four surface maps ~ -can be displayed together for comparative analysis. Patient exams can be archived to floppy disc and recal}ed at any time. Perrnanent records can be produced via optional Polaroid carnera or color graphics printer.
.~'' The colored ~raphics presentation can be utilized to show where ~o make - ~.
correc~ing incisions into to the cornea during a radial keratotomy or laser sculpturing procedure of the cornea. A video display monitor is utilized to view ; ~ -~
the graphic presentauon. Video ~raphics can be saved on the system printer or on -disc for archival purposes. ~-Graphical displays can also be useful to record the topo~raphic hislory of the cornea during the healing process. The cornea can take months and sometimes eYen years to heal: the cornea has no blood in it, so it repairs similar to a missing fin~ger nail; it does not scab over and heal within a week or so Such his~oricaltopographic data enables a doctor ~o make necessary adius~nents as the cornea heals. The doctor can d~hten or loosen sutures or make other correc~ing adjust~nents to op~imize the co~rective effects of surgery on the shape of the rr cornea.

Graphical presentations can also be used to compare the topo~raphic corneal characteristics before and after surgery. The difference between the twocan also be show so that a physician can observe how the sur~ery has affected the ~.... .. . . . . . .. . .

':
Wo ~3/24049 2 1 3 7 1 5 ~ Pcr/US93/05293 `

topography of the cornea. Examples of the graphic presentations are preserited in J
Figures 3A - 3L. ' The graphic display can be chosen from menus as shown in Figure 3A
5 using the "Select Display Forrnat" menu. Fi~ure 3B is an example display of keratometric data (orthogonal). Figure 3C is an exarnple display of keratometricdata showing astigmatism in a "torque display" in which the 3mm, 5mm and 7mm topographies are overlaid in one display. Figure 3D is a profile graph which canbe generated for any 2 meridians. Figure 3E is a tabular display of keratometric10 data which can be generated for any 2 meridians. Figure 3F is an example display of a contact lens fitting map showing ~he dicptric correction for different points on the cornea. Figure 3G is an example of a cornparative isodioptric rnapping that can be generated to compare 1, 2. 3 or 4 eyes. Figure 3H is a color map with normalized diop~ric scale. Figure 3I is an example of a data overview display.
15 Figure 3J is an example of display eye image whish is a display of the eye and ~he Placido ring i. .age upon it. Figure 3K is a~ exarnple of the contact lens fitting display. Figure 3L is an example of compara~ve iso-dioptric color mapping.
Figure 3M is an example of a tabular display of curvature data in any two selected meridians.
The data or~ganization and presentation software source code is listed in appendix 1.

PRECISE Placido PC)SIIIONING AND FOCUS NG ~AID

The size of the reflechon of the Placido in the cornea, and therefore the cal;culated perceived radius of curvature for a par~icular zone of the cornea, is a 30 function of the distance from the eye to the Placido. Therefore it is desirable that this distance be the same each time the doctor analyzes the topography of the WO 93/24049 2 :13 11 i ~ Pcr/us93/o5293 cornea. A change in the distance would render an erroneous calculation as to~he topography of the cornea. For instance, should the Placido be positioned slightly closer to the cornea on a second "snapshot," tlle ring~ would appear farther apart ~-and more pixels would be counted between the rings even though ~e shape of the cornea has not changed, and the results would erroneously indicate an increase in the millimeter radius of curvature.

ln the present embodiment the actual Placido is approximately 3" from the eye; however, a focus aid Is employed to exactly position the Placido to the sarne position for each diagnostic session; The focusing aid is much closer to the eye - ~-than the actual Placido and it projects focusing crosshairs on to the eye. These ~-focusing cross hairs consbtute a "synthetic Placido" which represents a Placido which is much closer co the eye than the actual Placido. Therefore when the `
focusing aid or "synthetic Placido" is positioned precisely the positional errors in -the actual Placido are negligible. Therefore the deviations in the position of the ~ -actual Placido become insignificant and aid accurate and reproducible posiuoningof ~he actual Placido, thus reducing inaccuracies in corneal topographic - -calculauons due to posi~ioning errors.

Ihe focusing aid projects focusin~ cross hairs onto the eye. The focusing aid acts as an optic~l range finding system to determine when the cornea is in focus. The focusing aid promotes accurate and reproducible eye placement to get exact compar~tive readings between pre-opera~ive and post-opera~ive comeal topography. Comparative readings are also useful in detelmining how the corneal shape may change over time dunng the healing process. The position of the ~:
Placido with respect to the eye is important in determining the corneal topography, in both an absolute or a comparative sense. The corneal topographic characteris~ics are also useful in determining and predicting the after effec~s of surgery and detecting possible errors that may have occurred in surgery using other diagnostic techniques than the system in accordance with the invenuon.

~ 21371~ 1 ~
Wo g3/24049 : , Pcr/vs93/05293 i The space between the reflected Placido rings is a function of the distance from the eye to the Placido 2. Because the Placido may appear in focus during ~ravel throu~h the depth of field for a particular lens, the.re can be significant variance in the distance from the Placido to the eye for tWO different points wi~hin 5 the depth of ~leld. A difference in this distance from the Placido to the eye causes a difference in the distance between the Placido concentric circles, inducin~ anerror in measurements of the dislance between the Placido lines. The Placido should be positioned at the same distance from the eye each time a ~neasurement is taken so that variations in the distance between reflecled Placido lines are caused 10 by variations in corneal topography and not by ~ariations in the distance from the Placido to the cornea.

Now referrirlg to Figures 4A and 4B, prior art systems use a trian~ulation method (100) as shown in Figure 4A. The prior an method employs converging laser beams 100 from lasers 102, to posiuon the apex of the cornea, 101 relativeto the optical assembly 58. This method introduces an error in post-surgery keratometric readin~s, as the tip or apex of the cornea 101 may be depressed substantially frorn its pre-opera~on position. This depression causes a flattening of the corneal apex as shown in figure 4B. This flattening causes the cornea to be 20 positioned closer to the optical system under the prior art and thus exaggera~ing the corneal flattening resulting from the surgery. The prior art triangula~ion focusing method induces an error in the distance to the reference point, the apex of the cornea. The prior art systerns therefore is less likely to give consistent and repeatable results or measurements because the dislance from the optical assembly 25 to the entire cornea chan~es af~er surgery inducing an error in postoperativemeasurement. Moreover, the use of lasers pro~ected onto the cornea is also dangerous as they can damage the tissue.

The illustrative system in accordance with the invention offers an 30 improvement in that these induced errors are reduced to enhance repea~able and accurate results. The present system in accordance with the invention uses two W O 93/24049 ~13 71 31 30 PCT/US93/05293 light emitting diodes (LEDs) 104, however an other illuminating source or means of projecting an image could be used. These LED projec~ed images do not converge but are pointed ~t the lirnbus area ~t the periphery of the eye. These LEDs project a focus aid image consisting of an "x" or cross hairs 103 onto the S outer portion or limbus area of the eye. This outer portion is less susceptible to -~
change through either fl~ttening or steepening ~han the apex area of the cornea.The change in this limbral area of the cornea after surgery is negligible compared to the change in the ape~. Therefore the rneasurements are more accurate and comparable using the system in accordance with the invention of the present :
system for pre and post opera~ive corneal curvature chan~es.

Figures SA, SB and 5C show the focusing aid in detail. An LED 121 is held in place by an LED holder 122. The tube 12~ encases the focusing aid. A
spacer 123 fits inside ~he tube 126 alon~ with lens one (f=84 mm~ 125 and lens two (f=48 mm) 124. -The focusing aid is secured to the op~ical assembly 58 by the focusing aid mounting collar 127. The LED holder 122 has 38 gau~e wire cross hairs 129 a~tached with epoxy. Focusing aid 130 projects these cross hairs 129 onto the limbus area of the eye. The cross hairs 129 are reflected by the eye back into the optics system and displayed on a video monitor for the operator to observe. In Fi~ure 9, the operator actuates joy s~ick 42 brin~ing the Placido 2 into focus. The operator via the joystick rnoves the optical assembly 58 along the optical a~;is 151 as shown in Figure 6A. This motion moves the optical assembly 58, focusing aid 130 and Placido 2 along the optical axis. The operator observes the focus aid ima~e 103 in Figure 4A on the video monitor 200 in Figure 1. The focus aid image is reflected off of ~he limbus region of the cornea into the optics assembly into the camera where it is displayed on the video monitor 200. Ihe angle of incidence 170 in Figure 6A of the focus ~id ~mage upon the eye changes a~ the focusin~ aid travels along the axis lSl. When the angle of incidence is proper, the cross ha~rs split the circle projec~ed from ~he focusing a~d into equal quadrants and the focusing aid is properly focused at ~he correct distance to t~se a shot of WO 93/24Q49 Pcr/us93/û~293 -31-:

the Placido properly focused on ~he cornea. That is when the focus aid is at ~heproper distance and in focus as indicated by the cross hairs positioned shown as in Fi~gure 6C, the Placido is also at the correct distance and properly in focus. This technique gives repeatable and consistent resul~s.

When the cross hairs 129 in figure SB are seen as shown in Figure 6C the Placido is focused at a repeatable distance from the eye each time before and afler corneal surgery because of this precise focusin~ technique upon the lirnbral region of the cornea. Changes in the central shape of the cornea have a negligible effect 10 upon the focus distance and therefore introduce little error into the analysis of the cornea. Hence the measurements are repeatable and negligible error is induced bya change in the reference point. The operator adjusts the focusing aid and placid reference distance using a calibrated sphere with a known radius of curvature.

FRAME GRABBER BO~RD

The present system in accordance with the invention takes a di~ital picture of the Placido as it is reflected by the cornea using the CCD camera. The frame 20 grabber board stores this image by grabbing two (even and odd) consecu~ive NTSC video fields 1/60 of a second apart, stor~ng them in memory to form a NTSC video fr~ne giving a composite image fo~ viewing by the operator~ The board also enables the operator to ætuate the frame grabber vi~ a foot switch.
The board is designed to work at high speed with the computer and so~tware. The 25 design de~ils and schematic, as well as the programmable logic array equations, are presel~ted in Figures lOA throu~h lOK.

L,~,,ij., ~
wo g3/24049 ~ 1 3 7 1 ~ I Pcr/lJS93/QS293 EDGE DETECTION AND ANALYSIS -The illustrative system in accordance wit.h the invention looks at the Placido reflection from the cornea and detennines the position of the edges of the S li~ht and dark pattern génerated by the Placido. The edge detection and analysis software is set out in the appendix.

Placido SET ECTION ANP DESIGN
' . '. ' '~
Different types and shapes for the Placido may be used. In a cylindrical Placido the rings are marked around the inside of the tubular surface to generate a pattern of rings when projected onto the cornea. However, in this arrangement the distance from the Placido to the eye is very short, usually less than 1" and15 most likely right on top of the eye. A planar Placido increases the distance from the Placido to the eye and in the present embodiment is at approximately 3".
Increasing this working distance from the Placido decreases the effect of positioning errors. That is an error of 1/10" is a much smaller percen~age of 3"than it is of 1" so that as an error of l/lOt' has much less effect on the 20 measùrements using a planar Placido with a worhng distar~ce of approximately 3", than a cylindrical Placido with a working distance of 1".
`~ :
The ~enelic design of the Placido is set out in the mathematical model below. In a planar Placido the inner bands of the Placido are thimler than $he 25 outer bands to generate a 50% duty cycle between light and dark edges in the reflected Placido image off of a normal cornea. The Placido can be designed to ', generate a Sû% duty cycle of light and dark edges in the reflected Placido ima~e ~`~
or any other duty cycle or variable duty cycle desired. The Placido can be designed for any shape also using the mathemadcal model set forth below. The -~
30 design of the Placido is a generalized design and is set out below as a ma~hema~ical model. This model works for any shape Placido. l~e design model ~ 1 3715~ ~
. !:
WO 93/24049 ` Pcr/uss3/o5293 ~ells the operator where to put the Placido ed~es on any shape Placido. For any shape Placido the operator must mark edges on the shape and the mathema~ical model tells the operator ~vbere to mark the edges on the shape.

S The Placido generates a virtual image on the convex cornea. The image actually exists behind the surface of the cornea, so when the operator focuses, the focus is on a point internal to the eye where the virtual image exists. This virtual image of the Placido is object of the camera. The vir~ual image is a series of rings. Using this design method and a planar Placido increases the working 10 distance, which is more comfortable for the pa~ent and less difficult to position.

MATHEMATICAL MODEL FOR PLACIDO

Each larger successive concentric Placido rin~ is wider to reflect a nominally uniform widtn set of rings in the cornea. The normal angle with respect to optical axis at point yl (2.yl dia zone) is given by a = sin -1 ~yl/7.937], where 7.937 is the radius of curvature at a 42.5 diopter surface. For a reflected ray from point yl to be parallel to the optical axis, it follows that the angle of 20 incidence of that ray ~on point yl) be < ia= ~ r. . :
- ~, This ray emanates from ~ ring ed~e on the Placido makin~ the center of 25 curvature of a 42.5 diopter surface our oAgin in a cartesian frame of reference, we have the locus for the Placido point yielding a reilec~ion at the 2Y diameter zone as '" ' ;' ' ' ' ~ ` '''-''`' (y-yl)--M (x-xl) (equation of a line) M = Tan 2a (angle of ~ncident ray with respecl to x axis) ~
Since (yl)~2 + (x1)^2 = (7.937)~2 (equation oi 42.5 Diopter surface) ;
.~'-:~ -.~ . .... .. . .

4~)49 2 1 3 7 1 ~ 1 -34- PCr/lJS93/05293 lherefore, Y = X tan 2a + [Y1 - (tan 2a) (7.937^2 - Y1^2)^1t2]

3) ie: Y = X [tan2 (sin-1 Y~ )] + ~YI - ~n2 (s~-1 Y~ )](7.95-Yl2)]1/:

is the focus of Placido points yielding a 2 Yl diameler reflect on a 42.5 D
surface.
The tip of the 42.5 D surface is at 7.937 mm = .3125".
Choosing an x (eye clearance is x - 0.3125 inches) yields an ordered pair (X,Y) for the Placido profile. Note that Y Max will be the overall diarneter of the Placido (X Max, Y Max) if Y1 = Max desired zone covered. ~--Choose Y2 = Min desired zone covered Y = 718"12 yields (X Min, Y Max) for -Pl~cido inside circle for a conical Placido, the focus of Placido points is X - X Max + X - X Min ~
Y - Max Y - Y Min :-4) i~ Y X (Y Max - Y Min~ + ¢~X ~ax Y Min - X Min Y Max~
~ Max - X M~n) ~X Ma~; - X A~in) ~ ., and the solution of 4) + 3) yield edge radii.

20 NOTE: Conical Placido profile has been used here but the theory obviously extends to ar~y desired profile, from cylindrical to planar 21371~
WO ~3/24û49 PCr~VS93/05293 OPTICAL ASSEMBLY -- The optical assembly houses a power supply and electronics, illuminating lamp, a camera, ~he optics, a Placido and the focusing aid. The c~nera sits inside S the optical assembly and behind a plate. The camera has an optical tube that cor~tains a lens whieh passes through ~he plate and projects all the way~forward to the Placido. The tube surrounds the optical path of the Placido ima~e. The fluorescent larnp that illuminates the Placido sits in front of the plate. The shape of the housing eliminates the need for a reflector pan as the housing serves as a 10 reflector behind the lamp that illuminates the Placido. The purpose is to have a homogeneous light source to illuminate the Placido.
.
The optical asse~nbly is detailed in Figures 8A-8I. The layout and design of the optical path is set out in Figures llA and llB. The optical pauh in the 15 current embodiment is a single lens system takin~ a ma~nification of .58 for 12 mm coverage so the doctor can see sli~htly more area than the eye itself. The design can accomrnodates various lens sizes. For example for a 75 mm lens, the total path length of the tube is approximately 8 inches. The outside diarneter of -the tube is 1 1/4" and has 3 baffles with 3/4" apertures.
Ma~nific~tiorl is impor~nt to the resolulion of the system. The pixel :~
resolution of the system is proportion~l to the ma~nification of the lens. More - -magnification means more pixels per millimeeer and less resolution. The more .::
pixels per millimeter that are present the better one can analyze small chan~es ' 2~ across that distance. For exampie, if you have 5 pixels per millimeter you can .... . , ~. -:
resolve a pixel 1/5 of a mi~limeter in size. If you have 10 pixels per millimeter you can resoive a pixel 1/10 of a miilimeter in size. ' ' .''` ~

' ~o 93/24049 2 1 3 7 1 ~ 1 36 PCr/USs3/052~3 - ' , ' ' POWER SUPPLY E~OARD ~ ~
, The power supply board is specifically designed to wor~ with the present system in accordance with the invention and is presented in detail in Fi~ure 9.
S

CONTACT LENS FI l-l lNG SYSTEM

The system in accordance with the invention includes a contact lens fitting 10 systern including software in which the corneal analysis generated inpu~s into a transformation function operating in software. The transforrnation function converts the corneal topographic profile pararneters into contact lens design parame~ers. These contact lens design parameters are sent to a contact lens lathe, well known in the art, to sculpt a custom contact lens to fit the eye that has been 15 analyzed. The contact lens design parameters may be checked for quality control before sendin~ the parameters to the lathe or the parameters can be sent to the lathe without such a quality control checking function and simply let the pa~ient and physician determine if the lens is sa~sfactory. A software function (or e~uivalent~ to transfer the contact lens pararnelers from the comeal analysis 20 computer to a lathe for sculpting a lens is necessary to implement the system.
One such quality control funclion has been developed by Polytech, Division of EMI-MEC, Limited, a Slmleaigh Comparly, School Lane, Chandler Ford, East Leigh, Hempshire, England, S05 3ZE. The present system in accordance with the inven~ion does not clairn the Polyteeh version of the quality control function 25 The software for the transforrnation from corneal parameters to contact lens design parameters and the link software from the design parameters are available in source listi~g form in the appendLx to the specification.

The communications software that sends a file from the corneal topography 30 analyzer computer to any other computer utilizes an off the shelf packa~e available ~ ~371~i1 ~
W0 93/~4049 . Pcr/us93to52~3 L
-37~

from Blase Compuung, Inc., 2560 Ninth St., Suite 316. Berkley, Californi~, (4 15) 540-5441 .

S CHECKERED_P ACIDO

A ray passing through a point on a checkered Placido, reflecled off a cornea, and detected by a C~D camera is graphically depicted in Figure 15. The focal plane 40 of the CCD camera, the plane of the lens 42, the plane of the Placido 44 and the planè 46 angential to the apex of the cornea are depicted in Figure lS. Each plane contains a local XY coordinate system. The origin of the XY coordinate system existing in each plane is intersected by a line 48 representing the optical axis of the eye. Each plane is parallel to the other planes. :
llle optical axis is coincident with~the origin of the coo;dinate system in eachplane. Point l'A" 50 lies on the Placido 4~. A line intersectin~ point "A" 50 and -the origin of the XY coordinate systern lying in the Placido plane 44 forns an - -angle "a" 5~ with the horizontal axis or X axis of the XY Placido coordinate ,- ~ , .
system.
., . ~
, .,,,'-~
As shown in Figure 18 the Placido In an illustrative embodiment is shaped ~ ~-like a cone. In an alte;native embodiment, the Placido could be a paraboloid. In --yet another alterrlatiYe embodiment, the Placido could be yet another shaped ~.
surface. The patient looks into the concave surface of the conical Placido in a ~ --pre~erred embodiment. The exterior or convex surface of the conical Placido in a ~ -~
25 pre~erred embodiment is backlit by a li~ht source. Point A SO represents a point on the Placido. A ray of li~ht from the light source will pass throu,gh point "A"
on the Placido and strike a reflection point 58. This ray is called the incident ray 56. The incident ray 56 passes throu~h Placido point l'A" ~0 and is reflected at ~he reflection point S8. The reflected ray 60 is detected point "A"' 62 on the CCD focal pla~}e 40. A line 64 passing throu~h detecled at point 62 and throu~h -~ 5 ~
WO93/~4049 21371 ~:1 38 PCr/USs3/~)5293 ~he origin of the coordinate system existing in CCD plane 40 forrns an angle ~al"
66 with the horizontal axis or X axis of the CCD plane coordinate system.

Referring now to Figure 19 a front view of the checkered Placido, the S Placido is la~d out in a checkered pattern. In a preferred embodiment, the checkered Placido is made up of black and white sec~ions. In an al-ernative embodiment. the checkered Placido could be made up of another set of contrastingcolors. The checkered pattern is designed so that black and white transitions are encountered when traveling along a radius drawn from the origin 74 to the outer 10 edge 76 of the Placido as concentric rings of conlrasting color are eneountered.
The design also provides for black and white transitions when traveling along anarc 7~. The arc 78 is generated by angularly rota~in~ a point drawn a distance Rfrom the origin 74 where R is less than the radius of the Placido perimeter 76.
Thus, edge transitions are encountered when traveling along a concentric circle 15 drawn inside the perimeter of the Placido circumference as adjacent sections of contrasting color are encountered. These sections are formed by drawing a ~-plurality of radii to form the triangular shaped sections shown in Figure l9.
. .
A benefit of the checkered Placido is that. as shown in Figure 15 with the 20 checkered Placido, the meridian of the incident rav can be determined by construction. Therefore when tbe meridian of the reflected ray is measured it ispossible to determine the precise orienta~ion of the sufface norrnal at the reflecting point. Referring again to Figure 15, in Ihe past it was assumed that the incident ray, the surface nonnal and the reflected ray were contained in a single plane.
25 This plane was assumed to contain the pr~nciple or op~ical axis. However, this ls not necessarily true. It depends on the precise orientation of the surface nolTnal at the reflecting point or the shape of the surface at the reflection point.

When the reflection point is located on a perfectly spherical surface the 30 principle axis or op~ieal axis is located in the plane containing the incident ray, the surface normal and the reflected ray. However. when the reflection point is `5~ WO 93/24049 Z ~ 3 ~ Pcr/us93/o~2s3 - 3 ~

located on a non spherical surface, such as a cornea having non spherical characteristicst ~hen ~he optical axis is not located in the plane contair~ing the ,~ -inciden~ ray the surface norrnal and the reflected ray.

In the checkered Placido the angle or rneridian of the incident ray can be dete~mined because the checkered Placido has a marlcin~ or identifyin~ line at the X axis in the coordinate system for the Placido plane. Thus, the deflection an~le 79 of a line drawn through a point "B" 50 on the Placido plane can be deee mined.
Thus, the XY coordinates of the point "A" 50 on the Placido plane are kllown. ~-]O :
Referring now to Figure 15, in a system with a Placido consisting only of concentric rings, not havin~ the checkered pattern of the present embodiment, itwas assumed that tne a~,~le "a" 52 measurin~ the angular deflection from the horizontal of the point "A" on the Placido plane. and the angle "a'" 66 measurin~
the angular deflection from horizonlal of the ~oint "a'" 62 the detected point on the CCD image plane, were the same. That is. it was assumed that the angular deflection of the point on the Placido piane and the an~ular deflection of the point on the detected CCD image were the same. However. this assumption is not necessarily true when the reflection point is located on a surface that is not perfectly spherical. -' ~
The point "A" ~0 is reflected at the refleclion point 58 and passes through the lens center represen2ed by the origin of the lens plane coordinate system 42and forms an image on ~e CCD focal plane. There is also a parallel ray from a virtual image, which is behind the eye. The parallel and the principle ray or chief ray converge at point 62 to determine where the irnage is formed. The system graphically depicted in Figure 15 has been desi~ned 20 forrn the image at the CCD ~-focal plane so that only the priraciple ray is a concern in the calculation. ~ ~:

Previously it was assumed that the angle ~2 was equal to the angle ~6 because there was no way easy to determine where the poin~ 50 was located in 2he W~ 93/240~9 Pcr/lJss3/os29~ I
2 1 3 7 ~ 40-Placido plane 44. However, with the checkered Placido the location of the point 50 on the Placido plane can be determined because the meridian or the angle "a" -52 is known by construction. Ille deflection angle or meridian 66 of the detected point can be measured on the detected CCD image. The angle "a" 52 is known by S construc~ion because it lies on or near the intersection of a black to white or color transition edge on the checkered Placido. The ~gle measured from horizontal to each edEe of the black to white or color transition on the Placido is known. Thus, points on or near these transition "edges" can be determined The deflection ari~le "a"' 66 of a detected poinl can be measured on the CCD. The angle 66 of the de~ected point will not equal the angle "a" 52 of the point on the Placido when Ihe reflection point is located on a nonspherical surface.
Also, when the reflec~ion point is located on an nonspherical surface, the surface normal will be twisted such that the surface norrnal at the reflection point 58 will no~ be contained in that plane containing the optical axis. It will be containedinstead in a s~ewed plane. When the an~le 52 is not equal to the angle 66, the surface normal is not contained in the plane of Ihe opùcal axis and the surface containing the reflection point is not spherical.

Therefore the location of the point on the Placido helps dete~nine more precisel~ the shape of the eye. The checkered Placido helps to deterrnine the location of a point on the Placido by construc~ion. The location of a point on the Placido can be determined because the Placido is constructed of black and white or conerasting sections whose edge transitions can be detected and mapped or located so that a map is formed of these known loca~ions of points on the Placido. The an~ular deflection from horizontal for each black to white or color transi~ion edge is known because the checl~ered Placido is manufactured wi~ a known deflection an~le for each of these transi~ion edges. Knowing the measured an~le 66 of the detected point, one can use solid geometry to go from point 62 on the CCD image through thé lens center back to the reflection point on the cornea of the eye and back ~o a known poinl "A" on the checkered Placido. The angle 52 determines 21371S ~
-` WO 93/24049 Pcr/us93/0529~ `

the surface norrnal of the reflection point in three-dimensional coordinates. T~ese three-dimensional coordinates define precisely the orientation of the surface normal ~ :
a~ the re~lection point. (Nx~ Ny~ and Nz) This triplet identifies the surface normal at the reflection poini. The surface normal triplet can be determined for every point on the cornea where is a measurement is taken. -Any line originatin,g from the center of a sphere and intersecting the surface of the sphere is a normal. In nonspherical volume there may be a ; ~;:
si~nificant perturbation away from a triplet for a normal on a spherical surface.
The checlcered Placido helps to deterrnine of this perturbation or delta.
Determining ~his perturbation or delta enables the corneal analysis sys~em to .:
deterrnine more precisely the topographical or non-spherical characteristics of the surface of the cornea at the reflection point. .~

Points on the Placido are mapped based on the angular deflection of the ;- :
point ~rom that zeroth meridian or horizontal axis. Each edge at a color transitions is a known number of degrees from the horizontal. The radial Placido j `~
sections are constructed by d~awing radii so that each section is a known numberof de~rees from horizontal. For example~ if each radial section is 10 de~rees wide 2û the angular deflection belween the horizontal or zeroth meridian and the ed~e of --the first section would be 10 degrees, 20 degrees to the second sec~ion edge, 30 ~-degrees to the third sec~ion edge, and so on. The black to white ed~es or color -;
transition edges formed by the adjoining radial sections encountered in the angular .
direction are cletected by the same edge detection and location method as used for the edges of the concentric circles encountered in the radial direc~ion. In a ~ -preferred embodiment, adjacent secuons on the Placido are alternately black and white, however, the adjacent sections can be another set of contras~in~ colors, as long a~ an detectable edge is formed between adjacent sec~ions, to facili~ate locating pomts on the Placido.

wo ~3/24049 Pcr/uss3/o~29~
2137 ~ 42- 1 ,.

The ed~es or color transitions are determined by the mathematical process of dif~erentiation. The derivative function highlights these edges by generating an impulsive change. The impulsive change is used to determine the precise positionof the edge of the black to white or color transition between two pixels. The 5 position is deterrnined to a sub-pixel position by a process of weighting and using ~he surrounding pixel information to detern;ine where between the two pixels theedge is precisely located.

The su*ace normal is calculated by drawin~ a line from the detected point 62 to the reflection point and drawing a line from the reflection poin~ to point 50 -on the Placido. The angle bisecting the angle between these two lines is the surface norrnal.

A successive approximation process is used to deterrnine the reflection point at which the surface normal intersects the eye.

.
Knowin~ ~e location of the de~ected point 62. the lens center point and the location of the Placido point 50, and reflection point one can calculate the surface normal. A line is drawn from point 62 throuPh a point at the ori~in of the lens coordinate system 42 or the center of the lens. This line 60 is extended to intersect the plane of the reflec~ion point. A plane which contains the line extended throu~h point 62 and the center of the lens is rota~ed until it touches the point 50 on the Placido. The X and the Y coordinate of the surface normal are 2 deterrnined. The Z coordinate of the surface normal is then determined. Once the2~ three coordinates of the surface nonnal are known for a number of points, a plane can be drawn ortho~onal to each surface normal. ~he planes can be joined ,~ .
together to form a multi-faceted surface area. This area of facets or joined planes can be smoothed to represent the su~ace contour of the cornea. That is, the faceted surface is integrated to srnooth, the faceted surface to represent the actual contour of the cornea. Points in between the surface normal are calcula~ed by the ..... .. . .

2 1 3 7 1 5 1 ?~ C
' WO 93J2404~ PCr/US93/0~293 -43- : ' :, ', process of interpolation. This process more precisely defirles the surface of ~eeye.

At tirnes it may be difficult to know e~actly what ring on the Placido S corresponds to the ring detected in the CCD digital image. This may be due tocorneal distortion, surgical scarring, or some other optical aberation i~hat ~-oblitera~es data in the digital image so that an ed~e becomes undetectable. As explained above, it iS advanta~eous to know which ring or section on the Placidocorresponds to the ring or section~ detected in the CCD digial image. Ring seven ~ --may be mistaken for ring six, for exarnple, if the edge between ring five and six is ~-not detected and not counted, thus skipped. In an illustrative embodiment, as shown in Fi~ure 19~ a reference mark 76 or numeral is placed on the Placido to aring or section on the Placido. ~ -., As shown in Figure 20, reference rnarks or numerals enhance correlauon of -points on the CCD digital image and corresponding points on the Placido. In an illustrative embodiment, reference marks or numerals are placed in each white rin&. Four lines of reference numerals are placed respectively at zero de~rees.
ninety degrees, one hundred eighty degrees, and two hundred seventy degrees tO
facilitate checking of each of the quadrants.
Even though the reference marks may undergo distortions, including scale, ~-perspective, and rota~ion, when reflected of a non-sphencal surface, the system can ~md the section con:aining the reference mark. The system will do a mapping back in~o a noImalized space to obtain a norrnali~ed detecled reference mark. Innvrmalized space there is a library in which templates are stored for the reference mar~s or numerals as detected when reflectPd from calibrated spheres. The system correlates the stored template mark or numeral from the library with the ?
normalized detected reference mark or numeral to confirm which r~n~ or section Oll the Placido corresponds to the detected ring or sec~ion.

WO 931~4049 2 1 ~ 7 1 ~ 1 44 Pcr/US93/05293 Ille norm~izahon of reference marks allows the sys~em to recognize - , ;
numerals or marks that have undergone translation, rotation, and rubber-sheeting - J -type of perspective distortion.

While an embodiment of the present system in accordance with the invention has been described herein, it ~ill be understood that a person skilled in the art may make minor alterna~ions or substitute circuitry and apparatus other than that described wi~hout departing from the spirit of the invention. For `~
exarnple~ those of ordinary skill having the benefit of this disclosure will of course reco~nized that the "hard-wired" discrete lo~ic function described herein may altematively and equivalently be implemented in sof~ware? i.e., throu,~h suitable programmin,~ of a processor system eyuipped with a suitable processor and a memory or other storage device. Such a software implementa~ion would be a matter of routine for those of ordinary skill havin~ the benefit of this disclosure and knowled~e of the processor system in question. Software functions disclosed in this application could liXewise be implemented in hardware by a person havingordinary skill and the benefi~ of this disclosure.

Claims

18. A checkered Placido.

19. A placido comprising a plurality of adjoining concentric rings divided into arcuate sections by radii extending from the center, adjacent sections differing in color to provide a checkered appearance.

20. A placido comprising a plurality of adjoining, concentric rings divided arcuately into arcuate sections, wherein each section has a common arcuate edge with a section in each adjoining ring and a common radial edge with each adjacent section in the same ring.

21. The placido of Claim 19 wherein adjacent arcuate sections differ in color to provide the placido with a checkered appearance.

22. The placido of Claim 20 wherein adjacent arcuate sections differ in color to provide the placido with a checkered appearance.

23. The placido of Claim 19 further comprising an indicia marking the surface of the placido for use in correlating a position on the placido to a position on a reflected image of the placido.

24. The placido of Claim 20 further comprising an indicia marking the surface of the placido for use ?

in correlating a position on the placido to a position on a reflected image of the placido.

25. A placido comprising a plurality of concentric rings divided into arcuate sections to define an arcuate lattice on the surface of the placido, and wherein adjacent sections differ in color to provide a checkered lattice.

26. A placido including a surface and plurality of adjoining, concentric rings on said surface; said rings sectioned along their length to define an arcuate lattice on said surface with adjacent sections differing in color.

27. The placido of Claim 26 further comprising an indicia marking on the surface to identify one axis of a coordinate system for the surface of the placido.

28. A placido having checkered concentric rings.