Abstract:
Apparatus for determining if a cornea (whether in vitro or in vivo) has been modified (either surgically or otherwise). The method includes the steps of: passing a beam of collimated light a (either coherent or incoherent) through the cornea to produce a distorted wavefront; determining the characteristics of the distorted wavefront; and analyzing the distorted wavefront for characteristics that identify the presence of a modification. The analysis of the distorted wavefront can be for the presence of higher order aberrations, or Gausian characteristics which are indicative of modifications. More particularly, the method includes the steps of providing an optical system that has a pupil plane and an image plane at a detector; positioning the cornea in the pupil plane; passing a collimated beam of light through the cornea to produce at least two images in the image plane; determining the characteristics of the distorted wavefront; and analyzing the distorted wavefront for characteristics that identify the presence of a modification. The apparatus includes: a source of collimated light: an optical system including a distorted grating and an imaging lens (which have a pupil plane, first and second virtual planes, and an image plane); structure for positioning the cornea in the pupil plane; and a computer. The structure for positioning the cornea (which is immersed in a suitable storage fluid) includes first and second plano/plano lenses. The first and second plano lens, which are substantially and perpendicular to and centered with respect to the axis, have less than total distortions.

Description:
RELATED U.S. APPLICATION DATA 
     This application is a continuation of application Ser. No. 09/895,309 filed Jun. 29, 2001 which, in turn, is a divisional of application Ser. No. 09/693,076, filed on Oct. 20, 2000, now U.S. Pat. No. 6,286,959 B1. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to the use of wavefront sensing to determine whether or not a cornea has been altered (due to corrective surgery, or accident). More specifically, the present invention relates to the use of wavefront sensing using a distorted defraction grating to identify corneas (whether in vitro or in vivo) that have been surgically modified (e.g., radical keratotomy (RK), excimer laser photorefractive keratectomy (PRK), laser-assisted in situ keratomileusis (LASIK) and automated lamellar keratoplasty (ALK)). 
     BACKGROUND OF THE INVENTION 
     In the United States about 40,000 corneal transplant operations are performed each year. While success of such surgery may depend upon a number of other factors, one factor that always has an effect on the outcome is the condition of the donor cornea. In the United States, a donor cornea must be transplanted within 7 days of harvesting. Outside the United States donor comeas may be used up to 14 days after harvesting. Additionally, it is essential to use only corneas which have not been modified (e.g., the subject of photorefractive surgery). 
     The growth of refractive surgery over the last five years has been dramatic. In the August 2000 issue of Archives of Ophthalmology, P. J. McDonnell, M.D. states that this year alone over 1,500,000 refractive procedures will be performed. As beneficial as these procedures are, the individual corneas are permanently altered, which makes them unsuitable for corneal transplanting. 
     The increase in refraction surgery increases the likelihood that a modified cornea will be harvested for transplant purposes. Unfortunately, it is generally not possible to conclusively tell, either visually or under a microscope, whether such a donor cornea has been subjected to a surgical procedure or otherwise altered. 
     Even when properly stored in a container (e.g., a Chiron Ophtholmics cornea container) filled with Optisol® or another appropriate solution, a donated cornea changes optically in the 14 day time period referenced above. The interior starts to develop optical scatter sources and the optical power of the cornea changes The scatter resources manifest themselves as randomly distributed optical aberrations which increase over time. It is believed that this is caused by the cells of the harvested cornea not being able to reject waste material. The change in optical power is believed to be caused by an overall relaxation of the tissue. Regardless of the cause, the net result is that these aberrations produce scintillation and static aberrations when a beam of light is passed through a donated cornea. 
     PCT/GB99/00658 (International Publication No. WO 99/467768), based on applications filed in Great Britain on Mar. 10, 1998 and Dec. 23, 1998, discloses a three dimensional imaging system including a lens and a distorted diffraction grating which images objects located at different distances from the grating simultaneously and spatially separated in a single image plane. The grating is distorted according to a quadratic function so as to cause the images to be formed under different focus conditions. It is stated that the system is useful for simultaneously imaging multiple layers within a three dimensional object field, and has applicability in a number of fields including optical information storage, imaging short-time scale phenomena, microscopy, imaging three dimensional object structures, passive ranging, laser beam profiling, wavefront analysis, and millimeter wave optics. The ability to make wavefront measurements is not disclosed or claimed. 
     P. M. Blanchard et al., “Multi-Plane Imaging With a Distorted Grating,” Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, World Scientific, pp. 296-301, Jul. 12-16, 1999, describe a technique for simultaneously imaging multiple layers within an object field onto the detector plane of a single detector. The authors, who are the named inventors in PCT/GB99/00658, state that the imaging of multiple layers within an object field is “useful in many applications including microscopy, medical imaging and data storage.” (See page 296.) The apparatus includes the use of a binary diffraction grating in which the lines are distorted such at each different level of defocus is associated with each diffraction order. When such a grating is placed in close proximity to a lens, the grating creates multiple foci of the image. This multi-foci effect enables the imaging of multiple object planes onto a single image plane. 
     L. J. Otten et al. “3-D Cataract Imaging System,” Proceedings of the 2nd International Workshop in Adaptive Optics for Industry and Medicine, World Scientific, pp. 51-56, describe optics and an associated diagnostic system for volumetric, in vivo imaging of the human lens to characterize or grade cataracts. The described method and apparatus are based on the use of a distorted grating (of the type disclosed in PCT/GB99/00658 and the Blanchard et al. paper, supra) in conjunction with a focusing lens and a re-imaging lens. (See FIG. 1 of this reference.) The quadratic phase shift, introduced by the grating, leads to a different degree of defocus in all diffraction orders, which produces a series of images of different layers of the cataract, each with different defocus conditions, simultaneously and side-by-side on the detector. Thus, in-focus images of different object planes are produced. 
     Analysis of the optical images referenced above requires the use of the Intensity Transport Equation (I.T.E.) and the employment of a Green&#39;s function to produce a wavefront map. S. Woods, P. M. Blanchard and A. H. Greenaway, “Laser Wavefront Sensing Using the Intensity Transport Equation,” Proceedings of the 2nd International Workshop on Adaptive Optics for Industry and Medicine, World Scientific, pp. 260-265, Jul. 12-16, 1999, describe both the I.T.E. and a Green&#39;s function solution thereto in conjunction with laser wavefront sensing. 
     OBJECTS OF THE INVENTION 
     It is an object of the present invention to determine, with wavefront sensing, whether or not a cornea has been altered (either deliberately or accidentally). 
     It is another object of the present invention to determine, with the use of wavefront sensing using a distorted grating, those donor corneas that have been modified by surgery or other methods. 
     It is another object of the present invention to provide a simple optical system (particularly including a light source, an imaging lens, a distorted grating and a data camera) to form, in the detector plane, images from which wavefront aberrations in the cornea can be derived. The beam of light that passes through a cornea (located in the pupil plane) and two virtual planes on opposite sides of and equidistant from such pupil plane. 
     It is an additional object of the present invention to provide a holder for a donor cornea which does not mask optical data from such cornea. 
     It is yet another object of the present invention to provide a holder for a donor cornea that has optical windows that are substantially free of distortion which would mask corneal optical data. 
     It is yet still another object of the present invention in which the optical windows have less than λ/10 distortions. 
     These and other objects will be apparent from the description which follows. 
     SUMMARY OF THE INVENTION 
     A method of determining if a cornea (whether in vitro or in vivo) has been modified (either surgically or otherwise). The method includes the steps of: passing a beam of collimated light a (either coherent or incoherent) through the cornea to produce a distorted wavefront; determining the characteristics of the distorted wavefront; and analyzing the distorted wavefront for characteristics that identify the presence of a modification. The analysis of the distorted wavefront can be for the presence of higher order aberrations, or Gausian characteristics which are indicative of modifications. More particularly, the method includes the steps of providing an optical system that has a pupil plane and an image plane at a detector; positioning the cornea in the pupil plane; passing a collimated beam of light through the cornea to produce at least two images in the image plane; determining the characteristics of the distorted wavefront; and analyzing the distorted wavefront for characteristics that identify the presence of a modification. 
     The apparatus for determining whether a cornea has been surgically modified includes: a source of collimated light, an optical system including a distorted grating and an imaging lens (which have a pupil plane, first and second virtual planes, and an image plane); structure for positioning the cornea in the pupil plane; means for recording the images of the first and second virtual planes; means for determining from the first and second images the distorted wavefront; and means for analyzing said wavefront for characteristics indicative of modified corneas. The first and second virtual planes are on opposite sides of and equally spaced from said pupil plane. 
     The structure for positioning the cornea (which is immersed in a suitable storage fluid) is a container which includes: a housing having first and second ends; structure positioned within the housing for supporting the perimeter of the cornea; a first plano/plano lens for closing the first end of the housing; and a cap for closing the second end of the housing. The cornea support is substantially symmetrical with respect to an optical axis. The first plano/plano lens is substantially perpendicular to the optical axis. Finally, the cap includes a second plano/plano lens which is substantially parallel to the first plano lens. The first and second plano/plano lens, which are substantially centered with respect to the axis, have less than λ/10 total distortions. The support structure includes a cage and a pedestal with the cage being supported by the pedestal. Preferably, the cage and pedestal are integrally formed with the housing. Finally, the cap has a top portion and a skirt which axially inwardly spaces the second lens from the top portion to create an annular area where air will collect when the container is holding a cornea and fluid, so that air will not interfere with a beam of light passing through the first and second plano/plano lenses and cornea. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic of the optical system of the instrument to characterize donor corneas; 
     FIG. 1A is the front view of the distorted grating used in the instrumentation to characterize comeas; 
     FIG. 1B is the front view of the detector plane of the detector of the instrumentation to characterize comeas, and the images in such plane; 
     FIG. 2 is a cross-section view of an optical cornea container of the present invention; 
     FIG. 3 is a cross-sectional, perspective view of an improved cornea container of the present invention; 
     FIG. 4 is a cross-sectional view of the improved optical cornea container of FIG. 3 in the open position; 
     FIG. 4A is a cross sectional view of the improved optical cornea container of FIG. 3 in the closed position. 
     FIG. 5 is a diagram showing the baseline date of the system of FIG. 1, with no cornea or container; 
     FIG. 6 is a diagram showing the baseline date of the system of FIG. 1, with the container of FIG. 2 filled with Optisol®, but with no cornea; 
     FIG. 7 is a diagram showing the data from an unmodified cornea L, held in the container of FIG. 2, positioned in the pupil plane of FIG. 1, and exposed to coherent and collimated light; 
     FIG. 8 is a diagram showing the data from a an unmodified cornea R, held in the container of FIG. 2, positioned in the pupil plane of FIG. 1, and exposed to coherent and collimated light; 
     FIG. 9 is a diagram showing the data from cornea L after it has been surgically modified, again held in the container of FIG. 2, positioned in the pupil plane of the system of FIG. 1, and exposed to the same coherent and collimated light; 
     FIG. 10 is a diagram showing the data from the cornea R after it has been surgically modified, again held in the container of FIG. 2, positioned in the pupil plane of FIG. 1, and exposed to the same coherent and collimated light; 
     FIG. 11 is a three dimensional presentation of the data set forth in FIG. 7; 
     FIG. 12 is a three dimensional presentation of the data set forth in FIG. 8; 
     FIG. 13 is a three dimensional presentation of the data set forth in FIG. 9; 
     FIG. 14 is a three dimensional presentation of the data set forth in FIG. 10; 
     FIG. 15 is a three dimensional presentation of the wavefront of cornea LL which was modified by a LASIK procedure (prior to the death of the donor), held in the container of FIG. 2, positioned in the pupil plane of FIG. 1, and exposed to coherent, illuminated light; 
     FIG. 16 is a three dimensional presentation of the wavefront of cornea LR which was modified by a LASIK procedure (prior to the death of the donor), held in the container of FIG. 2, positioned in the pupil plane of FIG. 1, and exposed to coherent, illuminated light; and 
     FIG. 17 is a schematic of the optical system used to characterize in vivo comeas. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     With reference to FIG. 1, the apparatus  11  for determining whether an in vitro cornea has been modified (either surgically or otherwise) includes a source of collimated coherent light  13 , a cornea container  15 , a distorted diffraction grating  17 , a high quality imaging lens (or lens set)  19 , and a detector  21  (either film or electronic) having a detector plane  23 . (Grating  17 , lens  19  and detector  21  are sometimes referred to as wavefront sensor  24 . ) Apparatus  11  also includes a beam path  25 , a pupil plane  27 , first virtual plane  29 , second virtual plane  31 , and a computer  33 . Computer  33  is connected to detector  21 , via a data acquisition device such as a frame grabber (located within the computer housing). Computer  33  stores the images form detector  21 , determines the wavefront from the stored images, and analyzes the wavefront for the characteristics that identify an altered cornea (e.g. compares the wavefronts to a stored norm). The representation of the virtual planes between source  13  and sensor  24  is for convenience only. In the preferred embodiment they are 73 cm on either side of pupil plane  27 . Source  13  is a coherent laser such as a 633 nm HeNe laser. As those skilled in the art will appreciate non-coherent sources, such as spectrally band filtered white light, could also be used. 
     With grating  17  in close proximity to lens  19  (typically these two elements would, in fact, be in contact with each other along beam path  25 ), the 0, +1 and −1 diffraction orders of grating  17 , image pupil plane  27 , virtual object plane  29  and virtual object plane  31  are projected onto detector plane  23 . The higher order diffraction orders are cut off by an appropriately placed field stop so as not to contaminate the image of the 0 and +1 and −1 orders. Further, with the zero order being an image of the pupil plane  27 , the images in the +1 and −1 diffraction orders correspond to virtual image planes equidistant from and an opposite sides of pupil plane  27 . The grating is distorted according to,            Δ   x          (     x   ,   y     )       ≂           W   20        d       λ                   R   2              (         x   2       +     y   2       )                              
     where λ is the optical wavelength, x and y are Cartesian co-ordinates with an origin on the optical axis and R is the radius of the grating aperture which is centered on the optical axis. The parameter W 20 , defines the defocusing power of the gratings, and is the standard coefficient of the defocus equivalent on the extra pathlength introduced at the edge of the aperature, in this case for the wavefront diffracted into the +1 order. The phase change (Ø m ) imposed on the wavefront diffracted into each order m is given by,            ϕ   m          (     x   ,   y     )       =     m          2      π                   W   20         λ                   R   2              (       x   2     +     y   2       )                              
     The various containers in which donor corneas are stored are unusable for optical diagnostics. The aberrations produced by the walls of such containers mask the aberrations exhibited by corneas both unaltered and altered. With reference to FIG. 2, optical cornea container  15  includes cylindrical housing  41 , first optical window  43 , second optical window  45 , and fluid containment ring  47 . Housing  41  and ring  47  are concentric rings, both bonded to optical window  43 . Window  43  is a plano/plano lens having surfaces  49 ,  51  which are substantially concentric with respect to beam path  25  and substantially perpendicular thereto. Similarly, window  45  is a plano/plano lens having surfaces  53 ,  55  which are also substantially concentric with and substantially perpendicular to beam path  25 . Collectively, windows  43  and  45 , including surfaces  49 ,  51  and  53 ,  55  have total aberrations of less than λ/10. In operation, cavity  57  is filled with Optisol®, or another solution suitable for the storage of donor corneas, to the top of housing  41  so that the meniscus causes such fluid to slightly over fill cavity  57 . Window  45  is then slid over housing  41  without trapping any air in cavity  57 . Excess fluid is collected between housing  41  and ring  47 . 
     With reference to FIGS. 3 and 4, improved cornea container  15   1  includes a cylindrical body portion  61 , a cornea support cage portion  63 , and a cap portion  65 . Body portion includes a bottom surface  67 , an upper skirt portion  69  having a groove  71  therein for supporting an o-ring seal  73  and threads (not shown), and a cavity  74 . Body portion  61  also includes a conical shaped skirt  75  integral with bottom surface  67  for centrally positioning cage portion  63  within body portion  61  as illustrated in FIGS. 3 and 4. Cage portion  63  includes a plurality of fingers  77 , which are supported by ring portion  79  of skirt  75  in a cylindrical pattern concentric with axis  81 . As best illustrated in FIG. 4, the free ends of fingers  77  include, inter alia, an inwardly sloping bevel  83  and notch  84  for supporting a donor cornea, such as illustrated at  85 . Finally, body-portion  61  includes a plano/plano lens  87  secured to ring portion  79 . Lens  87  has parallel plano surfaces  89  and  91  which are substantially centered with respect to axis  81  and substantially perpendicular thereto. Cap portion  65  includes a skirt portion  93 , a shoulder  95  which seats against  73 , a top portion  96 , and an inner skirt portion  97  having a circumferential lip  99 . Inner surface  100  includes threads (not shown) which mate with the threads (also not shown) on skirt  69 . Secured to lip  99  is a second plano/plano lens  101  having plano parallel surfaces  103  and  105 . When cornea container  15   1  is closed, with seal  73  received in circumferential recess  95 , surfaces  103  and  105  are substantially centered with respect to axis  81  and substantially perpendicular thereto. Collectively, the aberrations in lenses  87  and  101 , including surfaces  89 ,  91 ,  103  and  105 , have a total aberration of less than λ/10. 
     In operation, donor cornea  85  is placed in cage  63 , with a portion of the convex surface thereof in contact with bevels  83  and the perimeter received within notches  84 . In this position, donor cornea is substantially centered about axis  81 . Cavity  74  is then filled with a suitable storage fluid and capped by screwing on cap  65 . As can be seen from FIG. 4A, because inner skirt portion  97  projects inwardly, closure of cap  65  will force excess fluid out of cavity  74 . In the event that there is any under filling of cavity  74 , any air which might be trapped in cavity  74  is collected in annular area  107  (outside of the beam path). 
     With nothing in pupil plane  27  of apparatus  11  (e.g., cornea container  15  removed) and source  13  present, the images recorded on detector plane  23  are as illustrated in FIG  1 B. Data was collected without any disturbances (i.e., no cornea container, cornea storage solution, or cornea) to determine the residual errors in the optics and, thus, establish the base line for instrument  11 . With reference to FIG. 5, the raw images as recorded by detector  21  are shown along with the reduced Zernike terms, annotated to show where the various types of data are located in the figure. All the data are taken using a 633 nanometer HeNe laser as the illumination source. Most of the error is tip and tilt, which is the result of not accurately aligning wavefront sensor  24  and for not accurately accounting for where the distorted grating images were actually placed on detector plane  23 . These two terms can be made equal to zero by: (1) subtracting them in the analysis of the wavefront to accommodate images that are not exactly centered on the same line; or (2) a more precise alignment of wavefront sensor  24 . The other aberrations (e.g. focus) are seen to be small, on the order of or less than 0.1λ. All the baseline aberrations, including tip and tilt, can be subtracted from the cornea data. 
     Next, a baseline for optical system  11 , with cornea container  15  located in pupil plane  27  and cavity  57  filled with Optisol® solution, but without a cornea, was established. The baseline data is set forth in FIG.  6 . Again, all aberrations can be compensated for or eliminated using the criteria set forth above with regard to FIG.  5 . 
     After establishing the baseline, an unmodified donor cornea L was placed in cornea container  15 , centered as illustrated in FIG. 2, filled with Optisol® solution, and then closed with optical window  45  in the manner set forth above. Container  15  was then placed in instrument  11 , in optical beam path  25  and with cornea L in pupil plane  27 , as illustrated in FIG.  1 . If necessary, predetermined aberrations can be introduced into the beam path prior to the beam reaching the pupil plane and subsequently accommodated in the analysis of the data. The measured errors are illustrated in FIG.  7 . In this figure the tip and tilt terms are irrelevant since they are associated with cornea container  15  and, the orientation of cornea L therein. Cornea L is seen to have focus and astigmatism errors. 
     As with cornea L, cornea R was placed in container  15 , and centered as set forth above. Cavity  57  as was then filled with Optisol® and closed with optical window  45 . Cornea container  15  was then placed in the pupil plane of instrument  11 . The measured errors are illustrated in FIG.  8 . As with cornea L, the tip and tilt terms for cornea R are irrelevant since they are associated with container  15  and the specific orientation of cornea R therein, both of which are not controlled. As is evident from FIG. 8, cornea R has focus, astigmatism and coma errors. 
     The data illustrated in FIGS. 7 and 8 were collected using a 12 mm diameter collimated beam. The measurements were repeated with an 8 mm, and 5 mm collimated beams to see if the measured aberrations were being effected by the irregular outer edge of the corneas. The effect of reducing the beam size was to improve the quality of the images but at the expense of brightness and the area examined. All data were collected with the beam centered on the cornea. 
     To demonstrate the ability of apparatus  11  to detect surgically modified corneas, cornea L was then modified using a PRK procedure to add 4 diopters of focus change. Cornea R was also subjected to the same procedure to add 8 diopters of focus change. After modification each cornea was, in turn, again centered in cavity  57 , which was filled with Optisol® and closed, and container  15  placed in apparatus  11  with the modified cornea again in pupil plane  27 . 
     The measured errors for cornea L (modified) are illustrated in FIG.  9 . Again, tip and tilt are irrelevant since they are associated with cornea container  15  and the orientation of cornea L (modified) therein. Cornea L (modified) is seen to have considerably larger focus and astymatism errors then cornea L. The higher order errors (coma  1 , coma  2 , trifoil  1 , trifoil  2  and spherical) are also considerably larger and provide one of the basis for the determination that the cornea has been altered. 
     The measured errors for cornea R (modified) are illustrated in FIG.  10 . As before, tip and tilt are irrelevant. Cornea R (modified) is seen to have considerably larger focus and astymatism errors than cornea R. As with cornea L (modified) the higher order aberrations have also increased (again indicating that the cornea has been modified). A summary of the results is shown in Table 1. Note that the measured difference (in waves) between the two corneas is a factor of 2, the same amount of focus difference introduced by the PRK procedure. 
     
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Focus Term Before 
                 Focus Term After 
                 Difference 
               
               
                 Cornea 
                 Modification (waves) 
                 Modification (waves) 
                 (waves) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 L 
                 1.77 
                 3.23 
                 1.46 
               
               
                 R 
                 1.024 
                 4.132 
                 3.108 
               
               
                   
               
             
          
         
       
     
     An alternative way of illustrating the data set forth in conjunction with FIGS. 7-10 is to present the distorted wavefronts produced by the respective unaltered and altered corneas as three dimensional images. This type of presentation is illustrated in FIGS. 11-14, wherein: FIG. 11 corresponds to FIG. 7; FIG. 12, to FIG. 8; FIG. 13, to FIG. 9; and FIG. 14, to FIG.  10 . In FIGS. 11-16, the grey scale on the right is a representation of the distortion. Note the similarities of the Gaussian-like slope of the wavefront aberrations measured for the modified corneas, which provides another basis for determining whether a cornea has been modified. 
     Right (RL) and left (LL) corneas from a donor who had the LASIK corrective surgery prior to death were measured in the same manner as the unmodified corneas L and R (FIGS. 7 and 8) and the PRK modified corneas (FIGS.  9  and  10 ). FIG. 15 is the left (LL) LASIK modified cornea. FIG. 16 is the right (RL) LASIK modified cornea. The characteristic Gausian-like shape of the wavefront produced by the laser surgery is clearly present in both corneas. As with the PRK modified corneas (FIGS.  9  and  10 ), the hier order aberrations are considerably larger than those aberrations in the unmodified corneas (FIGS.  7  and  8 ). 
     The basis for extracting the wavefront from the data collected from detector  21  is to solve the Intensity Transport Equation (I.T.E.). The I.T.E. is derived by expressing the parabolic wave equation for complex amplitude in terms of intensity (I) and phase (Ø), and relates to the rate of change of intensity in the direction of the propagation to the transverse gradient and La Placian of the phase:            -       2      π     λ              ∂   I       ∂   z         =       I          ∇   2        ϕ       +       ∇   I     ·     ∇   φ                                
     For a uniformly illuminate aperture, R ′ , with perimeter P, the ITE simplifies to              2      π     λ          1     I   o              ∂   I       ∂   z         =         W   R            ∇   2        ϕ       -       δ   P            ∂   φ       ∂   η                                  
     where W R  is the aperture function (=1 inside R ′ =0 outside R), δ P  is a delta-function around P, and ∂φ/∂η is the normal derivative of Ø on P. 
     Consider the problem of finding the phase at a particular point r. We can express this in terms of an integral involving a delta-function as follows: 
     
       
         φ( r )=∫ R φ( r ′)( r−r ′) 
       
     
     If we have a Green&#39;s function satisfying            (             ∇   2          G        (     r   ,     r   ′       )         =     δ        (     r   -     r   ′       )         ,       ∂     G        (     r   ,     r   ′       )           ∂   η              )     p     =   0                          
     then we can say          φ        (   r   )       =       ∫   R            φ        (     r   ′     )              ∇   2          G        (     r   ,     r   ′       )                                    
     Applying Green&#39;s 2 nd  identify;          φ        (   r   )       =         ∫   R            G        (     r   ,     r   ′       )                         ∇   2          φ        (     r   ′     )             +       ∮   P            φ        (     r   ′     )              ∂     G        (     r   ,     r   ′       )           ∂   η           -       ∮   P            G        (     r   ,     r   ′       )              ∂     φ        (     r   ′     )           ∂   η                                    
     and the boundary condition on the Green&#39;s function;                φ        (   r   )       =         ∫   R            G        (     r   ,     r   ′       )                         ∇   2        φ          (     r   ′     )         -       ∮   P            G        (     r   ,     r   ′       )              ∂     φ        (     r   ′     )           ∂   η                         =       ∫   R            G        (     r   ,     r   ′       )            (         ∇   2          φ        (     r   ′     )         -       δ   P            ∂     φ        (     r   ′     )           ∂   η           )                                      
     we get the solution. The term in parenthesis is the right hand side of the ITE. The wavefront phase is thus obtained by measuring the intensity derivative (the left hand side of the ITE), multiplying by the Green&#39;s function and integrating;          φ        (   r   )       =       -       2      π     λ            1     I   O              ∫   R              (     G        (     r   ,   r     )       )     ′                       ∂     I        (     r   ′     )           ∂   z                                    
     The intensity derivative,          ∂     I        (     r   ′     )           ∂   z                            
     is obtained by the subtraction of two pixellated images. The Green&#39;s function is be pre-calculated on the appropriate grid and the solution obtained by the matrix multiplication:        φ   =       -       2      π     λ            1     I   O              ∑   J                       (       Gi   j          (       ∂   I       ∂   z       )       )     j                                
     The particular solution will vary, depending on the specifics of the optical design, the detector and the distorted grating used. 
     While the foregoing has dealt with donor comeas, the same basic procedure can also be used on in vivo comeas. With reference to FIG. 17, system  111  includes a source of collimated coherent light  113 , a beam splitter  115 , a distorted diffraction grating  117 , a high quality imaging lens or lens set  119 , and a detector  121  (either film or electronic) having a detector plane  123 . As with instrument  11 , grating  117 , lens  119  and detector  121  constitute wavefront sensor  124 . System  111  also includes a beam path  125 , a pupil plane  127 , a first virtual plane  129 , a second virtual plane  131 , and a computer  133  connected to detector  121  by a data acquisition device, such as a frame grabber located within the computer housing. As with the first embodiment, source  113  is a coherent laser whose energy, when projected into the eye meets FDA approved eye safe levels. Grating  117 , which is also distorted according to the grating equation set forth above, is in close proximity with or touching lens  119 . System  111  also includes apparatus, not shown, for positioning the patient&#39;s head such that his/her cornea is in pupil plane  127 . 
     In operation the beam from source  113  is directed through beam splitter  115 , through the cornea  135  and of eye  137 , onto the retina  139  where it is reflected back through the cornea and then directed, by beam splitter  115  to wavefront sensor  124 . As with instrument  11 , the 0, +1 and −1 diffraction orders of grating  117  image pupil plane  127 , virtual object plane  129  and virtual object plane  131  onto detector plane  123 . Again, the higher order diffraction orders are cut off by an appropriately placed field stop so as not to contaminate the image of the 0 and +1 and −1 orders. Further, with zero order being an image of the pupil plane  127 , the images in the +1 and −1 diffraction orders correspond to virtual image planes equidistant from and opposite sides of pupil plane  127 . Computer  133  stores the images from detector  121 , determines the wavefront from the stored images in the manner set forth above with the I.T.E. and a Green&#39;s function, and then analyzes the wavefront for the characteristics that identify an altered cornea (e.g., compares the wavefront to a stored norm). 
     Whereas the drawings and accompanying description have shown and described the preferred embodiment of the present invention, it should be apparent to those skilled in the art that various changes may be made in the form of the invention without affecting the scope thereof.