Patent Publication Number: US-2013253884-A1

Title: Method and apparatus for morphological analysis

Description:
TECHNICAL FIELD 
     The present disclosure relates generally to the field of analyzing structures and in particular to a method and apparatus for analyzing morphological properties of a structure. 
     BACKGROUND ART 
     The application of optical coherence tomography (OCT) has increased significantly over the past several years. OCT has been applied not only to ophthalmology, but also to other medical fields such as the investigation of skin diseases, endoscopy and colonoscopy. Moreover, it has been used for non-medical fields, such as evaluation of materials, for example in the evaluation of cracks in silicon nitride bearing balls and in the analysis of art objects. 
     Common OCT devices are based on Michelson interferometer principles. Specifically, a beam of light is split into two beams of light, where a first beam of light interacts with the sample and the second beam of light is reflected off a reference mirror to interfere with the first beam of light after the interaction of the first beam of light with the sample. The interference signal carries information about the layers forming the sample. The Michelson interferometer is very useful for optical analysis deep within the specimen, such as in the case of the human retina where it is typically positioned at about two centimeters from the human body surface. 
     Since some OCT applications, such as: the analysis of the cornea or skin; colonoscopy; analysis of materials; and the analysis of art objects, need to be analyzed at a relatively shallow depth, a simple and cheap analyzing tool arranged to provide optical analysis at shallow depths would be advantageous. 
     An article by G. E. Aizenberg, et al. entitled “A Digital Signal-Processing Analysis Technique for the Infrared Reflectivity Characterization of Ion Implanted Silicon”, published in Journal of Electronic Material, Vol. 21, No. 11, in 1992, describes a method for analyzing optical reflectance by performing a Fourier Transform of a Bilinear Transform of the reflectance data. An article by G. E. Aizenberg, et al. entitled “Optical characterization of semiconductors containing inhomogeneous layers”, published in Applied Surface Science, Vol. 63, in 1993, also describes the above analyzing method. However, the aforementioned articles do not teach or suggest how to build a practical apparatus for implementing the mathematical methods described therein. 
     SUMMARY OF INVENTION 
     In view of the discussion provided above and other considerations, the present disclosure provides methods and apparatus to overcome some or all of the disadvantages of prior and present methods of providing analysis of structures. Other new and useful advantages of the present methods and apparatus will also be described herein and can be appreciated by those skilled in the art. 
     In certain embodiments an apparatus arranged to analyze a structure is provided, the apparatus comprising: a control unit; a target focusing functionality; a light source in optical communication with the target focusing functionality and arranged to irradiate a target area of the structure in cooperation with the target focusing functionality; and a light detector, in communication with the control unit and arranged to detect the irradiated light from the light source after interaction with the target area. The control unit is arranged, for each of a plurality of target areas of the structure, to: control the target focusing functionality such that the target area is irradiated by the light source and the light detector detects the irradiated light from the light source after interaction with the target area; detect the amplitude of the detected light as a function of wavelength; perform a transform of a function of the detected amplitudes to the optical thickness domain; determine morphological information of the target area responsive to the performed transform; and output the determined morphological information. 
     In one independent embodiment, an apparatus arranged to analyze a structure is provided, the apparatus comprising: a control unit; a light source arranged to irradiate a target area of the structure; and a light detector in communication with the control unit, and arranged to detect the irradiated light from the light source after interaction with the target area, the control unit arranged to: transform amplitudes of the detected light to the optical thickness domain, the transform comprising a bilinear transform; determine morphological information of the target area responsive to the performed transform; and output the determined morphological information. 
     In one embodiment, the apparatus further comprises: a target focusing functionality in optical communication with the light source, wherein the arrangement of the light source to irradiate a target area is in cooperation with the target focusing functionality, wherein the control unit is further arranged, for each of a plurality of target areas of the structure, to control the target focusing functionality such that the target area is irradiated by the light source and the light detector detects the irradiated light from the light source after interaction with the target area, and wherein the arrangement of the control unit to transform, determine and output is for each of the plurality of target areas. In one further embodiment, the apparatus further comprises: a display, in communication with the control unit and arranged to display the output morphological information, wherein the morphological information comprises refractive index information of a plurality of layers of each target area, and wherein a three dimensional view of the target area is displayed on the display, the determined refractive index information of each layer of each target area being displayed within the three dimensional view. 
     In one embodiment, the morphological information comprises optical thickness information of the target area. In another embodiment, the morphological information comprises the refractive index of one layer of the target area. 
     In one embodiment, the morphological information comprises the thickness of at least one layer of the target area. In another embodiment, the control unit is further arranged to receive topographic information of a surface of the target area and adjust the calculated morphological information responsive to the received topographic information. 
     In one embodiment, the structure is a Cornea and the morphological information comprises the thickness of the Cornea. 
     In another independent embodiment, a method of analysis of a structure is provided, the method comprising: irradiating a target area of the structure with a first beam of light; detecting the amplitude of the first beam of light after interaction with the target area, the amplitude detected as a function of wavelength; transforming the detected amplitudes to the optical thickness domain, the transforming comprising performing a bilinear transform on the detected amplitudes; determining morphological information of the target area responsive to the transforming; and outputting the determined morphological information. 
     In one embodiment, the irradiating, detecting, transforming, determining and outputting is performed for each of a plurality of target areas of the structure. In one further embodiment, the morphological information comprises refractive index information of a plurality of layers of each target area and the method further comprises: displaying a three dimensional view of the target area; and displaying the determined refractive index information of each layer of each target area within the displayed three dimensional view. 
     In one embodiment, the morphological information comprises optical thickness information of a layer of the target area. In another embodiment, the morphological information comprises the refractive index of a layer of the target area. 
     In one embodiment, the morphological information comprises the thickness of a layer of the target area. In another embodiment, the method further comprises disposing a layer of optical material, exhibiting a known refractive index, on the structure. 
     In one embodiment, the method further comprises: receiving topographic information of a surface of the target area; and adjusting the calculated morphological information responsive to the received topographic information. In another embodiment, the structure is a Cornea and the morphological information comprises the thickness of the Cornea. 
     In one independent embodiment, a control unit arranged to analyze light reflected off a target area of a structure is provided, the amplitudes of the light reflected off the target area detected by a detector arranged to output information regarding the detected amplitudes as a function of wavelength, the control unit comprising: a transform functionality arranged to transform the detected amplitudes to the optical thickness domain, the transform comprising a bilinear transform; and a determining functionality arranged to determine morphological information of the target area responsive to the transform and further arranged to output the determined morphological information. 
     In one embodiment, the control unit further comprises: an irradiating control functionality arranged, for each of a plurality of target areas of the structure, to control a target focusing functionality such that the target area is irradiated by light, wherein the arrangement to transform, determine and output is for each of the plurality of target areas. In one further embodiment, the control unit is in communication with a display arranged to display the output morphological information, wherein the morphological information comprises refractive index information of a plurality of layers of each target area, and wherein the control unit is arranged to cause the display to display a three dimensional view of the target area and to display the determined refractive index information of each layer of each target area within the three dimensional view. 
     In one embodiment, the morphological information comprises optical thickness information of a layer of the target area. In another embodiment, the morphological information comprises the refractive index of a layer of the target area. 
     In one embodiment, the morphological information comprises the thickness of a layer of the target area. In another embodiment, the determining functionality is further arranged to receive topographic information of a surface of the target area and adjust the calculated morphological information responsive to the received topographic information. 
     In another independent embodiment, a method of measuring the thickness of a target portion of a Cornea is provided, the method comprising: irradiating the target portion of the Cornea with a first beam of light; detecting the first beam of light after interaction with the target portion of the Cornea; determining the thickness of the target portion of the Cornea responsive to a reflectometric analysis of the detected light; and outputting the determined thickness of the target portion of the Cornea. 
     In one embodiment, the detecting comprises detecting the amplitude of the detected light as a function of wavelength, and the method further comprises: transforming the detected amplitudes to the optical thickness domain, the transforming comprising performing a bilinear transform on the detected amplitudes; and determining morphological information of the target area responsive to the performed transform, the determined morphological information comprising the determined thickness. In one further embodiment, the irradiating, detecting, transforming, determining morphological information and outputting is performed for each of a plurality of target areas of the cornea. 
     In one embodiment, the morphological information comprises optical thickness information of the cornea. In another embodiment, the morphological information comprises the refractive index of a layer of the cornea. 
     In one embodiment, the morphological information comprises the thickness of a layer of the cornea. In another embodiment, the method further comprises: receiving topographic information of a surface of the cornea; and adjusting the calculated morphological information responsive to the received topographic information. 
     In one embodiment, the morphological information comprises refractive index information of a plurality of layers of each target area, and the method further comprises: displaying a three dimensional view of the target area; and displaying the determined refractive index information of each layer of each target area within the displayed three dimensional view. 
     Additional features and advantages of the invention will become apparent from the following drawings and description. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       For a better understanding of the invention and to show how the same may be carried into effect, reference will now be made, purely by way of example, to the accompanying drawings in which like numerals designate corresponding elements or sections throughout. 
       With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of the preferred embodiments of the present invention only, and are presented in the cause of providing what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the invention. In this regard, no attempt is made to show structural details of the invention in more detail than is necessary for a fundamental understanding of the invention, the description taken with the drawings making apparent to those skilled in the art how the several forms of the invention may be embodied in practice. In the accompanying drawings: 
         FIG. 1A  illustrates a high level schematic diagram of an apparatus arranged to determine morphological information of a structure responsive to light reflected off the structure, according to certain embodiments; 
         FIG. 1B  illustrates a high level block diagram of a processor of the apparatus of  FIG. 1A , according to certain embodiments; 
         FIG. 1C  illustrates a high level flow chart of the operation of the apparatus of  FIG. 1A  to determine morphological data of a target structure; 
         FIG. 1D  illustrates a high level flow chart of the operation of the processor of  FIG. 1B  to determine morphological data; 
         FIG. 1E  illustrates a high level diagram of a multi-layer structure; 
         FIG. 1F  illustrates a plot of reflectance data vs. wave number of a light beam reflected from the structure of  FIG. 1E ; 
         FIG. 1G  illustrates a plot of the reflectance data of  FIG. 1E  after performing a bilinear transform and a Fourier transform to the optical thickness domain; 
         FIG. 1H  illustrates a high level flow chart of the operation of the apparatus of  FIG. 1A  to determine the thickness of a target Cornea; 
         FIG. 2A  illustrates a high level schematic diagram of an apparatus arranged to determine morphological information of a structure responsive to light reflected off the structure and further responsive to topographic information of the surface of the structure, according to certain embodiments; 
         FIG. 2B  illustrates a high level flow chart of the operation of the apparatus of  FIG. 2A , according to certain embodiments; 
         FIG. 3A  illustrates a high level schematic diagram of an apparatus arranged to determine morphological information of a structure responsive to interference between light reflected off the structure and a reference light, according to certain embodiments; 
         FIG. 3B  illustrates a high level flow chart of the operation of the apparatus of  FIG. 3A , according to certain embodiments; 
         FIG. 4A  illustrates a high level schematic diagram of an apparatus arranged to determine morphological information of a multi-layer optical structure in a plurality of modes, according to certain embodiments; and 
         FIG. 4B  illustrates a high level flow chart of the operation of the apparatus of  FIG. 4A . 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Before explaining at least one embodiment in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of the components set forth in the following description or illustrated in the drawings. The invention is applicable to other embodiments or of being practiced or carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein is for the purpose of description and should not be regarded as limiting. In particular, the term connected as used herein is not meant to be limited to a direct connection, and allows for intermediary devices or components without limitation. 
       FIG. 1A  illustrates a high level schematic diagram of an apparatus  20  arranged to determine morphological information of a structure  30  responsive to light reflected off structure  30 . Apparatus  20  comprises: a control unit  40 , comprising a processor  45  and a memory  50 ; a light source  60 ; a light detector  70 ; a target focusing functionality  80 ; and a display  85 . Each of light source  60 , light detector  70  and target focusing functionality  80  is in one embodiment in communication with control unit  40 . Control unit  40  may be implemented in dedicated circuitry, or by a general purpose computing platform arranged to perform computer readable instructions read from a non-transitory storage device without limitation. In another embodiment, one or more of light source  60 , light detector  70  and target focusing functionality  80  is controlled by an internal control unit. 
     In one embodiment, light source  60  outputs a broad band light, and in another embodiment light source  60  is a tunable light source responsive to control unit  40 , particularly the wavelength of the light output by light source  60  is in such an embodiment responsive to an output of control unit  40 . In one embodiment, light source  60  comprises a plurality of super luminescent diodes (SLDs). A plethora of such light sources  60  are commercially available, such as: the SLD-MS-series commercially available from Superlum of County Cork, Ireland; any of a plurality of ultra wideband light source modules commercially available from INPHENIX of Livermore, Calif.; and a Super Luminescent Light Emitting Diode Device commercially available from INPHENIX of Livermore, Calif. In another embodiment, light source  60  comprises a Tungsten-Halogen lamp. In one non-limiting embodiment, light source  60  is arranged to output light exhibiting a wavelength range of 0.8-0.85 um. In another non-limiting embodiment, light source  60  is arranged to output light exhibiting a wavelength ranged centered about any of a plurality of wavelengths, such as: 1.3 um; 1.5 um; or 1.6 um, without limitation. 
     In one embodiment, light detector  70  comprises one or more of a diffraction grating and a charge-coupled device (CCD) array. In one non-limiting embodiment, light detector  70  comprises a spectrometer module. A plethora of such light detectors  70  are commercially available, such as: the HR4000 Spectrometer commercially available from Ocean Optics, Inc. of Dunnedin, Fla., which exhibits a 1200 grooves/mm grating and a 5 micron slit; the CCS100 Compact CCD Spectrometer commercially available from Thorlabs of Newton, N.J.; and a high resolution spectrometer such as the AvaSpec-ULS3648-USB2 High Resolution Fiber Optic Spectrometer, commercially available from Avantes Inc. of Broomfield, Colo. In another non-limiting embodiment, light detector  70  comprises any one, or a combination of, a plurality of detector types, such as: a Silicon (Si) based detector; an Indium Gallium Arsenide (InGaAs) based detector; and a Lead Selenide (PbSe) based detector. In one embodiment, light detector  70  is arranged to detect specular reflection of light sourced by light source  60  after interaction with structure  30  and in another embodiment light detector  70  is arranged to detect diffuse reflection of light sourced by light source  60  after interaction with structure  30 . In another embodiment, light detector  70  is arranged to detect both specular and diffuse reflection of light sourced by light source  60  after interaction with structure  30 , without limitation. 
     In one embodiment, target focusing functionality  80  comprises a plurality of motors arranged to translate target focusing functionality along three orthogonal axes responsive to control unit  40 . In one non-limiting example, target focusing functionality  80  may be translated along the three orthogonal axes by a GVS002 Scanning Galvanometer Mirror System, commercially available from Thorlabs of Newton, N.J. In one embodiment, target focusing functionality  80  comprises optical lenses arranged to focus light detected from light source  60  and further arranged to collect light reflected from structure  30  so that it is transferred to light detector  70 , as will be described below. In one embodiment, target focusing functionality  80  additionally includes isolation devices, such as optical circulators, that allow proper routing of incoming or reflected light to the proper direction. In one embodiment, light traveling between light source  60 , focusing functionality  80 , structure  30  and light detector  70 , travels through free space. In another embodiment, light traveling between light source  60 , focusing functionality  80 , structure  30  and light detector  70 , is guided through optical fibers. 
       FIG. 1B  illustrates a high level block diagram of processor  45  comprising: an irradiating control functionality  100 ; an optional amplitude detection functionality  110 ; a normalization functionality  120 ; a bilinear transform functionality  130 ; a domain transform functionality  140 ; an identification functionality  160 ; and a determination functionality  170 . Each of irradiating control functionality  100 , optional amplitude detection functionality  110 , normalization functionality  120 , bilinear transform functionality  130 , domain transform functionality  140 , identification functionality  160  and determination functionality  170  are in one embodiment implemented as automated processes within processor  45  of control unit  40 , instructions for the automated processes stored on memory  50  in a machine readable format, preferably on a computer readable medium of fixed form, which may be a local storage drive, or may be a remote storage drive accessed over a network connection. Alternatively, dedicated hardware may be provided for each, or some, of irradiating control functionality  100 , optional amplitude detection functionality  110 , normalization functionality  120 , bilinear transform functionality  130 , domain transform functionality  140 , identification functionality  160  and determination functionality  170  without exceeding the scope. 
     In an exemplary embodiment, light exiting light source  60  impacts structure  30 , via target focusing functionality  80 , at a near normal incidence, i.e. at about 90°+/−5% from a plane defined by the surface of structure  30 . Light detector  70  is secured so as to detect light sourced by light source  60  reflected from structure  30  at a near normal incidence. In a non-limiting example light source  60  and light detector  70  are provided as a single controllable optical block. In one non-limiting embodiment light detector  70  comprises a lens. In one embodiment target focusing functionality  80  comprises a scanning galvanometer mirror system, such as the GVS002 commercially available from Thorlabs of Newton, N.J., as described above. Target focusing functionality  80  is arranged to scan the surface of structure  30  and further comprises a lens arranged to focus a beam of light detected from light source  60  onto a target area  90  of structure  30 . In one embodiment the lens, or an additional lens, is also used to collect light reflected from structure  30  and transfer it to light detector  70 , as will be described below. In one optional embodiment (not shown), light source  60  and light detector  70  are placed within control unit  40  and are in optical communication with structure  30  via fiber optics. As indicated above, in one non-limiting embodiment, light source  60  is constituted of a tunable laser light, in another embodiment light source  60  is constituted of a narrow bandwidth light source and in another embodiment light source  60  is constituted of a broad range light source, such as a white light or a halogen lamp. Light detector  70  may be constituted of a light detector with a light filter, a light detector with a tunable light filter, or a simple detector without exceeding the scope. 
     In operation, as will be described further below, in one embodiment a structure  30 , such as the multi-layer structure illustrated in  FIG. 1E , is scanned at a plurality of target areas  90 . In another embodiment, a single target area  90  is scanned, as will be described below. Multi-layer structure  30  is comprised of a plurality of layers  35  numbered consecutively for identification from the external surface layer and proceeding away from the surface layer. For clarity, the surface layer is defined as the layer upon which light exiting light source  60  is first detected. In one non-limiting embodiment, each target area  90  exhibits a diameter of about 20 micrometers, the distance between the centers of adjacent target areas  90  is in one non-limiting embodiment about 10 micrometers. In one non-limiting embodiment, the plurality of target areas  90  forms an analysis area  95  of about 1 cm 2 . 
     The method of analyzing an analysis area  95  of a multi-layer structure  30  is described in the high level flow chart of  FIG. 1C  and is implemented by apparatus  20 . In optional stage  1000 , if the sign of the refractive index steps for each of the interfaces of layers  35  is known, the information is stored on memory  50 . In optional stage  1010 , in the event that the refractive indices of all layers  35  are unknown, an additional layer (not shown) with a know refractive index is added to structure  30 , preferably disposed on the surface thereof, i.e. on the surface of layer  1  thereof. In the embodiment where structure  30  is a cornea, the additional layer is in one embodiment liquid drops exhibiting a known refractive index. In stage  1020 , control unit  40 , via irradiating control functionality  100 , controls target focusing functionality  80  to scan the surface of structure  30  and select a target area  90 . 
     In stage  1030 , control unit  40 , in cooperation with irradiating control functionality  100 , controls light source  60  to output light. In one embodiment, as will be described below, control unit  40  is arranged to disable the output of light from light source  60  after light detector  70  detects the reflected light from target area  90 . In such an embodiment, control unit  40  is arranged to control light source  60  to initiate output of light for each analyzing of a target area  90 . In another embodiment, light source  60  is disabled only after all of the plurality of target areas  90  have been analyzed. The beam of light is focused by target focusing functionality  80  onto the selected target area  90  of stage  1020  responsive to control unit  40 . The diameter of the beam of light focused by target focusing functionality  80  is arranged such that the beam of light preferably covers the entirety of selected target area  90 . In stage  1040 , at least a portion of the light of stage  1030  is reflected from selected target area  90  and detected at light detector  70 . In one embodiment, the reflected light is focused by target focusing functionality  80  onto light detector  70 . 
     In stage  1050 , morphological data of selected target area  90  is determined, as will be described in stages  2000 - 2030  of  FIG. 1D . In stage  1060 , control unit  40  determines if all desired target areas  90  were scanned. In one embodiment, the desired target areas  90  are predetermined and stored on memory  50 . In the event that it is determined that all of the target areas  90  have not yet been scanned, stage  1020  as described above is performed. In the event that it is determined that all of the target areas  90  of interest have been scanned, or in the event that only a single target area  90  is scanned, in stage  1070  control unit  40  is arranged to display the determined morphological data of each target area  90 , as will be described further below, on display  85 . In one embodiment, the determined morphological data is transmitted by control unit  40  to an external computer via a local area network, wide area network, or the Internet, without limitation. In one embodiment, control unit  40  is arranged to display a 3 dimensional gray scale image of structure  30 , as will be described further below. In the event that structure  30  is a biological structure, such as a cornea, in one embodiment the determined morphological data is compared to previously stored morphological data from an earlier analyzation session. The comparison may provide an indication as to whether there has been an improvement or deterioration in structure  30 . 
       FIG. 1D  illustrates a high level flow chart of the operation of processor  45  to determine morphological data as described above in stage  1050 . In stage  2000 , in one embodiment, control unit  40  steps the wavelength of light output from light source  60  by discrete even intervals, and further determines, responsive to optional amplitude detection functionality  110 , the amplitude of the reflected light for each discrete wavelength. It is to be understood that stepping of the wavelength in discrete intervals is not meant to be limiting in any way, and sweeping of the wavelength may be performed, with samples taken at discrete intervals without exceeding the scope. In yet another embodiment, light source  60  continuously emits light in all desired spectra simultaneously. Light detector  70  may use an internal grating, prism or other tuning means in order to perform the spectrometric conversion so as to associate an amplitude with each discrete wavelength. In one non-limiting embodiment, light detector  70  is arranged to provide 2048 readings over the desired reflectance spectrum. In another embodiment, optional amplitude detection functionality  110  is integrated within light detector  70 , such that light detector  70  provides control unit  40  with the amplitude of the reflected light as a function of wavelength. 
     As described above, control unit  40  detects the amplitude of the detected light as a function of the wavelength of the light output by light source  60 . In one embodiment, control unit  40 , responsive to normalization functionality  120 , is further arranged to normalize the detected amplitude and preferably convert the measurements from wavelength to wave number for ease of calculation. The term wave number as utilized herein is defined as reciprocal of the wavelength, and is commonly used in spectroscopy, however this is not meant to be limiting in any way, and wavelength or frequency may be substituted, with the appropriate mathematical compensation, whenever the term wave number is utilized. Normalization is preferably performed based on the reflectance results measured for a known material with a known reflectance performance, such as aluminum, which has a reflectance of about 95%. A normalized value of the detected amplitude is thus determined. 
     In stage  2010 , control unit  40  is arranged to transform the detected amplitudes as a function of wave number to the optical depth domain, preferably by performing a domain transform, such as a Fourier transform, of a bilinear transform of the detected amplitudes. Specifically, control unit  40 , responsive to bilinear transform functionality  130 , is further arranged to perform a bilinear transform on the detected amplitudes as a function of wave number, with the term bilinear transform as a function of wave number denoted B[R(w)], preferably defined as: 
     
       
         
           
             
               
                 
                   
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     where R(w) is defined as the reflectance amplitude as a function of wave number w. In one embodiment, the amplitudes are determined as a fraction of light output reflected. B[R(w)] is illustrated in  FIG. 1F  as graph  200 . 
     For an inhomogeneous structure, EQ. 1 can be expressed as: 
     
       
         
           
             
               
                 
                   
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     where n(x) is the refractive index at depth x, w is the wave number, B 0  is given as: 
     
       
         
           
             
               
                 
                   
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     and B 1  is given as: 
     
       
         
           
             
               
                 
                   
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     where n 1  is the refractive index of the first layer of the structure, i.e. the layer at the surface of structure  30  as described above. 
     For a multi-layer structure with small refractive index steps between adjacent layers, EQ. 2 can be expressed as: 
     
       
         
           
             
               
                 
                   
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                   5 
                 
               
             
           
         
       
     
     where N is the number of layers exhibiting a respective thickness d i  of the multi-layer structure. 
     Control unit  40 , and particularly processor  45 , is further arranged, responsive to domain transform functionality  140 , to transform the bilinear transformed reflectance amplitudes to the optical thickness domain, preferably by performing a Fourier transform, even further preferably by performing a fast Fourier transform. There is no limitation to the domain transform, and autocorrelation or covariance methods may be used to determine optical thickness and amplitude relationships without limitation. In an exemplary embodiment a Fourier transform is performed by domain transform functionality  140 , wherein the data is interpolated at equi-spaced wave-number points, high-pass filtered, windowed, zero padded to a specific number of points and a fast Fourier transform (FFT) algorithm is applied. From EQ. 5 it is evident that the Fourier analysis of B(w) leads to a spectrum in the optical thickness domain. The term optical thickness is defined as two times the refractive index times the thickness, denoted “2nd”, wherein “n” denotes the refractive index and “d” denotes the thickness of the layer, with the factor of 2 added to take into account that light must pass through the layer in both directions for reflectance data. 
     The bilinear transformed reflectance amplitudes transformed to the optical thickness domain exhibit a plurality of peaks  210 , as illustrated in  FIG. 1G . Control unit  40 , and in particular processor  45 , in cooperation with identification functionality  160 , is preferably further arranged to identify the peaks from the bilinear transformed reflectance amplitudes transformed to the optical thickness domain. The amplitude of each peak is preferably given as: 
     
       
         
           
             
               
                 
                   A 
                   = 
                   
                     
                       B 
                       1 
                     
                      
                     
                       
                         
                           n 
                           
                             j 
                             + 
                             1 
                           
                         
                         - 
                         
                           n 
                           j 
                         
                       
                       
                         n 
                         j 
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   6 
                 
               
             
           
         
       
     
     In stage  2020 , control unit  40  is in one embodiment further arranged, in cooperation with determination functionality  170 , to determine morphological information of target area  90  responsive to identified peaks  210 . In one embodiment, the optical thickness of at least one layer of target area  90  is determined. In another embodiment the refractive index of at least one layer is determined. Specifically, the refractive indices are determined responsive to the known, or determined, refractive index of the first layer. In the event that optional stage  1010 , as described above, was performed and a first layer was externally added to structure  30 , the refractive index of the first layer, i.e. n 1 , is known. In the event that optional stage  1010  was not performed and the refractive indexes of all layers are unknown, the refractive index of layer n 1  is preferably determined responsive to the bilinear transform of EQ. 5. Specifically, as described above in relation to EQ. 1, B(w) is a function of the detected light amplitudes of stage  2010 . The average of B(w) is determined responsive to the detected light amplitudes. From EQ. 5 it is clear that the average of B(w) is equal to B 0 . From EQ. 3, n 1  is thus determined. The refractive indices of the subsequent layers are then determined responsive to the amplitudes of peaks  210  according to EQs. 4 and 6. The thickness of each layer can then be determined by dividing the respective peak  210  by twice the refractive index of the layer. 
     In one embodiment, the refractive index steps between each layer is determined and stored on memory  50 . In the event structure  30  contains only a single layer, structure  30  can be considered as a multi-layer structure with the thickness of each additional layer being zero. 
     In one embodiment, in the event the average refractive index of structure  30  is known, the optical depth domain (2nd) spectrum of  FIG. 1G  is divided by 2*n av , i.e. twice the average refractive index. The resultant spectrum is in the depth domain, i.e. is a function of the depth of structure  30 . The amplitude of the spectrum at any specific depth may be presented as a gray scale representation of the 3 dimensional coordinate, i.e. the specific depth at the specific target area  90 . 
     In stage  2030 , the determined morphological information is output from determination functionality  170  and preferably stored on memory  50  and/or output on display  85 . In stage  2040 , as described above in relation to stage  1050 , after all target areas  90  are analyzed, control unit  40  is in one embodiment arranged to display the stored morphological data on display  85 . In one embodiment, where the refractive indices of the layers of structure  30  are determined for each target area  90 , refractive index information of each layer  35  of each target area  90  is displayed on display  85  as a gray scale representation of a 3 dimensional view of target area  90 . In one embodiment, the displayed refractive index information is the refractive index step between each layer  35  of each target area  90  and the refractive index steps within each layer  35  between adjacent target areas  90 . 
     Advantageously, no interference is necessary to determine the morphological information responsive to the light reflected off of target area  90  and thus no reference mirrors are needed, reducing cost and complexity of apparatus  20  when compared to prior art OCT devices. 
     Analysis of Simulated Reflectance Data 
     A simulated example of the use of the above method on a structure consisting of 7 layers disposed on a substrate is given herein as a non-limiting example. Table 1 represents the refractive indices, the depth and the optical depth of each layer: 
     
       
         
           
               
               
               
             
               
                   
                 TABLE I 
               
             
            
               
                   
                   
               
               
                   
                 Layer # 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 Substrate 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Refractive Index 
                 1.52 
                 1.5 
                 1.49 
                 1.47 
                 1.45 
                 1.42 
                 1.38 
                 1.33 
               
               
                 Thickness [μm] 
                 49.50 
                 62.00 
                 71.00 
                 50.00 
                 63.00 
                 68.00 
                 74.00 
               
               
                 Optical Depth [μm] 
                 150.48 
                 336.48 
                 548.06 
                 695.06 
                 877.76 
                 1070.83 
                 1275.12 
               
               
                   
               
            
           
         
       
     
     A typical wavelength range of 0.8&lt;λ&lt;0.85 μm was assumed for the simulation. The reflectance data was interpolated at equi-spaced wave-number points, as illustrated in graph  200  of  FIG. 1F . The Bilinear Transformation of Eq. 2 was applied and the result was high-pass filtered, windowed, zero padded to a specific number of points and a Fast Fourier Transform (FFT) was performed. The resulting spectrum is illustrated in  FIG. 1G  as described above. 
     Observed peaks  210  are representative of the seven interfaces between layers. The optical depths of such peaks are indicated in Table 1. If n 1  or n S , i.e. the refractive index of the substrate, is known and there is structural information in regards of which indices are higher or lower at each interface, i.e. the sign of the refractive index steps at each interface are know, then all refractive indices and thicknesses can be determined, as described above. 
     For example, by averaging the bilinear transformed reflectance of EQ. 1 and responsive to EQ. 5, as described above, it is determined that n 1 =1.52. The leftmost peak  210  occurs at an optical depth θ 1 =151 μm and its amplitude is 0.0056. Therefore, the thickness of the first layer is d 1 =151 μm/(2*1.52)=49.5 μm. According to EQ. 4, B 1 =0.43 and according to EQ. 5, (n 2 −n 1 )=0.0056*1.52/0.43=0.02. Since n 1  is known to be 1.52, n 2 =1.52−0.02=1.5. The thickness of the second layer is thus determined to be d 2 =(θ2−θ1)/(2*1.5)=(337 μm−151 μm)/3=62 μm. This procedure is followed to determine the thickness of each of the various layers. 
     The minimal thickness of each layer which can be determined is given as: 
     
       
         
           
             
               
                 
                   
                     d 
                     
                       MI 
                        
                       
                           
                       
                        
                       N 
                     
                   
                   = 
                   
                     
                       
                         λ 
                         
                           MA 
                            
                           
                               
                           
                            
                           X 
                         
                       
                       · 
                       
                         λ 
                         
                           MI 
                            
                           
                               
                           
                            
                           N 
                         
                       
                     
                     
                       2 
                       · 
                       n 
                       · 
                       
                         ( 
                         
                           
                             λ 
                             
                               M 
                                
                               
                                   
                               
                                
                               AX 
                             
                           
                           - 
                           
                             λ 
                             
                               MI 
                                
                               
                                   
                               
                                
                               N 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   7 
                 
               
             
           
         
       
     
     where λ MAX  is the maximum wavelength of light detected by light detector  70 , λ MIN  is the minimum wavelength of light detected by light detector  70  and n is the refractive index of the respective layer. For example, if n˜1.5 and as described above the wavelength range is 0.8&lt;λ&lt;0.85 μm, d MIN  is about 4.5 μm. 
     The maximal depth of structure  30  which can be determined is given as: 
     
       
         
           
             
               
                 
                   
                     D 
                     
                       M 
                        
                       
                           
                       
                        
                       AX 
                     
                   
                   = 
                   
                     
                       λ 
                       
                         MI 
                          
                         
                             
                         
                          
                         N 
                       
                       2 
                     
                     
                       
                         4 
                         · 
                         
                           n 
                           av 
                         
                         · 
                         Δ 
                       
                        
                       
                           
                       
                        
                       λ 
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
     where n av  is the average refractive index of the structure and Δλ is the wavelength resolution of light detector  70 . For example, if n av −1.5, Δλ=50 pm and λ MIN =0.8 μm, the maximum depth which can be determined is approximately 2.1 mm. 
       FIG. 1H  illustrates a high level flow chart of a method of measuring the thickness of a Cornea, according to certain embodiments. Today complex measurement arrangements, such as Orbscan II, commercially available from Bausch &amp; Lomb of Aliso Viejo, Calif., are used for accurate analysis of the cornea before and after conducting LASIK (laser-assisted in situ keratomileusis) surgery. In addition to the full featured measurement suits, doctors use a simpler, single point cornea thickness measurement device. Each of these device types typically use an ultrasound measurement technique in order to measure the Cornea thickness, known also as “Ultrasound Pachymetry”. For example, the Kerasonix KSX-1000 ultrasound pachymeter, commercially available from DGH Technology of Exton, Pa., is used to measure the Cornea thickness. In the course of this measurement the doctor needs to apply anesthesia drops to the patient&#39;s eye. After waiting for a short period the doctor touches the approximate center of the cornea (where typically the Cornea reaches its minimal thickness) and the measurement is taken. The current ultrasound instruments are relatively simple and easy to use, but they involve application of drops and physical contact of the measuring tip with the patient&#39;s cornea. This involves some discomfort to the patient and the need to carefully sterilize the measurement tip in order to avoid contamination from one patient to another. 
     Apparatus  20  is in one embodiment utilized to perform Cornea thickness measurement. In stage  2100 , target focusing functionality  80  is used to focus the beam of light on one target area  90 , as described above in relation to stage  1030 , preferably located immediately in front of the measurement device. In stage  2110 , the reflected light is detected by light detector  70 , as described above in relation to stage  1040 . In stage  2120 , the Cornea thickness measurement is then performed, responsive to a reflectometric analysis of the detected light of stage  2110 . The term reflectometric analysis as used herein, refers to analysis of the detected light responsive only to interference of the light with itself at target area  90 . As described above, apparatus  20  does not utilize reference mirrors in the subject analysis and interference from a reference signal is not provided for the reflected light from target area  90 . Preferably, the reflectometric analysis is performed according to one of two methods. In a first method, morphological data of the target Cornea is determined, as described above in relation to stage  2000 - 2020 . As described above, the morphological information of each layer of the target Cornea is determined as a function of the thickness of the particular layer. In particular, as described above, the thickness of each layer can be determined by dividing the respective peak  210  in the optical thickness domain by twice the refractive index of the layer. In a second method, the thickness of each layer of the cornea is determined by the detected light at light detector  70  and responsive to a curve fitting technique. 
     In stage  2130 , the determined thickness of stage  2120  is output and preferably stored on memory  50  and/or output on display  85 . In one embodiment, display  85  comprises a small screen facing the doctor and in another embodiment a speaker is further provided and the determined Cornea thickness is communicated by a voice-like output generated by control unit  40  and the provided speaker. This device can be very useful for initial screening of potential patients of LASIK surgery. It can also be very helpful in the diagnosis of Glaucoma which is manifested by Cornea thickness reduction from a typical value of about 500 nm to a value of about 400 nm. 
     The above operation allows Pachymetry to be performed by apparatus  20  which is smaller and consumes less power than traditional Pachymeters and therefore the entire device can be packaged in a portable device. In one embodiment, the portable device is pistol shaped where the doctor aims the frontal narrow “barrel” at the patient&#39;s approximate center of Cornea. 
       FIG. 2A  illustrates a high level schematic diagram of an apparatus  300  arranged to determine morphological information of a structure  30  responsive to light reflected off structure  30 . The construction and arrangement of apparatus  300  is in all respects similar to the construction and arrangement of apparatus  20  of  FIGS. 1A-1B , with the addition of a surface topography functionality  310  in communication with control unit  40  and arranged to provide topographic information of the surface of structure  30 .  FIG. 2B  illustrates a high level flow chart of the operation of apparatus  300 ,  FIGS. 2A-2B  being described together. 
     In operation, in stage  3000 , stages  1000 - 1020  as described above are performed thereby selecting a target area  90  for analyses. In stage  3010 , surface topography functionality  310  is arranged to scan a selected target area  90  and provide topographic information of the surface of selected target area  90 . Preferably, surface topography functionality  310  defines a reference plane and determines the distance of the surface of selected target area  90  from the reference plane. Preferably, the defined reference plane is identical for all selected target areas  90 . In one embodiment, the topographic information is stored on memory  50 . 
     In stage  3020 , control unit  40  controls light source  60  to output light, as described above in relation to stage  1030 . In stage  3030 , the light output by light source  60  is reflected from selected target area  90  and detected at light detector  70 . In one embodiment, the reflected light is focused by target focusing functionality  80  onto light detector  70 , as described above in relation to stage  1040 . 
     In stage  3040 , morphological information of selected target area  90  is determined, as described above in relation to stage  1050  and stages  2000 - 2030 . In the event that the depth of selected target area  90  was determined, control unit  40  is further arranged to adjust the determined depth responsive to the topographic information of stage  3010 . Specifically, the depth is adjusted responsive to the determined distance between the reference plane and the surface of selected target area  90 . The adjusted depth is preferably stored on memory  50 , as described above in relation stage  2030 . 
     In stage  3050 , as described above in relation stage  1060 , control unit  40  determines if all desired target areas  90  were scanned. In one embodiment, the desired target areas  90  are predetermined and stored on memory  50 . In the event that it is determined that all of the target areas  90  have not yet been scanned, stage  3020  as described above is performed. In the event that it is determined that no more target areas  90  need to be analyzed, in stage  3060 , control unit  40  is arranged to display the determined morphological data of each target area  90 , stored on memory  50 , on display  85 . 
     In another embodiment, surface topography functionality  310  is arranged to scan the surface of structure  30  and provide topographic information of the entirety, or a portion, of the surface of structure  30  which is then preferably stored on memory  50 . Prior to display of the morphological information of stage  3060 , control unit  40  is arranged to adjust the determined depths of each target area  90  responsive to the topographic information, as described above. 
       FIG. 3A  illustrates a high level schematic diagram of an apparatus  400  arranged to determine morphological information of a structure  30  responsive to interference between light reflected off the structure and a reference light, both provided by a single light source  60 . Apparatus  400  comprises: a control unit  410 , comprising a processor  420  and a memory  50 ; a light source  60 ; a light detector  70 ; a target focusing functionality  80 ; a display  85 ; a light beam splitter  430 ; a reference mirror  440 ; and a focusing lens  450 . 
     Each of light source  60 , light detector  70 , target focusing functionality  80 , display  85  and reference mirror  440  is in one embodiment in communication with control unit  410 . In another embodiment, one or more of light source  60 , light detector  70 , target focusing functionality  80 , display  85  and reference mirror  440  is controlled by an internal control unit. Light beam splitter  430  is arranged to split a beam of light detected from light source  60  into a pair of light beams, a first light beam being directed to a target area  90  of structure  30  via target focusing functionality  80  and the second light beam being directed to reference mirror  440  via focusing lens  450 . Reference mirror  440  is arranged to reflect the second light beam to light detector  70  via light beam splitter  430 , the reflected second light beam performs an interference with light reflected off of structure  30 , as will be described below. Reference mirror  440  preferably comprises a displacement mechanism arranged to translate reference mirror  440  along an axis in order to adjust the depth where structure  30  is analyzed. 
       FIG. 3B  illustrates a high level flow chart of the method of the operation of apparatus  400 ,  FIGS. 3A-3B  being described together. In stage  4000 , in the event the spectrum of the light arranged to be output from light source  60  is known, the information is stored on memory  50 . In the event the spectrum is not known, it is measured in one of two methods. In the first method, control unit  410  controls light source  60  to output light which is detected by light detector  70 . Control unit  410  then analyzes the detected light and determines the spectrum thereof. In the second method, a structure exhibiting pre-determined high absorption properties (not shown), and exhibiting a pre-determined spectral absorption pattern, is positioned between light beam splitter  430  and reference mirror  440  and arranged to absorb light directed to reference mirror  440 . Additionally a structure exhibiting high reflectance properties is positioned to detect light from light source  60  via light beam splitter  430 , the light reflected therefrom being detected by light detector  70 . Control unit  410  then determines the spectrum of the detected light. 
     In stage  4010 , a-priori knowledge of structure  30 , specifically the sign of the refractive index steps between layer interfaces and the refractive index of at least one layer of structure  30 , is stored, preferably on memory  50 . In the event the refractive index of all layers of structure  30  are unknown, an external layer with a known refractive index is added on top of structure  30 , as described above in relation to stage  1010 . In stage  4020 , reference mirror  440  is positioned such that the desired depth of structure  30  is analyzed. Specifically, the position of reference mirror  440  causes the interference between the light beam reflected off of structure  30  and the light beam reflected off of reference mirror  440  to represent the morphological information of structure  30  at a specific depth. In stage  4030 , a target area  90  is selected by target focusing functionality, as described above in relation to stage  1020 . 
     In stage  4040 , morphological data of the selected target area  90  of stage  4030  is determined. In one embodiment, processor  420  contains dedicated circuitry to determine the morphological information of selected target area  90 . In another embodiment, processor  420  is a computer platform containing computer readable instructions for determining the morphological information of target area  90 . Specifically, control unit  410  controls light source  60  to output light. As described above, the output light is split by light beam splitter  430 . A first beam of light is directed towards reference mirror  440  and a second beam of light is directed towards target area  90 . Both beams of light are reflected off of their respective targets and interfere with each other, the interference being detected at light detector  70 . 
     The intensity of the interference signal detected at light detector  70 , denoted I(w) is given as: 
     
       
         
           
             
               
                 
                   
                     I 
                      
                     
                       ( 
                       w 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         I 
                         S 
                       
                        
                       
                         ( 
                         w 
                         ) 
                       
                     
                     + 
                     
                       
                         I 
                         R 
                       
                        
                       
                         ( 
                         w 
                         ) 
                       
                     
                     + 
                     
                       2 
                        
                       
                         
                           
                             
                               I 
                               S 
                             
                              
                             
                               ( 
                               w 
                               ) 
                             
                           
                            
                           
                             
                               I 
                               R 
                             
                              
                             
                               ( 
                               w 
                               ) 
                             
                           
                         
                       
                        
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           N 
                         
                          
                         
                           
                             α 
                             
                               j 
                               , 
                               
                                 j 
                                 + 
                                 1 
                               
                             
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 4 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 
                                   wn 
                                   j 
                                 
                                  
                                 
                                   x 
                                   j 
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   9 
                 
               
             
           
         
       
     
     where w is the wave-number, λ is the wavelength, I S  is the intensity of the light beam reflected off target area  90 , I R  is the intensity of the light beam reflected off reference mirror  440 , n j  is the refractive index of the layer j; and α j,j+1  is the square root of the reflectivity of the sample “r j,j+1 ” (at depth x j , between layers j and j+1). Depth information of structure  30  is preferably determined by means of an inverse Fourier transform on the signal detected at light detector  70 , the transformed signal being given as: 
     
       
         
           
             
               
                 
                   
                     
                        
                       
                         
                           F 
                           
                             - 
                             1 
                           
                         
                          
                         
                           [ 
                           
                             I 
                              
                             
                               ( 
                               w 
                               ) 
                             
                           
                           ] 
                         
                       
                        
                     
                     2 
                   
                   = 
                   
                     
                       
                         Γ 
                         2 
                       
                        
                       
                         ( 
                         x 
                         ) 
                       
                     
                     ⊗ 
                     
                       [ 
                       
                         
                           δ 
                            
                           
                             ( 
                             0 
                             ) 
                           
                         
                         + 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             N 
                           
                            
                           
                             
                               r 
                               
                                 j 
                                 , 
                                 
                                   j 
                                   + 
                                   1 
                                 
                               
                             
                              
                             
                               δ 
                                
                               
                                 ( 
                                 
                                   x 
                                   - 
                                   
                                     x 
                                     j 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         + 
                         
                           
                             ∑ 
                             
                               j 
                               = 
                               1 
                             
                             N 
                           
                            
                           
                             
                               r 
                               
                                 j 
                                 , 
                                 
                                   j 
                                   + 
                                   1 
                                 
                               
                             
                              
                             
                               δ 
                                
                               
                                 ( 
                                 
                                   x 
                                   + 
                                   
                                     x 
                                     j 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         + 
                         
                           A 
                            
                           
                             ( 
                             
                               x 
                               j 
                             
                             ) 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   10 
                 
               
             
           
         
       
     
     where γ(x) is the envelope of the coherence function, and δ(0) and A(x j ) represent reference and sample autocorrelations, respectively. The second and third terms within the brackets of EQ. 10 are produced by the interference between the reflected light beams of target area  90  and reference mirror  440 . Depth information is extracted responsive to the Dirac delta functions “δ(x−x j )”, whose spectral positions represent the depth “x j ” of structural interfaces. 
     A first order approximation of the reflectivity of an inhomogeneous refractive index profile is given as: 
     
       
         
           
             
               
                 
                   
                     r 
                      
                     
                       ( 
                       w 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         r 
                         01 
                       
                       - 
                       
                         
                           1 
                           2 
                         
                          
                         
                           
                             ∫ 
                             0 
                             ∞ 
                           
                            
                           
                             
                               1 
                               
                                 n 
                                  
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                              
                             
                               
                                  
                                 
                                   n 
                                    
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                               
                               
                                  
                                 x 
                               
                             
                              
                             
                                
                               
                                 
                                   - 
                                    
                                 
                                  
                                 
                                     
                                 
                                  
                                 4 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 w 
                                  
                                 
                                   
                                     ∫ 
                                     0 
                                     x 
                                   
                                    
                                   
                                     
                                       n 
                                        
                                       
                                         ( 
                                         ξ 
                                         ) 
                                       
                                     
                                      
                                     
                                        
                                       ξ 
                                     
                                   
                                 
                               
                             
                              
                             
                                
                               x 
                             
                           
                         
                       
                     
                     
                       1 
                       - 
                       
                         
                           
                             r 
                             01 
                           
                           2 
                         
                          
                         
                           
                             ∫ 
                             0 
                             ∞ 
                           
                            
                           
                             
                               1 
                               
                                 n 
                                  
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                              
                             
                               
                                  
                                 
                                   n 
                                    
                                   
                                     ( 
                                     x 
                                     ) 
                                   
                                 
                               
                               
                                  
                                 x 
                               
                             
                              
                             
                                
                               
                                 
                                   - 
                                    
                                 
                                  
                                 
                                     
                                 
                                  
                                 4 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 w 
                                  
                                 
                                   
                                     ∫ 
                                     0 
                                     x 
                                   
                                    
                                   
                                     
                                       n 
                                        
                                       
                                         ( 
                                         ξ 
                                         ) 
                                       
                                     
                                      
                                     
                                        
                                       ξ 
                                     
                                   
                                 
                               
                             
                              
                             
                                
                               x 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   11 
                 
               
             
           
         
       
     
     where r 01  is the reflectivity between air and the surface of the sample. When dealing with very small refractive index changes, for example those observed in retinal analysis, EQ. 11 can be approximated to: 
     
       
         
           
             
               
                 
                   
                     r 
                      
                     
                       ( 
                       w 
                       ) 
                     
                   
                   ≈ 
                   
                     
                       r 
                       01 
                     
                     - 
                     
                       
                         1 
                         2 
                       
                        
                       
                         
                           ∫ 
                           0 
                           ∞ 
                         
                          
                         
                           
                             1 
                             
                               n 
                                
                               
                                 ( 
                                 x 
                                 ) 
                               
                             
                           
                            
                           
                             
                                
                               
                                 n 
                                  
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                             
                                
                               x 
                             
                           
                            
                           
                              
                             
                               
                                 - 
                                  
                               
                                
                               
                                   
                               
                                
                               4 
                                
                               π 
                                
                               
                                   
                               
                                
                               w 
                                
                               
                                 
                                   ∫ 
                                   0 
                                   x 
                                 
                                  
                                 
                                   
                                     n 
                                      
                                     
                                       ( 
                                       ξ 
                                       ) 
                                     
                                   
                                    
                                   
                                      
                                     ξ 
                                   
                                 
                               
                             
                           
                            
                           
                              
                             x 
                           
                         
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   12 
                 
               
             
           
         
       
     
     Solving EQ. 12 for a multi-layer structure with small refractive index steps between layers, EQ. 12 becomes: 
     
       
         
           
             
               
                 
                   
                     r 
                      
                     
                       ( 
                       w 
                       ) 
                     
                   
                   ≈ 
                   
                     
                       r 
                       01 
                     
                     - 
                     
                       
                         1 
                         2 
                       
                        
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           N 
                         
                          
                         
                           
                             
                               
                                 n 
                                 
                                   j 
                                   + 
                                   1 
                                 
                               
                               - 
                               
                                 n 
                                 j 
                               
                             
                             
                               n 
                               j 
                             
                           
                            
                           
                              
                             
                               
                                 - 
                                  
                               
                                
                               
                                   
                               
                                
                               4 
                                
                               π 
                                
                               
                                   
                               
                                
                               w 
                                
                               
                                 
                                   ∑ 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   j 
                                 
                                  
                                 
                                   
                                     n 
                                     i 
                                   
                                    
                                   
                                     d 
                                     i 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   13 
                 
               
             
           
         
       
     
     EQ. 13 shows that “r(w)”, i.e. the reflectivity expressed as a function of the wave-number, possesses a spectrum in the optical thickness domain “2nd”. The positions of the spectrum peaks correspond to interfaces between layers and the peak amplitudes are proportional to the refractive index steps at the respective interfaces. 
     By taking into account the reflectivity of EQ. 13, EQs. 9 and 10 can be given a more appropriate expression, as functions of the optical depth “θj”, such that EQ. 9 is given as: 
     
       
         
           
             
               
                 
                   
                     I 
                      
                     
                       ( 
                       w 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         I 
                         S 
                       
                        
                       
                         ( 
                         w 
                         ) 
                       
                     
                     + 
                     
                       
                         I 
                         R 
                       
                        
                       
                         ( 
                         w 
                         ) 
                       
                     
                     + 
                     
                       2 
                        
                       
                         
                           
                             
                               I 
                               S 
                             
                              
                             
                               ( 
                               w 
                               ) 
                             
                           
                            
                           
                             
                               I 
                               R 
                             
                              
                             
                               ( 
                               w 
                               ) 
                             
                           
                         
                       
                        
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           N 
                         
                          
                         
                           
                             α 
                             
                               j 
                               , 
                               
                                 j 
                                 + 
                                 1 
                               
                             
                           
                            
                           
                             cos 
                              
                             
                               ( 
                               
                                 2 
                                  
                                 
                                   πθ 
                                   j 
                                 
                                  
                                 w 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   14 
                 
               
             
           
         
       
     
     and EQ. 10 is given as: 
     
       
         
           
             
               
                 
                   
                     
                        
                       
                         
                           F 
                           
                             - 
                             1 
                           
                         
                          
                         
                           [ 
                           
                             I 
                              
                             
                               ( 
                               w 
                               ) 
                             
                           
                           ] 
                         
                       
                        
                     
                     2 
                   
                   = 
                   
                     
                       
                         Γ 
                         2 
                       
                        
                       
                         ( 
                         θ 
                         ) 
                       
                     
                     ⊗ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 δ 
                                  
                                 
                                   ( 
                                   0 
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   1 
                                   2 
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       j 
                                       = 
                                       1 
                                     
                                     N 
                                   
                                    
                                   
                                     
                                       
                                         Δ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           n 
                                           j 
                                         
                                       
                                       
                                         n 
                                         j 
                                       
                                     
                                      
                                     δ 
                                      
                                     
                                       ( 
                                       
                                         θ 
                                         - 
                                         
                                           θ 
                                           j 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   1 
                                   2 
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       j 
                                       = 
                                       1 
                                     
                                     N 
                                   
                                    
                                   
                                     
                                       
                                         Δ 
                                          
                                         
                                             
                                         
                                          
                                         
                                           n 
                                           j 
                                         
                                       
                                       
                                         n 
                                         j 
                                       
                                     
                                      
                                     
                                       δ 
                                        
                                       
                                         ( 
                                         
                                           θ 
                                           + 
                                           
                                             θ 
                                             j 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               + 
                               
                                 A 
                                  
                                 
                                   ( 
                                   
                                     θ 
                                     j 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   15 
                 
               
             
           
         
       
     
     where θj is given as: 
     
       
         
           
             
               
                 
                   
                     θ 
                     j 
                   
                   = 
                   
                     2 
                      
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         j 
                       
                        
                       
                         
                           n 
                           i 
                         
                          
                         
                           d 
                           i 
                         
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   16 
                 
               
             
           
         
       
     
     The refractive index step between layers is Δn j =n j+1 −n j . For small refractive index steps the Fresnel reflectivity coefficient between layers j and j+1 of EQ. 10 approaches: 
     
       
         
           
             
               
                 
                   
                     r 
                     
                       j 
                       , 
                       
                         j 
                         + 
                         1 
                       
                     
                   
                   = 
                   
                     - 
                     
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           n 
                           j 
                         
                       
                       
                         2 
                          
                         
                           n 
                           j 
                         
                       
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   17 
                 
               
             
           
         
       
     
     EQ. 15 is expressed as: 
     
       
         
           
             
               
                 
                   
                     
                        
                       
                         
                           F 
                           
                             - 
                             1 
                           
                         
                          
                         
                           [ 
                           
                             I 
                              
                             
                               ( 
                               w 
                               ) 
                             
                           
                           ] 
                         
                       
                        
                     
                     2 
                   
                   = 
                   
                     
                       
                         Γ 
                         2 
                       
                        
                       
                         ( 
                         θ 
                         ) 
                       
                     
                     ⊗ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 δ 
                                  
                                 
                                   ( 
                                   0 
                                   ) 
                                 
                               
                               + 
                               
                                 
                                   1 
                                   
                                     2 
                                      
                                     
                                       n 
                                       av 
                                     
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       j 
                                       = 
                                       1 
                                     
                                     N 
                                   
                                    
                                   
                                     Δ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       n 
                                       j 
                                     
                                      
                                     δ 
                                      
                                     
                                       ( 
                                       
                                         θ 
                                         - 
                                         
                                           θ 
                                           j 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               + 
                             
                           
                         
                         
                           
                             
                               
                                 
                                   1 
                                   
                                     2 
                                      
                                     
                                       n 
                                       av 
                                     
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       j 
                                       = 
                                       1 
                                     
                                     N 
                                   
                                    
                                   
                                     Δ 
                                      
                                     
                                         
                                     
                                      
                                     
                                       n 
                                       j 
                                     
                                      
                                     
                                       δ 
                                        
                                       
                                         ( 
                                         
                                           θ 
                                           + 
                                           
                                             θ 
                                             j 
                                           
                                         
                                         ) 
                                       
                                     
                                   
                                 
                               
                               + 
                               
                                 A 
                                  
                                 
                                   ( 
                                   
                                     θ 
                                     j 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   EQ 
                   . 
                   
                       
                   
                    
                   18 
                 
               
             
           
         
       
     
     In EQ. 18, an average value n av  replaces n j  in the denominator of the second and third terms within the brackets. Based on the assumption of small refractive index steps, such replacement introduces negligible error, and a value for n av  may be obtained from known statistical values. For example, refractive index values around 1.38 are often used for cornea analysis. 
     In order to measure the refractive index steps at the layer interfaces, compensation for the influence of light source  60  and normalization of the spectrum amplitudes according to a known standard are preferred. 
     Compensation for source effects is accomplished by dividing the detected interference signal of EQ. 14 by its known spectrum. As described above in relation to stage  4000 , in the event that the spectrum of light from light source  60  is not known, it is measured. Alternatively, an inverse Fourier transform is performed on the detected light beam at light detector  70 , which leads to Γ 2 (θ) of EQ. 15. Thus, when analyzing a structure  30 , the amplitudes of the spectral peaks of interest (the second and third terms within the brackets of EQ. 15) are determined and divided by the correspondent Γ 2 (θ) associated values. 
     Normalization is achieved by performing the above analysis on a structure (not shown) exhibiting a known refractive index. Measuring the amplitude of the resultant inverse Fourier transform interface peak leads to a scaling factor for EQ. 18. 
     The refractive index steps between layers of structure  30  are calculated according to EQ. 17 or 18, i.e. the amplitude of the normalized spectral peak “j” is determined and multiplied by two times n av , leading to Δn j . Having calculated the refractive index steps between layers, the refractive indices can then be determined responsive to the known refractive index of one of the layers of structure  30  stored on memory  50  in stage  4010 . The sign of Δn j  indicates if the index of refraction increases or decreases at the interface. As this is not known from the Inverse Fourier transformation, a-priori knowledge of the sign of the refractive index are preferably utilized, as described above in relation to stage  4010 . 
     EQs. 14 and 16 reveal that the determination of the refractive index steps between interfaces improves thickness estimation. Thus, subsequent to the calculation of the refractive index steps, the thickness of each layer is preferably more accurately determined. 
     In stage  4050 , control unit  410  determines if all desired target areas  90  were scanned. In one embodiment, the desired target areas  90  are predetermined and stored on memory  50 . In the event that it is determined that that all of the target areas  90  have not yet been scanned, stage  4030  as described above is performed. In the event that it is determined that no more target areas  90  need to be analyzed, in stage  4060 , control unit  410  is arranged to display the determined morphological data of each target area  90  stored on memory  50 , as will be described further below, on display  85 . In the event that structure  30  is a biological structure, such as a cornea, the determined morphological data is preferably compared to previously stored morphological data from an earlier analysis session, with the comparison output to display  85 . The comparison can indicate whether there has been an improvement or deterioration in structure  30 . 
       FIG. 4A  illustrates a high level schematic diagram of an apparatus  500  arranged to determine morphological information of a structure  30  in a pair of modes. The construction and arrangement of apparatus  500  is in all respects similar to the construction and arrangement of apparatus  400  of  FIG. 3A , with the exception that a blocking mirror  510  is provided in communication with a control unit  520  (communication path not shown). Blocking mirror  510  is in communication with a translation mechanism  515  arranged to alternately: in a reflectance mode translate the blocking mirror  510  to a position so as to block any light from light beam splitter  430  from reaching reference mirror  440 ; and in an optical coherence tomography mode translate the blocking mirror  510  to a position so as to allow a light beam from light beam splitter  430  to impact reference mirror  440 , as described above in relation to  FIGS. 3A-3B . In one embodiment (not shown), a plurality of blocking mirrors  510  are provided, at least one of the blocking mirrors  510  in communication with a respective translation mechanism  515 . In one embodiment, control unit  520  comprises processor  45  of control unit  40  of  FIG. 1B  and processor  420  of  FIG. 3A .  FIG. 4B  illustrates a high level flow chart of the method of operation of apparatus  500 ,  FIGS. 4A-4B  being described together. 
     In operation, in stage  5000 , a mode of operation is selected. In one embodiment, the mode of operation is selected by a user via a user input device (not shown). In the event that the reflectance mode is selected, in stage  5010 , control unit  520  controls translation mechanism  515  to translate blocking mirror  510  to a position so as to block light from light beam splitter  430  from reaching reference mirror  440 . In one embodiment, blocking mirror  510  is arranged to direct light detected from light beam splitter  430  to a structure (not shown) exhibiting very high absorption properties. In another embodiment, blocking mirror  510  is arranged to direct light detected from light beam splitter  430  away from apparatus  500  such that the light beam doesn&#39;t interfere with the light beam directed towards structure  30 , or the light reflected therefrom. In stage  5020 , morphological information of a plurality of target areas  90  are determined and output, optionally by displaying the determined morphological information on display  85 , as described above in relation to stages  1000 - 1050 . 
     In the event that the OCT mode is selected, in stage  5030 , control unit  520  controls translation mechanism  515  to translate blocking mirror  510  to a position so as to allow a light beam from light beam splitter  430  to impact reference mirror  440 . In stage  5040 , morphological information of a plurality of target areas  90  are determined and output, optionally by displaying the determined morphological information on display  85 , as described above in relation to stages  3000 - 3040 . 
     It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable sub-combination. 
     Unless otherwise defined, all technical and scientific terms used herein have the same meanings as are commonly understood by one of ordinary skill in the art to which this invention belongs. Although methods similar or equivalent to those described herein can be used in the practice or testing of the present invention, suitable methods are described herein. 
     All publications, patent applications, patents, and other references mentioned herein are incorporated by reference in their entirety. In case of conflict, the patent specification, including definitions, will prevail. In addition, the materials, methods, and examples are illustrative only and not intended to be limiting. 
     The terms “include”, “comprise” and “have” and their conjugates as used herein mean “including but not necessarily limited to”. The term “connected” is not limited to a direct connection, and connection via intermediary devices is specifically included. 
     It will be appreciated by persons skilled in the art that the present invention is not limited to what has been particularly shown and described hereinabove. Rather the scope of the present invention is defined by the appended claims and includes both combinations and sub-combinations of the various features described hereinabove as well as variations and modifications thereof, which would occur to persons skilled in the art upon reading the foregoing description.