Patent Document

CROSS-REFERENCE TO RELATED APPLICATION(S) 
       [0001]    This application is based upon and claims the benefit of priority from U.S. Patent Application Ser. No. 60/885,652, filed Jan. 19, 2007, the entire disclosure of which is incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates generally to apparatus and method for controlling (e.g., increasing) ranging depth in optical frequency domain imaging by using one or more depth and frequency encoding (“DFE”) technique. 
       BACKGROUND INFORMATION 
       [0003]    Optical coherence tomography (“OCT”) techniques provide exemplary cross-sectional images of biological samples with resolution on the scale of several to tens of microns. Contrast in conventional OCT results from differences in the optical scattering properties of various tissues and permits imaging of tissue microstructure. It has been demonstrated that Fourier-Domain OCT (“FD-OCT”) provides significantly improved sensitivity, enabling high-speed imaging. FD-OCT has been implemented in two configurations, spectral-domain OCT (“SD-OCT”) and optical frequency domain imaging (“OFDI”). In exemplary SD-OCT arrangement as shown in  FIG. 1(   a ), a spectrometer can be used to record spectral fringes that result from the interference of a reference beam with light reflected from a sample. In the exemplary OFDI arrangement as shown in  FIG. 1(   b ), a narrowband wavelength-swept source and a single detector are used to record the same interferogram. 
         [0004]    The exemplary OFDI arrangements and methods, however, may become the preferred imaging modalities for several applications since they may be less prone to motion artifacts associated with endoscopy and can provide a larger depth range. However, the maximum ranging depth can typically be limited by the instantaneous line-width (coherence length) of the laser source. For a number of OFDI sources, there may be a tradeoff between instantaneous line-width, tuning speed, output power, and tuning range, which ultimately limits the useful ranging depth. Several methods have been described to avoid the ambiguity between positive and negative depths and increase ranging depth by measuring quadrature interference signals or using both sides of the coherence range. Continued development of wavelength-swept laser sources can provide further improvements in imaging speed and resolution. These advantages are important in several exemplary OCT applications, including Barrett&#39;s esophagus screening and coronary imaging. As such, imaging in many applications may require increasing ranging depth. 
         [0005]    One of the objects of the present invention is to overcome the above-described deficiencies. 
       SUMMARY OF EXEMPLARY EMBODIMENTS OF PRESENT INVENTION 
       [0006]    According to certain exemplary embodiments of the present invention, method and apparatus for making high ranging depth measurements by using depth and frequency encoding (“DFE”) in an exemplary OFDI system can be provided. For example, the exemplary embodiments of the method and apparatus can utilize a technique for increasing the ranging depth using depth and frequency encoding in OFDI. This exemplary technique can use, e.g., two (N) acousto-optic frequency shifters in two (N) different reference arms to provide two (N) constant frequency shifts in the detected signal. The path differences may divide the ranging depth into two (N) sections, where each section can be encoded by a different frequency. 
         [0007]    Measurement of amplitude and phase can be used to measure profile reflectivity of the sample, blood flow and other motion in a turbid or scattering media, can also be used to monitor optical thickness of materials over time or as a function of transverse location, and can be used to measure birefringence of the sample. An exemplary embodiment of the apparatus and method according to the present invention can be used for increasing ranging depth in the above measurement methods. In this exemplary embodiment, the OFDI system can be modified to simultaneously acquire, e.g., two (N) images of the sample at two (N) different sections where each image is encoded by a different frequency. 
         [0008]    Thus, exemplary embodiments of an apparatus according to the present invention are provided. For example, the exemplary apparatus can include at least one first arrangement providing at least one first electro-magnetic radiation to a sample, at least one second electro-magnetic radiation to a first reference and at least one third electro-magnetic radiation to a second reference. A frequency of radiation provided by the first arrangement generally varies over time. The exemplary apparatus may also include at least one second arrangement which is configured to detect a first interference between at least one fourth electro-magnetic radiation associated with the first electro-magnetic radiation and at least one fifth electro-magnetic radiation associated with the second radiation. The second arrangement is also configured to detect a second interference between at least one sixth electro-magnetic radiation associated with the first electro-magnetic radiation and at least one seventh electro-magnetic radiation associated with the third radiation. 
         [0009]    According to another exemplary embodiment of the present invention, an optical path length of the first reference may be substantially different from an optical path length of the second reference. The difference between the optical path length of the first reference and the optical path length of the second reference can be more than 500 μm. Further, the first reference may have a further arrangement to shift a frequency of the second electro-magnetic radiation. In addition, the first reference may have an additional arrangement to shift a frequency of the third electro-magnetic radiation. 
         [0010]    According to yet another exemplary embodiment of the present invention, the magnitude of the shift of the frequency of the second electro-magnetic radiation can be different from a magnitude of the shift of the frequency of the third electro-magnetic radiation. The first electro-magnetic radiation can have a spectrum whose mean frequency may change substantially continuously over time at a tuning speed that is greater than 100 Tera Hertz per millisecond. 
         [0011]    These and other objects, features and advantages of the present invention will become apparent upon reading the following detailed description of embodiments of the present invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    Further objects, features and advantages of the invention will become apparent from the following detailed description taken in conjunction with the accompanying figures showing illustrative embodiments of the invention, in which: 
           [0013]      FIG. 1A  is a schematic diagram of a conventional spectral-domain OCT system; 
           [0014]      FIG. 1B  is a schematic diagram of a conventional OFDI system; 
           [0015]      FIG. 1C  is a schematic diagram of a conventional OFDI system for increasing ranging depth by measuring quadrature interference signals; 
           [0016]      FIG. 1D  is a schematic diagram of a conventional OFDI system for increasing ranging depth using both sides of the coherence range; 
           [0017]      FIG. 2A  is a schematic diagram of an exemplary operation of an exemplary embodiment of a system according to the present invention implementing an exemplary embodiment of a depth and frequency encoding technique; 
           [0018]      FIG. 2B  is a plot of an exemplary crosstalk caused by two depths mapped to the same frequency; 
           [0019]      FIG. 3  is a block diagram of another exemplary embodiment of the system according to the present invention which utilized an exemplary depth and frequency encoding technique; 
           [0020]      FIGS. 4(   a )- 4 ( d ) are plots of variations of (a, b) SIR1 and (c, d) SIR2 due to A-line rate and frequency spacing; 
           [0021]      FIG. 5  is a plot of a minimum SIR for different tuning speeds; 
           [0022]      FIG. 6  is a plot of an exemplary signal power variation by moving a calibrated partial reflector (sample) throughout the total ranging depth; 
           [0023]      FIG. 7(   a ) is a side view of an exemplary OFDI image of the human aorta tissue ex vivo obtained with frequency shifts 25 and 50 MHz, with the exemplary image consisting of 1492 vertical×500 transverse pixels, whereas the depth and frequency encoding technique increased the ranging depth to 10 mm; 
           [0024]      FIG. 7(   a ) is an end view of the exemplary OFDI image of the human aorta tissue ex vivo of  FIG. 7(   b ); and 
           [0025]      FIG. 8  is an exemplary image of the tissue before the application of the exemplary embodiment of the technique according to the present invention, and an exemplary image thereof after the application of the exemplary technique. 
       
    
    
       [0026]    Throughout the figures, the same reference numerals and characters, unless otherwise stated, are used to denote like features, elements, components or portions of the illustrated embodiments. Moreover, while the subject invention will now be described in detail with reference to the figures, it is done so in connection with the illustrative embodiments. It is intended that changes and modifications can be made to the described embodiments without departing from the true scope and spirit of the subject invention. 
       DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0027]    Convention OFDI systems can create images based on the magnitude and phase of the reflectivity as a function of depth. In this OFDI system, the maximum ranging depth is typically limited by the instantaneous line-width (coherence length) of the laser source because one side of coherence range is used by placing the zero depth at the surface of the sample to avoid the ambiguity between positive and negative depths. Other methods have been discussed to avoid the ambiguity between positive and negative depths and increase ranging depth including: I) measuring quadrature interference signals shown in  FIG. 1(   c ) or II) using both sides of the coherence range shown in  FIG. 1(   d ). The first approach can unfold otherwise overlapping images associated with positive and negative depths, but tended to leave residual artifacts due to the difficulty of producing stable quadrature signals. The second approach can provide a 2-fold increase of the effective ranging depth. 
         [0028]    According to the exemplary embodiment of the present invention, method and apparatus can be provided for an N-fold increase of the effective ranging depth. N different frequency shifts are applied into N different reference arms to provide N constant frequency shifts in the detected signal. The path differences divide the ranging depth into N sections, where each section is encoded by a different frequency.  FIG. 2  ( a ) depicts a schematic of the depth and frequency encoding setup. By assuming a Gaussian coherence function, the fringe visibility has a peak value at the zero path difference point and decreases as the path difference increases. The coherence length l c  indicates the depth around the zero path difference point where the visibility drops to 0.5 and thereby the SNR drops by 6 dB. In the proposed technique, the number of zero path difference points (depths) inside the sample is increased by a factor of N (points A 1  and A N ) using N reference arms biased relative to each other (Δz). As shown in the example of  FIG. 2  ( a ), with one frequency shifter only a single coherence region can be used. However, N coherence regions can be utilized by dividing the sample into N sections and frequency multiplexing each section. 
         [0029]    While this exemplary technique can provides a N-fold increase of the effective ranging depth of a conventional OFDI system, two factors can degrade the image quality including: I) crosstalk (interference) between adjacent encoded images at different frequencies and II) crosstalk between a specific depth that corresponds to a frequency 
         [0000]    
       
         
           
             ( 
             
               
                 ( 
                 
                   
                     f 
                     i 
                   
                   - 
                   
                     f 
                     j 
                   
                 
                 ) 
               
               + 
               
                 
                   2 
                    
                   
                       
                   
                    
                   Δ 
                    
                   
                       
                   
                    
                   z 
                    
                   
                       
                   
                    
                   Δ 
                    
                   
                       
                   
                    
                   λ 
                 
                 
                   
                     λ 
                     0 
                     2 
                   
                    
                   T 
                 
               
             
             ) 
           
         
       
     
         [0000]    and the third term in equation (5), where Δλ,λ 0 , and T are the source tuning range, center wavelength, and tuning period. 
         [0030]    Explanation of OFDI in Frequency Domain 
         [0031]    Exemplary Fourier-Domain OCT systems and methods generally use the interference between two arms of an interferometer to measure depth-dependent reflections in a turbid, semi-turbid, or transparent medium. An input light source is split into a reference arm and a sample arm. The light in the sample arm is directed to the sample to be imaged, and reflections from the sample are directed to a first port of an output coupler. The reference arm light is directed to the second port of the same output coupler. Spectral interference between the beams is measured by recording the interferometer output power as a function of wave-number (or time). The balanced detected current can be expressed as: 
         [0000]        i   s ( t )=2η√{square root over ( P   r ( t ) P   s ( t ))}{square root over ( P   r ( t ) P   s ( t ))}∫√{square root over ( R ( z ))} G (| z   r   −z |){cos(2 k ( t )( z   r   −z )+φ z ) dz   (1) 
         [0000]    where η, Pr(t), Ps(t), R(z), G(|z r   −z |), k(t), φ z  and Δz=z r −z are the quantum efficiency of the detector, the reference arm optical power, the sample arm optical power, the sample reflectivity profile, coherence function corresponding to the fringe visibility, wavenumber, the phase of the reflection at position z and the path difference between reference arms and an scatterer at position z. By assuming the output wavenumber is tuned linearly in time i.e. k(t)=k 0 −k 1 t, where k=2π/λ is the wavenumber, λ is the optical wavelength, t is the time spanning from −T/2 to T/2, and T is the tuning period or equivalently A-line period. Further we assume a Gaussian tuning envelope given by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       out 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                   = 
                   
                     
                       P 
                       out 
                     
                      
                     
                       exp 
                       ( 
                       
                         - 
                         
                           
                             
                               ( 
                               
                                 4 
                                  
                                 
                                     
                                 
                                  
                                 ln 
                                  
                                 
                                     
                                 
                                  
                                 2 
                               
                               ) 
                             
                              
                             
                               t 
                               2 
                             
                           
                           
                             
                               ( 
                               
                                 σ 
                                  
                                 
                                     
                                 
                                  
                                 T 
                               
                               ) 
                             
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where P out (t) denotes the output power of the source and σT the full width at half maximum (FWHM) of the tuning envelope. Eq. (2) also describes the Gaussian spectral envelope of the source, where σk 1 T corresponds to the FWHM tuning range in wavenumber. A Fourier transform of Eq. (1) with respect to t yields a complex-valued depth profile (A-line). 
         [0032]    Assuming: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       P 
                       r 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                    
                   
                     
                       P 
                       s 
                     
                      
                     
                       ( 
                       t 
                       ) 
                     
                   
                 
               
               = 
               
                 
                   P 
                   out 
                 
                  
                 
                   exp 
                   ( 
                   
                     - 
                     
                       
                         
                           ( 
                           
                             4 
                              
                             
                                 
                             
                              
                             ln 
                              
                             
                                 
                             
                              
                             2 
                           
                           ) 
                         
                          
                         
                           t 
                           2 
                         
                       
                       
                         
                           ( 
                           
                             σ 
                              
                             
                                 
                             
                              
                             T 
                           
                           ) 
                         
                         2 
                       
                     
                   
                   ) 
                 
               
             
             , 
             
               
                 k 
                 1 
               
               = 
               
                 
                   2 
                    
                   
                       
                   
                    
                   π 
                    
                   
                       
                   
                    
                   Δ 
                    
                   
                       
                   
                    
                   λ 
                 
                 
                   
                     λ 
                     0 
                     2 
                   
                    
                   T 
                 
               
             
           
         
       
     
         [0000]    and σ&lt;1, we can approximate the range of the integral to [−∞, +∞], which results in 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           I 
                            
                           
                             ( 
                             f 
                             ) 
                           
                         
                         = 
                           
                          
                         
                           F 
                            
                           
                             { 
                             
                               
                                 i 
                                 s 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                             } 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             ∫ 
                             
                               - 
                               
                                 T 
                                 2 
                               
                             
                             
                               T 
                               2 
                             
                           
                            
                           
                             
                               
                                 i 
                                 s 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                    
                                    
                                   
                                       
                                   
                                    
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   π 
                                    
                                   
                                       
                                   
                                    
                                   f 
                                    
                                   
                                       
                                   
                                    
                                   t 
                                 
                                 ) 
                               
                             
                              
                             
                                 
                             
                              
                             
                                
                               t 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           2 
                            
                           
                               
                           
                            
                           η 
                            
                           
                               
                           
                            
                           
                             P 
                             out 
                           
                            
                           
                             ∫ 
                             
                               
                                 
                                   R 
                                    
                                   
                                     ( 
                                     z 
                                     ) 
                                   
                                 
                               
                                
                               
                                 G 
                                  
                                 
                                   ( 
                                   
                                      
                                     
                                       
                                         z 
                                         r 
                                       
                                       - 
                                       z 
                                     
                                      
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             ∫ 
                             
                               - 
                               
                                 T 
                                 2 
                               
                             
                             
                               T 
                               2 
                             
                           
                            
                           
                             cos 
                              
                             
                               [ 
                               
                                 
                                   2 
                                    
                                   
                                     ( 
                                     
                                       
                                         k 
                                         0 
                                       
                                       - 
                                       
                                         
                                           k 
                                           1 
                                         
                                          
                                         t 
                                       
                                     
                                     ) 
                                   
                                    
                                   
                                     ( 
                                     
                                       
                                         z 
                                         r 
                                       
                                       - 
                                       z 
                                     
                                     ) 
                                   
                                 
                                 + 
                                 
                                   φ 
                                   z 
                                 
                               
                               ] 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           
                             exp 
                             ( 
                             
                               
                                  
                                  
                                 
                                     
                                 
                                  
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 π 
                                  
                                 
                                     
                                 
                                  
                                 f 
                                  
                                 
                                     
                                 
                                  
                                 t 
                               
                               - 
                               
                                 
                                   
                                     ( 
                                     
                                       4 
                                        
                                       
                                           
                                       
                                        
                                       ln 
                                        
                                       
                                           
                                       
                                        
                                       2 
                                     
                                     ) 
                                   
                                    
                                   
                                     t 
                                     2 
                                   
                                 
                                 
                                   
                                     ( 
                                     
                                       σ 
                                        
                                       
                                           
                                       
                                        
                                       T 
                                     
                                     ) 
                                   
                                   2 
                                 
                               
                             
                             ) 
                           
                            
                           
                              
                             t 
                           
                            
                           
                              
                             z 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               η 
                                
                               
                                   
                               
                                
                               
                                 P 
                                 out 
                               
                                
                               σ 
                                
                               
                                   
                               
                                
                               T 
                             
                             2 
                           
                            
                           
                             
                               π 
                               
                                 ln 
                                  
                                 
                                   ( 
                                   2 
                                   ) 
                                 
                               
                             
                           
                            
                           
                             ∫ 
                             
                               
                                 
                                   R 
                                    
                                   
                                     ( 
                                     z 
                                     ) 
                                   
                                 
                               
                                
                               
                                 G 
                                  
                                 
                                   ( 
                                   
                                      
                                     
                                       
                                         z 
                                         r 
                                       
                                       - 
                                       z 
                                     
                                      
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           [ 
                           
                             exp 
                              
                             
                               { 
                               
                                 
                                   - 
                                   
                                     
                                       
                                         
                                           
                                             ( 
                                             
                                               σ 
                                                
                                               
                                                   
                                               
                                                
                                               T 
                                             
                                             ) 
                                           
                                           2 
                                         
                                         
                                           16 
                                            
                                           
                                               
                                           
                                            
                                           
                                             ln 
                                              
                                             
                                               ( 
                                               2 
                                               ) 
                                             
                                           
                                         
                                       
                                       [ 
                                       
                                         
                                           2 
                                            
                                           
                                               
                                           
                                            
                                           π 
                                            
                                           
                                               
                                           
                                            
                                           f 
                                         
                                         - 
                                         
                                           
                                             
                                               4 
                                                
                                               
                                                   
                                               
                                                
                                               π 
                                                
                                               
                                                   
                                               
                                                
                                               Δ 
                                                
                                               
                                                   
                                               
                                                
                                               λ 
                                             
                                             
                                               
                                                 λ 
                                                 0 
                                                 2 
                                               
                                                
                                               T 
                                             
                                           
                                            
                                           
                                             ( 
                                             
                                               
                                                 z 
                                                 r 
                                               
                                               - 
                                               z 
                                             
                                             ) 
                                           
                                         
                                       
                                       ] 
                                     
                                     2 
                                   
                                 
                                 + 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                             
                            
                           
                              
                              
                             
                               ( 
                               
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   
                                     
                                       k 
                                       0 
                                     
                                      
                                     
                                       ( 
                                       
                                         
                                           z 
                                           r 
                                         
                                         - 
                                         z 
                                       
                                       ) 
                                     
                                   
                                 
                                 + 
                                 
                                   φ 
                                   z 
                                 
                               
                               ) 
                             
                           
                           } 
                         
                         + 
                       
                     
                   
                   
                     
                       
                           
                          
                         
                           exp 
                            
                           
                             { 
                             
                               
                                 - 
                                 
                                   
                                     
                                       
                                         
                                           ( 
                                           
                                             σ 
                                              
                                             
                                                 
                                             
                                              
                                             T 
                                           
                                           ) 
                                         
                                         2 
                                       
                                       
                                         16 
                                          
                                         
                                             
                                         
                                          
                                         
                                           ln 
                                            
                                           
                                             ( 
                                             2 
                                             ) 
                                           
                                         
                                       
                                     
                                     [ 
                                     
                                       
                                         2 
                                          
                                         
                                             
                                         
                                          
                                         π 
                                          
                                         
                                             
                                         
                                          
                                         f 
                                       
                                       + 
                                       
                                         
                                           
                                             4 
                                              
                                             
                                                 
                                             
                                              
                                             π 
                                              
                                             
                                                 
                                             
                                              
                                             Δ 
                                              
                                             
                                                 
                                             
                                              
                                             λ 
                                           
                                           
                                             
                                               λ 
                                               0 
                                               2 
                                             
                                              
                                             T 
                                           
                                         
                                          
                                         
                                           ( 
                                           
                                             
                                               z 
                                               r 
                                             
                                             - 
                                             z 
                                           
                                           ) 
                                         
                                       
                                     
                                     ] 
                                   
                                   2 
                                 
                               
                               - 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           
                               
                              
                             
                                
                                
                               
                                 ( 
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     
                                       
                                         k 
                                         0 
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             z 
                                             r 
                                           
                                           - 
                                           z 
                                         
                                         ) 
                                       
                                     
                                   
                                   + 
                                   
                                     φ 
                                     z 
                                   
                                 
                                 ) 
                               
                             
                             } 
                           
                           ] 
                         
                          
                         
                            
                           z 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0000]    As show in the above equation (3), the backscattering coefficient of the scatterer at position z is given by the magnitude of the signal at frequency 
         [0000]    
       
         
           
             
               ± 
               
                 
                   2 
                    
                   
                       
                   
                    
                   Δ 
                    
                   
                       
                   
                    
                   λ 
                 
                 
                   
                     λ 
                     0 
                     2 
                   
                    
                   T 
                 
               
             
              
             
               
                 ( 
                 
                   
                     z 
                     r 
                   
                   - 
                   z 
                 
                 ) 
               
               . 
             
           
         
       
     
         [0000]    There is interference between frequency components correspond to ±(z r −z) depths limiting using both side of coherence function (G(|z|)). 
         [0033]    Depth and Frequency Encoding in OFDI 
         [0034]    Exemplary FD-OCT techniques of SD-OCT and OFDI systems and methods can measure the discrete spectral interference i(k) but differ in the implementation of this measurement. OFDI uses a wavelength-swept source and a single-element photoreceiver (or set of single-element photoreceivers) to record i(k) as a function of time.  FIG. 3  shows an exemplary embodiment of a high-speed OFDI imaging system. This exemplary system can include, e.g., three modules: a wavelength-swept source  85 , an interferometer  90 , and acquisition electronics  95 . The wavelength-swept source (hereafter referred to as swept source) is constructed as a ring-cavity laser with a semiconductor optical amplifier (SOA)  125  as the gain element and a polygon mirror filter  101  comprising a polygon mirror  100 , telescope  105 , diffraction grating  110 , and fiber collimator  113 . A polarization controller  120  can be inserted to optimize the laser polarization and output coupler  130  provides the laser output. The output coupler can nominally split light equally between the output port  132  and laser port  131 . An optical circulator  115  directs light from the laser port  131  to the polygon mirror filter  101 , and may direct light returning from the polygon mirror filter  101  to the polarization controller  120 . As the polygon mirror rotates, the wavelength reflected from the polygon mirror filter  101  sweeps in wavelength, causing the laser output to sweep in wavelength in a similar manner. 
         [0035]    The laser output at  132  can therefore be wavelength swept in time. This output is input to the interferometer coupler  135  which splits the light into a reference arm port  135   a  and sample arm port  135   b . Coupler  165  splits the reference arm light. Light from the output  165   a  is directed to a second circulator  145  which passes light to a fiber Bragg grating (FBG)  150 . The FBG has a narrowband reflection at a discrete wavelength within the wavelength-sweep range of the source. As the source tunes past this reflection wavelength, a reflected optical pulse is generated. This pulse is directed by the circulator  145  to the photoreceiver  155  after which it is converted into a TTL pulse by 160. This TTL pulse is used as a trigger signal for the data acquisition electronics  200 . Light from output port  165   b  is directed to a third circulator which directs light to a variable optical delay  210 . This variable optical delay is used to path-match the interferometer. Return light is directed by the circulator  170  to the first port  220   a  of the input coupler  220 . The light at the Nth port  220 N of the output coupler  220  is directed to the polarization controller  225 N and frequency shifter  230 N at frequency fs N  and the polarizer  235 N. The frequency shifter  230 N in the reference arm is driven through a signal carried on line  203  which is derived from the DAQ sample clock output  204 . 
         [0036]    This output clock is down-shifted in frequency using a “Divide by N” digital logic circuit  201  and the resulting signal passes through an amplifier and filter stage  202  to produce a single tone on line  203 . Because the drive signal for the frequency shifter is driven by the DAQ sample clock output, the phase of the frequency shift is synchronous with the sample clock and thus does not induced additional phase noise. Then, light is directed to the polarization controller  240 N and the Nth port  245 N of the input coupler  245 . All N frequency shifted lights are combined at the first port  245  of the output coupler  245  and directed to the first port  250   a  of the input coupler  250 . By assuming the path difference between the i-th port  220   i  of the input coupler  220  and the i-th port  245   i  of the input coupler  245  is Li, we set the difference between Li and Lj to 4*(N−M)*Lc, where Lc is the coherence length of the source. The sample arm light at port  135   b  is directed to a fourth circulator  205  which directs the light on fiber  206  to the sample to be imaged. Imaging optics  215  focuses the light on the sample and provide for beam translation. 
         [0037]    Light reflected from the sample is collected by the same fiber  206  and returned to circulator  205  which directs the light to a frequency shifter and the second port  250   b  of the input coupler  250 . This frequency shifter that is not driven is used to compensate for the dispersion of the driven frequency shifters. The combined sample arm light and reference arms light at the first port  250   c  and  250   d  of the output coupler  250  are directed to polarization controllers  260  and  270  and polarization beam splitter  280  and  290 , respectively. By adjusting the polarization controllers  240   i , the polarization states of shifted light become parallel to each other at the input ports of polarization beam splitters  280  and  290 . By adjusting the polarization controllers  260  and  270 , The power of the output coupler  250  correspond to the Nth reference arm power equally splits between the first and second ports  280   a ,  280   b ,  290   a , and  290   b  of the output polarization beam splitters  280  and  290 . Reference arms and sample arm light interferes at the first and second ports  280   a ,  280   b ,  290   a , and  290   b  of the output polarization beam splitters  280  and  290 . The interference signal at the first ports  280   a  of the output polarization beam splitters  280  and the first ports  290   a  of the output polarization beam splitters  290  are detected by the photoreceiver  295   a  and  295   b , respectively. 
         [0038]    The interference signal at the second ports  280   b  of the output polarization beam splitters  280  and the second ports  290   b  of the output polarization beam splitters  290  may be detected by the photoreceiver  300   a  and  300   b , respectively. The signals from the photoreceiver  295   a  and  295   b  are subtracted and directed toward an analog-to-digital (A2D) input port of the data acquisition (DAQ) board  200 . The signals from the photoreceiver  300   a  and  300   b  are subtracted and directed toward an analog-to-digital (A2D) input port of the data acquisition (DAQ) board. The DAQ board  200  acquires n (n is predetermined) samples at a clock rate f c1 . The clock signal is internally generated in the DAQ board  200 . The trigger signal from the TTL pulse generator  160  originates from the optical pulse produced by the FBG  150 . 
         [0039]    With frequency shifts f 1 , . . . , f i  . . . , f N  in the reference arms  1100   i  iε{1, . . . N} and an interferometer path-length differences (or depths) of z r1 -z, z r2 -z, z rN -z, Signals at the output of the 295 and 300 photo-receivers can be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             i 
                             s 
                           
                            
                           
                             ( 
                             t 
                             ) 
                           
                         
                         = 
                         
                           
                             2 
                              
                             
                                 
                             
                              
                             η 
                              
                             
                               
                                 
                                   
                                     P 
                                     r 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                  
                                 
                                   
                                     P 
                                     s 
                                   
                                    
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                               
                             
                              
                             
                               ∫ 
                               
                                 
                                   
                                     R 
                                      
                                     
                                       ( 
                                       z 
                                       ) 
                                     
                                   
                                 
                                  
                                 
                                   { 
                                   
                                     
                                       
                                         
                                           
                                             ∑ 
                                             
                                               i 
                                               = 
                                               1 
                                             
                                             N 
                                           
                                            
                                           
                                             G 
                                              
                                             
                                               ( 
                                               
                                                  
                                                 
                                                   
                                                     z 
                                                     ri 
                                                   
                                                   - 
                                                   z 
                                                 
                                                  
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                     
                                     
                                       
                                         
                                           cos 
                                            
                                           
                                             ( 
                                             
                                               
                                                 
                                                   
                                                     
                                                       2 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       k 
                                                        
                                                       
                                                         ( 
                                                         t 
                                                         ) 
                                                       
                                                        
                                                       
                                                         ( 
                                                         
                                                           
                                                             z 
                                                             ri 
                                                           
                                                           - 
                                                           z 
                                                         
                                                         ) 
                                                       
                                                     
                                                     + 
                                                   
                                                 
                                               
                                               
                                                 
                                                   
                                                     
                                                       2 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       π 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       
                                                         f 
                                                         i 
                                                       
                                                        
                                                       t 
                                                     
                                                     + 
                                                     
                                                       φ 
                                                       z 
                                                     
                                                   
                                                 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   } 
                                 
                                  
                                 
                                    
                                   z 
                                 
                               
                             
                           
                           + 
                           
                             2 
                              
                             
                                 
                             
                              
                             η 
                              
                             
                                 
                             
                              
                             
                               
                                 P 
                                 r 
                               
                                
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                              
                             
                               
                                 ∑ 
                                 
                                   j 
                                   = 
                                   1 
                                 
                                 N 
                               
                                
                               
                                 
                                   ∑ 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   N 
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       2 
                                        
                                       
                                           
                                       
                                        
                                       
                                         k 
                                          
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                        
                                       
                                         ( 
                                         
                                           
                                             z 
                                             ri 
                                           
                                           - 
                                           
                                             z 
                                             rj 
                                           
                                         
                                         ) 
                                       
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           + 
                           
                             2 
                              
                             
                                 
                             
                              
                             
                               π 
                                
                               
                                 ( 
                                 
                                   
                                     f 
                                     i 
                                   
                                   - 
                                   
                                     f 
                                     j 
                                   
                                 
                                 ) 
                               
                             
                              
                             t 
                           
                         
                       
                       ) 
                     
                      
                     
                       
 
                     
                      
                     
                         
                     
                      
                     
                       
                         for 
                          
                         
                           
                               
                           
                            
                           
                               
                           
                         
                          
                         i 
                       
                       ≠ 
                       
                           
                       
                        
                       j 
                     
                   
                    
                   
                       
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       I 
                        
                       
                         ( 
                         f 
                         ) 
                       
                     
                     = 
                     
                       
                           
                           
                       
                        
                       
                           
                         
                             
                             
                         
                           
                       
                        
                       
                         
                           η 
                            
                           
                               
                           
                            
                           
                             P 
                             out 
                           
                            
                           σ 
                            
                           
                               
                           
                            
                           T 
                         
                         2 
                       
                        
                       
                         
                           π 
                           
                             ln 
                              
                             
                               ( 
                               2 
                               ) 
                             
                           
                         
                       
                        
                       
                         ∫ 
                         
                           
                             
                               R 
                                
                               
                                 ( 
                                 z 
                                 ) 
                               
                             
                           
                            
                           
                             { 
                             
                               
                                 
                                   ∑ 
                                   
                                     i 
                                     = 
                                     1 
                                   
                                   N 
                                 
                                  
                                 
                                   
                                     G 
                                      
                                     
                                       ( 
                                       
                                          
                                         
                                           
                                             z 
                                             ri 
                                           
                                           - 
                                           
                                               
                                           
                                            
                                           z 
                                         
                                          
                                       
                                       ) 
                                     
                                   
                                    
                                   
                                       
                                     
                                       [ 
                                       
                                           
                                       
                                        
                                       
                                         
                                           
                                             
                                               
                                                 exp 
                                                  
                                                 
                                                   { 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             - 
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             ( 
                                                             
                                                             σ 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             T 
                                                             
                                                             ) 
                                                             
                                                             2 
                                                             
                                                             
                                                             16 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             ln 
                                                              
                                                             
                                                             ( 
                                                             2 
                                                             ) 
                                                             
                                                             
                                                             
                                                             
                                                             [ 
                                                             
                                                             
                                                             2 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             f 
                                                             
                                                             - 
                                                             
                                                             
                                                             
                                                             4 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             Δ 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             λ 
                                                             
                                                             
                                                             
                                                             λ 
                                                             0 
                                                             2 
                                                             
                                                              
                                                             T 
                                                             
                                                             
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             z 
                                                             r 
                                                             
                                                             - 
                                                             z 
                                                             
                                                             ) 
                                                             
                                                             
                                                             + 
                                                             
                                                             2 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             f 
                                                             i 
                                                             
                                                             
                                                             
                                                             ] 
                                                             
                                                             2 
                                                             
                                                           
                                                           + 
                                                         
                                                       
                                                     
                                                     
                                                       
                                                         
                                                            
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             2 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             
                                                             
                                                             k 
                                                             0 
                                                             
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             z 
                                                             ri 
                                                             
                                                             - 
                                                             z 
                                                             
                                                             ) 
                                                             
                                                             
                                                             i 
                                                             
                                                             
                                                             + 
                                                             
                                                             φ 
                                                             z 
                                                             
                                                             
                                                             ) 
                                                           
                                                         
                                                       
                                                     
                                                   
                                                   } 
                                                 
                                               
                                               + 
                                             
                                           
                                         
                                         
                                           
                                             
                                               exp 
                                                
                                               
                                                 { 
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           - 
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             ( 
                                                             
                                                             σ 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             T 
                                                             
                                                             ) 
                                                             
                                                             2 
                                                             
                                                             
                                                             16 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             ln 
                                                              
                                                             
                                                             ( 
                                                             2 
                                                             ) 
                                                             
                                                             
                                                             
                                                             
                                                             [ 
                                                             
                                                             
                                                             2 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             f 
                                                             
                                                             + 
                                                             
                                                             
                                                             
                                                             4 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             Δ 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             λ 
                                                             
                                                             
                                                             
                                                             λ 
                                                             0 
                                                             2 
                                                             
                                                              
                                                             T 
                                                             
                                                             
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             z 
                                                             ri 
                                                             
                                                             - 
                                                             z 
                                                             
                                                             ) 
                                                             
                                                             
                                                             - 
                                                             
                                                             2 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             f 
                                                             i 
                                                             
                                                             
                                                             
                                                             ] 
                                                             
                                                             2 
                                                           
                                                         
                                                         - 
                                                       
                                                     
                                                   
                                                   
                                                     
                                                       
                                                          
                                                          
                                                         
                                                           ( 
                                                           
                                                             
                                                             2 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             
                                                             k 
                                                             0 
                                                             
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             z 
                                                             ri 
                                                             
                                                             - 
                                                             z 
                                                             
                                                             ) 
                                                             
                                                             
                                                             
                                                             + 
                                                             
                                                             φ 
                                                             z 
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                   
                                                 
                                                 } 
                                               
                                             
                                           
                                         
                                       
                                        
                                       
                                           
                                       
                                       ] 
                                     
                                      
                                     
                                         
                                     
                                     } 
                                   
                                    
                                   
                                       
                                   
                                    
                                   
                                      
                                     
                                         
                                     
                                      
                                     z 
                                   
                                 
                               
                                
                               
                                   
                               
                               + 
                               
                                 
                                   
                                     η 
                                      
                                     
                                         
                                     
                                      
                                     
                                       P 
                                       out 
                                     
                                      
                                     σ 
                                      
                                     
                                         
                                     
                                      
                                     T 
                                   
                                   2 
                                 
                                  
                                 
                                   
                                     π 
                                     
                                       ln 
                                        
                                       
                                         ( 
                                         2 
                                         ) 
                                       
                                     
                                   
                                 
                                  
                                 
                                   
                                     ∑ 
                                     
                                       j 
                                       = 
                                       1 
                                     
                                     N 
                                   
                                    
                                   
                                     
                                       ∑ 
                                       
                                         i 
                                         = 
                                         1 
                                       
                                       N 
                                     
                                      
                                     
                                       exp 
                                        
                                       
                                         { 
                                         
                                           
                                             
                                               
                                                 
                                                   - 
                                                   
                                                     
                                                       
                                                         
                                                           
                                                             ( 
                                                             
                                                             σ 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             T 
                                                             
                                                             ) 
                                                           
                                                           2 
                                                         
                                                         
                                                           16 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           
                                                             ln 
                                                              
                                                             
                                                             ( 
                                                             2 
                                                             ) 
                                                             
                                                           
                                                         
                                                       
                                                       [ 
                                                       
                                                         
                                                           
                                                             
                                                             
                                                             2 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             f 
                                                             
                                                             - 
                                                             
                                                             
                                                             
                                                             4 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             Δ 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             λ 
                                                             
                                                             
                                                             
                                                             λ 
                                                             0 
                                                             2 
                                                             
                                                              
                                                             T 
                                                             
                                                             
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             z 
                                                             ri 
                                                             
                                                             - 
                                                             
                                                             z 
                                                             rj 
                                                             
                                                             
                                                             ) 
                                                             
                                                             
                                                             + 
                                                             
                                                           
                                                         
                                                         
                                                           
                                                             
                                                             2 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             
                                                             ( 
                                                             
                                                             
                                                             f 
                                                             i 
                                                             
                                                             - 
                                                             
                                                             f 
                                                             j 
                                                             
                                                             
                                                             ) 
                                                             
                                                             
                                                           
                                                         
                                                       
                                                       ] 
                                                     
                                                     2 
                                                   
                                                 
                                                 + 
                                               
                                             
                                           
                                           
                                             
                                               
                                                  
                                                  
                                                 
                                                   ( 
                                                   
                                                     
                                                       2 
                                                        
                                                       
                                                           
                                                       
                                                        
                                                       
                                                         
                                                           
                                                             k 
                                                             0 
                                                           
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             z 
                                                             ri 
                                                             
                                                             - 
                                                             
                                                             z 
                                                             rj 
                                                             
                                                             
                                                             ) 
                                                           
                                                         
                                                         i 
                                                       
                                                     
                                                     + 
                                                     
                                                       φ 
                                                       z 
                                                     
                                                   
                                                   ) 
                                                 
                                               
                                             
                                           
                                         
                                         } 
                                       
                                     
                                   
                                 
                               
                               + 
                               
                                 exp 
                                  
                                 
                                   { 
                                   
                                     
                                       
                                         
                                           
                                             - 
                                             
                                               
                                                 
                                                   
                                                     
                                                       ( 
                                                       
                                                         σ 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         T 
                                                       
                                                       ) 
                                                     
                                                     2 
                                                   
                                                   
                                                     16 
                                                      
                                                     
                                                         
                                                     
                                                      
                                                     
                                                       ln 
                                                        
                                                       
                                                         ( 
                                                         2 
                                                         ) 
                                                       
                                                     
                                                   
                                                 
                                                 [ 
                                                 
                                                   
                                                     
                                                       
                                                         
                                                           2 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           π 
                                                            
                                                           
                                                               
                                                           
                                                            
                                                           f 
                                                         
                                                         + 
                                                         
                                                           
                                                             
                                                             4 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             π 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             Δ 
                                                              
                                                             
                                                               
                                                             
                                                              
                                                             λ 
                                                             
                                                             
                                                             
                                                             λ 
                                                             0 
                                                             2 
                                                             
                                                              
                                                             T 
                                                             
                                                           
                                                            
                                                           
                                                             ( 
                                                             
                                                             
                                                             z 
                                                             ri 
                                                             
                                                             - 
                                                             
                                                             z 
                                                             rj 
                                                             
                                                             
                                                             ) 
                                                           
                                                         
                                                         - 
                                                       
                                                     
                                                   
                                                   
                                                     
                                                       
                                                         2 
                                                          
                                                         
                                                             
                                                         
                                                          
                                                         
                                                           π 
                                                           ( 
                                                           
                                                               
                                                           
                                                            
                                                           
                                                             
                                                             f 
                                                             i 
                                                             
                                                             - 
                                                             
                                                             f 
                                                             j 
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                   
                                                 
                                                 ] 
                                               
                                               2 
                                             
                                           
                                           - 
                                         
                                       
                                     
                                     
                                       
                                         
                                            
                                            
                                           
                                             ( 
                                             
                                               
                                                 2 
                                                  
                                                 
                                                     
                                                 
                                                  
                                                 
                                                   
                                                     k 
                                                     0 
                                                   
                                                    
                                                   
                                                     ( 
                                                     
                                                       
                                                         z 
                                                         ri 
                                                       
                                                       - 
                                                       
                                                         z 
                                                         rj 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               + 
                                               
                                                 φ 
                                                 z 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   } 
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0000]    Equation (5) shows that the sample reflectivity profile is encoded at N different frequency shifts while zero depths of N interferometers correspond to f 1 , . . . , f N . The third term of equation (5) is the beat terms between N reference arm signals. 
         [0040]    Signal to Interference Ratio (SIR) 
         [0041]    Crosstalk between two adjacent encoded images causes degradation of sensitivity and ranging depth. However, appropriate spacing between frequency shifts can avoid crosstalk. As shown in  FIG. 2(   b ), two depths mapped into the same frequency range can cause crosstalk. For two frequency shifts, the theoretical results in  FIG. 3  shows that the proper frequency spacing for required SIR depends on the A-line rate (assuming crosstalk is dominant term in the presence of noise).  FIGS. 4(   a ), ( b ), (c), and (d) show the variation of SIR due to depth for different frequency spacings and A-line rates. SIR1 and SIR2 are signal to interference ratios of two sections around corresponding zero depths (z r1 , z r2 ). When the A-line rate increases, SIR decreases. For example SIR1 increases around 30 dB at zero depth when the tuning speed decreases from 75 KHz to 50 KHz with frequency spacing 50 MHz. In addition, SIR at each depth grows when the frequency spacing increases for a determined A-line rate. 
         [0042]    The appropriate frequency spacing for a preferred SIR can depend on not only the A-line rate but also coherence length. As shown in  FIG. 2(   b ), the SIR increases by increasing coherence length. In theoretical, simulation, and experimental results, we assume the source instantaneous coherence length and Δz are 2.5 mm and 5 mm respectively.  FIG. 5  shows the minimum SIR for different tuning speeds and frequency spacings (25 MHz and 50 MHz). The simulation results in  FIG. 6  shows signal power versus depth using a calibrated partial reflector at various depth locations in the sample arm. The lens and sample can be moved so that the sample reflectivity profile was uniform from −5 mm to 5 mm. The sampled data acquired at each depth may be processed with mapping and dechirping procedures. The minimum SIR through the depth may be greater than 60 dB using an OFDI system with 25 KHz A-line rate, frequency spacing 50 MHz, coherence length 2.5 mm, and tuning range 100 nm. 
         [0043]    Exemplary Processing Procedure 
         [0044]    Nonlinearity in the tuning frequency of the source results in a chirping of the signal at a constant depth and causes a degradation of axial resolution. It is possible to a modify an exemplary interpolation method based on frequency shifting and zero padding to achieve nearly transform limited axial resolution over the entire ranging depth. An exemplary embodiment of a procedure to perform such exemplary function is shown in  FIG. 9 . 
         [0045]    In particular, as illustrated in  FIG. 9 , P samples of the signal are obtained with uniform time interval during each wavelength sweep of the source (procedure  910 ). DFT of P data points is then determined in the electrical frequency domain (procedure  920 ). Further, 2P frequency bands are separated below and above frequency shifts f i ε{f 1 , . . . , f N } corresponding negative and positive depths, respectively (procedure  930 ). Each frequency band can be shifted such that the zero depth is aligned the zero electrical frequency (procedure  940 ). In addition, zero-padding can be applied to each frequency band and calculate inverse resulting in an array of increased number of samples in the time domain with smaller time interval for each frequency band (procedure  950 ). The number of zeroes can be determined based on required ranging depth. Each array in the time domain can be interpolated into a uniform v space using a mapping function calibrated to the nonlinearity of the source with linear interpolation (procedure  960 ). Then, DFT of each interpolated array can be determined (procedure  970 ). Further, the 2P arrays (e.g., images) can be combined by shifting the array index (procedure  980 ). 
         [0046]    Exemplary Applications of DFE OFDI 
         [0047]    In a further exemplary embodiment, the DFE-OFDI system can be used to image intravascular. A device capable of imaging increasing ranging depth is shown in  FIG. 7 . The optical probe  310  is placed inside the artery  320  and the imaging beam  330  is emitted from the side of the probe. By moving probe into the artery, the imaging beam  330  hits artery  320  at two different points A and B. DFE-OFDI is able to image artery at A and B while the images are encoded with different frequency. The end view illustrates how DFE-OFDI is able to increase ranging depth. 
         [0048]    It can be appreciated by those skilled in the art that one of the embodiments can be used in combination with other embodiments to construct DFE-OFDI systems with increasing ranging depth. 
       EXAMPLE 
       [0049]    The exemplary embodiment of the method according to the present invention was verified in the laboratory by the following experiment. 
         [0050]      FIG. 1(   a ) depicts the experimental setup of the conventional OFDI system employing two acousto-optic frequency shifters (25 MHz and 50 MHz). A swept laser was constructed to provide a tuning range of 117 from 1240 nm to 1357 nm. The laser was operated at rates of 12.5 KHz, 25 KHz and 50 KHz so that 15872, 7936, 3968 samples could be acquired (sampling rate ˜4 times of the maximum frequency shift). The probe, comprising a galvanometer mirror and an imaging lens, produced a 40 μm 1/e 2  diameter focal spot on the sample with a confocal parameter of 2 mm. An image of a human aorta was acquired ex vivo at an A-line rate of 12.5 KHz with the depth and frequency-encoded OFDI system. This image was reconstructed using the mapping algorithm described above. The surface of the tissue was placed at an angle with respect to the probe beam axis, and the reference mirrors were positioned such that the path difference between them was 5 mm. The sample lens was configured to focus the light 5 mm inside the tissue at the center of the image.  FIG. 7  ( a ) depicts an image of the aorta when we used a single frequency shifter at 25 MHz for resolving positive and negative depth ambiguity.  FIG. 7  ( b ) depicts the same image after depth and frequency encoding. The left and right sides of image were encoded at 25 MHz and 50 MHz frequencies, respectively. The ranging depth was increased by a factor of two compared to the single frequency shifter case. 
         [0051]    The foregoing merely illustrates the principles of the invention. Various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein. Indeed, the arrangements, systems and methods according to the exemplary embodiments of the present invention can be used with any OCT system, OFDI system, spectral domain OCT (SD-OCT) system or other imaging systems, and for example with those described in International Patent Application PCT/US2004/029148, filed Sep. 8, 2004, U.S. patent application Ser. No. 11/266,779, filed Nov. 2, 2005, and U.S. patent application Ser. No. 10/501,276, filed Jul. 9, 2004, the disclosures of which are incorporated by reference herein in their entireties. It will thus be appreciated that those skilled in the art will be able to devise numerous systems, arrangements and methods which, although not explicitly shown or described herein, embody the principles of the invention and are thus within the spirit and scope of the present invention. In addition, to the extent that the prior art knowledge has not been explicitly incorporated by reference herein above, it is explicitly being incorporated herein in its entirety. All publications referenced herein above are incorporated herein by reference in their entireties.

Technology Category: 3