angle - resolved fd - oct is described herein below in a context of fourier - domain oct . for example , in fd - oct , the interference between reference light and the light backscattered from the imaging sample can be measured in the frequency domain in order to obtain the depth - resolved reflectance of a turbid , semi - turbid , or transparent medium . electro - magnetic radiation ( e . g ., light , laser beam , etc .) of the input light source can be split into a reference beam and a sample beam . the sample beam light may be directed to the sample to be imaged , and backscattered light from the sample may be interfered with reference beam light . in the case of angle - resolved fd - oct , the reference beam can be spatially expanded such that it can be made larger in a cross - sectional area than the cross - sectional area of the sample beam in order to allow for the interference with a range of backscattering angles beyond those subtended by the incident sample beam . the interference between the reference beam and the backscattered light can be measured using , e . g ., a detector array , which may consist of ( i ) detectors integrated onto a single integrated circuit element , and / or ( ii ) individual detectors provided together in space . the angular dependence of the detected backscattered light with respect to the incident beam may be encoded in the spatial domain , as the distribution of light intensities along at least one dimension of the detector array . the wavelength dependence of the interfered light may be measured , and fourier analysis axial reflectivity profiles corresponding to different ranges of backscattering angles can be obtained . for example , the interference signal s i detected by an ith pixel of the detector array as a function of the frequency of laser light v n can be given by the following proportionality expression : s i ⁡ ( v n ) ∝ p ⁡ ( v n ) ⁢ γ r , i ⁡ ( v n ) ⁢ γ s , i ⁡ ( v n ) ⁢ ∫ 0 ∞ ⁢ r ⁡ ( z ) ⁢ cos ⁡ ( 4 ⁢ π ⁢ ⁢ v n ⁢ z / c + ϕ ⁡ ( z ) ) ⁢ ⁢ ⅆ z ( 1 ) where p ( v n ) is the total power of the source . r ( z ) and φ ( z ) are the amplitude and phase terms of the reflectance profile , respectively . an axial distance z may be expressed as a relative distance , with z = 0 corresponding to zero optical path difference between the sample and reference arms . the amount of the sample arm and reference arm electro - magnetic radiation ( e . g ., light ) that reaches pixel i , expressed as fractions of p ( v n ) can be denoted γ s , i and γ r , i , respectively . the reflectivity profile r ( z ) can be obtained as the discrete fourier transform of the sampled interference signal along the dimension i : speckle results from distortions of the backscattered wavefront , which are likely caused by low - angle multiple forward scattering and diffuse multiple backscattering from closely separated refractive index heterogeneities . angular compounding techniques are generally obtained from an observation that as a result of this interference , fields originating from different backscattering angles are de - correlated . by averaging the signals from different scattering angles incoherently , e . g ., averaging of the magnitude of the reconstructed reflectance profiles , a reflectance signal with reduced speckle can be obtained . the speckle signal - to - noise ratio (“ snr ”) can be a measure of the speckle reduction , as the ratio of the mean to the square - root of the variance of pixel intensities within a medium with homogenous scattering properties : snr = 〈 s k 〉 〈 ( s k - 〈 s k 〉 ) 2 〉 , ( 3 ) where the angular brackets denote an average over a collection of pixels indexed by k . the speckle snr can be a normalized measure of the variance of the signal obtained from a homogenous sample . as such , the speckle snr may differ from the system sensitivity , which can be defined without the presence of speckle as the minimum detectable reflectance . for the exemplary angular compounding method , the snr may increase proportionally to the square - root of the number of uncorrelated , incoherent averages , n : an extent to which the snr can be increased by angular compounding may therefore be dependent on the level of angular decorrelation . in general , higher levels of decorrelation for oct sample volumes containing large numbers of scatterers can be obtained , as well as those at large optical depths . in comparison , sharp interfaces and scatterers with dimensions that are similar to those of the sample volumes are likely to indicate a small amount of contrast enhancement from angular compounding . principle of extraction of parameters from angular backscattering distributions for image contrast the angular backscattering patterns of light , which may be measured by the angle - resolved fd - oct methods and systems , can contain information about the scatterer size and the density of the imaging sample . this information may be relevant in , e . g ., a clinical imaging context in order to distinguish between different regions of tissue that have very similar scattering properties that may be used in optical methods that measure the reflectance of light that is backscattered within a single angular range . image contrast measures can be generated from angular backscattering distributions at each pixel , and such measures can be spatially smoothed , and / or image contrast measures can be generated from spatially smoothed angular backscattering distributions . the fd - oct techniques of sd - oct and ofdi systems and method can measure a discrete spectral interference , and may differ in the implementation of this measurement . the ofdi systems and methods can use a wavelength - swept source to record the interference as a function of time , whereas the sd - oct systems and methods may generally use a spectrometer to image interference spectra onto a detector array or a portion of an array . fig7 shows a schematic diagram of an exemplary embodiment of the angle - resolved fd - oct imaging system in accordance with the present invention . this exemplary system can include the following modules : a wavelength - swept source 705 , an interferometer 707 , and an acquisition camera 765 with corresponding electronics 785 . for example , the laser output can be directed to the optical coupler 710 which may split the light into two arms of the interferometer 707 . a collimated light provided from a reference arm collimator 725 may be incident on a cylindrical lens telescope with elements 735 , 740 , 745 , and this telescope can which expand the beam in the dimension of the line - scan camera 765 . a free - space coupler of variable length 712 can be placed within the reference arm before the collimator 725 to facilitate reference arm length adjustments . the collimated light from the sample arm collimator 730 can be directed through a linear polarizer 755 and the beam splitter 750 , where such light may be incident on imaging optics 770 , 775 which focus the light on a sample 780 . polarization controllers 715 , 720 provided before the collimators 725 , 730 , respectively , can be positioned to maximize the fringe modulation across the frequency range of the wavelength - swept source 705 . the imaging optics 770 and 775 consists of a galvanometer mirror 770 with its axis parallel to the plane of the interferometer 707 and perpendicular to the beam which is incident upon it from the beam splitter 750 , and a focusing lens 775 that is placed one focal length from the sample 780 . the incident beam contacts the horizontal and vertical centers of the galvanometer mirror 770 . the light back - reflected from the sample 780 can pass back via the mirror 770 and the focusing lens 775 , and may subsequently interfere with the reference beam at the beam splitter 750 . the interfered light may be incident on a cylindrical lens 760 which focuses the light onto the line - scan camera 765 . the light from a he — ne laser 700 can be injected into the fiber coupler 710 , and may act as a guide beam during the imaging procedure . the signals from the line - scan camera 765 can be directed toward analog - to - digital ( a - d ) input ports of a data acquisition (“ daq ”) board 785 . for example , in a time period corresponding to one a - line , the daq board 785 can obtain m data points from n exposures , where m may be the number of detectors in the line scan camera 765 , and n can be the number of frequencies sampled per a - line . the a - line acquisition rate can be determined as the quotient of the line scan camera readout rate and n . the readout from the daq board 785 may be synchronized to the frequency - swept laser source 705 using , e . g ., ttl trigger signals by the line - scan camera 765 at the beginning of each readout phase . as shown in the diagram of fig8 , the exemplary embodiment of the wavelength - swept source can be constructed as a ring - cavity laser with a semiconductor optical amplifier (“ soa ”) 845 as the gain element and a galvanometer mirror filter 800 that may include a galvanometer mirror 802 , a telescope 805 , 810 , a diffraction grating 815 , and a fiber collimator 820 . two polarization controllers 825 , 840 can be provided to optimize a laser polarization and output coupler 835 which thus provides the laser output . the output coupler 835 can nominally split the light approximately equally between the output port 836 and the laser port 837 . an optical circulator 830 may direct light from the laser port 837 to the galvanometer mirror filter 800 via the polarization controller 840 , and can direct the light returning from the galvanometer mirror filter 800 back to the soa 845 via the polarization controller 825 . as the galvanometer mirror 802 rotates , the wavelength reflected from the galvanometer mirror filter 800 generally changes . an optical isolator 850 can be used to separate the laser from the rest of the exemplary system . according to a second exemplary embodiment of the present invention , the detection of the interfered light can be performed using a two dimensional array of detectors , with both dimensions corresponding to the angular distribution of backscattered light . the light incident on the sample may be provided by a wavelength - tunable , narrow line - width source . the light backscattered from the imaging sample is interfered with a reference beam that has been expanded along two spatial dimensions . each detector array element can correspond to a unique range of polar and azimuthal angles of the backscattered light . by sweeping the laser across its tuning range , while acquiring readouts of the detector array , a vector for each discrete azimuth - polar angular pair can be obtained . fourier - domain optical coherence tomographic reconstruction techniques may be applied the vectors , which can generate depth - resolved reflectance profiles . by scanning the beam across the sample or moving the sample relative to the beam while acquiring readouts of the array , angle - resolved reflectance profiles for different locations on the tissue may be obtained . these profiles can be combined to form two - or three - dimensional cross - sectional reflectance images . according to a third exemplary embodiment of the present invention , a detection of the interfered light can be performed using , e . g ., a two dimensional array of detectors , with one dimension corresponding to wavelength , and the other to the angle of the backscattered light , as shown in the operational and block diagram of fig9 . the light incident on the sample may be provided by a broadband source . the light backscattered from the sample can be interfered with a reference beam that has been expanded along one spatial dimension , and this dimension can correspond to the angle of the backscattered light . the interfered light 900 may be incident on a diffraction grating 905 , which can separate light along another dimension corresponding to wavelength . subsequently , this separated light 910 can be incident on the two - dimensional detector array 915 . along each one - dimensional portion of the detector array readout which corresponds to a particular backscattering angular range , fourier - domain optical coherence tomographic reconstruction techniques can be applied to the interference spectrum , thereby providing a depth - resolved reflectance profile . by scanning the beam across the sample , or moving the sample with respect to the beam while acquiring readouts of the array , the angle - resolved reflectance profiles for different points on the tissue may be obtained . these profiles can be combined to form two - or three - dimensional cross - sectional reflectance images . a fourth exemplary embodiment suitable for applications using small probe geometries in accordance with the present invention can be used with a fiber bundle , a shown in the operational and block diagram of fig1 . according to this exemplary embodiment , an array of optical fibers 1025 can be used to transmit and receive the light to and from an imaging sample 1000 . one or more fibers in the array 1025 can be designated as “ delivery fibers ,” through which light 1010 may be transmitted to and received from the sample 1000 . each fiber in the array 1025 can correspond to a unique , narrow range of angular backscattering angles . lenses placed before the fibers 1020 may serve to enhance the amount of light collected by each fiber . a lens 1015 placed in front of the lenses 1020 serves to focus light onto the sample 1000 , and to collimate light backscattered from the sample 1000 prior to the collection by the lenses 1020 . polarimetric measurements in the context of optical coherence tomography may be useful for spatially resolving birefringence in biological tissue . according to a fifth exemplary embodiment according to the present invention , polarimetric measurements can be performed by one or more of the following : a ) varying the polarization of the light prior to the receipt thereof at the interferometer , and by fixing the polarization state of the reference arm and / or the sample arm ; b ) varying the polarization of only the sample beam as a function of time ; c ) varying the polarization of only the reference beam as a function of time ; d ) varying the polarization state of one or more parts of the reference beam as a function of space , such that there may be at least two distinct parts of the reference beam that differ in the polarization state ; e ) varying the polarization state of one or more parts of the backscattered light as a function of space prior to interference with the reference beam , such that there may be at least two distinct parts of the sample beam that differ in the polarization state ; f ) varying the polarization state of one or more parts of the interfered light as a function of space , such that there may be at least two distinct parts that differ in the polarization state . using the exemplary techniques ( a ), ( b ) and / or ( c ), the birefringence maps of the sample can be obtained by comparing a - lines received at different times , such that the polarization states from which they originated are likely different . using the exemplary techniques ( d ), ( e ) and / or ( f ), the birefringence maps of the sample can be obtained by comparing a - lines obtained from different backscattering angular ranges such that the polarization states from which they originated are likely different . the angular frequency content obtained from the angle - resolved fd - oct system and / or method can be analyzed using a computational framework of mie scattering , provided that the deviations of the beam from planar waves can be accounted for in the analysis . in particular , as the angular scattering distributions which can originate from spherical dielectric scatterers may be determined using the mie theory , the inverse problem of determining the size distributions of the scatterers from the angular scattering distributions can be performed . the mie scattering analyses of angular backscattering distributions can enable a measurement of scatterer distributions within epithelial tissues , which may be correlated with dysplastic transitions that precede cancerous lesions . another method of processing angular backscattering distributions acquired from angle - resolved fd - oct involves analysis of their angular frequency content . image contrast measures include the angular frequency bin with maximum power and the width of the peak with the highest power . analysis of the power - spectral density of the angular backscattering distributions is equivalent to analysis of the auto - correlation function by the wiener - kinchine theorem . the normalized auto - correlation function c can be provided by : c i = ∑ j ⁢ ⁢ ( s j - 〈 s j 〉 ) ⁢ ( s j - i - 〈 s j 〉 ) ∑ j ⁢ ⁢ ( s j - 〈 s j 〉 ) 2 . ( 5 ) where j and i can be angular indexes . for example , the width of the central lobe of the autocorrelation function , measured relative to the first minimum , can indicate the extent of the correlation between successive angular samples . this exemplary width can be determined for each pixel of a cross - sectional image obtained using the angle - resolved fd - oct system and method , thus providing an image with the contrast for the de - correlation level of the angular backscattering distributions . the exemplary embodiment of the system and method according to the present invention which can be used for reducing speckle was verified by the following experiment . two - layer tissue phantoms were constructed from aqueous agar gel ( 0 . 5 % agar by weight ) and polymer microspheres of diameter 0 . 3 mm ( duke scientific ). the phantoms were contained in silicone isolators ( sigma ). an initial scattering layer with an approximate depth of 2 mm was formed . a second scattering layer , designed to have a lower scattering coefficient than the first , was funned on top of the first and had an approximate depth of 450 mm . by analyzing the exponential signal attenuation with respect to depth , the total scattering coefficients were estimated to be 24 cm - 1 and 12 cm - 1 for the first and second layers , respectively . the two - dimensional image generated from a single angular sample shows significant speckle , as shown in fig1 ( a ) , in which the boundary between the two layers is not clearly visible . speckle is greatly reduced in the angularly compounded image , with the boundary between the two layers clearly visible , as shown in fig1 ( b ) . by a qualitative inspection , the resolution in the image in fig1 ( b ) is not likely to be significantly lower than that of the image of fig1 ( a ) . graphs of exemplary representative angular distributions obtained from a point that is 500 mm below the surface of the phantom and the corresponding autocorrelation function are shown in fig1 ( a ) and 12 ( b ) . the effects of angular compounding are striking when applied to esophagus tissue , as shown in the images of fig1 a - 13d . these images were obtained from a swine ex vivo , and the imaging sample was lightly compressed by a coverslip to enhance the visibility of the layers underlying the epithelium . in particular , as shown in fig1 a , the image generated from a single angular sample is qualitatively similar to that obtained by a state - of - the art conventional ofdi system , e . g ., in terms of the features that are resolved and the graininess resulting from speckle . in this exemplary image , a scattering layer within the epithelium is only faintly apparent ( see arrow ). with three compounded angles as shown in the image of fig1 b , the level of speckle reduction is such that this layer can be resolved only in certain parts of the image . with 30 or more angular averages as shown in the images of fig1 c and 13d , the scattering layer clearly resolved across the length of the image . similar increases in detail afforded by angular compounding are seen within the regions of lamina propria and submucosa underlying the epithelium . 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 .
arrangements , apparatus and methods are provided according to exemplary embodiments of the present invention . in particular , at least one first electro - magnetic radiation may be received and at least one second electro - magnetic radiation within a solid angle may be forwarded to a sample . the second electro - magnetic radiation may be associated with the first electro - magnetic radiation . a plurality of third electro - magnetic radiations can be received from the sample which is associated with the second electro - magnetic radiation , and at least one portion of the third electro - magnetic radiation is provided outside a periphery of the solid angle . signals associated with each of the third electro - magnetic radiations can be simultaneously detected , with the signals being associated with information for the sample at a plurality of depths thereof . the depths can be determined using at least one of the third electro - magnetic radiations without a need to utilize another one of the third electro - magnetic radiations .