Abstract:
Exemplary embodiments of systems and methods can be provided which can generate data associated with at least one sample. For example, using at least one first arrangement, it is possible to forward at least one first radiation to the sample(s) so as to cause at least one second radiation to be provided from the sample(s) that can be based on the first radiation(s). In addition, using at least one second arrangement, it is possible to receive the second radiation from the sample(s), generate a plurality of distinct measurements regarding at least one portion of the sample(s) based the second radiation(s), and characterize the portion(s) over a plurality of continuous resolvable depth points thereof which are associated with the distinct measurements. Further, the characterization of the at least one portion can be resolved and distinctly characterized at a number of the depth points which is greater than a number of the distinct measurements.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
     This application is based upon and claims the benefit of priority from U.S. Patent Application Ser. No. 61/121,312, filed on Dec. 10, 2008, the entire disclosure of which is incorporated herein by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     The invention was made with the U.S. Government support under Grant Nos. CA127465 and HL076398 awarded by the Public Health Services/National Institutes of Health. Thus, the U.S. Government has certain right in the invention. 
    
    
     FIELD OF THE DISCLOSURE 
     The present disclosure relates to exemplary embodiments of optical imaging systems, apparatus and methods, and more specifically to methods, systems and apparatus associated with measuring scattering profiles of a sample over a large depth range with a small amount of acquired data through the use of, e.g., optical sub-sampling. 
     BACKGROUND INFORMATION 
     Optical coherence tomography (OCT) provides cross-sectional images of biological samples with resolution on the scale of several to tens of microns. Conventional OCT, referred to as time-domain OCT (“TD-OCT”), can use low-coherence interferometry techniques to achieve depth ranging. In contrast, Fourier-Domain OCT (“FD-OCT”) techniques can use spectral-radar techniques to achieve depth ranging. FD-OCT techniques have been shown to facilitate higher imaging speeds through improved signal-to-noise performance and elimination of a mechanically scanned interferometer reference arm. 
     FD-OCT systems generally operate by separating a light source into a sample beam and a reference beam. The sample beam can be directed at a sample to be imaged, and the reflected light from the sample is recombined with light from the reference beam (i.e., returning from the reference arm), resulting in an interference signal, which can provide information about the structure, composition and state, for example, of the sample. Light in the sample path and or light in the reference path can be modified by, for example, a phase modulator or frequency shifter, altering the characteristics of the interference and enhancing the information content of the signal or making the signal easier to detect. FD-OCT systems can sample the interference signal as a function of wavelength. 
     In one exemplary embodiment of the FD-OCT system, the interference signal as a function of wavelength can be obtained by using a light source that has an output wavelength which sweeps or steps as a function of time. A detection of the interference signal as a function of time thereby yields the interference signal as a function of wavelength. This exemplary embodiment can be referred to as optical frequency domain imaging (“OFDI”) technique. 
     In another exemplary embodiment of the FD-OCT system, the interference signal as a function of wavelength can be obtained by using a broadband light source and a spectrally dispersing unit or a spectrometer that spatially separates the recombined sample and reference light according to wavelength such that a one-dimensional or two-dimensional camera can sample the signal as a function of the wavelength. This exemplary embodiment can be referred to as spectral-domain OCT technique. In both such exemplary embodiments, the detected interference signal as a function of wavenumber k (k=1/wavelength) can be used to provide information related to the depth profile of scattering in a turbid or semi-turbid sample, or a transparent sample. Such information can include information regarding, e.g., the structure of the sample, composition, state, flow, and birefringence. 
     A scatterer at a given depth can induce a modulation in the amplitude or polarization of the interfered signal. The frequency of such modulation in wavenumber-space can be related to the location of the scatter or the time delay of the light reflected from that scatter relative to the time delay of the light in the reference arm. Scatterers located at a depth that causes reflected signals with no net time delay relative to the reference arm light can induce an interference signal that may not modulate with wavenumber. As the location of the scatterers moves from this zero-delay point, the magnitude of the frequency can increase. To image over large delay windows, e.g., to detect and localize reflections within large time delay window, the interference signal may often be sampled with sufficiently high resolution in wavenumber-space to facilitate an unambiguous detection of the range of modulation frequencies that are associated with the large delay window. 
     To accommodate the sampling at high resolution in wavenumber, increasingly fast analog-to-digital converters (“ADC”) can be used in the OFDI systems, and increasingly high pixel count cameras can be used in the SD-OCT systems. In both OFDI and SD-OCT systems, the increased data volume resulting from imaging over large extents can often result in the use of increasingly-high bandwidth data transfer buses and data storage units. 
     Thus, there may be a need to overcome at least some of the deficiencies associated with the conventional arrangements and methods described above. 
     SUMMARY OF EXEMPLARY EMBODIMENTS OF THE DISCLOSURE 
     To address and/or overcome such deficiencies, exemplary embodiments of systems and methods according to the present disclosure can be provided, e.g., using optical subsampling in Fourier-Domain OCT to acquire signals over a large depth range with a reduced volume of acquired data. 
     For example, exemplary embodiments of the present disclosure can provide systems and methods for registering the interference signals over a large delay window in FD-OCT systems but requiring reduced ADC rates for OFDI, lower pixel count cameras for SD-OCT techniques, and lower bandwidth data buses and data storage units for both OFDI and SD-OCT techniques. Such exemplary embodiments of the present disclosure can be based on a use of optical subsampling of the interference signal. Subsampling has been used in telecommunications and wireless transmissions to convert high-frequency, bandwidth-limited signals to baseband through direct digital down-conversion. According to certain exemplary embodiments of the present invention, it is possible to utilize optical subsampling to acquire a reduced volume of data that characterizes the location of scatters within a large delay window but with a distribution of delays that may be predominately localized to a limited sub-range of the overall delay window. 
     In one exemplary embodiment according to the present disclosure, exemplary embodiments of systems and methods can be provided which can generate data associated with at least one sample. For example, using at least one first arrangement, it is possible to forward at least one first radiation to the sample(s) so as to cause at least one second radiation to be provided from the sample(s) that can be based on the first radiation(s). In addition, using at least one second arrangement, it is possible to receive the second radiation from the sample(s), generate a plurality of distinct measurements regarding at least one portion of the sample(s) based the second radiation(s), and characterize the portion(s) over a plurality of continuous resolvable depth points thereof which are associated with the distinct measurements. Further, the characterization of the at least one portion can be resolved and distinctly characterized at a number of the depth points which is greater than a number of the distinct measurements. 
     According to another exemplary embodiment of the present disclosure, the number of the distinct depth points can be at least twice the number of the distinct measurements. Further, the second arrangement(s) can include at least one interferometric arrangement which can receive the second radiation(s) from the sample(s) and at least one third radiation from a reference arrangement, and interfere the second and third radiations to generate at least one interference signal. Such exemplary second arrangement(s) can be configured to generate the distinct measurements based on the interference signal(s). 
     According to still another exemplary embodiment, at least one third arrangement can be provided which is configured to (a) generate at least one image of the sample(s) based on the distinct measurements, whereas the image(s) can comprise a plurality of sections which are associated with respective multiple continuous segments of the sample(s), and (b) connect at least two adjacent ones of the sections of the image(s) to one another to form at least one continuous and uninterrupted portion of the image associated with at least two respective ones of the segments. 
     In a further exemplary embodiment of the present disclosure, the second arrangement(s) can be configured to generate the distinct measurements at as a function of wavelengths of the at least one first radiation. For example, the wavelengths at which the distinct measurements are made can be equally spaced in K-space. According to a still another exemplary embodiment of the present disclosure, the first arrangement(s) can be configured to vary a wavelength of the at least one first radiation over time. 
     These and other objects, features and advantages of the exemplary embodiment of the present disclosure will become apparent upon reading the following detailed description of the exemplary embodiments of the present disclosure, when taken in conjunction with the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWING(S) 
       Further objects, features and advantages of the present invention will become apparent from the following detailed description taken in conjunction with the accompanying figures showing illustrative embodiments of the present disclosure, in which: 
         FIG. 1  is a graph of an exemplary performance of a wavelength-stepped source and a block diagram associated therewith; 
         FIG. 2  is a diagram of a conventional wavelength stepped source; 
         FIG. 3  is a block diagram of an exemplary optically sub-sampled OFDI system arrangement according one exemplary embodiment of the present disclosure; 
         FIG. 4  is a graph of an exemplary use of subsampling to down-convert signals over a large frequency range to a more limited baseband frequency range that can be described by a smaller volume of acquired data, according to one exemplary embodiment of the present disclosure; 
         FIG. 5  is a set of exemplary images generated by exemplary optical subsampling so as to image a sample over a large depth extent by measuring a sub-sampled image and then using the wrapping properties of the image in the sub-sampled image along with a surface finding routing to unwrap the acquired sample according to an exemplary embodiment of the present disclosure; 
         FIG. 6  is a diagram illustrating exemplary characteristics of an optical comb source used to perform optical subsampling in SD-OCT (along with a block diagram associated therewith) in accordance with an exemplary embodiment; 
         FIG. 7  a block diagram of an exemplary embodiment of an arrangement of a spectrometer according to the present disclosure which can facilitate mapping(s) of each of the discrete wavenumber channels of a optical comb source to a unique pixel on a camera, enabling optical subsampling in SD-OCT; and 
         FIG. 8  is a set of drawings including a block diagram of an exemplary embodiment and use according to the present disclosure of exemplary sub-sampled OFDI techniques and/or exemplary sub-sampled SD-OCT techniques to increase the acquired depth range in an endoscopic application in a data efficient manner, and exemplary images associated therewith. 
     
    
    
     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 disclosure 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 exemplary embodiments without departing from the true scope and spirit of the subject disclosure as defined by the appended claims. 
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     In one exemplary embodiment of the present disclosure, an imaging system can be provided that can be based on optical frequency domain imaging (“OFDI”) technique(s), and which can utilize, e.g., a wavelength-stepped source. For example, unlike conventional OCT systems that generally utilize wavelength-swept sources, whereas the source wavelength varies substantially continuously with time, exemplary embodiment of the imaging system according to the present disclosure can use a wavelength-stepped source which can have a wavelength that varies in a stepwise fashion, e.g., with discrete jumps in wavelength separating periods where the wavelength may be substantially constant. 
       FIG. 1  illustrates an exemplary graph of an exemplary output wavenumber as a function of time of an exemplary wavelength-stepped source  100  in accordance with an exemplary embodiment of the present disclosure. This exemplary source  100  can provide an optical output  110  (e.g., laser light) that may be time-varying in wavenumber. An exemplary graph of a wavenumber  132  versus time  131  trace is illustrated in a graph  130  of  FIG. 1 . For example, the trace can be characterized by periods of stability (i.e., periods  133   a - 133   f ) in the k of the laser, separated by periods during which the source wavenumber is rapidly switching  135   a - 135   f.  The step size in wavenumber-space can be provided as Δk  134 . Each of the stable periods  133   a - 133   f  can define a wavenumber value k_a to k_f ( 137   a - 137   f ) for a specific channel of the source. 
     The graph  130  illustrates, e.g., 6 exemplary channels, which can be a subset of the total channel count of the source  100 . It should be understood that other number of channels can be provided. The output power of the source  100  can be configured to provide appreciable power in each of the channels. For example, the power trace can be flat as a function of wavelength, can vary according to, e.g., the spectral response of the gain medium used in the source  10 , and/or can be made to follow a particular (e.g., predetermined) profile. 
       FIG. 2  shows a diagram of a conventional wavelength-stepped source. This conventional source can include a fiber laser cavity  220  containing a linear array of fiber Bragg gratings (FBGs)  230 , a booster optical amplifier  210 , and an output coupler  240 . The BOA  210  can be modulated with a particular waveform generated by an arbitrary waveform generator (AWG)  200 . Each FGB  230  can define a wavelength channel of the system. A multi-channel pulse can propagate through the BOA  210  in one direction, and may be converted upon a reflection from the FBGs  230  to a pulse train with each pulse having a particular wavelength defined by the FBGs  230 . Such pulse train can be amplified upon traveling in the opposite direction through the BOA  210 , and may be reconstituted into a single pulse by reflection from the FBG  230  array from the opposite direction. The output coupler  250  can select a portion of the pulse train, providing a wavelength-stepped source. 
     In one exemplary embodiment of the present disclosure which is shown as a block diagram in  FIG. 3 , an exemplary wavelength-stepped source  300  can provide at least one electro-magnetic radiation (e.g., light) which can be divided into a reference arm  310  and a sample arm  320  by an optical splitter  305 . The electro-magnetic radiation (e.g., the light) in the reference arm can be directed to a first port  340   a  of a complex demodulator  340 . The electro-magnetic radiation (e.g., the light) in the sample arm  320  can be directed to and collected from a sample  350 . This exemplary procedure can be accomplished by, e.g., directing the sample arm  320  electro-magnetic radiation to a first port  330   a  of an optical circulator which can direct such electro-magnetic radiation (e.g., light) preferentially to a second port  330   b.  The electro-magnetic radiation from the second port  330   b  can be directed by an optical fiber  335  toward the sample  350 . The optical fiber  335  can include various probes, catheters, endoscopes, and microscopes, which are known in the art for controlling the location and other characteristics of the sample arm light on the sample  350 . The backscattered electro-magnetic radiation (e.g., light) from the sample  350  can be collected by the fiber  335 , and returned to the second port  330   b  of the circulator  330 , and preferentially directed to a third port  330   c.  This electro-magnetic radiation (e.g., light) can then be directed to the second port  340   b  of the complex demodulator  340 . 
     The exemplary complex demodulator  340  can include, e.g., optical components, digitizers, and digital processing components and arrangements. The complex demodulator  340  can be configured to measure for each wavenumber channel signals that can be associated with the interference between the reference arm  310  and the sample arm  320 . For example, the complex demodulator  340  can be configured to provide, corresponding to each wavenumber channel, a complex signal S  370 , which is proportional to complex reflected sample field,
 
 S   i ∝√{square root over ( P ( k   i ))} e   (√{square root over (−1)})θ(k     i     )    Eq. 1
 
where P(k i  ) is the reflected signal power can correspond to wavenumber k i  and θ(k i ) may be the phase difference between the reference arm light and reflected sample light corresponding to wavenumber k i . The complex signal S  370  can be forwarded to the data processing and recording arrangement  360 . Such data processing and recording arrangement can include one or more processor(s) (e.g., microprocessor(s)), and computer-accessible medium (e.g., hard drives, memory sticks, floppy disks, RAM, ROM, etc.) which can store data and software thereon to execute certain procedures using such one or more processor(s) when such software is obtained from the computer accessible medium.
 
     In one exemplary embodiment of the present disclosure, the complex demodulator  340  can be based on a polarization-based demodulation, as described in Vakoc, Optics Letters 31(3), pp. 362-364 (2006) and U.S. Patent Publication No. 2007/0035743. In another exemplary embodiment of the present disclosure, a phase modulator can be placed in either the reference arm  310  or the sample arm  320 . The exemplary phase modulator can be configured to induce a phase shift of π/2 radians or 0 radians such that two measurements can be made at each of these phase shifts for each wavenumber channel. This can provide, e.g., time-multiplexed in-phase and quadrature signals preferable to construct the complex signal S  370 . In yet another exemplary embodiment of the present disclosure, the complex demodulator  340  can based on the use of a 3×3 coupler, e.g., as described in Choma, Optics Letters 28(22), pp. 2162-2164. 
       FIG. 4  illustrates a graph associated with a frequency conversion that can occur by subsampling the interference at the discrete wavenumbers ki in accordance with an exemplary embodiment of the present disclosure. An exemplary frequency of the complex signal S  370  shown in  FIG. 3  can be plotted as a function of delay between the sample arm  320  and the reference arm  310 . For example, the solid curve  400  shown  FIG. 4  illustrates an exemplary frequency for a continuously swept wavelength source, while a dashed curve  410  indicates the measured frequency using optical subsampling at wavenumbers ki. In an exemplary frequency range centered at zero delay  440 , no conversion may be induced. 
     At exemplary frequency ranges corresponding to larger magnitudes of delay, frequencies can be down-converted to a baseband signal. For example, the frequencies in the delay range  420 , which appear between +F/5 and +3*F/5 when using a wavelength-swept source, can be down-sampled (e.g., to a delay range  410 ) to the range −F/5 to F/5 using optical subsampling. Further, the frequencies in the delay range  450  can be up-sampled (e.g., in a delay range  460 ) again to the range of −F/5 to F/5. By detecting, e.g., only the limited frequency range from −F/5 to F/5, signals over the full depth characterized by −2.5 ΔT to 2.5 ΔT can be acquired with reduced data volume. 
     In the exemplary embodiment described herein, the data processing and data storage arrangement  360  shown in  FIG. 4  (e.g., which can include a computer-accessible medium as described above, a processor, a multitude thereof, etc.) can generate a scattering profile in depth from each of the acquired complex signal arrays Si according to exemplary approaches utilizing discrete Fourier transforms, which are known in the art. These exemplary profiles can be concatenated to generate exemplary images.  FIG. 5  illustrates an exemplary procedure and subimages for a generation of an exemplary sub-sampled image resulting from the sample  350  that can span an extent greater the depth range of the sub-sampled image. 
     Turning to a sample that is arranged at an angle as depicted in an image  600 , e.g., the exemplary image of this sample can be acquired with an OFDI system using a complex demodulation technique, and without a subsampling technique. For example, by discarding at least some of the sampled datapoints within each A-line, a sub-sampled image can be generated as shown in the exemplary image  610  of  FIG. 5 . The image depth range can be significantly reduced, and signals occurring outside the baseband can be down-converted to appear within this reduced depth range. By tiling this exemplary image  610 , e.g., concatenating copies of the image vertically to provide a tiled subsampled image  620 , it is possible to recognize the original structure. Using a surface-finding procedure, a single representation of the object can be isolated from the duplicate representations  630 , recovering the actual image of the sample. The exemplary imaging results can be effectively achieved over a range sufficient to encompass the tilted sample, e.g., with at a reduced data volume corresponding to the depth range depicted in the exemplary subsampled image  610 . 
     In an another exemplary embodiment of the present disclosure, optical subsampling can be achieved using exemplary SD-OCT systems and methods by utilizing an optical comb source  700  shown in  FIG. 6 , which can have an output  710  that comprises a series of narrow lines arranged at discrete wavenumbers  720 .  FIG. 7  shows a block diagram of an exemplary embodiment of an arrangement/system according to the present disclosure which can comprise a spectrometer such that each of wavenumber channels  820   a - 820   e  of an interferometric signal output  800  obtained using SD-OCT technique(s) can be diffracted from a grating  810 , and each of the channels  820   a - 820   e  can be mapped to a unique pixel  830   a - 830   e  of a one- or two-dimensional camera  825  (which can include an LCD camera which can include or be connected to one or more processors and/or computer accessible medium (that can store software thereof that can configure the processor(s) to perform the indicated technique as described herein). Thus, it is possible to utilize such processor(s) such that the information regarding each pixel can be used to measure the signal from one wavenumber channel  820   a - 820   e.  Alternatively or in addition, a broadband source can be used in conjunctions with a periodic filter, such a Fabry-Perot transmission filter, which can be placed between the source and the grating  810  to generate the channelized electro-magnetic radiation (e.g., light). 
     An exemplary use of sub-sampled optical imaging to increase the effective depth range is illustrated in  FIG. 8 . For example, an exemplary imaging arrangement  900  shown in  FIG. 9  can comprise an endoscope  901  that can convey the imaging electro-magnetic radiation (e.g., light) from an imaging system  902  to a sample  910 , and the backscattered light returns to such imaging system  902 . The endoscope  901  can include or be made using a single bidirectional waveguide such as an optical fiber, or alternatively can include or be made using a pair of waveguides, e.g., one that propagates the electro-magnetic radiation (e.g., light) from the imaging system  902  to the sample  910 , and another that returns scattered or reflected electro-magnetic radiation (e.g., light) from the sample  910  to the imaging system  902 . The endoscope  901  can include, e.g., near its distal tip, a beam scanner  940  that can be configured to scan an exemplary angle  930  of the electro-magnetic radiation (e.g., light) exiting the endoscope  901 . The beam scanner  940  can be based on a micro-electromechanical scanner, e.g., as described in Kim, et. al, Opt. Express 15, pp. 18130-18140 (2007). 
     For the sample  910  oriented at an angle to the endoscope  901 , the distance from the beam scanner  940  to a surface of the sample  910  for one angle may be relatively shorter, for example, d 1    920   a,  while for another angle relatively longer, for example d 2    920   b.  Using conventional OCT or OFDI techniques, the imaging system  902  can be configured to acquire data over the full depth range (d 2 −d 1 +δ), where the parameter δ  922  describes the imaging depth into the sample  910 . 
     A conventional OCT procession of the image  950  generated by the OFDI technique can be established as a function of a depth  921  and an angle  923 . The exemplary image can occupy a depth range provided by d 2 −d 1 +δ. Acquiring data over such large area in a short time can utilize fast digitization and data transmission capabilities. For example, the acquisition can be inefficient in that large areas of the acquired image may have no information content either above the tissue surface  933   a  or a depth greater than δ below the tissue surface  933   b.  The use of sub-sampled optical frequency domain imaging or sub-sampled SD-OCT procedure(s) can facilitate an acquisition of the same or similar information content and with a greater efficiency. 
     In an exemplary illustration  960 , a sub-sampled OFDI image is shown in  FIG. 8  as a function of a depth  961  and an angle  964 . This exemplary imaging system can provide an imaging range of δ  962 . Such exemplary imaging range does not have to be greater than the imaging penetration depth into the sample, and can alternatively be less if information is desired over a more shallow region. The wrapping properties of sub-sampled imaging can facilitate the capture of information from the superficial depth δ of the sample at all angles. Furthermore, imaging acquisition bandwidth does not have to be dedicated to the empty space above the tissue surface, or below the imaging penetration into the tissue. 
     It is possible to locate the tissue surface as provided in a surface portion  970  of an exemplary image using surface-finding procedures, including, e.g., snake procedures)—see, e.g., Yezzi, et. al., IEEE Tran Med Imag 16,2; pp. 199-209 (1997), and to unwrap the image to generate an image where the tissue is shown with a surface that is approximately constant in a depth  990 . 
     The foregoing merely illustrates the principles of the present disclosure. Various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein. For example, more than one of the described exemplary arrangements, radiations and/or systems can be implemented to implement the exemplary embodiments of the present disclosure Indeed, the arrangements, systems and methods according to the exemplary embodiments of the present invention can be used with and/or implement any OCT system, OFDI system, SD-OCT system or other imaging systems, and for example with those described in International Patent Application PCT/US2004/029148 filed Sep. 8, 2004 (which published as International Patent Publication No. WO 2005/047813 on May 26, 2005), U.S. patent application Ser. No. 11/266,779 filed Nov. 2, 2005 (which published as U.S. Patent Publication No. 2006/0093276 on May 4, 2006), U.S. patent application Ser. No. 10/861,179 filed Jun. 4, 2004, U.S. patent application Ser. No. 10/501,276 filed Jul. 9, 2004 (which published as U.S. Patent Publication No. 2005/0018201 on Jan. 27, 2005), U.S. patent application Ser. No. 11/445,990 filed Jun. 1, 2006, International Patent Application PCT/US2007/066017 filed Apr. 5, 2007, and U.S. patent application Ser. No. 11/502,330 filed Aug. 9, 2006, 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 present disclosure and are thus within the spirit and scope of the present disclosure. 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.