Abstract:
Systems and methods according to exemplary embodiments of the present disclosure can be provided that can efficiently detect the amplitude and phase of a spectral modulation. Such exemplary scheme can be combined with self-interference fluorescence to facilitate a highly sensitive depth localization of self-interfering radiation generated within a sample. The exemplary system and method can facilitate a scan-free depth sensitivity within the focal depth range for microscopy, endoscopy and nanoscopy.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
       [0001]    The present application relates to and claims priority from U.S. Patent Application Ser. No. 61/822,669 filed May 13, 2013, the entire disclosure of which is incorporated herein by reference. 
     
    
     FIELD OF THE DISCLOSURE 
       [0002]    The present disclosure relates obtaining information regarding a sample, and more particular to system and method for an efficient detection of a phase and an amplitude of a periodic modulation associated with a self-interfering fluorescence. 
       BACKGROUND INFORMATION 
       [0003]    Self-Interference Fluorescence Microscopy (SIFM) is a technique that facilitates depth sensitive and lateral position sensitive fluorescence detection in epi-illuminated confocal microscopy without the need for depth scanning [see, e.g., M. De Groot et al. “Self-interference fluorescence microscopy: three dimensional fluorescence imaging without depth scanning,” Optics Express, 20, 15253 (2012) and C. L. Evans et al., U.S. Pat. No. 8,040,608]. This technique can use a phase plate that converts the wavefront curvature in the back-focal plane of the imaging system into a spectral modulation by via a self-interference. For example, an amplitude modulation on an electromagnetic spectrum that is periodic in the wavenumber domain can be considered as a spectral modulation. 
         [0004]    SIFM makes it possible to detect the depth location or lateral position of an emitter with localization error much smaller than the Rayleigh length or the beam diameter, respectively, of the imaging beam or even the wavelength of the detected light. 
         [0005]    In the context of biomedical imaging, an efficient implementation of SIFM can facilitate imaging of, for example, near-infrared labeled monoclonal antibodies for tumor detection. The depth sensitivity can strengthen the diagnostic potential with respect to standard confocal microscopy for example by allowing more effective staging of tumors. 
         [0006]    In the context of, e.g., single molecule biophysics, an efficient SIFM implementation can facilitate the three-dimensional tracking of particles with nanometer sensitivity. 
         [0007]    Previously, the spectral modulation that includes the SIFM signal has been detected with traditional spectrometers that (i) disperse the spectrum in space according to wavelength and (ii) detect the various wavelength components with a large number of detector elements. Although this configuration can facilitate the characterization of the phase and amplitude of the spectral modulation, the use of a spectrometer with numerous detector elements may not be optimal in terms of speed, efficiency and sensitivity. 
         [0008]    Traditionally most methods can make use of either spatially or temporally encoded detection of the spectrum with a spectrometer [see, for example A. F. Fercher et al. “Measurement of intraocular distances by backscattering spectral interferometry,” Optical Communications 117, 43 (1995)] or swept-source respectively [see, for example, S. H. Yun et al. “High-speed optical frequency-domain imaging,” Optics Express 11, 2953 (2003)]. Other methods that have been proposed, based on a conversion of a broad-band pulse to a time-domain chirp, can also detect the full spectrum at high sampling density [see, for example Y. Tong et al. “Fibre dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electronics Letters, 33, 983 (1997), P. V. Kelkar et al. “Time-domain optical sensing,” Electronics Letters 35, 1661 (1999) and J. Chou et al. “Time-wavelength spectroscopy for chemical sensing,” IEEE Photonics Technology Letters 16, 1140 (2004)] 
         [0009]    There may be a need to overcome at least some of the deficiencies and/or issues associated with the conventional arrangements and methods described above. 
       SUMMARY OF EXEMPLARY EMBODIMENTS 
       [0010]    To address and/or overcome such deficiencies and/or issues, exemplary embodiments of the system and method for an efficient detection of a phase and amplitude of a periodic modulation associated with a self-interfering fluorescence according to the present disclosure can be provided. 
         [0011]    The exemplary system and method according to the exemplary embodiments of the present disclosure as described herein are certainly not limited to light from a fluorescent source. Indeed, such exemplary system and method can be applied in all cases where it is desirable to determine the amplitude and/or phase of the spectral modulation on an electromagnetic spectrum. For example, such exemplary application can include, but is not limited to, Optical Coherence Phase Microscopy [see, for example C. Joo et al. “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Optics Letters, 30, 2131 (2005) and M. A. Choma “Spectral-domain phase microscopy,” Optics Letters, 30, 1162 (2005)], Doppler Optical Coherence Tomography (OCT) [see, for example X. J. Wang et al. “Characterization of fluid flow velocity by optical Doppler tomography,” Optics Letters, 20, 1337 (1995) and B. Braaf et al. “Angiography of the retina and the choroid with phase-resolved. OCT using interval-optimized backstitched B-scans”, Optics Express, 20, 20516 (2012)]] and transverse scanning OCT [see, for example M. Pircher et al. “Transversal phase resolved polarization sensitive optical coherence tomography,” Physics in Medicine and Biology, 49, 1257 (2004)] 
         [0012]    In general, according to certain exemplary embodiments of the present disclosure, the exemplary system and method can facilitate the phase detection of the spectral modulation using, e.g., a two-stage interferometer with properly tuned optical path delays. A beam carrying the spectrum of interest can be split into two or more beams using a beam splitting element/arrangement. These beams can then be recombined at either a second beam splitting element/arrangement or at the same beam splitting element/arrangement after travelling different optical paths. Such exemplary configuration describes a first stage of the interferometer. For an input beam with a smooth un-modulated spectrum, this transport of the beam(s) can lead to two output spectra with a spectral modulation frequency and phase that can be characteristic for an optical path length difference (OPD 1 ). The phase of one of the output spectra can be shifted by, e.g., about 180 degrees with respect to the phase of the other spectrum. The two-output beams from the first stage can then be transmitted/provided into the two input ports of the second stage including a three way beam splitter assembly/arrangement with a specifically tuned second optical path difference (OPD 2 ) leading to three output beams carrying spectra with spectral modulations that are shifted in phase by, for instance, about 0, 120 and 240 degrees, respectively. When the input beam/radiation carries a spectrum with a spectral modulation, and the path length difference OPD 1  of the first stage is tuned to match the frequency of this spectral modulation, the phase of the modulation can be determined by comparing the spectrally integrated total intensities of the three output beams. 
         [0013]    According to one exemplary embodiment of the present disclosure, the three way beam splitter assembly of the second stage described above can be constructed by combining a 33/67 beam splitter with two 50/50 beam splitters. The input beams impinge on the first 50/50 beam splitter that allows half of the light (three sixths) to travel to a 33/67 beam splitter that transmits two thirds of the light (two sixths of the total power, this is output beam one). The other three sixths from the first 50/50 beam splitter is recombined with the one sixths reflected by the 33/66 beam splitter at the second 50/50 beam splitter leading to two more output beams (two and three) each containing two sixths of the power like output beam one. 
         [0014]    According to another exemplary embodiment of the present disclosure, the three way beam splitter assembly of the second stage described above can be constructed from a 3×3 all fiber 33/33/33 coupler as described in e.g. Mi. A. Choma et al. “System and method for low coherence broadband quadrature interferometry”; U.S. Pat. No. 7,019,838; M. A. Choma et al. “Instantaneous quadrature low-coherence interferometry with 3×3×3 fiber-optic couplers,” Optics Letters 28, 2162 (2003); and L. K. Cheng, et al. “Alternative fringe sensor for DARWIN mission,” Proceedings of SPIE 5905 59051E-1 (2005). 
         [0015]    According to still another exemplary embodiment of the present disclosure, it is possible to provide the second stage three way beam splitter assembly described above as a monolithic prism as described in references [Hess, U.S. Pat. No. 7,916,304 B2 and G. Shtengel “Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure,” PNAS 106, 3125 (2009)]. 
         [0016]    In still another exemplary embodiment of the present disclosure, not only the second stage, but also the first stage of the interferometer can be produced and/or constructed from the optical fiber. In this case the first stage consists of two 2×2 50/50 fiber couplers that are linked in series the light from the input port being split at the first 2×2 coupler into two arms of different optical length that are recombined at the second 2×2 50/50 coupler. 
         [0017]    According to a further exemplary embodiment of the present disclosure, the amplitude and phase of the spectral modulation on the input spectrum can be determined by treating the measured intensities at the three outputs of the two stage interferometer as three samples of a signal. Transforming this signal with a simple discrete Fourier transform (DFT) gives the required amplitude and phase in a complex representation as either the second or the third sample in the DFT (these carry the same information since they are complex conjugates of one another). 
         [0018]    In yet another exemplary embodiment of the present disclosure, the modulated spectrum may be obtained from a beam or sample scanning microscope equipped with a phase plate for self-interference fluorescence microscopy as described in [M. De Groot et al. “Self-interference fluorescence microscopy: three dimensional fluorescence imaging without depth scanning,” Optics Express, 20, 15253 (2012) and C. L. Evans et al, U.S. Pat. No. 8,040,608 B2]. The excitation and emission beam paths may be separated by a beam splitter or a dichroic mirror. 
         [0019]    According to still another exemplary embodiment of the present disclosure, the excitation beam may be combined with a second beam which may be shaped with a phase plate or other optical element for super resolution imaging by depletion or state-switching [see, for example, S. Hell et al. “Breaking the diffraction resolution limit by stimulated-emission—stimulated-emission-depletion fluorescence microscopy,” Optics Letters 19, 495 (1995) and M. Hofmann et al. “Breaking the diffraction barrier in fluorescence microscopy at low light intensities by using reversibly photoswitchable proteins,” Proceedings of the National Academy of Sciences of the United States of America 102, 17565 (2005)]. The shaped second beam provides increased lateral resolution while a phase plate for self-interference fluorescence microscopy in the emission path provides axial depth localization. 
         [0020]    In yet a further exemplary embodiment of the present disclosure, the modulated spectrum can be obtained from a catheter or endoscopic device using a single optical fiber for light delivery and collection, an optional spacer, a gradient index (GRIN) lens for focusing, a miniature phase plate, a mirror to deflect the beam, and/or a micromechanical motor to move the mirror and scan the beam over the sample. 
         [0021]    According to yet another exemplary embodiment of the present disclosure, the catheter or endoscopic device can utilize a first GRIN lens to collimate the imaging beam before the phase plate and a second GRIN lens to focus it after the phase plate. 
         [0022]    In accordance with still another exemplary embodiment of the present disclosure, the excitation light/radiation can be delivered with a first optical fiber, while the fluorescence can be detected via a second optical fiber. 
         [0023]    According to a further exemplary embodiment of the present disclosure, the fiber for delivery and detection can be scanned laterally, and the fiber tip can be relayed with an optical system in order to scan the beam across the sample. 
         [0024]    In yet a further another exemplary embodiment of the present disclosure, the fluorescence source can be a targeted fluorescent label, including, for example, a near-infrared labelled monoclonal antibody. 
         [0025]    Various other exemplary phase plate and pin hole configurations that can be used for SIFM have been described in U.S. Pat. No. 8,040,608, the disclosure of which is incorporated herein by reference in their entireties. 
         [0026]    Thus, exemplary apparatus and/or method can be provided using which, it is possible to provide information associated with an electromagnetic radiation of interest. For example, at least one electro-magnetic radiation received can be split into a plurality of radiations, one of the radiations having a spectral modulation with a phase that is different from the spectral phase of another of the radiations. Further, it is possible to detect the radiations and generate information regarding the spectral modulation of the at least one electro-magnetic radiation. 
         [0027]    According to another exemplary embodiment, it is possible to provide system, method and computer accessible medium, in which data associated with an electro-magnetic radiation is obtained, and the information regarding the spectral modulation of the electro-magnetic radiation is generated. 
         [0028]    Thus, according to an exemplary embodiment of the present disclosure, exemplary apparatus and method can be provided to obtain at least one electro-magnetic radiation from at least one portion of a sample. For example, with at least one optical first arrangement, it is possible to receive the electro-magnetic radiation(s) from the portion(s), and generate at least one first radiation based on the electro-magnetic radiation(s). The electro-magnetic radiation(s) can be separated and recombined to be self-interfered after exiting the portion (s). In addition, with at least one interference second arrangement, it is possible to receive and further separate and recombine the first radiation so as to further self-interfere and generate at least one second radiation. Further, with at least one computer third arrangement, it is possible to determine information regarding the portion(s) based on the second radiation(s). 
         [0029]    For example, a path-length difference of the separated and recombined electro-magnetic radiation(s) can be substantially the same as a path-length difference of the separated and recombined first radiation. With the second arrangement, it is possible to generate a plurality of second radiations. Using at least one detector fourth arrangement, it is possible to detect at least one particular radiation of the second radiations. Using at least one combiner fifth arrangement, it is possible to recombine at least two of the second radiations to generate a plurality of self-interfered third radiations. With at least one detector sixth arrangement, it is possible to detect the third radiations. Using the third arrangement, it is possible to generate Fourier-transform data associated with the at least one particular radiation and the third radiations into transformed data, whereas the transformed data is indicative of amplitude and phase of the self-interfered first radiation. The second and fifth arrangements can be optical fiber arrangements. 
         [0030]    In a further exemplary embodiment of the present disclosure, the information can include data regarding a position of a source of the electro-magnetic radiation(s) provided from the portion(s) of the sample. The first arrangement(s) can be a catheter arrangement, and/or can include a phase-plate which introduces a path-length difference between portions of the separated and recombined electro-magnetic radiation so as to produce the self-interfered first radiation. In addition, with at least one radiation-providing arrangement, it is possible to provide a particular radiation having characteristics to excite at least one fluorophore within the portion(s) so as to cause the electro-magnetic radiation(s) to be provided from the portion(s). 
         [0031]    These and other objects, features and advantages of the present disclosure will become apparent upon reading the following detailed description of embodiments of the present disclosure, when taken in conjunction with the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]    Further objects, features and advantages of the present disclosure will become apparent from the following detailed description taken in conjunction with the accompanying figures showing illustrative embodiments of the present disclosure, in which: 
           [0033]      FIG. 1  is an exemplary graph illustrating a typical self-interference spectrum to explain a spectral modulation; 
           [0034]      FIG. 2  is an exemplary graph illustrating a dependence of a phase of the self-interference spectrum on the axial position with respect to the focal plane of the objective of a thin emitting layer, whereas each data point in the graph represents the mean phase calculated from 1024 recorded spectra, the error bars indicate ±1 standard deviation, the imaging NA for this measurement was 0.086 and the Rayleigh length zR was 128 μm, and a linear fit of the central section between −2 and 2 zR yields a slope dφ/dz=−1.31 rad/zR; 
           [0035]      FIG. 3  is an exemplary graph illustrating a dependence of the standard deviation of a phase measurement on the signal to noise ratio, whereas the dots are the measured standard deviations of 1024 phase measurements, and the solid line is the theoretical curve σ φ =1/√{square root over ( 2 )}·SNR; 
           [0036]      FIGS. 4(   a )- 4 ( e ) are a set of illustrations of a comparison of SIFM and confocal microscopy on a three-dimensional distribution of fluorescent microspheres; 
           [0037]      FIG. 5  is an exemplary SIFM image of microvasculature in a mouse heart, whereas the image represents a 500×500×60 μm volume of tissue, starting at 15 μm below the tissue surface, the depth of the vessels is grayscale/color-coded, and the deepest layers are displayed in violet and the top layers are displayed in a bright shade; 
           [0038]      FIG. 6  is an exemplary SIFM image of 100 nm fluorescent beads in agarose gel, whereas the data represents a 40×40×2 μm volume and the grayscale/color coding shows the detected depth; 
           [0039]      FIG. 7  is a diagram of a first exemplary embodiment of a system with a free space two-stage interferometer configuration according to the present disclosure. 
           [0040]      FIG. 8  is a diagram of a second exemplary embodiment of a fiber based two-stage interferometer in accordance with the present disclosure. 
           [0041]      FIG. 9  is a diagram of a third exemplary embodiment of a fiber based two-stage interferometer in accordance with the present disclosure implemented with a 3×3 fiber coupler as the second stage. 
           [0042]      FIG. 10(   a ) is a graph of a simulated detector response for the three output channels of a two-stage interferometer according to the exemplary embodiment shown in  FIG. 1  as a function of the phase of the spectral modulation of the input spectrum; 
           [0043]      FIG. 10(   b ) is a graph of the phase information that is obtained from the information of  FIG. 10(   a ) via a discrete Fourier transform; 
           [0044]    In particular,  FIG. 11  shows the detector response (in counts per second) and the defocus (in micrometer) applied to the microscope sample stage as a function of time applying the exemplary system and method according to the exemplary embodiments of the present disclosure; 
           [0045]      FIG. 12  is a graph providing similar or same results as shown in  FIG. 11  and instead of an absolute intensity, an exemplary fractional contribution of each channel to the total intensity is shown in order to take out the effect of the confocal point spread function on the signal intensity; 
           [0046]      FIG. 13  a graph of the phase obtained by taking the discrete Fourier transform of the normalized channel data from  FIG. 12  and applying the exemplary system and method according to the exemplary embodiments of the present disclosure; 
           [0047]      FIG. 14  is a diagram of an exemplary embodiment of the apparatus and system according to an exemplary embodiment of the present disclosure that uses a laser scanning microscope, including a phase plate, to collect the modulated SIFM spectrum; 
           [0048]      FIG. 15  is a diagram of an exemplary embodiment of the apparatus and system according to an exemplary embodiment of the present disclosure that uses a STED microscope including a stimulated emission depletion beam in order to perform lateral super resolution imaging combined with SIFM depth localization; 
           [0049]      FIG. 16  is a diagram of an exemplary embodiment of the apparatus and system according to an exemplary embodiment of the present disclosure that uses a catheter or endoscopic device to collect the SIFM spectrum; 
           [0050]      FIG. 17  is a diagram of still another exemplary embodiment of the apparatus and system according to an exemplary embodiment of the present disclosure that uses two GRIN lenses in a catheter or endoscopic device to collect the SIFM spectrum; 
           [0051]      FIG. 18  is a diagram of yet another exemplary embodiment of the apparatus and system according to an exemplary embodiment of the present disclosure that uses two separate optical fibers for excitation and detection in a catheter or endoscopic device using to collect the SIFM spectrum; 
           [0052]      FIG. 19  is a diagram of an additional exemplary embodiment that scans the fiber for delivery and detection laterally and relays the fiber tip with an optical system to the sample in order to scan the beam across the sample. 
           [0053]      FIG. 20  is a diagram of a further exemplary embodiment of the apparatus and system according to an exemplary embodiment of the present disclosure that rotates the whole assembly of fiber and the imaging optics inside of the catheter sheet in order to scan the beam across the sample. 
       
    
    
       [0054]    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 embodiments without departing from the true scope and spirit of the subject disclosure. 
       DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0055]    Thus, detection system and method according to the exemplary embodiment of the present disclosure can be provided, where the phase of a spectral modulation on the spectrum of interest can be obtained with, e.g., only three single point detectors. In addition, the exemplary system according to the present disclosure can include different schemes for an implementation, as well as exemplary methods for processing such data. 
         [0056]      FIGS. 4(   a )- 4 ( e ) show a set of illustrations of a comparison of SIFM and confocal microscopy on a three-dimensional distribution of fluorescent microspheres. For example,  FIG. 4(   a ) illustrates an exemplary SIFM intensity image (100×100 μm), square ( 4 ) which can indicate that the area that was compared to a standard confocal stack.  FIG. 4(   b ) illustrates an exemplary SIFM phase image,  FIG. 4(   c ) illustrates an exemplary slice from the SIFM 3D reconstruction,  FIG. 4(   d ) illustrates a corresponding slice from a confocal stack, and FIG.  4 ( e ) shows exemplary SIFM and confocal slices overlapped, with SIFM data displayed in darker and confocal in lighter, and the lightest dots indicating an overlap of both datasets. 
         [0057]    In a system according to a first exemplary embodiment of the present disclosure, as shown in  FIG. 7 , light or other electro-magnetic radiation ( 10 ) from a measurement system can be optically processed by a two-stage interferometer to facilitate a determination of both phase and amplitude of a spectral modulation with just three single point detectors. In particular, an electromagnetic spectrum of the light/electro-magnetic radiation ( 10 ) can enter the system via a 50/50 beam splitter element ( 20 ), and can be partly reflected and partly transmitted. Such spectrum ( 10 ) can be transmitted via two mirrors ( 30 ), ( 40 ) through two variable retarders including rotatable plates ( 50 ), ( 60 ) onto a second 50/50 beam splitter ( 70 ). The retarders ( 50 ), ( 60 ) can be independently tuned to make it possible to match the optical path difference to the modulation frequency of the input spectrum. The beams/spectrum/radiations exiting the second beam splitter pass through two more variable retarders ( 80 ), ( 90 ) after which at least one beam is partially transmitted (e.g., about 67%) and partially reflected (e.g., about 33%) by a third beam splitter ( 100 ), while the other beam is transmitted to a the last 50/50 beam splitter ( 120 ) via a mirror ( 110 ). The beam/radiation reflected at the beam splitter  100  can be provided to the beam splitter  120 , as well. The three output beams can be provided onto detectors ( 130 ), ( 140 ), ( 150 ). 
         [0058]    As shown in  FIG. 8  which illustrates another system according to a second exemplary embodiment of the present disclosure, the spectrum of interest can be coupled into the two-stage interferometer via an optical fiber ( 160 ). A 50/50 2×2 fiber coupler ( 170 ) can couple the light/radiation into two different fibers, at least one of which can extend through a fiber stretcher ( 180 ) that can be used to match the optical path difference to the frequency of the spectral modulation on the input spectrum. The light/radiation can be recombined at a second 50/50 2×2 fiber coupler ( 190 ). The light/radiation exiting the 2×2 coupler ( 170 ) via two fibers then can pass through a 33/67 2×2 coupler ( 200 ) and another fiber stretcher ( 210 ), respectively, and can be (e.g., partially) recombined at the final 50/50 2×2 fiber coupler ( 220 ). The three output fibers can be connected to the detectors ( 130 ), ( 140 ), ( 150 ). The fiber stretchers ( 180 ), ( 210 ) can be used to tune the optical path lengths OPD 1  and OPD 2  to the correct value or the desired value. 
         [0059]    A first part of the system according to a third exemplary embodiment of the present disclosure is shown in  FIG. 9 , which can be substantially identical to the system according to the second exemplary embodiment, and instead of two 2×2 couplers ( 200 ), ( 220 ), a single 33/33/33 3×3 coupler can be used. 
         [0060]      FIG. 10(   a ) shows a graph of an exemplary simulated detector response for the three output channels of a two-stage interferometer according to the exemplary embodiment shown in  FIG. 1  as a function of the phase of the spectral modulation of the input spectrum.  FIG. 10(   b ) is a graph of the phase information that is obtained from the information of  FIG. 10(   a ) via a discrete Fourier transform. Thus,  FIGS. 10(   a ) and  10 ( b ) illustrate a simulation of the spectrally integrated detector signals provided by the exemplary system of the first exemplary embodiment of the present disclosure illustrated in  FIG. 7 , as the phase of the spectral modulation of the input spectrum is varied. For each input phase, e.g., the three detectors can contribute different ratios to the total signal. 
         [0061]    By treating these exemplary ratios as three samples in a short signal, the phase and amplitude of the modulation can be obtained in a complex representation as either the second or the third sample in the discrete Fourier transform of this signal (e.g., which can carry the same information since they are complex conjugates of one another). The calculation/determination of this complex number representing the amplitude and phase of the modulation can also be expressed as a sum of the three channels following multiplication of the channels signals by the three discrete complex exponentials 1, 
         [0000]    
       
         
           
             
               e 
               
                 - 
                 
                   
                     2 
                      
                     
                         
                     
                      
                     π 
                      
                     
                         
                     
                      
                     i 
                   
                   3 
                 
               
             
              
             
                 
             
              
             and 
              
             
                 
             
              
             
               e 
               
                 - 
                 
                   
                     4 
                      
                     
                         
                     
                      
                     π 
                      
                     
                         
                     
                      
                     i 
                   
                   3 
                 
               
             
           
         
       
     
         [0000]    respectively: 
         [0000]    
       
         
           
             z 
             = 
             
               
                 ∑ 
                 
                   k 
                   = 
                   0 
                 
                 2 
               
                
               
                   
               
                
               
                 
                   I 
                   k 
                 
                  
                 
                   e 
                   
                     - 
                     
                       
                         2 
                          
                         
                             
                         
                          
                         π 
                          
                         
                             
                         
                          
                         ik 
                       
                       3 
                     
                   
                 
               
             
           
         
       
     
         [0000]    where I k  is the relative intensity on channel k. The squared magnitude and phase can now be obtained by conversion of the complex number z to the polar representation. 
         [0062]      FIGS. 11-13  illustrate a set of exemplary graphs for applying the exemplary system and method according to the exemplary embodiments of the present disclosure to a depth sensitive fluorescence detection with Self Interference Fluorescence Microscopy, as described in, e.g., U.S. Pat. No. 8,040,608. 
         [0063]    For example, as shown in the graph of  FIG. 11 , the measured detector response (in counts per second) and the defocus (in micrometer) is applied to the microscope sample stage as a function of time. This measurement was obtained with a 20× objective from a thin layer of fluorescent dye (a 5 μl drop of a 25 μM LiCor IrDye-800CW solution with 0.1% bovine serum albumin in phosphate buffered saline between cover slips). The sample was scanned in depth by applying a voltage to the z-drive of a piezo-driven microscope stage. The amplitude of the modulation was 45 μm. The sample was excited with a 785 nm laser and the power at the sample was 10 μW. The signals were detected with a 4 channel photon counting module (Excelitas SPCM-AQ4C). The three channels were acquired in parallel at a sampling rate of 10 Hz. The sampling rate was limited by the speed of the piezo stage only, in principle much higher sampling rates of 1 MHz or more can easily be achieved. The spectral modulation on the input spectrum was induced using a coverslip with a 4 mm diameter hole positioned in the back-focal plane of the microscope objective, similar to the description provided in M. De Groot et al. “Self-interference fluorescence microscopy: three dimensional fluorescence imaging without depth scanning,” Optics Express, 20, 15253 (2012). 
         [0064]      FIG. 12  shows a graph providing the same or substantially the same results as provided  FIG. 11 . Further, instead of the absolute intensity, the fractional contribution of each channel to the total intensity is shown in order to take out the effect of the confocal point spread function on the signal intensity. For each time point provided in the illustration of  FIG. 6 , the sum of the signals of the three channels was calculated, and the signal of each channel was divided by this sum. This exemplary graph illustration of  FIG. 12  shows the phase differences in the signals for the three channels which is approximately 120 degrees. 
         [0065]      FIG. 13  shows a graph providing the phase obtained by taking the discrete Fourier transform of the normalized channel data from  FIG. 12  as described above. The phase can be unambiguously mapped to a certain depth. The phase response may not be completely linear, which is partly due to the imperfect balance between the three channels. This can be improved by better/further alignment and or post processing of the data if required) and partly this is a characteristic of Self-Interference Fluorescence Microscopy. Thus, as shown therein, the phase can be unambiguously mapped to a certain depth. 
         [0066]      FIG. 14  shows a diagram of the system according to a fourth exemplary embodiment of the present disclosure. For example, with the exemplary system illustrated in  FIG. 14 , the SIFM spectrum can be obtained via a laser scanning microscope. An excitation beam/radiation ( 330 ) can be deflected by a dichroic mirror ( 340 ) to an X,Y scanner ( 350 ). The beam/radiation can then be transmitted via a scan lens ( 360 ), a folding mirror ( 370 ), and a tube lens ( 380 ) to a microscope objective ( 390 ). The beam/radiation focused on the sample ( 320 ) can excite the fluorophores, and the emitted fluorescence can be collected and descanned in the opposite direction. The emission beam/radiation then passes the dichroic mirror, and is transmitted via a SIFM phase plate ( 280 ) and a lens ( 400 ) through a spatial filter ( 410 ) toward the detection interferometer. 
         [0067]    The system according to a fifth exemplary embodiment of the present disclosure is shown in  FIG. 15 . With this exemplary system, the SIFM spectrum can be obtained via a stimulated emission depletion microscope. For example, an excitation beam ( 330 ) can be deflected by a dichroic mirror ( 340 ). The beam/radiation can then be combined with a second beam ( 335 ) that passes through a phase plate ( 337 ) to create a donut beam for stimulated emission depletion. Both beams/radiations together can pass through an X,Y scanner ( 350 ), and may be transmitted via a scan lens ( 360 ) a folding mirror ( 370 ) and a tube lens ( 380 ) to a microscope objective ( 390 ). The two beams/radiations focused together onto the sample can induce fluorescence only from a spot smaller than the diffraction limit. The emitted fluorescence can be collected and descanned in the opposite direction. The emission beam/radiation can then pass the dichroic mirror, and may be transmitted via a SIFM phase plate ( 280 ) and a lens ( 400 ) through a spatial filter ( 410 ) towards the detection interferometer. 
         [0068]      FIG. 16  shows the system according to a sixth exemplary embodiment of the present disclosure. With this exemplary system of  FIG. 16 , the SIFM spectrum can be obtained via a catheter or endoscopic device. For example, a catheter housing ( 240 ) can host and/or include an optical fiber ( 250 ) that can be used both for excitation and detection. The optical fiber can be a standard single mode fiber or a multiclad fiber that provides light guidance both through the core and multiple claddings. The excitation light/radiation can be provided through the cladding or through the core. The detected fluorescence can be guided through the core to provide the SIFM signal, and the light guided through the claddings can provide additional information on the total fluorescence of the sample. An optional spacer ( 260 ) can facilitate the imaging beam/radiation exciting the fiber ( 320 ) to expand before it passes through a GRIN lens ( 270 ) and a SIFM phase plate ( 280 ). Thereafter, the beam/radiation can be deflected by a rotating mirror ( 290 ) mounted on a micromechanical motor ( 300 ). An end cap ( 310 ) can seal the catheter housing. 
         [0069]      FIG. 17  illustrates the system according to a seventh exemplary embodiment of the present disclosure. With this exemplary system, the SIFM spectrum can be obtained via a similar catheter or endoscopic device and instead of a single GRIN lens that focuses the beam/radiation, this exemplary system can use two GRIN lenses ( 270 ), ( 285 ) to focus the beam/radiation onto the sample which can provide a collimated beam at the SIFM phase plate ( 280 ). 
         [0070]      FIG. 18  shows the system according to an eighth exemplary embodiment of the present disclosure. With this exemplary system, the SIFM spectrum can be obtained via a similar catheter or endoscopic device, and instead of a single optical fiber, two separate fibers can be used for an excitation ( 285 ) and detection ( 280 ). This configuration uses, e.g., three GRIN lenses ( 270 ), ( 275 ), ( 285 ), and facilitates a separation according to the wavelength with two dichroic mirrors ( 282 ), ( 283 ). 
         [0071]      FIG. 19  illustrates the system according to a ninth exemplary embodiment of the present disclosure. With this exemplary system, the SIFM spectrum can be obtained via a catheter or endoscopic device similar to the exemplary system of the fifth exemplary embodiment, and instead of a rotating mirror that scans the beam/radiation across the sample, the fiber for delivery and detection ( 250 ) can be laterally scanned and relayed to the sample with an optical system consisting of two lenses ( 272 ), ( 315 ) in order to scan the beam/radiation across the sample. 
         [0072]      FIG. 20  shows the system according to a further exemplary embodiment of the present disclosure. With this exemplary system, the SIFM spectrum can be obtained via a catheter or endoscopic device similar to the exemplary system of the fifth exemplary embodiment described herein, and instead of a rotating mirror that scans the beam across the sample, the whole assembly of fiber and imaging optics can be rotated inside the stationary catheter housing to scan the beam/radiation across the sample. At least part of the assembly can include an optional spacer ( 287 ) and a polished ball lens ( 292 ) that can be used to deflect and focus the beam/radiation onto the sample. 
         [0073]    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. Indeed, the arrangements, systems and methods according to the exemplary embodiments of the present disclosure can be used with imaging systems, and for example with those described in U.S. Pat. No. 8,040,608, the disclosure of which is 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.