Abstract:
Exemplary apparatus and/or method can be provided using which, it is possible to provide information associated with at least one portion of a sample. For example, at least one electro-magnetic radiation received from the at least one portion of the sample can be separated into a plurality of first radiations, one of the first radiations having a phase delay that is different from a phase delay of another of the first radiations. In addition, at least one of the first radiations can be received and separated into second radiations according to wavelengths of the received at least one of the first radiations. Further, it is possible to detect the second radiations and generate information regarding a position of the at least one portion of the sample as a function of at least one characteristic of at least one interference of the first radiations. According to another exemplary embodiment, it is possible to provide system, method and computer accessible medium, in which data associated with first radiations can be obtained, and the information regarding a position of the at least one portion of the sample may be generated. Such information can be generated based on the data by separating second radiations associated with the portion(s) of the sample according to wavelengths of at least one of the second radiations. For example, one of the second radiations can have a phase delay that is different from a phase delay of another one of the second radiations, and the second radiations may be interfering.

Description:
CROSS-REFERENCE TO RELATED APPLICATION(S) 
       [0001]    The present invention relates to U.S. Provisional Application No. 60/969,396 filed Aug. 31, 2007, the entire disclosure of which is incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates to system and method for optical imaging and computer-accessible medium associated therewith. In particular, it is possible to utilize a light beam emitted from a sample, whereas the emitted light is passed through a spatial phase retarding optic to cause self-interference of the beam wherein the self-interference allows for high-resolution microscopic imaging. 
       BACKGROUND INFORMATION 
       [0003]    A number of optical methods have demonstrated microscopic resolutions beyond the diffraction limit. These methods, which all requiring fluorescent labeling, include Scanning Near-field Optical Microscopy (SNOM) (see I. Horsh et al. “A stand-alone scanning near-field optical microscope,” Photons and Local Probes, NATO ASI Series E:300:139 (1995)), Stimulated Emission Depletion (STED) (see S. Hell et al. “Breaking the diffraction resolution limit by stimulated-emission—stimulated-emission-depletion fluorescence microscopy,” Optics Letters. 19:495 (1995)) and Ground State Depletion (GSD) (see S. Hell et al. “Ground-State-Depletion fluorescence microscopy—a concept for breaking the diffraction resolution limit,” Applied Physics B. 60:780 (1994)) fluorescence microscopy, photo-activated localization microscopy (PALM) (see E. Betzig et al. “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313:1642 (2006)), stochastic optical reconstruction microscopy (STORM) (see M. Rust et al. “Sub-diffraction-limited imaging by stochastic optical reconstruction microscopy (STORM),” Nature Methods 3:783 (2006)), and structured illumination microscopy (SIM) (see B. Bailey et al. “Enhancement of Axial Resolution in Fluorescence Microscopy by Standing-Wave Excitation,” Nature 366:44 (1993); see M. Gustafsson “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” Journal of Microscopy 198:82 (2000); and see M. Gustafsson “Nonlinear structured illumination microscopy: Wide-field fluorescence imaging with theoretically unlimited resolution,” PNAS 102:13081 (2005)). In addition, it is possible to improve the position accuracy beyond the diffraction limit in linear fluorescence microscopy and two-photon microscopy (see W. Denk et al. “2-Photon Laser Scanning Fluorscence Microscopy,” Science 248:73 (1990)) by fitting the point spread function (see R. Thompson et al. “Precise nanometer localization analysis for individual fluorescent probes,” Biophysical Journal 82:2775 (2002)). 
         [0004]    Optical coherence tomography, Spectral Domain OCT and Optical Frequency Domain Imaging include certain imaging techniques that measure the interference between a reference beam of light and a detected beam reflected back from a sample. A detailed system description of traditional time-domain OCT has been described in D. Huang et al., “Optical Coherence Tomography,” Science 254: 1178 (1991). Exemplary detailed descriptions for spectral-domain OCT and optical frequency domain interferometry systems are provided in U.S. patent application Ser. Nos. 10/501,276 and 10/577,562, respectively. 
         [0005]    Another exemplary technique that can achieve resolution beyond the diffraction limit can be called self-interference fluorescence microscopy (SIFM). This exemplary technique is related to the work described in K. Drabe et al. “Localization of Spontaneous Emission in front of a mirror,” Optics Communications 73:91 (1989) and Swan et al. “Toward nanometer-scale resolution in fluorescence microscopy using spectral self-interference,” IEEE Quantum Electronics 9:294 (2003). It has been demonstrated that the position of a fluorophore located in front of a reflecting surface can be determined with nanometer resolution by analyzing the self-interference of the emitted fluorescence light with the reflection from the surface. The exemplary technique is related to Optical Coherence Phase Microscopy (OCPM), another technique derived from OCT (see C. Joo, et al. “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Optics Letters 30:2131 (2005); and see C. Joo, et al. “Spectral Domain optical coherence phase and multiphoton microscopy,” Optics Letters 32:623 (2007)), where the phase of the interference between a sample and a reference arm is used to determine motion on a (sub) nanometer length scale. 
         [0006]    In OCPM, an external light source is used, and the light is scattered by structures in tissue or within a cell. OCPM has demonstrated a phase sensitivity corresponding to 25 picometers. In SIFM, the light source is the fluorophore itself, which is excited by an excitation source. Fluorescent light emitted in different directions is captured and made to interfere with itself after passing through a spatial phase retarding optical element. The interference can be spectrally resolved in a spectrometer, generating an interference pattern with a periodicity corresponding to the path length differences experienced by the light traversing the phase retarding element. A Fourier transform of the spectrally resolved interference may generate a profile as in Spectral Domain Optical Coherence Tomography (SD-OCT), with a point spread function determined by the fluorescence bandwidth. By using the phase term of the transform, the fluorophore can be localized with a resolution far better than the diffraction limit. This exemplary approach generally makes use of a single microscope objective and a specially designed wave plate that collect the emitted light the epi-direction with a high numerical aperture and dividing the beam in 4 sections, each with different delays, for three-dimensional triangulation. 
         [0007]    There may be a need to overcome certain deficiencies associated with the conventional arrangements and methods described above. 
       SUMMARY OF EXEMPLARY EMBODIMENTS OF THE PRESENT INVENTION 
       [0008]    To address and/or overcome such deficiencies, exemplary embodiments of the present invention can be provided. 
         [0009]    In general, certain exemplary embodiments of the system and method according to the present invention can facilitate high-resolution imaging by collecting the emission of a fluorophore by a lens, collimating the light into a beam that is passed through a phase element that imparts multiple, distinct wavelength-dependent phase delays over the beam wavefront. This beam is then wavelength dispersed by a prism, a grating, or other dispersive element and focused onto a spectrometer. For example, when the individual wavelength components of the beam are focused to a point on the spectrometer, the phase-delayed components of their wave fronts interfere with each other, likely producing a wavelength-dependent, fluorescence self-interferogram. This self-interferogram can then be analyzed by way of a Fourier transform to extract sub-diffraction resolution information. The sub-diffraction limited information is contained in the relative phase, as may be determined from the complex Fourier component of the interference. 
         [0010]    According to one exemplary embodiment of the present invention, a full three-dimensional localization can be accomplished by utilizing infinity collimated objective lenses. In such optic, a fluorophore located at the axial center of the focal spot can give rise to a collimated beam at the objective back aperture. If the fluorophore is located above or below the axial center, the output beam can be slightly convergent or divergent, respectively. Based on an exemplary embodiment of the present invention, a phase plate can be provided with an additional phase delay segment in the center to convert path length changes caused by changes in divergence into axial fluorophore localization. 
         [0011]    Thus, exemplary apparatus and/or method can be provided using which, it is possible to provide information associated with at least one portion of a sample. For example, at least one electro-magnetic radiation received from the at least one portion of the sample can be separated into a plurality of first radiations, one of the first radiations having a phase delay that is different from a phase delay of another of the first radiations. In addition, at least one of the first radiations can be received and separated into second radiations according to wavelengths of the received at least one of the first radiations. Further, it is possible to detect the second radiations and generate information regarding a position of the at least one portion of the sample as a function of at least one characteristic of at least one interference of the first radiations. 
         [0012]    According to another exemplary embodiment of the present invention, the first radiations can be self-interfering. Further, it is possible to detect the second radiations and generate information regarding a position of the at least one portion of the sample as a function of at least one characteristic of the self-interference of the first radiations. The position information can include a lateral position and/or depth of the portion(s). The characteristic(s) can include a phase of the self-interference and/or an intensity of the self-interference, and the information may be generated based on a spectral modulation of the self-interference of the first radiations. 
         [0013]    According to still another exemplary embodiment of the present invention, it is possible to use at least two optical elements having optical thicknesses to effectuate a first path length difference between any of the at least two optical elements which is different from a second path length difference in any of other of the optical elements. An optical path length difference between any of the at least two optical elements can produce approximately an integer number of modulations of a spectrum of a self-interference of the first radiations. The integer number can be different for any combination of path length differences between the optical elements. It is also possible to provide an excitation radiation so as to generate the electro-magnetic radiation(s). Further, it is possible to receive the excitation radiation and provide radiation which is associated with different locations on the portion(s) of the sample based on the excitation radiation. 
         [0014]    According to a further exemplary embodiment of the present invention, the spatial filter can include a pin hole, an array of pin holes, a optical fiber and/or a fiber array. The optical fiber can be a single mode fiber, and the fiber array can include single mode fibers. It is also possible to provide radiation which is associated with different locations on the portion(s) of the sample. Such radiations can be provided using scanning mirrors. The electro-magnetic radiation(s) can include a plurality of radiations provided from a plurality of portions of the sample. Further, it is possible to detect a plurality of spectra of the second radiations associated with the plurality of portions of the sample. Further, the first radiations can be interfering. 
         [0015]    According to another exemplary embodiment, it is possible to provide system, method and computer accessible medium, in which data associated with first radiations is obtained, and the information regarding a position of the at least one portion of the sample is generated. Such information can be generated based on the data by separating second radiations associated with the portion(s) of the sample according to wavelengths of at least one of the second radiations. For example, one of the second radiations can have a phase delay that is different from a phase delay of another one of the second radiations, and the second radiations may be interfering. 
         [0016]    In still another exemplary embodiment, the second radiations can be self-interfering. The information can be generated by performing a Fourier transformation of the data. The Fourier transformation may be performed to generate at least one of a phase or an amplitude of at least one interference of the second radiations. For example, the information may be generated based on the phase and/or the amplitude of the interference(s) of the second radiations. Further, the information can include a position information of the one portion(s). 
         [0017]    These and other objects, features and advantages of the present invention will become apparent upon reading the following detailed description of embodiments of the invention, when taken in conjunction with the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]    Further objects, features and advantages of the invention will become apparent from the following detailed description taken in conjunction with the accompanying figures showing illustrative embodiments of the invention, in which: 
           [0019]      FIG. 1  is a diagram of a first exemplary embodiment of a system with a spectrometer configuration according to the present invention; 
           [0020]      FIG. 2  is a diagram of an exemplary embodiment of a phase plate ( 30 ) for two-dimensional imaging in accordance with the present invention; 
           [0021]      FIGS. 3(   a )- 3 ( d ) are exemplary diagram of an example of an interference profile from the exemplary embodiment of the phase plate shown in  FIG. 2 , illustrating interferogram pattern(s) resulting from the interference between segments; 
           [0022]      FIG. 4(   a ) is a diagram of an exemplary embodiment of a power spectrum profile resulting from a Fourier transform of the interferogram illustrated in  FIGS. 3(   a )- 3 ( d ) according to an exemplary application of the exemplary embodiment shown in  FIG. 1  and the exemplary embodiment of the phase plate shown in  FIG. 2 ; 
           [0023]      FIG. 4(   b ) is a diagram of an exemplary embodiment of a phase profile resulting from a Fourier transform of the interferogram illustrated in  FIGS. 3(   a )- 3 ( d ) according to an exemplary application of the exemplary embodiment shown in  FIG. 1  and the exemplary embodiment of the phase plate shown in  FIG. 2 ; 
           [0024]      FIG. 5(   a ) is a diagram of an exemplary embodiment of the system according to the present invention utilizing a fourth phase plate element to discern out-of-focus light using a four-part phase plate; 
           [0025]      FIG. 5(   b ) is a diagram of an exemplary embodiment of the system according to the present invention utilizing a fourth phase plate element to discern out-of-focus light to perform three-dimensional imaging; 
           [0026]      FIG. 6(   a ) is a graph of an exemplary interferogram from the exemplary embodiment shown in  FIGS. 5(   a ) and  5 ( b ); 
           [0027]      FIG. 6(   b ) is a graph of an exemplary power spectrum profile resulting from a Fourier transform of the interferogram shown in  FIG. 6(   a ); 
           [0028]      FIG. 6(   c ) is a graph of an exemplary phase profile resulting from a Fourier transform of the interferogram shown in  FIG. 6(   a ); 
           [0029]      FIG. 7  is a diagram of a third exemplary embodiment of the system according to the present invention; 
           [0030]      FIG. 8  is a diagram of a fourth exemplary embodiment of the system according to the present invention; 
           [0031]      FIG. 9  is a diagram of an fifth exemplary embodiment of the system according to the present invention; 
           [0032]      FIG. 10  is a diagram of a sixth exemplary embodiment of the system according to the present invention; 
           [0033]      FIG. 11  is a diagram of a seventh exemplary embodiment of the system according to the present invention; 
           [0034]      FIG. 12  is a diagram of an eight exemplary embodiment of the system according to the present invention; 
           [0035]      FIG. 13  is an exemplary embodiment of a four-element phase plate with relative optical thicknesses; 
           [0036]      FIG. 14  is a simulation of an exemplary self-interference spectrum using the exemplary embodiment of the phase plate shown in  FIG. 13 ; 
           [0037]      FIG. 15  is a graph of an exemplary power spectrum (e.g., a complex Fourier transform) of the spectrum shown in  FIG. 14 ; and 
           [0038]      FIG. 16  is a graph of exemplary phases determined at peaks of the power spectrum shown in  FIG. 15 . 
       
    
    
       [0039]    Throughout the figures, the same reference numerals and characters, unless otherwise stated, are used to denote like features, elements, components or portions of the illustrated embodiments. Moreover, while the subject invention will now be described in detail with reference to the figures, it is done so in connection with the illustrative embodiments. It is intended that changes and modifications can be made to the described embodiments without departing from the true scope and spirit of the subject invention. 
       DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
       [0040]    Thus, the exemplary embodiments of the present invention can provide an imaging system method, where the light emitted from a sample can be used to access sub-diffraction limited information. In addition, the exemplary embodiment of the system according to the present invention provides different scanning and detection schemes for signals obtained with such a device, as well as exemplary methods for processing such data. 
         [0041]    According to a first exemplary embodiment of the present invention diagramed in  FIG. 1 , emitted light from a sample ( 10 ) is optically processed through a phase element PE ( 30 ) and a dispersive element DE ( 40 ) to achieve high resolution imaging. In particular, a fluorescence emission from the source ( 10 ) can be collected by an objective ( 20 ), passed through a phase element ( 30 ) before being wavelength dispersed by a dispersive element ( 40 ) and focused by a lens ( 50 ) through an optional spatial mask ( 60 ), onto a spectrometer ( 70 ). 
         [0042]    An exemplary layout of the phase element determines the nature of the self-interferogram and the information that can be extracted from its analysis. For example, the spatial mask ( 60 ) before the detector array ( 70 ) may improve the phase sensitivity. For two-dimensional localization, a phase plate (e.g., the phase element PE ( 30 )) with, e.g., three elements may be preferable, as shown in the example of  FIG. 2 . As shown in  FIG. 2 , e.g., each segment of the phase plate can have a particular thickness and facilitate a phase ramp as a function of a wavelength. Interferograms can result from light that has transmitted through the different segments. 
         [0043]    As a beam passes through this phase plate, e.g., each portion of the wavefront passes through a different plate segment. The path length difference generated by the phase plate segments generate a modulation of the spectrum through interference, as shown in  FIGS. 3(   a )- 3 ( d ). In particular,  FIG. 3(   a ) shows interferogram pattern(s) resulting from the interference between segments  1  and  2 ,  FIG. 3(   b )—between segments  2  and  3 , and  FIG. 3(   c )—between segments  1  and  3 . Figure (d) illustrates exemplary summed interferograms of  FIGS. 3(   a )- 3 ( c ) as collected on the spectrometer. For example, the emission spectrum can be provided as a Gaussian, which is shown in  FIGS. 3(   a )- 3 ( c ) as a dotted line. In these exemplary figures, segment  1  provides no delay, segment  2  has a thickness of L resulting in a single 2π phase ramp over the wavelength range, and segment  3  has a thickness of 3 L resulting in a 6π phase ramp over the wavelength range. 
         [0044]    To obtain meaningful phase information from the interferogram(s) shown in one or more of  FIGS. 3(   a )- 3 ( d ), according to one exemplary embodiment, the thicknesses of each segment can be set to generate interference patterns that are preferably orthogonal, whereas the periodicity of the interference modulation can differ by an integer number over the emission spectrum of the fluorophore. Orthogonality can be preferable such that the contributions from different phase plate segments may be separated from each other, such as, e.g., through a multivariate analysis. A complex Fourier transform of the interferogram can contain both intensity and relative phase information, as shown in  FIGS. 4(   a ) and  4 ( b ). 
         [0045]    For example,  FIGS. 4(   a ) and  4 ( b ) show diagrams of exemplary embodiments of a power spectrum profile and a phase profile, respectively, resulting from a Fourier transform of the interferogram illustrated in  FIGS. 3(   a )- 3 ( d ) according to an exemplary application of the exemplary embodiment shown in  FIG. 1  and the exemplary embodiment of the phase plate ( 30 ) shown in  FIG. 2 . The relative phase of the three interference peaks and the knowledge of the objective lens numerical aperture and magnification can provide spatial localization information. The use of a four element plate, as shown in  FIG. 5 , can provide a third dimension of the localization. 
         [0046]    In particular,  FIGS. 5(   a ) and  5 ( b ) illustrate diagrams of exemplary embodiment of the system utilizing, e.g., a fourth phase plate element to discern out-of-focus light using a four-part phase plate ( 30 )— FIG. 5(   a ), to perform three-dimensional imaging— FIG. 5(   b ). An exemplary fluorophore ( 10 ) located at the exact axial focal center of the objective ( 20 ) can likely produce, e.g., a perfectly-collimated output. When a fluorophore is located above or below the focus, the output divergence can likely change. For example, the phase plate can be provided with a fourth segment for the axial localization, as shown in  FIG. 5(   b ). 
         [0047]    Additional interferences between phase plate elements can yield relative phase information for an axial high-resolution imaging, as shown in  FIGS. 6(   a )- 6 ( c ). In particular,  FIG. 6(   a ) illustrates a graph of an exemplary interferogram from the exemplary embodiment shown in  FIGS. 5(   a ) and  5 ( b ).  FIG. 6(   b ) shows a graph of an exemplary power spectrum profile resulting from a Fourier transform of the interferogram shown in  FIG. 6(   a ). Further,  FIG. 6(   c ) illustrates a graph of an exemplary phase profile resulting from a Fourier transform of the interferogram shown in  FIG. 6(   a ); 
         [0048]    In another embodiment of the system according to the present invention shown in  FIG. 7 , a set of relay lenses ( 31 / 39 ) and a pinhole DH ( 60 ) is used in order to spatially filter the light before it passes through a transmission grating TG ( 40 ) and is focused by an imaging lens ( 50 ) onto the detector ( 70 ). In particular, the exemplary system of  FIG. 7  has a pinhole or a (single mode) optical fiber ( 60 ) for spatial filtering, a relay lens system ( 31 ,  39 ), and transmission grating ( 40 ) for dispersing the spectrum of light, a focusing lens ( 50 ), and a spectrometer array ( 70 ) such as a charge-coupled device or photomultiplier tube array. In addition, the system includes a dichroic mirror and the phase plate PP ( 30 ). 
         [0049]      FIG. 8  shows a diagram of another exemplary embodiment of the system according to the present invention. This exemplary system is similar to the exemplary system shown in  FIG. 7 , and adds an extra pinhole ( 27 ) and relay lens system ( 26 ,  29 ) for spatial filtering before the phase plate ( 30 ). In  FIG. 8 , the dichroic mirror DM ( 25 ), the pinhole PH or (single mode) optical fiber ( 27 ,  60 ), the phase plate ( 30 ), the transmission grating TG ( 40 ), the focusing lens ( 50 ), and the pectrometer array ( 70 ) as shown. In particular, as provided in  FIG. 8 , two sets of relay lenses ( 26 , 29 ) and ( 31 , 39 ) can be used to place the phase plate ( 30 ) and a transmission grating ( 40 ) at conjugate planes of the objective ( 20 ) back aperture. 
         [0050]    This exemplary configuration can facilitate that any motion of the fluorophore ( 10 ) in the focal plane can result, e.g., only in changes to the beam angle, instead of beam displacement, on the phase plate ( 30 ) and transmission grating ( 40 ). In this exemplary embodiment, a pulsed IR source may be used to two-photon excite the fluorophore, though one-photon or ultraviolet lamp excitation can also be used for fluorescence pumping. For example, the dichroic mirror ( 25 ) can be used to separate the epi-fluorescence from the excitation beam. The pinhole ( 27 ) may also be used at the first plane conjugate to the objective focal plane for confocal rejection of out-of-plane fluorescence and scattered light. The spectrometer ( 70 ) can be a charge-coupled device array and/or a multi-anode photomultiplier tube. 
         [0051]      FIG. 9  shows still another exemplary embodiment of the system according to the present invention. In particular, the exemplary system of  FIG. 9  can include the pinhole or (single mode) optical fiber ( 27 ) and utilizes a combined phase plate and transmission grating element ( 30 / 40 ) and an optional spatial mask ( 60 ). For example, the optional spatial mask ( 60 ) provided before the detection array ( 70 ) may improve the phase sensitivity. 
         [0052]      FIG. 10  shows yet another exemplary embodiment of the system according to the present invention. For example, the exemplary system of  FIG. 10  can include a set of scanning mirrors SM ( 23 ) for raster-scanning the excitation beam ( 80 ) over the sample and descanning the fluorescence emission. Elements  21  and  22 , and  26  and  29  shown in  FIG. 10  can be relay lenses. In particular, the excitation laser beam can be angle scanned using the scanning mirrors ( 23 ), e.g., galvanometric mirrors. The scan and tube lens ( 21 ,  22 ) can direct the beam into the objective, where the angle scan may be translated into a positional scan over the focal plane. Light generated at the focus may travel back along the illumination path, and can be descanned into a stationary beam by traveling through the scanning mirrors ( 23 ). This fluorescence beam may be separated from the excitation beam using a dichroic mirror ( 25 ). The pinhole ( 27 ) can be used for confocal detection or to separate the fluorescence from the focus from scatter or other out-of-focus light. The exemplary system can then use the phase plate ( 30 ) and the transmission grating ( 40 ) to generate the self-interferogram. 
         [0053]      FIG. 11  shows a further exemplary embodiment of the system according to the present invention. For example, the exemplary system of  FIG. 11  can include a multilens array ( 81 ) and scanning mirror system ( 23 ) for scanning a line of focal points over a sample. This exemplary system can a pinhole array ( 90 ) as a spatial filter and a 2 dimensional CCD camera ( 70 ) for the detection. In particular, multiple excitation foci can be scanned across the sample to increase the imaging rate. For example, instead of scanning a single point, a line of points can be scanned at once to speed up data acquisition. Each beamlet, generated by the multilens array ( 81 ), can be scanned over a different sample position, producing beamlets of the emitted light that can traverse back through the scanning mirrors ( 23 ). 
         [0054]    The phase plate ( 30 ) and the dispersive element ( 40 ) can be placed at planes conjugate to the back aperture ( 24 ) of the objective ( 20 ), facilitating a common phase plate and dispersive element pair to be used, e.g., for all beamlets. Between the phase plate and the dispersive element, the pinhole array (or a spatial mask) ( 90 ) may spatially filter the light. As each beamlet has a distinct angle at this conjugate plane, a lens placed after the transmission grating can generate separate interferograms for each beamlet spaced along the perpendicular axis. A two-dimensional array, such as a CCD chip ( 100 ), can be used to collect such interferograms, facilitating multi-point SIFM at rapid scanning speeds. 
         [0055]    An illustrative numerical simulation of a self-interference measurement is described as follows. The optical components referred to herein relate to another exemplary embodiment of the system according to the present invention as shown in  FIG. 12 . For example, the exemplary system of  FIG. 12  can include an objective ( 20 ) with a back aperture ( 24 ), a pinhole PH or a (single mode) optical fiber ( 60 ) for spatial filtering, a relay lens system ( 31 ,  39 ), and transmission grating ( 40 ) for dispersing the spectrum of light, a focusing lens ( 50 ), and a spectrometer array ( 70 ), e.g., a charge-coupled device or photomultiplier tube array. The dichroic mirror DM ( 25 ), the phase plate PP ( 30 ), and the transmission grating TG ( 40 ) of this exemplary system are also illustrated in  FIG. 12 . In particular, the complex electric field distribution E p (x, y, λ)=I(x, y, λ)e iφ(x,y,λ)  at the objective pupil ( 24 ) shown in  FIG. 12  can be defined. For a point source ( 10 ) in the focus of the microscope objective ( 20 ), both intensity and phase functions can be flat: E p (x, y, λ)=I 0 (λ)e iφ     0     (λ) . The phase plate ( 30 ) can retard the field into sections with different phases. 
         [0056]      FIG. 13  shows an exemplary embodiment of a simulated four-element phase plate with the numbers (0, 1, 3, 7) indicating the optical thickness of the different sections. For example, the retarded field E r (x, y, λ)=E p e iφ(x,y,λ)  can be determined from the optical thickness of the wave plate at position (x, y) and the wavelength λ. As shown in the exemplary embodiment of the system of  FIG. 12 , the lens ( 31 ) focuses the field onto the accepting fiber tip/spatial filter ( 60 ). The field E f (x, y, λ) distribution at the accepting fiber tip/spatial filter ( 60 ) can be determined by Fourier transformation of E s . This exemplary field distribution E f0  of the unretarded field E r0  can be defined as the accepting fiber mode. The field coupling efficiency between the sheared field and the fiber mode pattern may be determined as the overlap integral C(λ)=∫E f (x, y, λ)E f0 (x, y, λ)dxdy. The power coupling can be the square modulus of the field coupling |C| 2 . 
         [0057]    The determination of the power coupling for each wavelength λ can provide the simulated self-interference spectrum, as shown in  FIG. 14 . The Fourier transform of this spectrum can provide the power spectrum and phase of the self interference modulations (as shown in  FIGS. 15 and 16 , respectively). The position of the point source can be obtained from the phase of these exemplary modulations. A movement of the source ( 10 ) in the (x,y) plane away from the focus of the objective ( 20 ) can be simulated by the addition of a linear phase ramp to the field EP. The movement of the source ( 10 ) along the z-axis away from the focus of the objective ( 20 ) can be simulated by the addition of a spherical phase term to the field E p . For the exemplary simulation described herein, it is possible to assume an objective (e.g., modeled as a thin lens) is used with an acceptance angle of, e.g., about 64 degrees and a focal length of, e.g., about 0.18 mm. The displacement of the fluorophore can be, e.g., about 60 nm in both x and y direction. This exemplary displacement can provide clear phase shifts, as shown in the graphs of  FIG. 16 . For a fluorophore in focus, it is possible for, e.g., all phases to be 0. 
         [0058]    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 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.