Patent Description:
Exemplary embodiments of the present disclosure relate generally to optical measurements of velocities, and more particularly to methods, systems and apparatus for providing multidimensional velocity measurements using amplitude and phase information in an optical interferometry.

Optical interferometric techniques to measure velocities can rely on the Doppler effect. The Doppler effect can describe a change in the frequency of light when it is reflected from a moving object. This permits the determination of the relative velocity of a sample, multiple samples or different parts of a sample with respect to the illuminating probe when it is shined with radiation that is analyzed in the frequency domain after reflection.

In some fields, it can be important to know a velocity map of a sample, for example when viscoelastic objects move with time. In these cases, the object can be considered as being composed of different parts that move independently, and therefore it can be valuable to make use of the Doppler effect in optical techniques that have higher imaging dimensionality, such as 2D and/or 3D imaging with a depth discrimination, so as to obtain a complete profile of the velocity distribution of the object of interest. In particular, Doppler Optical Coherence Tomography (D-OCT) is a technique known in the art for determining the velocity distribution as a function of depth in biological or other types of samples, with the potential of providing 2D and 3D velocity profiles when combined with multidimensional imaging or scanning systems. An optical system capable of performing D-OCT measurements consists of a phase-stable interferometer and data acquisition system that is able to detect changes in phase with time that come exclusively from the sample, without phase errors induced by fluctuations in the interferometer itself or by the acquisition process. D-OCT is very sensitive but has a limited range, being able to detect velocities as low as tens of micrometers per second up to millimeters per second. In the limited cases in which the sample of interest has a smooth velocity pattern and the spatial resolution of the Doppler phase map is sufficiently high, phase unwrapping algorithms can be used to extend the limits of the velocity range.

Currently, the fastest OCT imaging systems can be provided with a light source that sweeps the optical Fourier domain, known as Optical-Frequency Domain Imaging (OFDI) systems. The sources used on OFDI impose stringent requirements on the timing of the data acquisition, which may not be easy to satisfy in order to have a phase stable measurement, due to drift in the timing clocks of the high-frequency data acquisition systems used in OFDI. Some solutions for this problem have been proposed, but they usually add important complexity to the light source, such as an additional interferometer with its own data acquisition system, This has limited the mainstream implementation of D-OCT in swept-source systems, which has hindered the use of OFDI for the fast measurement of multidimensional velocity profiles in many fields.

D-OCT procedures and/or configuration are capable of establishing the sign of the direction of the movements, but can be directly sensitive only to movement in the line of sight (LOS). This has been another limitation for the use of D-OCT systems, because the angle that the D-OCT light beam makes with the moving object must be known in order to accurately determine the velocity. When the sample of interest has a map of velocities with varying orientation, such as those found in the most general flow of a liquid, it is not possible to know the angle of the velocities with respect to the light beam without a priori knowledge of the complete vectorial distribution of the velocities that the measurement intends to determine. Errors in the knowledge of this angle translate into errors in the measured velocities. This has been a very important drawback of the D-OCT method that makes it difficult to use in applications where an accurate description of the velocity profile is needed.

For example, one of these applications consists of determining the velocity profile in the blood flow inside blood vessels, and determining the total flow rate. Only when the flow is well-behaved unidirectional laminar flow, D-OCT is able to quantify the flow rate. Unfortunately, these conditions are rarely met in biological tissue. This inhibits, in principle, the use of D-OCT for characterizing blood flow inside blood vessels with branches and ramifications, as well as its use for quantifying the total flow rate in these conditions. For the reasons described above, it would be highly desirable to have a method that is able to determine velocity distributions without a prior knowledge of the velocity directional distribution.

There have been proposals for the use of Doppler analysis to determining a movement out of the LOS direction, in particular the use of the Doppler variance. However, Doppler variance is strongly linked with the signal-to-noise ratio (SNR) and the focusing optics, and depends on zero or a calibrated constant variance in the LOS direction, which makes it undesirable for use in real-world scenarios.

Another set of techniques use different quantities based on the speckle that forms when radiation is scattered from the sample in a coherent imaging system. In a coherent optical or acoustic system, speckle forms due to the interference between multiple signals scattered from different parts of the object under study inside the resolution volume, and speckle evolves as a stochastic process whose statistics are related to the movement of the scatterers. Speckle-based techniques do not rely on the phase information of the signal, only on the statistical fluctuations of speckle intensity. For example, it is possible to relate the variance of the speckle above a given threshold to the presence of moving scatterers in the sample, such as those occurring in a flowing liquid. However this technique is purely qualitative, as it is only capable of discriminating moving and static areas. Other speckle techniques are based on cross-correlation between speckle taken at different times, or on the time autocorrelation of speckle. Although in this case it is theoretically possible to quantify speed, so far there have been no known reliable systems for the measurement of speed distributions based on speckle statistics.

Dynamic light scattering (DLS) is a technique that analyzes statistics of complex OCT speckle. DLS can obtain quantitative information regarding the LOS and transverse motion of the scatterers by analyzing the complex speckle signal, but it relies on the phase of the OCT signal. Therefore, DLS requires a phase-stable OCT system to determine vectorial speed profiles. The use of the complex signal is at the core of the technique, which cannot be separated into distinct amplitude and phase analyses. It can be highly valuable to provide technique, system, method, apparatus and/or computer-accessible medium that can carry out the same measurements of DLS, depending only on the amplitude of the OCT signal.

Gradients in the LOS velocity can likely impact speckle statistics, and the effects can be severe when the velocity is mainly aligned. A known technique for addressing this problem relies on measuring the axial velocity using the phase information of the signal. However, this makes it difficult to make quantitative measurements when only the amplitude of the signal is available. It can be valuable to provide technique, system, method, apparatus and/or computer-accessible medium that, having access to only the amplitude signal, can determine the axial gradient distribution and to compensate for its effects on the decorrelation of the signal. Bringing the speckle correlation techniques to obtaining quantitative measurements would be useful for the widespread use of coherent systems for determining speed distributions, and could enable the use of OFDI systems for multidimensional velocity measurements.

Speckle techniques can be sensitive to speed in any direction, but no technique, system, method, apparatus and/or computer-accessible medium based on amplitude speckle statistics have been able to determine the axis in which the movement occurs. It would be valuable to develop a speckle technique that, although sensitive to velocity in any direction, is at the same time able to discriminate between flow in the LOS and out of the LOS. For example, in the viscous flow of a liquid, turbulence can appear at some regimes and the determination of the level of turbulence is highly valuable in some fields of study. Doppler would not be able to identify the areas with turbulent flow as it only identifies flow in the line of sight. Current speckle techniques could potentially be sensitive to the turbulent flow but cannot provide the directional information that is necessary to assess the total flow rate, which produces an overestimation of the total flow rate.

Apart from tracking the motion of a sample, in some areas, it can be of interest to track the motion of the probe that is being used to measure the sample interferometrically. In some fields, the motion of the probe cannot be completely controlled, with unexpected discontinuities during the scanning process. These discontinuities can appear in translating and rotating degrees of freedom, and without correction, can severely distort the images acquired. It would be valuable to provide technique, system, method, apparatus and/or computer-accessible medium that can use speckle amplitude statistics and/or phase to track the motion of the probe so as to compensate for image distortion.

Accordingly, there may be a need to address and/or overcome at least some of the issues of deficiencies described herein above.

Indeed, based on the above, it would be desirable to provide system, apparatus, methods and techniques that overcomes the limitations of the phase-based velocity measurements in high-speed interferometry systems, and address the line-of-sight problems of Doppler techniques, and overcome the lack of reliable quantitative and directionality information in intensity-based speckle speed measurements.

The scientific articles "<NPL>) and "<NPL>) are pertinent to the understanding of the present invention. Furthermore, the following patent application is also pertinent to the understanding of the present invention: <CIT> <CIT>).

A first embodiment of the invention is the optical frequency domain imaging apparatus defined in claim <NUM>. A second embodiment of the invention is the optical frequency domain imaging method defined in claim <NUM>. Preferred embodiments of the apparatus are defined in claims <NUM>, <NUM> and <NUM>. Preferred embodiments of the method are defined in claims <NUM> and <NUM>.

Further objects, features and advantages of the present disclosure will become apparent from the following detailed description taken in conjunction with the accompanying figures in which:.

<FIG> illustrates the invention defined in the appended claims.

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.

Referring to <FIG>, a conventional coherence imaging system can include a coherent source <NUM> which provides a temporally coherent electromagnetic or acoustic signal to a sample <NUM> and a reference sample <NUM>. The radiation propagates through the radiation coupling 100a, which can consist of free-space components or of wave-guiding components. 100a can be fitted with means to perform multidimensional imaging, such as lenses or scanning systems. After radiation is scattered by <NUM> one more radiation coupling component 100c transmits the radiation to a coherent detector <NUM>. Due to the coherent nature of the source and of the detection, when the sample <NUM> includes many subresolution scatterers, the image of sample <NUM> can likely be composed of speckle.

It is possible to analyze the statistical variations of the speckle amplitude in order to gain information on the movement of the sample. Such techniques usually rely on implementing 100a as a two-dimensional detector, and the analysis performed on the acquired amplitude of speckle as a function of time is known as laser speckle contrast imaging. These techniques usually provide qualitative information on whether a part of the object is moving or not, but determining actual speeds is not possible.

Referring now to <FIG>, an exemplary interferometric imaging system can include a coherent source <NUM> which can provide an electromagnetic and/or acoustic signal to a multiport coupler 260a. This coupler 260a, in the case of the electromagnetic radiation, can be a beam splitter, as is generally known in the art. The radiation can propagate through a radiation coupling 200a, which can include free-space components or of wave-guiding components. After the radiation coupling 260a, the radiation can be separated in two couplings 200b and 200c. Radiation going into the coupling 200b is delivered to the sample <NUM>. The coupling 200d can be fitted so as to perform multidimensional imaging, such as lenses or scanning systems. After radiation is scattered by <NUM>, radiation is coupled back into the coupling 200b and transmitted through a multiport coupler 260a. Radiation is also delivered through 200c to the reference reflection <NUM>, which can have means to change the effective optical path length as is known in the art. Coherent radiation reflected by the sample <NUM> and the reference <NUM> can be mixed by multiport coupler 260a and delivered by a coupler 200f into a coherent detector <NUM>. Due to the coherent mixing of the signals, by appropriate measurement schemes as it is known in the art, it is possible to determine both the amplitude and phase of the radiation reflected from sample <NUM>. In the case that sample <NUM> can include many subresolution scatterers, the amplitude and phase detected can present speckle.

It is possible to perform a Doppler analysis on the phase variations of the reflected radiation in order to gain information on the movement of the sample. Such techniques are generally only sensitive to the LOS movement of the sample, which inhibits the reconstruction of a complete velocity profile. As Doppler can be sensitive to the sign of the movement, movement that occurs in many directions in a determined region of the sample (such as that movement that appear in the turbulent flow of a liquid) may not be accurately determined, and such regions with rapid velocity direction changes cannot be identified. Furthermore, Doppler techniques have a defined limit given by the phase wrapping effect.

Referring now to <FIG>, an exemplary OFDI imaging system is shown as a block diagram that can include a wavelength-swept coherent source <NUM> which can provide an electromagnetic signal to a multiport coupler 360a. This coupler 360a can be or include a beam splitter, as is generally known in the art. The radiation propagates through the radiation coupling 300a, which can consist of free-space components or of wave-guiding components. After the multiport coupler 360a, the radiation can be separated in two couplings 300b and 300c, which can comprise a sample and a reference arm, respectively. The radiation provided into a coupling 300b can be further split into couplers 300d and 300c. The coupler 300d can provide the radiation to a fiber Bragg grating that, upon going to an optical circulator <NUM>, provides a clock signal at a detector 350b that can be further digitized in a data acquisition (DAQ) system <NUM>. The portion of light/radiation that continues through a path 300e feeds the polarization and/or frequency shifter 390a for polarization diverse sensing and/or for removal of the depth degeneracy, as is well known in the art. Coupling 300f can feed a circulator <NUM> to provide radiation to the reference reflection <NUM> via a coupler <NUM>, and the coupler/path <NUM> delivers reflected light/radiation into a multiport coupler 360b.

Similarly, the sample arm is comprised of circulator <NUM> that collects light reflected from sample <NUM>, which is delivered via <NUM>. Coupling 300j can guide the radiation into the polarization and/or frequency shifter 390b which are used as it is well known in the art. Coupling 300i can deliver the sample light/radiation into the multiport coupler 360b, which can mix light/radiation from the reference reflection, reference sample and sample, and balance detector assembly <NUM> consists of detectors and optionally multiport couplers to have polarization sensitive detection. <NUM> can be fitted with means to perform multidimensional imaging, such as lenses or scanning systems. The reference reflection <NUM> can have a way to change the effective optical path length as is known in the art. A signal from <NUM> can be digitized by the data acquisition board (DAQ) <NUM>. Due to the coherent mixing of the signals, by appropriate measurement schemes, it is possible to determine both the amplitude and phase of the radiation reflected from the sample <NUM> as a function of depth. In the case that sample <NUM> consists of many subresolution scatterers, the amplitude and phase detected will present speckle.

It is possible to perform a Doppler analysis on the phase variations of the reflected radiation in order to gain information on the movement of the sample in a similar way to the exemplary embodiment shown in <FIG>. The same or similar limitations can apply, e.g., the sensitivity to only LOS movement of the sample, the inability to accurately determine regions with movement in many directions (such as that movement that appear in the turbulent flow of a liquid) and the well-defined limit given by the phase wrapping effect.

<FIG> shows an exemplary OFDI imaging system according to an exemplary embodiment of the present disclosure with a similar configuration to the conventional system depicted in <FIG>, configured to further subdivide the radiation in the light coupling <NUM> into couplings/paths <NUM> and <NUM> due to a multiport coupler 360a.

For example, as shown in <FIG>, the light coupling and scanning system <NUM> can have many implementations. For example, in the case of OFDI systems used in cardiovascular applications, the exemplary system <NUM> can be configured and/or provided in the form of a catheter that is well known in the art, as shown in <FIG>. The sample <NUM>, e.g., in cardiovascular applications, can be or include blood inside a vessel, the vessel wall itself, or a combination of both. An exemplary scanning system based on a catheter can perform one-dimensional measurements of the reflectance of the sample with depth (known as A-lines), and mechanical rotation allows for scanning of the transversal plane. At the same time the catheter can be "pulled-back" to provide sectioning along the longitudinal direction to gather three-dimensional data from the sample.

<FIG> shows a flow diagram of an exemplary embodiment of a method for correcting the absolute phase acquired from the sample using the exemplary embodiment of <FIG>. An exemplary embodiment for this correction is as follows:.

In the exemplary embodiment of the exemplary systems shown in <FIG> and <FIG>, it is possible to define two coordinate systems to which the velocity profiles can be referred. It should be understood that other exemplary embodiments can be used to determine multidimensional velocity profiles in accordance with an exemplary embodiment of the present disclosure. For example, the first coordinate system can define z as the light propagation direction, and its associated perpendicular xy plane. The second system can be defined with respect to the sample <NUM>, which in case of the exemplary embodiment shown <FIG> has a cylindrical shape, however it is not limited in any way to this geometry. In this exemplary coordinate system, z̃ is looking forward in the longitudinal direction of the catheter and the x̃ỹ defines the plane of rotation of the beam. It is possible to define x and z̃ as parallel, so an ideal laminar flow inside the tube flows along the x direction which is independent of the rotation angle θ of the beam, while the y direction depends on θ.

<FIG> shows a flow diagram of an exemplary embodiment of a method according to the present disclosure for calculating and/or otherwise determining a speed profile based on an analysis of the autocorrelation of the speckle amplitude acquired from the sample. The steps/procedures are explained in detail herein below.

In a coherent optical system where fully developed speckle is formed after reflection of light by moving particles, the speckle-decorrelation time is inversely proportional to the speed of the particles. In the case of OFDI, there is a speckle size in the axial direction that can be related to the axial resolution of the system (given by the bandwidth of the light source). At each depth, the speckle can evolve as a function of time so that its decorrelation time is inversely proportional to the particles reflecting light at that depth. <FIG> shows a set of illustrations providing examples of this relation, where the tomogram of a tube is shown that is filled with flowing scattering liquid (e.g., intralipid) at two different flow rates. Reference <NUM> in <FIG> indicates an M-mode tomogram of phantom fluid at <NUM> / min with low flow velocities and large speckle size, while reference <NUM> in <FIG> shows the same sample at <NUM> / min yielding high flow speeds and small speckle size. These tomograms are so called M-mode measurements, which consist of the measurement of A-lines as a function of time of the same position in the sample.

Thus, the horizontal axis shown in <FIG> corresponds to time, while the vertical axis to depth. The catheter is provided at the top, clearly identified by the strong reflections of the collimating ball lens and the protective sheath. The exemplary catheter can be placed near a center of the tube (e.g., <NUM> diameter), and the liquid-tube interface can correspond to the weak reflection at the bottom of the tomograms. It is easily seen that the speckle-decorrelation time (the speckle size in the horizontal direction) matches the expected relationship with particle speed. In particular, the horizontal speckle size gets bigger near the interfaces due to the no-slip condition of the flow.

For example, the speckle correlation time can be inversely proportional to the modulus of the velocity (the speed) of the particles <MAT>.

The way of calculating the autocorrelation for speckle statistics can include, e.g., the use of the Pearson correlation function, either between A-lines at two consecutive times, or at a single or a group of depths as a function of time. This determination can produce an estimation of the decorrelation time that is highly influenced by noise, especially in the case of using the cross-correlation coefficient. Instead, according to an exemplary embodiment of the present disclosure, it is possible to utilize a modified correlation function tailored for the determination of speckle size, and analyze the speckle size at each depth as a function of time. The exemplary normalized correlation function can be defined as <MAT> where <> denotes an ensemble average, I is the intensity, and the summation is along the discrete time dimension. In a system with unity speckle contrast and in absence of noise, this definition of the autocorrelation function has a maximum value of <NUM>, totally decorrelated signals have a value of <NUM>, and anti-correlated signals have values below <NUM>. The ensemble average allows taking into account multiple correlation windows in the calculation, reducing the statistical fluctuations on speckle size and the effect of noise.

After certain testing, with the use of the above-defined autocorrelation function on the scattered radiation amplitude, as opposed to the traditional approach on the scattered radiation intensity, decorrelation profiles can be produced that can be significantly more homogeneous. This can be linked to the effect that the square has on outliers in the statistical fluctuations of speckle intensity. When this square is avoided, the outliers likely have a smaller weight on the autocorrelation function which produces more homogeneous results. A side effect of this can be that the autocorrelation no longer reaches a value of <NUM> for speckle with perfect contrast.

As noise is the most important factor in the accuracy of speckle decorrelation times, it is possible to define another exemplary autocorrelation by performing the following exemplary transformations: for example, it is possible to remove the value at Δt = <NUM>, optionally apply a small Gaussian smoothing filter (FWHM = <NUM> px), renormalize the autocorrelation by defining the value at Δt = <NUM> px as one, and define the median of the value in a certain range of the autocorrelation as zero
<MAT>
where g̃ ≡ g * c-ln2Δt<NUM>/(FWHM/<NUM>)<NUM> is the Gaussian filtered version, and w is defined based on the autocorrelation properties. This corresponds to step <NUM> in the exemplary method shown in <FIG>. For example, by defining such exemplary autocorrelation, most if not all functions can have similar contrast and cover the range from <NUM> to approximately <NUM>. The contrast C is defined before the final normalization as <MAT> C can be a good indicator of presence of flow, similar to the speckle variance technique. This corresponds to step <NUM> in the exemplary method of <FIG>.

It may be preferable to estimate the noise floor of the exemplary system. This can be possible, e.g., if the system is fitted with a mechanism to block the sample arm of the interferometer while taking a measurement of scattered radiation. Then, a tomogram reconstruction on this data can be performed, and an average over all depths can provide an estimation for the noise floor. Further, most if not all scattered radiation measurements can be converted from intensity into SNR by subtracting the estimated noise floor value, corresponding to step <NUM> in the exemplary method shown in <FIG>.

In this exemplary embodiment, the decorrelation time for each region of the sample can be determined by calculating the time it takes the autocorrelation function calculated in step <NUM> to reach the value <NUM>. This corresponds to step <NUM> in the exemplary method shown in <FIG>.

<FIG> show exemplary illustrations of complete inverse autocorrelation profiles for a solid material moving at a known and stable speed. The profiles were measured using the conventional autocorrelation method. The complete inverse autocorrelation profiles shown in <FIG> correspond to the same set of speeds and are measured by the exemplary embodiment of the speckle-amplitude statistics OFD1 system according to an exemplary embodiment of the present disclosure. <FIG> illustrate a significant improvement in the homogeneity of the profile using the exemplary embodiments of the present disclosure.

With respect to determining the speckle speed from the speckle decorrelation time (e.g., step <NUM> in the exemplary method shown in <FIG>), it is possible to consider a movement in the x direction. In this exemplary case, the total apparent mean speed can be, e.g.: <MAT> where KBM denotes an offset given by stochastic movement, such as that produced by Brownian motion of the scatterers. The speckle-decorrelation time τ is inversely proportional to this speed. For example, zero speed may provide an infinite decorrelation time. However, because the autocorrelation can be calculated using a window of finite width, even at zero velocity, there may be a finite decorrelation time (equal to the window size). If necessary, an offset can be added to account for this effect to the KBM constant outside the radical to define a new offset kc. Finally, <MAT> where the k proportionality constant has been absorbed into the new Brownian motion contribution constant.

Considering the exemplary embodiment shown in <FIG> in which the scanning mechanism is a rotating catheter, the rotation of the catheter with angular velocity ωR can produce decorrelation that is linked to motion in they direction. However, there will not be a pure dependence on the tangential velocity υy = ωRz because as the catheter rotates, the light beam is not only displaced an amount υydt but light is entering the material at a different angle θ(t + dt) = θ(t) + ωRdt. As the speckle pattern is also dependent on incident angle, the combination of these exemplary movements can produce a speckle pattern whose size is mostly independent of z. It is possible to consider this exemplary decorrelation as arising directly from the angular velocity ωR via another proportionality constant kR, which can have some z dependence. It is possible to see why the dependence is with the angular velocity of the catheter: if the whole sample were made to rotate at exactly the same speed, the decorrelation due to the rotation of the catheter would be exactly canceled. Therefore, in a rotating catheter system with sample movement only in x, the speckle-decorrelation time can be described by, e.g.: <MAT> and the sample speed |υx| can be found using, e.g.: <MAT> where it is made explicit that it is not possible to determine the sign of the flow velocity. This corresponds to step <NUM> in the exemplary method of <FIG> when sample motion happens only in the x direction.

Considering, e.g., the corrected decorrelation time <MAT>, the equation above indicates that at high flow speeds, the rotation between <MAT> and speed is linear <MAT> while it can be non-linear at low flow speeds with an offset at zero flow speed given by Brownian motion and catheter rotation <MAT>.

This indicates that speckle-decorrelation flow measurements can be better suited for quantifying high flow speeds than Doppler, while the opposite can be the case when the rotational speed of the catheter is significant.

In the general case of sample motion in any direction, the proportionality constants can be different if the voxel that corresponds to the point spread function (PSF) is asymmetric. This can be usually the case, unless some post-processing on the OFDI data is performed. This exemplary case is described by, e.g.: <MAT> where kpp is the proportionality constant for flow perpendicular to the beam, kpl the constant for flow parallel to the beam, υy is the tangential speed of the flow in the y direction, and <MAT> is a term that represents the decorrelation due to the angular scanning, and can be dependent on depth and tangential speed. To understand the effect of the two constants that depend on the sample velocity, it is possible to assume for simplicity no motion in the y direction. Therefore <MAT> where it is clear that <MAT> due to the different constants. In order to avoid this it is necessary to rescale the tomogram in the axial direction to make the axial and transversal PSFs of the system equal. If the tomogram is rescaled to have a symmetric PSF and define now k ≡ kpp = kpl in the case of no flow in the y direction, e.g.: <MAT>.

The case of flow in the y direction can be more complex because of the coupling with the rotational contribution. However, many exemplary methods for determining the total speed can be utilize, such as, e.g., measuring at different rotational speeds solving the equations for υ<NUM>.

Further exemplary embodiments can be provided with a usage of a signal-to-noise (SNR) ration calibration method. The rationale for the parametrization can be the following: when measuring a solid sample with a static catheter kBM = ωR = <NUM>, so τ-<NUM> as a function of speed should be a linear function, although when reaching <MAT> the slope should increase to indicate that higher speeds will all produce values close to the maximum inverse correlation time given by the time resolution of the system. The exemplary illustrations in <FIG> were used as calibration data to parametrize sample speed as a function of inverse correlation time and SNR. The best parametrization for this behavior was a fourth order polynomial where the linear term dominates except for correlation times near the limit of the system. The exemplary behavior of the SNR. can be mostly linear for > <NUM> dB SNR and higher-order for lower SNR.

Therefore, the speed was parametrized as a fourth order polynomial of the two variables τ-<NUM> and SNR and a fit of this exemplary model to the data can be performed by minimizing the mean absolute value error, instead of the mean quadratic error, to minimize the influence of outliers. An exemplary parametrization based on the present exemplary material as measured by the exemplary embodiment of the speckle-amplitude statistics OFDI system according to an exemplary embodiment of the present disclosure is shown in an exemplary illustration of <FIG>. <FIG> shows a set of an exemplary illustrations of speed profiles for a moving solid phantom as measured using the exemplary parametrization of speed as a function of τ-<NUM> and SNR based on the present exemplary material as measured by the exemplary embodiment of the speckle-amplitude statistics OFDI system according to an exemplary embodiment of the present disclosure. The solid phantom was translated by using a motorized linear stage at a fixed speed, corresponding to <NUM>/s (illustration <NUM>), <NUM>/s (illustration <NUM>), <NUM>/s (illustration <NUM>) and <NUM>/s (illustration <NUM>). The measured speed by our technique matches extremely well the expected values.

Another exemplary calibration relates the newly defined inverse correlation time with the velocity of a given material. As a matter of illustration, the scattering liquid used in the exemplary configuration can be intralipid and the results from this fitting procedure are: <MAT>.

The system and methods described above allows for the accurate measurement of speeds from speckle-amplitude statistics as described in the present disclosure. <FIG> shows illustrations of measurements taken of Intralipid flow through a tube at different flow rates when the catheter is not rotating. In particular, <FIG> provide exemplary illustrations of speed profiles for a flowing liquid as measured by the exemplary embodiment of the speckle-amplitude statistics OFDI system according to an exemplary embodiment of the present disclosure. Further, <FIG> show exemplary illustrations of the flow speed as measured by Doppler analysis using the exemplary embodiment of the phase-correction OFDI system according to an exemplary embodiment of the present disclosure.

<FIG> shows a set of illustrations of exemplary two-dimensional speed profile measurements when the catheter is rotating where the contribution from rotation has been calibrated as <MAT>.

In particular, <FIG> show exemplary illustrations of the conventional structural image from OFDI of the tube and the liquid. <FIG> show exemplary illustrations of two-dimensional speed profiles for a flowing liquid as measured by the exemplary embodiment of the speckle-amplitude statistics OFDI system and method according to an exemplary embodiment of the present disclosure. Further, Figures I3G-13I show exemplary illustrations of two-dimensional flow speeds as measured by Doppler analysis using the exemplary embodiment of the phase-correction OFDI system and method according to an exemplary embodiment of the present disclosure.

The system according to an exemplary embodiment of the present disclosure can be further configured to provide an additional scanning mechanism in <NUM> in <FIG>. For example, a pullback mechanism can provide longitudinal scanning of the sample <NUM>. If the measurements described above can be carried out while the pullback system is in operation, it is possible to obtain three-dimensional speed profiles of the sample. <FIG> provide a set of illustrations of three-dimensional speed profile measurements when the catheter is rotating using the above-described exemplary embodiment of the systems and methods according to the present disclosure. In particular, <FIG> show exemplary illustrations of three-dimensional speed profiles for a flowing liquid at different planes in the tube longitudinal direction as measured by the exemplary embodiment of the speckle-amplitude statistics OFDI system and method according to an exemplary embodiment of the present disclosure. In addition, <FIG> show exemplary illustrations of three-dimensional speed profiles for a flow velocity measured by Doppler analysis using the exemplary embodiment of the phase-correction OFDI system and method according to an exemplary embodiment of the present disclosure. Further, <FIG> show exemplary illustrations of conventional structural images from OFDI of the tube and the liquid.

For example, the scanning speed can contribute to the decorrelation time. The equivalent in a tabletop scanning system can correspond to a translational speed, which can have a simpler relationship with decorrelation, In this exemplary case, the angle of incidence does not change, although there can be a scanning translational speed in the xy plane. If the scanning speeds are much lower than sample speeds, this correction can be small and can be ignored. If they are, or are made comparable it is possible to make use of different scanning speeds to determine the individual components of the velocity vector in the transversal plane. For example, by scanning in the y direction with velocity υs we have <MAT>.

By measuring with different scanning speeds in x and y, several of these equations can be obtained and solved for υ<NUM>, υx, υy and υz.

Following the reasoning of Eq.(<NUM>), an exemplary embodiment of a method according to the present disclosure as shown in <FIG> can be provided as follows:.

In a further exemplary embodiment, it is possible to extract two- and three-component vectorial velocity profiles of the sample, depending on the scanning/imaging implementation. In the case of a mechanically scanning system in which time and the transversal coordinates are coupled a two-component vectorial profile can be determined, where the two components correspond to the longitudinal speed and the transversal speed. Eq.(<NUM>) can be written as <MAT> where the transversal speed is <MAT> and the longitudinal speed is
<MAT>
kpl can be synthetically modified by different methods after measuring, because its value depends on the axial resolution of the tomogram. For different axial resolutions, its value can be calibrated. One possibility includes splitting the raw spectrum and reconstructing different realizations of the tomogram with a reduced bandwidth, which results in a tomogram with reduced longitudinal resolution. In general, it is possible to consider such exemplary process as signal filtering in k-space, and the use of several filters in k-space can be considered as k-space filtering diversity. Multiple possibilities of k-space filtering are possible, which can provide numerous diversities, such as, e.g., axial resolution diversity, group velocity dispersion diversity, quartic dispersion diversity, etc. For axial and lateral flow discrimination, we will focus on axial resolution diversity. This exemplary step/procedure does not require a phase stability, as all A-lines can be inherently phase-stable with respect to points inside the same A-line. Exemplary different realizations can be used in the calculation of the autocorrelation function (step <NUM> in <FIG>) to improve the SNR. As each realization will be described by an Eq.(<NUM>) with a different kpl, a system of equations can be created and solved for <MAT> and <MAT>. In general, modifications to the k-space signal can produce a different kpl, which can then be used to provide an exemplary system, method and/or computer-accessible medium which can be configured and/or programmed to utilize equations, and solve for axial and lateral speeds.

Following the reasoning of Eq.(<NUM>), an exemplary embodiment of a method according to the present disclosure as shown in <FIG>, can be provided as follows:.

There can be other figures of interest that can be determined in a similar manner, e.g., by k-space filtering. In general, interferometric systems can have varying degrees of dispersion mismatch between the reference and sample arms. Furthermore, it is possible to add or subtract the dispersion mismatch synthetically after measuring. As a particular exemplary embodiment, consider the case of so-called group velocity dispersion (GVD). A variation in GVD influences the decorrelation produced by axial velocity gradients, which can then be used to determine them. Consider that the system has a GVD given by a quadratic dispersion of amplitude 2πγ. This can be produced either by, e.g., physical GVD between the two arms of the interferometer, and/or synthetically in post processing (e.g., k-space filtering producing GVD diversity). In presence of GVD, the complex amplitude spread function (ASF) of the system is <MAT> where z is the axial direction, k<NUM> the central wave number of the spectrum, wz the diffraction-limited axial <NUM>/e size of the point spread function (PSF), and ŵz the actual <NUM>/e size of the PSF due to the quadratic dispersion.

Assu ming an axial speed profile inside the ASF with a linear gradient of the form vz(z) = vz<NUM> + zvz<NUM> / wz. After some approximations, the autocorrelation function becomes <MAT> where xy are the transverse directions, n is the refraction index, D the diffusion constant of the scatterers, and wxy the lateral <NUM>/e size of the PSF. By defining the speckle decorrelation time τc as the time when the second-order autocorrelation function reaches the threshold <NUM> + gc, the following is provided: <MAT> where the diffusion constant is <MAT>, the group velocity dispersion contributions are
<MAT>
and <MAT>. We identify the axial velocity gradient contribution to decorrelation as the last term in Eq. (<NUM>). It is easy to see that by varying γ synthetically, we can find the decorrelation contribution from vz<NUM> by producing different values of the decorrelation time due to GVD<NUM>(γ) and GVD<NUM>(γ). The data can be assembled in an exemplary system, method and/or computer-accessible medium which can be configured and/or programmed to utilize equations to find the axial velocity gradient contribution to decorrelation. Further, e.g., when physical dispersion mismatch is present, its effects persist even when compensated synthetically. This can be found by performing an exemplary calibration when the axial velocity gradient is known, which produces the GVD<NUM>(γ) and GVD<NUM>(γ) baseline contributions from the physical dispersion mismatch.

In the case of an imaging system (in which the tomograms of transversal one- or two-dimensional regions are taken simultaneously, for example using a camera in which each pixel corresponds to different transversal positions of the sample), the A-lines taken simultaneously can be phase-coherent. For this reason, it is possible to synthetically alter the transversal resolution in one of the two transverse dimensions (for example, by calculating the convolution of the two- or three-dimensional complex-valued tomogram with a kernel in one of the transverse directions), and generate a number of realizations of the tomogram which can be described by an equation similar to Eq.(<NUM>) where the proportionality constant that changes is the kpp in the transversal direction where the filter is applied. It is possible to determine a three-dimensional profile if the above-explained technique is performed first, so the values for <MAT> and <MAT> are already known. Then ,using the exemplary technique for transversal manipulation of the resolution, an exemplary embodiment of the system of equations can be provided and can be used solve for <MAT> or <MAT> (depending on which one has the filter applied) and given that <MAT> is known, solve for the remaining transversal component.

Following the reasoning above, a method according to another exemplary embodiment of the present disclosure shown in <FIG> can be provided as follows;.

In another exemplary embodiment, it is possible to extract two-component vectorial velocity profiles of the sample, where the two components correspond to the longitudinal speed and the transversal speed using amplitude-based and phase-based velocity measurements. Speckle amplitude-based analysis provides information about the total speed of the sample v, while phase-based Doppler analysis provides vz = vpl, which can then be used to determine the transversal speed profile <MAT>.

Following the reasoning above, a method according to an exemplary embodiment of the present disclosure shown in <FIG> can be provided as follows:.

The exemplary systems, methods, techniques and computer-accessible medium described herein above facilitates an accurate measurement of speeds from speckle-amplitude statistics in presence of axial velocity gradients, as well as the determination of the axial and lateral components as described in the present disclosure. <FIG> shows a set of illustrations of measurements taken of Intralipid flow through a tube at different flow rates to correct for axial velocity gradient errors in speckle decorrelation speed measurements as measured by the exemplary embodiment of the speckle-amplitude statistics OFDI system and method according to the present disclosure.

For example, image <NUM> of <FIG> are exemplary illustrations of axial velocity gradient determination using the exemplary embodiment of the k-space GVD diversity analysis for a flowing liquid as measured by the exemplary embodiment of the speckle-amplitude statistics OFDI system and method according to the present disclosure. Indeed, the exemplary image <NUM> is the expected parabolic speed profile, the exemplary image <NUM> is the uncorrected speckle flow speed profile, the exemplary image <NUM> is the rotation between data in images <NUM> and <NUM>, the exemplary image <NUM> is the expected GVD_1 due to axial velocity gradient, <NUM> is the GVD_1 as determined by the methods according to the exemplary embodiments shown in <FIG> (<NUM>, <NUM>, <NUM>), the exemplary image <NUM> is the expected GVD_2 due to axial velocity gradient, the exemplary image <NUM> is the GVD_2 as determined by the methods according to the exemplary embodiments of <FIG> (<NUM>, <NUM>, <NUM>), the exemplary image <NUM> is the corrected speckle flow speed profile, and the exemplary image <NUM> is the relation between data in the images <NUM> and <NUM>.

<FIG> shows a set of illustrations of exemplary speed profile measurements of axial, lateral and total flow speed, in which the axial gradient velocity correction was used for more accurate results, e.g., of the k-space bandwidth diversity analysis for a flowing liquid as measured by the exemplary embodiment of the speckle-amplitude statistics OFDI system and method according to the present disclosure. In particular, the exemplary set of images <NUM> shows on the left column thereof the speckle determined flow, on the right column the parabolic expected flow, the top row - the axial flow, in the center row - the lateral flow, and at the bottom row - the total flow speed, e.g., as determined by the method according to the exemplary embodiments of Figures (see exemplary procedures/steps <NUM>, <NUM>, <NUM>). The exemplary set of images <NUM> indicate average profiles and expected profiles shown in the exemplary images of <NUM>. The exemplary image <NUM> shows the corresponding flow angle as a function of depth as determined for <NUM> different angles in the region of interest using the exemplary embodiment of lateral and axial flow determination according to an exemplary embodiment of the present disclosure.

There can be different approaches for determining turbulence when the speed profile corresponds to a flowing material. The method shown as a flow diagram in <FIG> illustrates the invention defined in the appended claims. The steps/procedures shown in <FIG> are as follows:.

For example, by implementing a method for determining a vectorial velocity profile based on speckle decorrelation (such as the exemplary method shown in <FIG>), no assumptions on the direction of the flow inside a cavity are needed in order to detect turbulent flow. The vectorial profile can provide a directional information, and analysis of this information (such as a velocity direction variance profile) can provide direct information on turbulence.

For example, by measuring the relative motion of the probe and sample, instead of determining the velocity profile of the sample, if the sample corresponds to a monolithic structure, this information can be used to track the motion of the probe during measurements. In the exemplary embodiment of the system shown in <FIG>, although the blood flow inside the vessel carries information of interest, the vessel wall is a monolithic landmark that can be used to track the movement of the catheter while it is performing measurements. This can be important when performing a pullback scan (scanning in the longitudinal direction of the vessel), as unwanted motion of the tissue can lead to structural imaging and flow imaging artifacts. The exemplary embodiment of the method according to the present disclosure can be used to track the motion of the probe without the need of additional radiation apart from the configuration and/or technique used for imaging. It is also possible to track not only displacements, but also the rotational speed of the catheter as it scans the tissue. Irregular rotational scanning, known in the literature as non-uniform rotation distortion (NURD), is a prevalent problem in catheter-based imaging. The exemplary embodiment of the method according to the present disclosure can track the rotational speed of the catheter to compensate for such distortions.

Another exemplary embodiment of a method according the present disclosure is shown in <FIG>, and provided as follows:.

Using the information from the longitudinal motion of the catheter and the transversal motion derived from image analysis, e.g., the motion of the catheter in three-dimensional space can be obtained. This can be used, for instance, to correct image artifacts from inhomogeneous pullback speeds, unwanted vessel motion, patient motion, among other applications.

Another exemplary embodiment of a method according to another exemplary embodiment of the present disclosure is shown in <FIG>, and provided as follows:.

The exemplary systems, methods and computer-accessible medium described herein can facilitate a performance of accurate tracking of the measuring probe. <FIG> shows a set of illustrations of images and graphs of measurements taken of a probe undergoing stable motion except for a single perturbation during scanning. For example, the exemplary image <NUM> is an exemplary frame of reference surface (wall) tracking; the exemplary graph <NUM> indicates a transverse position of the probe in time from the reference tracking surface tracking; the exemplary graph <NUM> - estimated transverse speed of the probe from the results in the graph <NUM>; the exemplary image <NUM> - estimated Doppler shift from the transverse speed in the graph <NUM>; the exemplary image <NUM> - experimental Doppler shift at the reference surface as a function of frame; the exemplary graph <NUM> - residual longitudinal velocity of the probe after subtraction from the graph <NUM> of the estimated Doppler shift in the image <NUM>. The longitudinal velocity of the probe as determined by the exemplary embodiment shows the expected behavior.

<FIG> shows a set of illustrations of exemplary rotational probe speed tracking and compensation of image deformation, according to the present disclosure. For example, a set of images/graph <NUM> provides an exemplary analysis of the transverse speed of the probe from speckle decorrelation, translation into rotational speed and correction of a deformed image due to NURD. The exemplary images <NUM> indicate a projection of a group of <NUM> images, before and after NURD detection and correction, as explained in the various exemplary embodiments of the methods according to the present disclosure. Although only a few exemplary embodiments of the present disclosure have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible in the exemplary embodiments without materially departing from the novel and non-obvious teachings and advantages of the present disclosure. Accordingly, all such modifications are intended to be included within the scope of the present disclosure as defined in the following claims.

Indeed, the arrangements, systems and methods according to the exemplary embodiments of the present disclosure 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 <CIT> which published as International Patent Publication No. <CIT>, <CIT> which published as <CIT>, and <CIT> which published as <CIT>, and <CIT>.

Claim 1:
An optical frequency domain imaging apparatus comprising:
a swept source (<NUM>) providing a radiation;
a splitter structure (360a, <NUM>) which separates the radiation into at least one first electro-magnetic radiation directed to a sample (<NUM>) and at least one second electro-magnetic radiation directed to a reference arm (<NUM>),
wherein a frequency of the radiation provided by the swept source is controlled thereby to vary over time; and
at least one detector second arrangement (<NUM>) configured to detect different interferences between at least one third radiation that is a return radiation from the sample which is based on the at least one first radiation and at least one fourth radiation that is a return radiation from the reference arm which is based on the at least one second radiation as a function of time; and
a computer (<NUM>) configured to generate an image, and determine information for measuring a motion within the sample based on a difference between amplitude values of the respective different interferences,
characterized in that the apparatus is configured to:
determine a Doppler velocity profile in the line of sight,
determine a total speed profile using speckle decorrelation,
subtract the Doppler profile from the speckle profile, and
determine areas with turbulent flow based on the result of the subtraction.