The rheological properties of fluids are complex and controlled by many parameters. For example, biological fluids, such as blood, are viscoelastic, i.e., they exhibit both viscosity and elasticity.
A number of techniques have been developed or suggested for evaluating the rheological properties of fluids on a microscopic scale. This area of science has become known as microrheology. Several microrheological techniques rely on applying a strain to the fluid through application of an external force, such as a mechanical force or a magnetic field. Such techniques may be undesirable, however, because the fluid under evaluation is evaluated under artificial conditions.
In a more recent approach described in U.S. Pat. No. 6,958,816, microrheological properties of a fluid are observed through low-coherence light scattering. In such analysis, a very small volume of the fluid under evaluation is observed by collecting backscattered rays that are reflected from scattering centers suspended in the volume when light is radiated into the fluid via a single-mode optical fiber. Such an arrangement is depicted in
Although the light scattering approach described above has significant advantages over previous techniques, the signal-to-noise ratio for the received signals is relatively small given that the number of scattering centers from which reflected light is collected is relatively small.
Disclosed is a light scattering sensing system and method. In one embodiment, the system comprises a sample branch configured to collect light signals backscattered from scattering centers contained in a coherence volume of a medium under evaluation, the sample branch comprising a multi-mode optical waveguide. In one embodiment, the method comprises radiating low-coherence light into a scattering medium using a multi-mode optical waveguide, and collecting light signals backscattered by the scattering centers and light reflected by an end surface of the multi-mode optical waveguide using the multi-mode optical waveguide.
The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. In the drawings, like reference numerals designate corresponding parts throughout the several views.
As described above, the microrheological properties of a fluid can be observed by collecting backscattered rays that are reflected from scattering centers suspended in the fluid when light is radiated into the fluid via a single-mode optical fiber. In such an approach, a very small volume of the fluid under evaluation is observed, in part due to the small cross-sectional area of the single-mode optical fiber core. Observation of a very small volume of fluid has been considered preferable given that the received optical signals can become very complex, and therefore difficult to evaluate, when a high concentration of scattering centers is observed due to multiple ray scattering that occurs between the scattering centers. Specifically, rays resulting from multiple inter-reflection between individual scattering centers can unduly complicate the received signals and therefore analysis of the fluid. Therefore, increasing the depth of the observed volume (see volume 110,
Although the effects of such multiple scattering are reduced when a very small volume of fluid is evaluated in the manner described in the foregoing, the signal-to-noise ratio of the received signals is relatively low. That is, because a very small volume of fluid is observed, reflected light is only collected from a relatively small number of scattering centers. Given that the few observed scattering centers are used as probes that are indicative of the microrheological properties of the fluid as a whole, it would be preferable to obtain reflected light signals from a greater number of scattering centers, without a significant increase in multiple-scattered signals.
As is described in the following, light can be collected from a greater number of scattering centers when multi-mode optical waveguides are used due to the larger cross-sectional area of the cores of such multi-mode optical waveguides. As a result, the signal-to-noise ratio is increased due to greater collection efficiency. However, because the depth of the observed volume is not increased, multiple scattering is not significantly increased even for optically dense suspensions.
Before describing the disclosed embodiments in detail it is noted that the invention is not limited in its application to the details of those particular embodiments since the disclosed systems and methods are capable of other embodiments. Also, the terminology used herein is for the purpose of description and is not intended to limit the disclosure.
In the techniques described herein, light backscattered from scattering centers suspended within from a small volume of media localized at the end of an optical waveguide is collected. The collected light is detected and analyzed, for example in the frequency domain. Owing to the refractive index contrast between the fiber core and the medium in which the scattering centers are suspended, the signal that is detected has two components: (i) the light that is backscattered from the dynamic system, and (ii) the component that is due to the Fresnel reflection at the fiber-medium interface. The coherence length and the transverse dimension of the fiber core define a coherence volume in which the optical fields preserve relative phase correlations. Considering the terms that survive the time averaging, we were able to derive the expression for the intensity autocorrelation function as
In Equation 1, I0 and Is=ΣjIj are the average intesities of the specular and the scattered components, respectively, and Ij is the intensity associated with the backscattered component of trajectory j. The term gj represents the normalized first-order correlation function corresponding to the backscattered component, defined as gj(τ)=(Ej(τ)Ej(t+τ)*)/Ij, with the angle brackets denoting time averaging and the symbol * representing complex conjugation. The optical path lengths associated with the scattered component j and the specular field are denoted sj and s0, respectively, and lc is the coherence length. An important consequence of Equation 1 is that for scattering media with the mean free paths longer than lc/2, the backscattered light undergoes on average only one scattering event in the coherence volume, which is defined approximately by the coherence length and the area of the fiber core. Consequently, the autocorrelation functions gj are independent of the length of the scattering trajectory and are given by the well-established formula for quasi-elastic light scatter. If Is<<I0, the last (self-beating) term of Equation 1 becomes negligible. With these assumptions, Equation 1 can be arranged to give the normalized autocorreclation function
In Equation 2, g(1)(τ)=exp(−q2Dτ), where D is the particle diffusion coefficient and q is the scattering vector, which, for our backscattering geometry, equals twice the wave number (4π/λ). For Brownian particles of diameter d, the diffusion coefficient relates to the temperature T and the viscosity η of the medium through the well-known Stokes-Einstein expression D=kBT/3πηd, where kB is Boltzmann's constant. The quantity IsCV in Equation 2 represents the average intensity of the light scattered from the coherence volume, IsCV=ΣjIj exp[−2(sj−s0)2/lc2]. For all the real light sources, the coherence length has a finite value, and therefore the inequality IsCV<Is always applies.
The investigated media can be optically dense but can still be analyzed by a single scattering model, as described in Equation 2. The fluctuations of the scattered light have been analyzed in the frequency domain based on the Fourier-transform relationship between the intensity autocorrelation function G2(τ) and the power spectrum P(ω). The associated power spectrum has a Lorentzian shape,
where Ω=Dq2 and A0 is the spectrum amplitude proportional to the product I0IsCV . Thus the amplitude A0 of the power spectrum can be expressed in simple form as A0=αρQb/d where d is the diameter of the particle, Qb is the backscattering efficiency, ρ is the density of the particles by volume, and α is an experimental constant. Since the dimension of the particle can be determined from the width of the power spectrum, as described above, the backscattering efficiency Qb, can be calculated for particles with known optical properties. Consequently, the particle concentration is obtained by the measurement of the A0 and calibration for the experimental constant, α.
The system 200 is capable of various specific configurations. In one such configuration, the light source 202 emits low-coherence light into a single-mode optical fiber 216 of the source branch 204. By way of example, the light source 202 comprises a broadband light source, such as a Hamamatsu Model #L3302, that produces light having a central wavelength of approximately 830 nm and a coherence length of approximately 5 μm to 20 μm, for instance 10 μm. In alternative embodiments, the light source can comprise an edge-emitting light emitting diode (LED), a superluminescent diode, multiple quantum well LEDs, a mode-locked Ti:AL203 laser, or a superfluorescent optical fiber. The light is transmitted through the single-mode optical fiber 216 and into a multi-mode optical waveguide 218, such as a multi-mode optical fiber, that is connected to the single-mode fiber optical with a coupler 220.
The optic coupler 206 is a 2×1 optic coupler and, in some configurations, comprises a graded index multi-mode coupler. Optionally, the sample branch 208 and the detector branch 210 comprise part of the optic coupler 206. In the system 200, both the sample branch 208 and the detector branch 210 comprise multi-mode optical waveguides, such as multi-mode optical fibers. By way of example, the detector 212 comprises a NewFocus Nirvana detector.
Light emitted from the light source 202 and delivered to the scattering medium 214 (
With the increased cross-sectional area of the multi-mode optical waveguide core 302, rays are collected by a greater number of scattering centers 306 such that a greater collection efficiency is achieved and a higher signal-to-noise ratio is obtained at the detector 212 (
When the light in the single-mode optical fiber 216 is launched into the coupler 220 (
E(r,ω,L)=√{square root over (PTU1)}(r,ω)exp(iβ1L) [Equation 4]
where PT is the total input power, β1 is the propagation constant of the eigenmode U1, and L is the propagation distance between the source and the medium under evaluation.
The reference field ER(r,ω,z) is obtained from the reflection of E(r,ω,L) at the end surface of the fiber 300. Due to the change of the propagation angle after the Fresnel reflection, a strong mode coupling occurs. The reference field is therefore a superposition of eigenmodes Um(r,ω) and can be expressed as
where βm is the propagation constant of mode Um, σ1m is the coupling efficiency from mode U1 to mode Um and N is the total number of propagating modes in the multimode fiber. One can notice from Equation 5 that all the mode are phase matched at z=0.
The portion RfPT of the total power in the reference field is obtained by integrating ER(r,ω,z) over the fiber surface as follows
RrPT=∫|ER(r,ω,z)|2d2r [Equation 6]
Using Equation 5, Equation 6 becomes
Since the eigenmodes Un of the fiber are orthonormal and satisfies the relation
∫U*m(r,ω)Un(r,ω)d2r=δnm [Equation 8]
equation 7 simplifies to
RfPT=PTm|σ1m|2 [Equation 9]
Assuming the power is evenly coupled in all the modes then σ1m=σ and
the non-reflected part of the incident field exits the fiber 300 and follows an optical path s in the medium. The part of the scattered light coupled back in the fiber 300 into the mode Un is characterized by the coefficient γn. The scattered field can then be written as a superposition of all the modes:
The portion of the power coming back in the fiber 300 after diffusion in the medium is determined by the coupling efficiency C. The power launched into the medium being PT(1−Rf), it follows from Equation 11 that we have the relation
CPT(1−Rf)=PTn|γn|2 [Equation 12]
Assuming that all the modes are equally excited, γn is independent of n and we deduce that
The frequency modulation of the intensity measured by the detector 212 arises from the interference between the reference field and the field scattered by the medium's flow. This modulated intensity is given by the real part of
IRS=∫S(ω)∫E*R(r,ω,z)Es(r,ω,z,s)d2rdω [Equation 14]
where S(ω) is the spectrum of the source. Using Equations 5 and 11, Equation 14 can be expressed as
Using the orthogonal property of the modes, Equation 15 simplifies to
One can see from this last relation, that the different propagation constants βn of the modes are canceled and therefore do not introduce intermodal dispersion, which can reduce the detection efficiency. Most of the power coupled from the single mode optical fiber 216 to the multi-mode fiber 218 is indeed concentrated in the fundamental mode and almost no mode coupling occurs during the propagation to the scattering medium. At the fiber-medium interface, the modes are excited in phase and contribute constructively to the interference signal. Assuming that the coupling coefficients σ1m and γ1m are independent of ω and the mode number m, then, using Equations 10 and 13, Equation 16 can be expressed as
IRS=PT√{square root over (C(1−Rf)Rf)}×Γ(S) [Equation 17]
where the self-coherence function Γ(s) is defined as
When a single-mode coupler is used instead of multi-mode fiber, the modulated intensity has an expression similar to Equation 17, namely
IRS=PT√{square root over (CSM(1−RfRf))}×Γ(S) [Equation 19]
where C has been replaced by the power coupling efficiency CSM of the single mode fiber. Due to their larger cores and numerical apertures, multi-mode optical waveguides have a much higher coupling efficiency than single-mode fibers, resulting in larger amplitude of the detected signal.
The improvement to signal amplitude and signal-to-noise ratio when a multi-mode optical waveguide is used instead of a single-mode optical fiber is evident in the graph of
Referring to
Other embodiments for the light scattering sensing system are possible. Example alternative embodiments can include features described in U.S. Pat. No. 6,958,816, which is hereby incorporated by reference into the present disclosure. For instance, the system could be arranged to incorporate one or more reference mirrors, as in the embodiment shown in FIG. 9 of that patent, or to comprise an open-air configuration as in the embodiments shown in FIGS. 10 and 11 of that patent.
While the above-described embodiments have been described to identify example implementations of the disclosed systems and methods, other embodiments are feasible. For example, in some embodiments, one or more of the light source, detector, analyzer, and optical waveguide(s) can be integrated together in a single device. Such an integrated device may be of particular interest for evaluating colloidal or polymer solutions.