Distributed sensing using continuous fiber bragg grating (FBG)

Abstract

This disclosure teaches launching input light into an optical fiber at two (2) different center wavelengths (λl and λh), with each center wavelength having a corresponding wavelength range (Δλl and Δλh, respectively). The fiber into which the input light is launched has a continuous fiber Bragg grating (FBG) and exhibits a higher-than-Rayleigh backscattering in a high-backscattering-fiber wavelength range (Δλf). The Δλf includes the λl +Δλl / 2and the λh - Δλh / 2. The λf shifts as a function of strain (ε), temperature (T), pressure (P), or other detectable parameter (X). Both the λl input light and the λh input light are backscattered by the optical fiber. The backscattered light at λl has a total power of Pb(λl). The backscattered light at λh has a total power of Pb(λh). Because λf shifts as a function of X (or ε, T, P, etc.), the Pb(λl) and the Pb(λh) correspondingly changes as a function of X.

Description

DISTRIBUTED SENSING USING CONTINUOUS FIBER BRAGG GRATING (FBG)BACKGROUNDFIELD OF THE DISCLOSURE

[0001] The present disclosure relates generally to optical fiber sensors and, more particularly, to systems and methods for sensing using a continuous fiber Bragg grating (FBG).DESCRIPTION OF RELATED ART

[0002] Fiber-optic sensors have been used for temperature and strain measurements. However, current systems may not be sufficient for measurements that require high spatial resolution, high temperature resolution, and short measurement time. Thus, there are ongoing efforts to improve optical fiber sensors.SUMMARY

[0003] The present disclosure provides systems and methods for optical-fiber-based sensing. Briefly described, one embodiment comprises launching input light into an optical fiber at two (2) separate center wavelengths (a lower center wavelength (Xi) and a higher center wavelength (Xh)), with each center wavelength having a corresponding wavelength range (AXi and AXh, respectively). The optical fiber into which the input light is launched has a continuous fiber Bragg grating (FBG) and exhibits a higher-than-Rayleigh backscattering in a high-backscattering fiber wavelength range (AXf) with a center wavelength (Xf). The spectra of the lights only partially overlap with AXf. Specifically, AXf overlaps with an upper edge of AXi and, further, AXf overlaps with a lower edge of AXh. Thus, (Xi+AXi / 2) and (Xh- AXh / 2) (meaning the upper edge of AXi the lower edge of AXh, respectively) are found within AXf,, while (Xi-AXi / 2) and (Xh+AXh / 2) (meaning a lower edge of AXi and an upper edge of AXh, respectively) are outside AXf . The Xf shifts as a function of strain (E), temperature (T), pressure (P), or other detectable parameter (X). Thus, Xf is dependent on parameters that affect X (e.g., E, T, P, etc.). Both the Xi input light and the Xh input light are backscattered by the optical fiber. The backscattered light at Xi has a total power of Pb(Xi), while the backscattered light at Xh has a total power of Pb(Xh). Because Xf shifts as a function of X (or£, T, P, etc.), the Pb(Xi) and the Pb(Xh) correspondingly changes as a function of X (or £ or T or P or whatnot). Specifically, Pb(Xi) decreases as Xf increases, while Pb(Xh) increases as Xf increases. Consequently, changes in X (e.g., £, T, P, etc.) correspond to the difference between Pb(Xi) and Pb(Xh). Since Pb(Xi) and Pb(Xh) change in opposite directions, measuring both Pb(Xi) and Pb(Xh) increases the sensitivity. Furthermore, the system becomes self- refencing (meaning, measurements will be largely immune to errors that can be caused by launching power fluctuations, connection loss change, fiber loss, etc.).

[0004] Other systems, devices, methods, features, and advantages will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present disclosure, and be protected by the accompanying claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0005] Many aspects of the disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure.Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

[0006] FIG. 1 is a system diagram 100 showing one embodiment of an optical fiber 110 having a continuous fiber Bragg grating (FBG), in which backscattered light 120 is measured in response to input light 130 being launched into the optical fiber 110.

[0007] FIG. 2 is a is a graph 200 showing a high-backscattering spectrum (R(X,X)) for an optical fiber having a higher-than-Rayleigh backscattering region, with the R(X,X) having a high-backscattering center wavelength (Xf) and a high-backscattering wavelength range (AXf).

[0008] FIG. 3 is a system diagram 300 showing one embodiment of an optical fiber 310 with a continuous FBG, into which both a lower wavelength input light 320 (centered at Xi) and a higher wavelength input light 325 (centered at Xh) are launched, and the total power for the respective backscattered light 330, 335 (Pb(Xi) and Pb(Xh), respectively) are measured.

[0009] FIG. 4 is a graph 400 showing one embodiment with an overlap between theAXf with AXi and A h.

[0010] FIG. 5A is a diagram 500a showing one embodiment having a lower- wavelength spectrum (AXi) and a higher- wavelength spectrum (AXh) at a baseline temperature (T).

[0011] FIG. 5B is a diagram 500b showing changes in the spectra of the embodiment of FIG. 5 A when there is a change in temperature (AT).

[0012] FIG. 6 is a graph showing changes in measured total power (in units of decibels (dB)) as a function of changes in T (in units of Celsius (°C)) for both Pb(Xi) 610 and Pb(Xh) 620.

[0013] FIG. 7 is a diagram 700 showing a high-backscattering spectrum 710 for one embodiment of an optical fiber comprising two (2) regions with higher-than-Rayleigh backscattering, along with example input wavelength ranges 720, 730.

[0014] FIG. 8 is a system diagram 800 showing another embodiment of an optical fiber 810 having a continuous fiber Bragg grating (FBG), in which backscattered light 820 is measured in response to input light 830 being launched into the optical fiber 810.DETAILED DESCRIPTION OF THE EMBODIMENTS

[0015] Fiber-optic sensors have been used for temperature and strain measurements. Conventional systems that employ distributed Raman-based sensing suffer from low signal- to-noise ratio (SNR) because back-scattered Raman signals are low. Conventional FBG systems collect backscattering from an optical fiber at a single center wavelength and, thus, require frequency-scanning processes (or wavelength-scanning processes), such as optical frequency domain reflectometry (OFDR), time-domain wavelength division multiplexing (TD-WDM), or other lengthy data acquisition methods.

[0016] Furthermore, Raman-based backscattering systems typically have very low signal-to-noise ratio (SNR) with backscattering coefficients of approximately negative 95 decibels-per-meter (-95dB / m) for its Stokes signal and -lOOdB / m for its anti-Stokes signal for a single-mode fiber (SMF) with a 1550 nanometer (nm) pump signal at room temperature. Consequently, these conventional Raman-based systems often require long time-averaging (on the order of several minutes) or larger spatial resolution to increase SNR for sufficient temperature resolution (on the order of ~0.1 degrees Celsius (°C)).

[0017] Other systems, such as optical-fiber-based distributed temperature sensing (DTS) systems use discrete gratings and a scanning light source, which have the ability to provide higher SNR and better temperature resolution (on the order of -0.01 °C). But the number of gratings for such conventional DTS systems is limited (usually, to less than 1,000 gratings). Additionally, conventional DTS systems are complicated and not well-suited for longer-length or higher-spatial-resolution applications.

[0018] Ultimately, current Raman-based DTS systems or discrete gratings systems are largely insufficient for higher-spatial resolution measurements and higher-temperature resolution measurements in shorter measurement times.

[0019] To these and other limitations, this disclosure teaches systems and processes that permit higher spatial resolution, higher temperature resolution, and shorter measurement times.

[0020] Unlike conventional systems and processes, the present disclosure teaches embodiments of systems and methods that collect backscattering from two (2) different wavelength ranges (not a single backscattering wavelength range), thereby permitting faster and simpler measurements. Specifically, the present disclosure provides systems and methods in which input light is launched into an optical fiber at two (2) separate center wavelengths (a lower center wavelength (Xi) and a higher center wavelength (Xh)), with each center wavelength having a corresponding wavelength range (AXi and AXh, respectively). The optical fiber into which the input light is launched has a continuous fiber Bragg grating (FBG) and exhibits a higher-than-Rayleigh backscattering in a high-backscattering fiber wavelength range (AXf) with a center wavelength (Xf). The spectra of the lights only partially overlap with AXf. Specifically, AXf overlaps with an upper edge of AXi and, further, AXf overlaps with a lower edge of AXh. Thus, (Xi+AXi / 2) and (Xh-AXh / 2) (meaning the upper edge of AXi the lower edge of AXh, respectively) are found within AXf„ while (Xi-AXi / 2) and (Xh+AXh / 2) (meaning a lower edge of AXi and an upper edge of AXh, respectively) are outside AXf . The Xf shifts as a function of strain (s), temperature (T), pressure (P), or other detectable parameter (X). Thus, Xf is dependent on parameters that affect X (e.g., a, T, P, etc.). Both the Xi input light and the Xh input light are backscattered by the optical fiber. The backscattered light at Xi has a total power of Pb(Xi), while the backscattered light at Xh has a total power of Pb(Xh). Because Xf shifts as a function of X (or a, T, P, etc.), the Pb(Xi) and thePb( h) correspondingly changes as a function of X (or s or T or P or whatnot). Specifically, Pb(Ai) decreases as Af increases, while Pb(Ah) increases as f increases. Consequently, changes in X (e.g., s, T, P, etc.) correspond to the difference between Pb(Ai) and Pb(Ah). Since Pb(Ai) and Pb(Ah) change in opposite directions, measuring both Pb( i) and Pb(Ah) increases the sensitivity. Furthermore, the system becomes self-refencing (meaning, measurements will be largely immune to errors that can be caused by launching power fluctuations, connection loss change, fiber loss, etc.).

[0021] Having provided a broad technical solution to a technical problem, reference is now made in detail to the description of the embodiments as illustrated in the drawings. While several embodiments are described in connection with these drawings, there is no intent to limit the disclosure to the embodiment or embodiments disclosed herein. On the contrary, the intent is to cover all alternatives, modifications, and equivalents.

[0022] FIG. 1 is a system diagram 100 showing one embodiment of an optical fiber 110 having a continuous fiber Bragg grating (FBG), in which backscattered light 120 is measured in response to input light 130 being launched into the optical fiber 110. As shown in FIG. 1, when input light 130 is launched into an optical fiber 110 having a continuous FBG, the launched light is backscattered and returns as backscattering light 120 to the launch point. The backscattered light 120 is affected by the characteristics of the optical fiber 110, as well as the properties of the input light 130. One example of the optical fiber 110 is AcoustiSens® optical fiber, manufactured by OFS Fitel, LLC, which exhibits higher-than- Rayleigh backscattering coefficient of approximately -63dB / m to approximately -53dB / m at a pump wavelength of 1550nm. These backscattering values are approximately 30dB higher (and sometimes even higher) than Raman Stokes (approximately -95dB / m) and anti-Stokes (approximately -lOOdB / m) backscattering.

[0023] FIG. 2 is a is a graph 200 showing a high-backscattering spectrum (R(X,A)) for an optical fiber having a higher-than-Rayleigh backscattering region, with the R(X,A) having a high-backscattering center wavelength (Af) and a high-backscattering wavelength range (AAf). R(X,A) depends on characteristics of the fiber, which in turn depend on changes to measurable parameters (X), such as strain (e), temperature (T), pressure (P), etc. Specifically, as E, T, P, or X changes, the R(X,A) changes proportionally.

[0024] This is demonstrated in the embodiment of FIG. 3, which is a system diagram300 showing one embodiment of an optical fiber 310 with a continuous FBG, into which both a lower wavelength input light 320 (centered at Xi) and a higher wavelength input light 325 (centered at Xh) are launched, and the total power for the respective backscattered light 330, 335 (Pb( i) andPb(Xh), respectively) are measured.

[0025] When pulsed light with an input spectrum of P(X) is launched into the high- backscattering fiber, the total power of the backscattered (or back-reflected) light can be represented as:with Pb representing the total power of the backscattered light (reflected back from the optical fiber), Pi representing the total power of the input light (launched into the optical fiber), X representing a center wavelength of the input light (and also the backscattered light), AX representing the wavelength range of the input light, and X representing the parameter of interest (e.g., E, T, P, etc.).

[0026] Specifically, as shown in FIG. 3, pulsed input light 320, 325 at two (2) different wavelengths is launched into a high-backscattering optical fiber 310 with a continuous FBG (with a backscattering spectrum of R(X,X), which is centered at Xf and has a wavelength range of AXf). The two pulsed inputs are at a lower center wavelength Xi (with a lower wavelength range AXi) and a higher center wavelength Xh (with a higher wavelength range AXh). Because the pulsed input comprises two (2) different input wavelengths, the optical fiber 310 produces two (2) different backscattered signals 330, 335, each with its own measurable total power:and

[0027] Significantly, R(X,Xi) and R(X,Xh) are sensitive to changes in X (or AX) and, thus, shift correspondingly with AX. Thus, if AXi overlaps with the AXf and Xi is located within the AXf, then AX directly affects Pb(Xi). Similarly, if AXh overlaps with the AXf and Xh is located within the AXf, then AX directly affects Pb(Xh). Furthermore, the degree to whichAX affects Pb(Xi) is different than the degree to which AX affects Pb(Xh). Consequently, by measuring both Pb(Xi) and Pb(Xh), one can determine AX based on how much Pb(Xi) and Pb(Xh) have changed.

[0028] As an example, FIG. 4 shows a graph 400 of one embodiment with an overlap between the AXf with AXi and AXh (with both Xi and Xh being located within AXf), thereby allowing for measurements of Pb(Xi) and Pb(Xh). Also, FIGS. 5 A and 5B show embodiments 500a, 500b in which X is a temperature (T). Specifically, FIG. 5A shows backscattering 500a at a baseline T and FIG. 5B shows backscattering 500b at AT (showing how AXi decreases as a function of AT, while AXh increases as a iunction of AT). Because AXi decreases as a function of AT while AXh increases as a function of AT, the difference in total power (in units of decibels (dB)) can be plotted as a iunction of AT (in degrees Celsius (°C)) for both Pb(Xi) 610 and Pb(Xh) 620, as shown in FIG. 6.

[0029] For purposes of clarity, a non-limiting example for strain (E) or temperature (T) are provided for a distributed sensing process. Again, the optical fiber has a continuous FBG and, also, a higher-than-Rayleigh backscattering in AXf, with the higher-than-Rayleigh backscattering having a R(T,X). Here, the R(T,X) is dependent on T and on a center wavelength of the light launched into the fiber. For this particular example, the process launches a lower wavelength pulsed input light into the optical fiber, with the lower wavelength pulsed input light comprising a AXi that is between approximately 1532 nanometers (~1532nm) and approximately 1540 nanometers (~1540nm) and a Xi of approximately 1536 nanometers (~1536nm). The input light has a lower wavelength input light spectrum Pi(Xi). The process also launches a higher wavelength pulsed input light into the optical fiber concurrently with the launching of the lower wavelength pulsed input light. The higher wavelength pulsed input light comprises a AXh that is between ~1553nm and ~1561nm. The higher wavelength pulsed input light also comprises Xh of ~1557nm and a higher wavelength input light spectrum (Pi(Xh)).

[0030] After launching the light with Pi(Xi) and Pi(Xh), the process measures Pb(Xi) and Pb(Xh), which are represented as:andfrom which AT can be calculated.

[0031] For the same parameters, s can be measured (rather than T) by simply substituting R(E,X) for R(T,X). In other words, as one having ordinary skill in the art will appreciate, any measurable parameter (X) that is dependent on R(X,X) can be substituted for £ or T, thereby permitting measurements of AX, AT, As, or whatnot, based on known inputs of Pi(Xi) and Pi(Xh) and direct measurements of Pb(Xi) and Pb(Xh).

[0032] As shown in FIGS. 1 through 6, the disclosed embodiments collect backscattering from two (2) different wavelength ranges (not a single backscattering wavelength range), thereby permitting faster and simpler measurements. Specifically, light is launched into an optical fiber at Xi and Xh. Thereafter, Pb(Xi) and Pb(Xh) are measured, both of which correspondingly change as a iunction of X (or E or T or P or whatnot). Consequently, changes in X (e.g., s, T, P, etc.) correspond to the difference between Pb(Xi) and Pb(Xh), thereby allowing for faster measurements with higher spatial resolution and higher measurement resolution of X (or s or T or P or whatnot).

[0033] Continuing, FIG. 7 is a diagram 700 showing a high-backscattering spectrum 710 for one embodiment of an optical fiber comprising two (2) regions with higher-than- Rayleigh backscattering, along with example input wavelength ranges 720, 730. As shown in FIG. 7, if an optical fiber has R(X,X) with two (2) high-backscattering regions (which exhibit higher-than-Rayleigh backscattering), then AXi and AXh can be situated strategically to maximize the resulting changes in Pb(Xi) and Pb(Xh) with changes in X (or E, or T, or P, or whatnot).

[0034] FIG. 8 is a system diagram 800 showing another embodiment of an optical fiber 810 having a continuous fiber Bragg grating (FBG), in which backscattered light 820 is measured in response to input light 830 being launched into the optical fiber 810. For comparison, FIG. 3 provides input light 320, 325 at two (2) wavelength bands (AXi and AXh), but FIG. 8 provides a single broadband input light 820 with a wavelength band (AX) and a center wavelength (X). Thus, to obtain Pb(Xi) and Pb(Xh), bandpass filtering is applied to the reflect light at two different wavelength ranges to produce a filtered reflected light 830. Because that filtered reflected light has been band-pass filtered, the resulting filtered reflected light 830 provides Pb(Xi) and Pb(Xh). Furthermore, because X is still dependent on X (or E or T or P or whatnot), changes in Pb(Xi) and Pb(Xh) will correspond to the changes in X(or s, T, P, etc.).

[0035] Thus, as shown in FIGS. 1 through 8, collecting backscattering information from two (2) different wavelength ranges (not a single backscattering wavelength range) permits faster and simpler measurements with higher spatial resolution and higher measurement resolution of the parameter-of-interest.

[0036] Any process descriptions or blocks in flow charts should be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps in the process, and alternate implementations are included within the scope of the preferred embodiment of the present disclosure in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the iunctionality involved, as would be understood by those reasonably skilled in the art of the present disclosure.

[0037] Although exemplary embodiments have been shown and described, it will be clear to those of ordinary skill in the art that a number of changes, modifications, or alterations to the disclosure as described may be made. All such changes, modifications, and alterations should therefore be seen as within the scope of the disclosure.

Claims

What is claimed is:

1. A distributed sensing process using an optical fiber, the optical fiber having a continuous fiber Bragg grating (FBG), the optical fiber having a higher-than-Rayleigh backscattering in a high-backscattering wavelength range (AXf), the higher-than-Rayleigh backscattering having a high backscattering spectrum (R(T,X)), the R(T,X) being dependent on a temperature (T), the R(T,X) further being dependent on a center wavelength (X) of the light launched into the fiber, the process comprising: launching a lower wavelength pulsed input light into the optical fiber, the lower wavelength pulsed input light comprising: a lower wavelength range (AXi) that is between approximately 1532 nanometers (~1532nm) and approximately 1540 nanometers (~1540nm); a lower center wavelength (Xi) of approximately 1536 nanometers (~1536nm); and a lower wavelength input light spectrum (Pi(Xi)); launching a higher wavelength pulsed input light into the optical fiber concurrently with launching the lower wavelength pulsed input light, the higher wavelength pulsed input light comprising: a higher wavelength range (AXh) that is between approximately 1553 nanometers (~1553nm) and approximately 1561 nanometers (~1561nm); a higher center wavelength (Xh) of approximately 1557 nanometers (~1557nm); and a higher wavelength input light spectrum (Pj(Xh)); measuring a first total power of a lower wavelength backscattered light (Pb(Xi)), the lower wavelength backscattered light having a center wavelength of Xi, wherein:PM = I M ■ RCW • dXi;measuring a second total power of a higher wavelength backscattered light (Pb(Xh)), the higher wavelength backscattered light having a center wavelength of Xh, wherein:determining changes in the temperature (AT) as a function of Pb(Xh) - Pb(Xi).

2. A distributed sensing process using an optical fiber, the optical fiber having a continuous fiber Bragg grating (FBG), the optical fiber having a higher-than-Rayleigh backscattering in a high-backscattering wavelength range (AXf), the higher-than-Rayleigh backscattering having a backscattering spectrum (R(X,X)), the R(X,X) being dependent on a parameter of interest (X), the R(X,X) further being dependent on a center wavelength ( ) of light launched into the optical fiber, the process comprising: launching a lower wavelength pulsed input light into the optical fiber, the lower wavelength pulsed input light having a lower wavelength range (AXi) that overlaps with the AXf, the AXi comprising: a lower center wavelength (Xi) such that Xz+is located within the AXr, anda lower wavelength input light spectrum (Pj(Xi)); launching a higher wavelength pulsed input light into the optical fiber concurrently with launching the lower wavelength pulsed input light, the higher wavelength pulsed input light having a higher wavelength range (AXh) that overlaps with the AXf, the AXh comprising: a higher center wavelength (Xh) such that Xh—is located within the AXf,and a higher wavelength input light spectrum (Pi(Xh)); measuring a first total power of a lower wavelength backscattered light (Pb(Xi)), the lower wavelength backscattered light having a center wavelength of Xi, wherein:measuring a second total power of a higher wavelength backscattered light (Pb(Xh)), the higher wavelength backscattered light having a center wavelength of Xh, wherein:determining changes in the parameter of interest (AX) as a fimction of Pb(Xh) and Pb(Xi).

3. The process of claim 2, wherein the X is a temperature (T) and the AX is a change in temperature (AT).

4. The process of claim 3, wherein:R(T,λ) shifts to longer wavelengths as T increases; and R(T,λ) shifts to shorter wavelengths as T decreases.

5. The process of claim 3, wherein:Pb(λh) increases as T increases; and Pb(λi) decreases as T increases.

6. The process of claim 3, wherein:Pb(λh) decreases as T decreases; and Pb(λi) increases as T decreases.

7. The process of claim 3, wherein AT is directly proportional to Pb(Xh) - Pb(Xi).

8. The process of claim 2, wherein the X is a strain (E) and the AX is a change in strain (As).

9. The process of claim 8, wherein:R(ε,λ) shifts to longer wavelengths as E increases; andR(ε,λ) shifts to shorter wavelengths as E deceases.

10. The process of claim 8, wherein:Pb(λh) increases as E increases; and Pb(λi) decreases as E increases.

11. The process of claim 8, wherein:Pb(λh) decreases as E decreases; and Pb(λi) increases as s decreases.

12. The process of claim 8, wherein As is directly proportional to Pb(λh) - Pb(λ1).

13. The process of claim 2, wherein the AXf is greater than approximately ten nanometers (~10nm) in width.

14. The process of claim 2, wherein the AXf is less than approximately twenty nanometers (~20nm) in width.

15. The process of claim 2, wherein the AXf is from approximately 1535 nanometers (~1535nm) to approximately 1560 nanometers (~1560nm).

16. The process of claim 2, wherein:Xi is approximately 1536 nanometers (~1536nm); andAXi is approximately eight nanometers (~8nm).

17. The process of claim 2, wherein: approximately 1540 nanometers (~1540nm); and approximately 1532 nanometers (~1532nm).

18. The process of claim 2, wherein: h is approximately 1557 nanometers (~1557nm); andAXh is approximately eight nanometers (~8nm).

19. The process of claim 2, wherein: approximately 1561 nanometers (~1561nm); and approximately 1553 nanometers (~1553nm).

20. A distributed sensing process using an optical fiber, the optical fiber having a continuous fiber Bragg grating (FBG), the optical fiber having a higher-than-Rayleigh backscattering in a high-backscattering wavelength range (AXf), the higher-than-Rayleigh backscattering having a backscattering spectrum (R(X,X)), the R(X,X) being dependent on a parameter of interest (X), the R(X,X) further being dependent on a center wavelength ( ) of light launched into the optical fiber, the process comprising: launching a broadband pulsed input light into the optical fiber, the broadband pulsed input light having a wavelength range (A ); receiving backscattered light; filtering the backscattered light to produce a lower- wavelength backscattered light and a higher-wavelength backscattered light, wherein: the lower- wavelength backscattered light comprises a lower wavelength range (AXi) that overlaps with the AXf, the AXi comprising: a lower center wavelength (Xi) such that Xz4- is located within AXf,and a lower- wavelength backscattered light spectrum (Pb(Xi)); the higher-wavelength backscattered light comprises a higher wavelength range (AXh) that overlaps with the AXf, the AXh comprising: a higher center wavelength (Xh) such that Xh—is located withinAXf, and a higher-wavelength backscattered light spectrum (Pb(Xh)); and determining changes in the parameter of interest (AX) as a function of Pb(Xh) and Pb(Xi).

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