Fiber-based distributed bolometry

Optical fibers are inherently designed to allow no interaction between the guided light and the surrounding optical radiation. Thus, very few optical fiber-based technologies exist in the field of optical radiation sensing. Accomplishing fully-distributed optical radiation sensing appears then as even more challenging since, on top of the lack of sensitivity explained above, we should add the need of addressing thousands of measurement points in a single, continuous optical cable. Nevertheless, it is clear that there exist a number of applications which could benefit from such a distributed sensing scheme, particularly if the sensitivity was sufficiently high to be able to measure correctly variations in optical radiation levels compatible with the earth surface. Distributed optical radiation sensing over large distances could be employed in applications such as Dynamic Line Rating (DLR), where it is known that solar radiation can be an important limiting factor in energy transmission through overhead power cables, and also in other applications such as thermo-solar energy. In this work, we present the proof-of-concept of the first distributed bolometer based on optical fiber technology and capable of detecting absolute changes of irradiance. The core idea of the system is the use of a special fiber coating with high emissivity (e.g., carbon coating or black paint). The high absorption of these coatings translates into a temperature change that can be read with sufficiently high sensitivity using phase-sensitive reflectometry. To demonstrate the concept, we interrogate distinct black-coated optical fibers using a chirped-pulse ΦOTDR, and we readily demonstrate the detection of light with resolutions in the order of 1% of the reference solar irradiance, offering a high-potential technology for integration in the aforementioned applications. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Several engineering applications are currently seeking for measurement methods providing continuous distributed measurements of optical radiation over large distances, typically around a few tens of kilometers.One of the most interesting and promising applications for large-scale spatially-resolved optical radiation detection is the optimization of power transmission along overhead power lines [1].The electrical line ratings are often kept below the optimum values, due to reliability and security concerns.A possible option to optimize the grid and improve efficiency is based on the concept of Dynamic Line Rating (DLR) [2].DLR replaces the traditional static ratings by updating the ampacity values in real time based on weather conditions and cable temperature.In DLR, temperature acquisition over the cable is often combined with meteorological measurements, which allow for precise models of behavior of the line conductor and therefore optimal values of transmission line limits [3].As recently reported [4], one of the environmental conditions that can considerably increase the temperature of the conductor in low wind speed conditions is solar radiation.Solar radiation has a direct influence in the ampacity of the conductor, and therefore should be monitored.However, very few dedicated technologies exist to enable this measurement in the power cable itself, and additionally, a single-point measurement of effective incident radiation is not sufficient to fully characterize the global combined effect of solar irradiance along the whole span [4].Therefore, there is a great interest in the dynamic and continuous monitoring of solar radiation along the conductor using distributed fiber sensing technology.
In other domains, Distributed Fiber Optic Sensors (DFOS) are gaining increasing attention due to their ability to perform continuous position-resolved measurements of different physical quantities along a certain monitored element.Distributed sensors allow replacing thousands of independent detectors which would be discretely disposed along a monitored structure or perimeter, by a single optical fiber cable connected to a single interrogation unit [5].This way, DFOS allow for an increase in space and weight efficiency, and lead to a reduction in the overall complexity, energy consumption and cost-per-sensor of the monitoring system, particularly when large numbers of detectors are required.Thanks to this, DFOS have proven to be convenient and cost-effective solutions for several problems in engineering, being currently a standard monitoring tool in certain types of large infrastructures [6,7].They have been shown to be particularly well-suited for the measurement of temperature [8][9][10], strain [11][12][13] and vibration/intrusions [14][15][16][17][18][19].In the energy domain, they have been extensively used to monitor long-distance pipelines [20] and also hot spots in power lines, as a tool for preventing failures related to high-temperature degradation inside the conductors [21].
The core idea of optical fiber distributed sensing consists in exploiting scattering effects intrinsic to the optical fiber (in order to sense different physical variables) and localize such interaction by means of time or frequency-domain techniques.The scattering processes appearing in fibers are Rayleigh, Brillouin or Raman [22].Since these phenomena are mostly temperature and/or strain dependent, DFOS are particularly well suited for the distributed measurement of these two physical quantities.Thus, distributed measurement of other parameters typically requires some type of transducing layer to convert the targeted physical quantity into a temperature or strain change in the fiber core.In the case of optical radiation, a possible solution might come by developing a photothermal-based distributed sensor, whose temperature changes in the presence of a certain irradiance.This could be accomplished by using a conventional optical fiber cable with a high emissivity coating.However, temperature resolutions of conventional distributed temperature sensors (e.g.Brillouin-based DFOS) are typically around 1 K [18].With this low temperature resolution, this idea becomes impractical, as the amount of radiation needed to have a measurable change in the cable temperature would be too high.Considering the expected temperature increase experienced by the fiber due to the absorbed radiation at the earth surface, this would yield an approach with very poor sensitivity, and inconvenient for a practical use.
Recently, the use of linearly chirped pulses in phase-sensitive optical time domain reflectometry (CP-ΦOTDR) has allowed achieving fast (kHz), robust and high sensitivity (mK) distributed fiber temperature measurements over distances of up to 70 km [23,24].With these sensitivities, the aforementioned ideas to develop a distributed bolometer are now made possible and practical.This is the starting point of our work.In this work, we make the proofof-concept of the first distributed optical radiation sensor, operating as a distributed bolometer interrogated by a CP-ΦOTDR.To this end, we make use of black-coated fibers for increased absorption.The proposed method readily achieves a resolution compatible with solar radiation detection (≈1% of the reference solar spectral irradiance on earth [25]), achieving an important milestone in optical radiation sensing technology.This demonstration opens the door for important applications in industries related to solar radiation, creating a highpotential feasible solution which can be applied in different engineering sectors.

Developing a bolometer
A bolometer can be implemented by connecting an absorptive element to a thermal reservoir with a constant temperature through a thermal link.Radiation reaching the absorber causes an increase in its temperature to a higher value than the reservoir temperature.Let us consider a heat sink with a temperature 0 T , assumed constant, weakly connected to an absorptive element which has a temperature 0 ( ) T T ≥ .The temperature T depends on the incident irradiance reaching the absorber, inc E .In the case of no incident radiation, 0 inc E = , then the temperature of the absorber will be equal to the temperature of the reservoir, 0 T T = .When 0 inc E > , the absorber element absorbs an optical power abs proportional to the absorber area inc A , and the absorption of the absorber, α.Consequently, T increases to a higher value than the heat sink temperature, so 0 T T > .Assuming a small temperature difference 0 T T − between the elements, the absorber dissipates power to the heat sink, as described by Newton's law of cooling [24]: where h is the heat transfer coefficient between the absorber element and the reservoir, and A is the heat transfer surface area.The rate equation describing the balance of energy occurring in the bolometer system in these conditions is given by: , where c and m represent the absorber's specific heat and mass, respectively.The terms Therefore, the energy gained in the system depends on the optical power absorbed by the element, which increases for higher values of incident radiation, while the energy lost depends on the dissipated optical power to the reservoir.By replacing the previous relations in Eq. ( 2), we obtain: which, in a simpler way, can be described as: being . The solution to this differential equation can be easily derived, and it has the form of: 0 ( ) exp .
Considering that at 0 t = the temperature of the absorptive element is equal to the heat sink's temperature, 0 ( 0) T t T = = , we can calculate the value of the constant K , which is given by: .
Finally, replacing the result from Eq. ( 8) in Eq. ( 7), we arrive to the general rate equation of the system which describes the temporal evolution of the element's temperature with relation to the applied irradiance: Furthermore, as it was seen from Eqs. ( 3) and ( 4), as the element's temperature increases due absorption, so does the dissipation, which is proportional to the difference in the temperatures between the element and the reservoir.Therefore, the system eventually evolves towards a thermal equilibrium state where Hence, by equaling 0 ( -) , or simply by considering a large value of t in Eq. ( 9), it is derived the following relation at the thermal equilibrium state: where ¢ is a constant which depends on the system parameters.This way, given a certain system at the thermal equilibrium condition where all the necessary constants are known, the incident radiation inc E can be calculated using the relation shown in Eq. ( 10).

Proposed fiber-based distributed bolometer
In this work, we recreate the bolometer operation principle using an optical fiber system.In the proposed configuration, a black-coated optical fiber is used as the absorbing element and the surrounding air is used as the heat sink, at T 0 .A second fiber with much lower absorptance to the incident radiation (and hence different temperature) is connected to the same interrogation system.The temperature of both optical fibers is monitored with mK resolution using a CP-ΦOTDR, allowing for a highly accurate tracking of the temperature difference between both fibers.The proposed system can be analyzed considering that the two fibers present different absorptance values (α 1 , α 2 ) to the incident radiation, and also (possibly) different heat transfer coefficients h 1 , h 2 .By monitoring the temperature difference between the two fibers simultaneously, it is possible to determine the value of irradiance reaching the fibers.In this case, the equilibrium state with the surrounding air will be reached at different temperatures, T 1 , T 2 , for the fibers 1 and 2: By replacing Eq. ( 11) in Eq. ( 12), it is then derived that: This way, by using two fibers with different coating (and therefore distinct optical absorption coefficients), an incident irradiance E inc can be measured given an unknown external temperature value, T 0, by simply measuring the difference between the temperature shifts obtained for the two fibers.Additionally, the values of ¢1 and ¢2 can also accommodate for different values of the heat transfer coefficient h and are not really needed individually, but only the value of the difference 2 1 ¢ ¢ − .This can easily be obtained by applying a known inc E to the reference and the absorber fiber, and by measuring the resulting 2 1 T T − in equilibrium.

CP-φOTDR: Distributed temperature sensor
The experimental setup proposed for the proof-of-concept demonstration of a distributed bolometer is depicted in Fig. 1.A CP-ΦOTDR interrogator [23] was used to monitor the temperature of the reference and the absorber optical fibers.This monitoring tool allows for high sensitivity and fast distributed measurements of temperature variations.Further information on the operation of this measurement technique can be found in [23].The specific interrogation scheme used in this work is very similar to the one used in one of our former works [24].It consists of a block responsible for generating linearly-chirped pulses and sending them towards the Fibers Under Test (FUTs); and a second block responsible for the detection of the Rayleigh backscattered light generated during the process.To generate the linearly-chirped pulses, a Laser Diode (LD) working in continuous emission, driven by a standard temperature and current controller (I&T), was modulated in current through an electrical ramp signal from a Signal Generator (SG).By synchronizing the laser current modulation with a square-wave to the driver of a Semiconductor Optical Amplifier (SOA), linearly-chirped pulses could be formed.The pulses were then amplified by means of an Erbium-doped Fiber Amplifier (EDFA).The pulse power was controlled with a tunable attenuator in order to prevent the advent of non-linear effects in the optical fiber, and filtered using a Dense Wavelength-division Multiplexer (DWDM) to reduce the amplified spontaneous emission (ASE) produced by the amplifier.The pulses were launched into the FUTs through an optical circulator.The generated Rayleigh backscattered light was then collected, amplified and filtered before reaching the photodetector, after which it was recorded by a high-speed digitizer.
In this case, the CP-ΦOTDR measurements were performed using 100 ns pulses, corresponding to a 10-meter spatial resolution.These pulses were linearly chirped with ≈1 GHz of total pulse frequency content.The detection scheme enables a temperature sampling period of 40 ms, resulting in a temperature resolution of ≈2 mK.Although a simple proof-ofconcept of a distributed bolometer is intended in this work, this method could be readily extended to match the limits set by the interrogation technique (CP-ΦOTDR), which could reach mK resolutions over up to 70 km, with metric spatial resolution and sampling rates in the order of 1 kHz [23].A more detailed description of the FUTs interrogated with this method is found in section 3.3.

Fiber-based bolometer system
In Fig. 2, a more detailed representation of the irradiance detection part of the setup is presented.It refers to the optical radiation emission/absorption mechanism, which can be found after the optical circulator in Fig. 1.As mentioned above, the distributed bolometer system consists in monitoring the temperature difference between two standard fibers with different coatings (and thus, different absorption coefficients).Therefore, a normal transparent-coating single-mode fiber (lower absorption coefficient) was used as the temperature reference fiber, FUT 1 .Three distinct black-coated fibers with higher absorption coefficients were tested as the absorptive-sensitive fiber, FUT 2 .All the FUTs had an outer diameter of ~0.25 mm, and each FUT had an overlapping section of ~10 m, corresponding to the interrogator spatial resolution.The ~10m of the reference FUT 1 and of each absorbing FUT 2 were wrapped in concentric circles with a radius of ~10 cm.They were placed contiguous to each other with the transparent fiber in front, as shown in Fig. 2.This ensured that both fibers experienced the same environmental conditions and that they received the same uniform radiation along, at least, the length of the interrogator spatial resolution.The two optical fibers were spliced together, so that they could be simultaneously monitored by the CP-ΦOTDR interrogator.A warm white LED lamp, operating at 12 V with 800-1000 total lumens, was used as optical radiation source emitting visible radiation towards the fibers.The lamp was disposed on a translation stage, enabling it to move and to be placed at difference discrete positions.This way, by changing the distance between the optical radiation source and the FUTs, different irradiance values could be applied to the fibers.The applied irradiance values were also monitored by a calibrated optical radiometer placed at the FUTs position.

Absorptive optical fibers
As it was mentioned above, different black-coated fibers were interrogated using the proposed method, in order to study the temperature response obtained under different absorption conditions.One of the highly-absorptive optical fibers tested was simply a blackpainted fiber, which consists of a normal SMF with the coating dyed in black.The layer of black dye is estimated to be ~40 μm thick, giving the fiber a total coating thickness of ~102.5 μm.A multi-mode and a single-mode carbon-coated fibers were also interrogated [26].These have a ~20 nm thick carbon film deposited between the glass surface and the primary coating, and were used since, in addition of having a dark-coating (i.e.high absorptance to the incident radiation) as seen in Fig. 3, they are widely industrialized fibers, which means that they can offer a reliable and feasible solution for a ready implementation.The single-mode carboncoated fiber used in these tests has an acrylate primary coating with a thickness of 62.5 μm, while the multi-mode carbon-coated fiber includes a polyimide primary coating with a thickness of 2 top of the dar mode fiber.operation sho

Proof-of-
In the proofirradiance, in studied under in cycles of 2 of irradiance v = 43.8W/m 2 , Note that all F that the radiat obtained can experienced b fiber, respecti FUT's temper inciple is FUT 1 and lues.This bsorption q. ( 13)), a e carbon-Wm −2 K −1 ) −2 K −1 ) for a greater mpared to o carbontween the he singlered to the he singley of more , we also verified as well that the experimentally obtained value of α/h was within the range of expectable theoretical values (according to the large variability of α and h).Also note that the sensitivity of one of the carbon fibers was characterized at three different positions, obtaining an equal sensitivity within the error of our measuring system.This indicates that we can rely on a constant sensitivity of the carbon-coated fibers along its length, as it was expected.Anyway, a reasonable sensitivity was achieved with the industrially fabricated fibers, in particular with the single-mode carbon-coated fiber, showing that this sensor can potentially be used in long distance applications.However, the ratio between applied radiances and temperature shifts for each set of fibers should be constant.The error in the measurements can have occurred since the temperature signals do not reach a perfect equilibrium state in the short cycles between irradiance stages (3.33 to 10 seconds).In any case, note that the step between the irradiances applied (≈15 W/m 2 ) corresponds to only ≈1.5% of the reference solar spectral irradiance on earth at surface level [25].This is an important result, since it demonstrates the compatibility between our proposed method and real solar-based applications.

Dynamic optical radiation measurements
After demonstrating the working principle, dynamic measurements were performed to the fibers in the transient-regime, in order to characterize the system linearity.Instead of using only one cycle of 25s or 35s for each given irradiance, the fibers were characterized without reaching the thermal equilibrium.They were interrogated under shorter irradiance cycles of 10s, 5s and 3.33 s, periodically applied over several minutes.The driving motivation behind this method is that by computing enough short cycles in a sufficiently long measurement (considering the time of temperature drifts), the amplitude of the signal obtained by a Fourier transform already compensates for the external fluctuations occurring during the measurements.Also, this amplitude provides a measurement which is proportional to the absorption coefficient of the fiber.This way, the use of a second fiber is not necessary, and it is also possible to characterize the absorption coefficients (α in Eq. ( 7)) of individual fibers separately.Therefore, the dynamic optical radiation was applied using a square wave at the LED electrical input.This results in alternating "on" and "off" states of the lamp, with a specific amplitude.The distinct values of irradiance were applied by moving the lamp with the translation stage, and they were applied to the absorptive fibers, being the reference temperature fiber removed.Since thermal equilibrium is never reached along the multiple cycles, the fiber temperature oscillates around a certain mean value.The amplitude of these temperature oscillations is expected to be linearly proportional to the amplitude of the applied irradiance, as it is proportional to the absorbed optical power ( abs Or, in a different way, the linearity can be expected from the rate equation outside equilibrium (Eq.( 9)), considering the same time for each incident irradiance at the absorber.
Figure 7 shows the results obtained for the amplitude of the temperature sensor regarding the different applied irradiances, using three square wave signals with periods of 10 s, 5 s and 3.33 s.Once again, a higher sensitivity was achieved using the black-painted fiber, followed by the single-mode carbon-coated fiber.These results are in agreement with the ones obtained in the previous section, which are directly linked to the absorption coefficient values of each structure.All tested fibers showed a linear amplitude response to the applied irradiance, as expected.The amplitude of the temperature oscillations depends on the period of the applied square function, since for larger periodic cycles the fiber will undergo a larger exposure time, increasing, therefore, the absorbed optical power (and also the time to cool down, so it starts again from a lower value).The different slopes obtained for each fiber were expected from Eq. ( 9), since for a certain fixed value of irradiance, the linear relation between the temperature a times, accordi

Conclusio
In this work, was presented absorptance t between the tw and the inciden ing to the expr irradiance without knowledge of the surrounding temperature.The interrogation technique used (CP-ΦOTDR) enabled high-sensitivity measurements of this temperature difference, while enabling to monitor tens of km-long distances in a spatially continuous fashion.Three different optical fibers were interrogated, showing that the proposed method is sufficiently sensitive using both multi-mode and single-mode fibers, showing a slightly increased sensitivity in the single-mode case.Employing a black-painted single-mode fiber (with higher emissivity and a slightly thicker coating) endows greater sensitivity in the optical irradiance absorption when compared to the other tested coatings, though new and/or existing enhanced fiber-coatings may as well be tested with this method.The sensor was readily demonstrated to be able to measure absolute values of irradiance with sensitivities of the order of 10 W/m 2 (equivalent to ≈1% of the reference solar spectral irradiance at the earth surface), and corresponding to temperature differences of ≈150 mK.However, the available sensitivities with the CP-ΦOTDR can reach ~2mK over tens of km with meter scale spatial resolutions.Therefore, the proposed sensor can be further explored in order to match its full capability.
Overall, the demonstrated detector has a high potential for integration in solar radiationbased applications, such as DLR forecasting or photovoltaic industries, becoming the first but feasible solution in distributed fiber-based optical radiation sensing.In this sense, the presented photothermal optical radiation sensor has been proven to work with already industrially available fibers, offering a reliable and ready-to-implement solution.Considering that the interrogated quantity is the temperature, the proposed system also provides the possibility of working at conventional telecom wavelengths, being feasible to integrate using conventional communication components.To approach practical applications, it is necessary to assess the operation of this method at a real time-scale.Further studies should be developed evaluating the response of the sensor in a 24h time-scale evaluation, in order to demonstrate the compatibility with real daily solar irradiance values along a whole day.Nevertheless, considering the average irradiance change along a full day and the sensitivity of our system (1% of the irradiance reference), this method should be compliant with those standards.Other experimental conditions should as well be improved in future studies in order to better approach the applied irradiation to normal solar conditions, as for example the integration of a lamp whose features are closer to solar irradiation and farther from the blue-emission zone.
Lastly, it could also be envisaged that optical fibers with different coating-colors might also be interrogated by CP-ΦOTDR, in order to achieve a spectral footprint associated with each fiber color and more advanced distributed bolometry based on spectral discrimination.
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