2.1.

Basic Concept and Its Proof

In this section, we describe the operation principle and the proof-of-concept experiment reported previously.¹³ In a luminescent solar concentrator (LSC),^14,15 a luminescent material embedded in a transparent plate converts sunlight to PL photons and they are harvested by the solar cells attached to the edge surfaces of the plate. Some of them are lost during the waveguiding process due to absorption by the luminescent material. This problem of self-absorption has been recognized since the early days.¹⁶ Because it limits the power conversion efficiency of an LSC, its large-scale deployment remains unpractical. Self-absorption manifests in other negative manners. For a uniform luminescent layer where scattering events can be neglected, it causes an emission spectrum to vary with the emission angle.¹⁷ It complicates the measurement of quantum yield of luminescent materials.

We proposed to utilize this unwanted effect for 1-D position sensing. As illustrated in Fig. 1(a), an optical fiber is coupled to the edge surface of a waveguide in which a luminescent material is uniformly dispersed. We call such a waveguide “fluorescent waveguide (FWG)” in this paper. For the moment, we work with a planar waveguide for simplicity of the experiment described below although a linear waveguide would suffice for 1-D position sensing. When an excitation beam of light is incident at $y=L$, PL photons are emitted. Some of them propagate this distance and enter the optical fiber. A spectrometer records the spectrum of the PL photons in which shorter-wavelength photons are lost due to self-absorption. The degree of this redshift in the PL spectra depends on the distance $L$. Hence, we can determine the incident position of the beam by quantifying it. These procedures are analyzed in the following three steps.

Fig. 1

One-dimensional PSD based on redshift in PL spectra. (a) A bird’s eye view. (b) The cross section of the coupling section.

First, we derive the probability of collecting the PL photons by the spectrometer. Assume isotropic emission of PL photons at $y=L$. The angle $\theta$, as defined in Fig. 1(b), is expressed as $\theta ={\tan }^{-1}\frac{D}{2L}$, where $D$ is the core diameter. Numerical aperture of the optical fiber (NA) determines the acceptance angle ${\theta }_{\max }$. Denoting the refractive index of the waveguide as $n$, the relation $n\sin {\theta }_{\max }=\mathrm{NA}$ holds. We assume that the refractive index is matched at the core and the waveguide. Then, the condition for the PL photon reaching the optical fiber and propagating inside is expressed as $\theta <{\theta }_{\max }$, i.e., ${\tan }^{-1}\frac{D}{2L}<{\sin }^{-1}\frac{\mathrm{NA}}{n}$. This condition is rewritten as

Second, we express the spectrum as a function of the distance $L$. Let $\mu (\lambda )$ be the absorption coefficient of this waveguide at wavelength $\lambda$ and $S_i(\lambda )$ be the initial spectrum before redshift. The PL photon emitted with an angle $\theta$ propagates the distance $L/\cos \theta$ to reach the optical fiber. The Lambert–Beer’s law gives the following expression for the spectrum of the PL photons entering the optical fiber:

In case of $D/L\ll 1$, Eqs. (2) and (3) are approximated as follows:

Third, we have some options about how to quantify the degree of redshift. In the following experiment, we calculate the chromaticity coordinates with the CIE1931 color-matching functions.

To prove this basic concept, we carried out a simple experiment using the planar FWG, which is shown in the inset of Fig. 2(a). This was supplied by Nitto Jushi Kogyo Co. Ltd. The dimension and transmittance at 450 nm of this FWG were $40\mathrm{mm}\times 40\mathrm{mm}\times 2.9\mathrm{mm}$ and 0.0018, respectively. The hole at the upper left corner was meant for bundling multiple samples and it did not affect our measurement. In a darkroom, we excited a single point on the FWG with a laser (Z-Laser, Model Z30M18-F-450-pe). The optics built in this laser module focused the beam, and its spot size was about 0.1 mm. The wavelength of the excitation light was 450 nm and its power was set to $83\mu \mathrm{W}$. The core diameter and numerical aperture of the optical fiber (Ocean Optics, Model P400-21-VIS/NTR) were $400\mu \mathrm{m}$ and 0.22, respectively. The integration time of the spectrometer (Ocean Optics, Model FLMS02760) was set to 2 ms. These experimental conditions allowed us to acquire the PL spectra and they were not necessarily optimized in terms of signal-to-noise ratio. We varied the incident position of the beam along the $y$ axis with a 2-mm step and recorded each PL spectrum. The result is shown in Fig. 2(a). As the $y$ coordinate of the incident position ($L$) increases, the spectral intensity below 500 nm decreases more rapidly. This is due to self-absorption. The rate of change in the spectral intensity tends to saturate as $L$ approaches 20 mm. In addition, we integrate each spectrum to obtain a value proportional to the PL intensity. As shown in Fig. 2(b), it is roughly proportional to the inverse of the distance $L$. Also shown is a fit by Eq. (4), where $A$ is a constant. Note that the values in Fig. 2(b) are proportional to the power of the incident radiation times the integration time. Hence, once we know the incident position of radiation with unknown power, we can use Fig. 2(b) to estimate its power.

Fig. 2

PL spectrum and its integrated value corresponding to each incident point of the excitation light at 450 nm. (a) The spectral intensity below 500 nm decreases more rapidly than that above it as the distance $L$ increases. A photograph of the planar fluorescent waveguide is shown in the inset. (b) The value obtained by integrating each spectrum in (a).

To quantify the redshift in Fig. 2(a), we used the CIE1931 color-matching functions [$\overline{x}(\lambda )$, $\overline{y}(\lambda )$, and $\overline{z}(\lambda )$] to calculate the $x$ and $y$ chromaticity coordinates. As shown in Fig. 3(a), the chromaticity coordinate $x$ increases monotonically with the distance $L$, while the chromaticity coordinate $y$ shows a peak. In Fig. 3(b), we plot the distance $L$ as a function of the ratio $x/y$. The solid circles represent the measured data and they are well fit by the following equation:

Fig. 3

Chromaticity coordinates calculated from each spectrum in Fig. 2(a). (a) The coordinates shift to a redder region as the incident position moves away from the edge surface. (b) The ratio of the chromaticity coordinates $x/y$ is almost proportional to the distance $L$. The line represents a linear fitting.

2.2.

Linear Fluorescent Waveguide

In the previous section, we used a planar FWG to prove the basic concept of utilizing redshift in PL spectra for 1-D position sensing. The next step was to demonstrate it with a linear FWG, which paves a way for applying this technique to a 2-D PSD. In fact, two linear FWGs were used to configure a 2-D PSD, as described in Ref. 18.

We fabricated a linear FWG by filling a hollow transparent tube with a fluorescent material. Its structure is illustrated in Fig. 4(a). In the experiment, we put a syringe needle half way into a heat-shrink tubing (Ohm Electric Inc., Tokyo, OHM 2.0C) and heated the tube by blowing hot air on it for about 10 s. We injected a mixture of a UV-curable resin (Norland, NOA81) and a luminescent material (BASF, Lumogen F Red 305) into the shrunk tube through the syringe. The concentration of Lumogen F Red 305 was 0.02 wt. % in this experiment. The resin was cured by ultraviolet (UV) light irradiation. Finally, we cut the tube to detach the needle and filed the surface of the linear FWG with an abrasive paper.

Fig. 4

Experimental setup and a photograph of 1-D position sensing. (a) The structure of a linear FWG.¹⁸ (b) The linear FWG is butt-coupled to the optical fiber head and its single spot is irradiated. (c) A photograph of the linear FWG coupled to the optical fiber head.

As in the previous experiment, the following measurement was carried out in a darkroom. We recorded the redshift in the PL spectrum when we varied the distance $L$ from 1 to 33 mm with a 2-mm step. The integration time of the spectrometer was set to 11 ms and data acquisition was repeated 20 times for averaging to suppress noise. As shown in Figs. 4(b) and 4(c), we excited a single point on the linear FWG by the laser emitting at 450 nm with its power of $348\mu \mathrm{W}$.

The recorded spectra are shown in Fig. 5. We measured the spectrum for $L\le 33\mathrm{mm}$ beyond which the signal became so small. Compared to Fig. 2(a), the monotonic decrease of the intensity with the distance $L$ is more gradual. This is expected from the geometrical confinement effect for the PL photons by the tubing configuration. The chromaticity coordinates calculated from these spectra are shown in Fig. 6(a). Here, we set the range of the distance $L$ such that the change in the chromaticity coordinate $y$ is monotonic. The coordinates calculated from the spectra measured at $L\ge 23\mathrm{mm}$ have large uncertainties, indicating that the redshift is almost completed at $L=23\mathrm{mm}$. By limiting the detection range to $3\mathrm{mm}\le L\le 21\mathrm{mm}$, the distances $L$ and $y$ are well correlated, as shown in Fig. 6(b). Because the redshift in the spectrum, measured at $L=1\mathrm{mm}$, is small, we also exclude the corresponding coordinate to improve the fitting. The fitting equation is given as

Fig. 5

Spectrum corresponding to each incident position of the excitation beam at 450 nm.

Fig. 6

Chromaticity coordinates calculated from the spectra in Fig. 5 and the CIE1931 color-matching functions. (a) The coordinates shift to a redder region as the distance $L$ increases. (b) The distance $L$ is well fitted by a cubic function of $y$.

Calculating the chromaticity coordinates is not the only means for determining $L$. For example, we define the following index $I_2/I_1$ based on the measured spectrum $S(\lambda )$

Now, we try to relate $I_2/I_1$ to the distance $L$. Setting the integration range to $630\mathrm{nm}<\lambda <640\mathrm{nm}$ for $\mathrm{\Delta }{\lambda }_{\mathrm{SA}}$ and $650\mathrm{nm}<\lambda <655\mathrm{nm}$ for $\mathrm{\Delta }{\lambda }_{\mathrm{NSA}}$, we have calculated this index and the result is shown in Fig. 7. When we limit the range of $L$ to $3\mathrm{mm}\le L\le 29\mathrm{mm}$, the distance is well fit by the following equation:

Fig. 7

The index $I_2/I_1$ calculated from the spectra in Fig. 5.

2.3.

Extending the Detection Range

Our position-sensing technique relies on the spectral change. Once the redshift is completed, propagation over a further distance does not alter the shape of the PL spectrum. Hence, to extend the detection range further, we expect that the transmission loss within an FWG must be low. A commercial scintillating fiber has much lower transmission loss than our homemade linear FWG. As in the previous experiments, we have investigated the relation between the redshift of the PL spectrum and the distance $L$. The experimental setup is shown in Fig. 8. We used a scintillating fiber (Kuraray Co., Ltd., Japan, Model SCSF-78) for this experiment. Its length was 300 cm. A laser emitting at 377 nm was used as the excitation light source to excite the luminescent material inside the fiber more efficiently. We varied the distance $L$ from 10 to 290 cm with a 10-cm step. The power of the excitation light incident on the fiber through the neutral-density filter was measured to be $120.9\mu \mathrm{W}$. The measurement was done in a darkroom.

Fig. 8

A photograph of the experimental setup of PSD utilizing a scintillating fiber.

As shown in Fig. 9, the intensity of the recorded spectra monotonically decreases as the distance $L$ increases. Note that the range of $L$ is much wider in this experiment.

Fig. 9

Dependency of the spectrum on the distance $L$ for the Kuraray scintillating fiber excited at 377 nm.

In Fig. 10, we have plotted the distance $L$ as a function of the chromaticity coordinate $y$ calculated from the measured spectra. The distance $L$ is well fit by the following equation:

Fig. 10

The relation between the chromaticity coordinate $y$ and the distance $L$.

Again, we tried the index $I_2/I_1$ defined by Eq. (3) with the integration range of $440\mathrm{nm}\le \lambda \le 455\mathrm{nm}$ for $\mathrm{\Delta }{\lambda }_{\mathrm{SA}}$ and $500\mathrm{nm}\le \lambda \le 505\mathrm{nm}$ for $\mathrm{\Delta }{\lambda }_{\mathrm{NSA}}$. The result is shown in Fig. 11. The distance $L$ is well fit by the following equation:

Fig. 11

The index $I_2/I_1$ calculated from the spectra in Fig. 9.

2.4.

Discussions

First, we discuss the signal-to-noise ratio of the PSDs based on this technique. Because the noise is essentially determined by the electronics involved, we focus on the signal size. There are two aspects here: the sensor-head design and the signal extraction process. The sensor-head design is specific to each application at hand. The PL spectrum at the end of a linear FWG is proportional to (a) the energy of the incoming radiation absorbed by the luminescent material, (b) its conversion efficiency to PL photons (quantum yield), and (c) the probability of the PL photons reaching the end of the linear FWG. These factors need to be considered specifically for each application. In addition, the signal extraction process plays an important role in determining the signal size. Calculating chromaticity coordinates is one option, which requires a spectrometer. It has a built-in slit, and the diffraction efficiency of its grating is limited. Hence, the PL photons are not efficiently utilized. In this regard, the index $I_2/I_1$ is preferred because we can measure this quantity directly. Namely, a photodiode covered by a bandpass filter would give $I_1$ and another photodiode with another bandpass filter would give $I_2$. A transistor connected to a photodiode enables the integration-mode operation, where the photo-generated charges are accumulated for a certain period of time. This is the building block of an image sensor.²¹ If the radiation is incident at a constant rate, the signal size is proportional to this integration time. This condition applies for x-rays and also for decays of a radioactive material as long as its halftime is much longer than the integration time. In fact, low-intensity gamma-ray imaging was demonstrated with a long integration time.²²

Second, we discuss the possibility of applying this sensing technique for radiation monitoring. When a 1-MeV gamma ray deposits its full energy in an evaporated CsI(Tl) layer, more than 25,000 electrons are generated in a crystalline Si photodiode coupled to it.²³ Photon yields of various scintillators are measured and expressed in units of photons/MeV.²⁴ The number for plastic scintillators is about $\mathrm{10,000}\text{photons}/\mathrm{MeV}$. Compton scattering is the dominant interaction for a matter with a low atomic number.¹ Let us start a rough calculation of signal size by assuming that a Compton event by a 1-MeV photon deposits 500 keV in a luminescent material. About 5000 photons are generated in the visible range. A photodiode would convert these photons to 2500 electrons if its quantum efficiency is 0.5. A charge-sensitive amplifier is often used for radiation detection. Its equivalent noise charge is as small as 38 electrons.²⁵ Therefore, we expect that single photon counting of 1-MeV gamma rays is possible. If appropriate, we can resort to the integration-mode operation to increase the signal. One might wish to increase the detection efficiency by surrounding the sensing medium with a high atomic-number material such as lead glass tubing.²⁶ This would induce Compton scattering events more efficiently and the luminescent material would have a higher chance of interaction with the scattered x-rays. From these arguments, we expect that the basic concept described in Sec. 2.1 can be applied for radiation monitoring, although this needs to be confirmed by future experiments. In the experiments described in this paper, luminescent materials convert blue and UV photons from the lasers to PL photons. This phenomenon mimics the radioluminescence in a scintillator.

3.1.

Two-Stage Photoluminescence Conversion

As illustrated in Fig. 12(a), we configure a 2-D PSD by coupling two linear FWGs to the left and right edge surfaces of a planar FWG. The planer FWG contains a first fluorescent material. The linear FWG contains a second fluorescent material. We choose the fluorescent materials such that the PL photons of the first fluorescent material excite the second fluorescent material.

Fig. 12

Configuration of a 2-D PSD based on two-stage PL conversion with FWGs.¹⁸ (a) A planar FWG and two linear FWGs constitute a sensor head. (b) The PL photons generated by the planar FWG enter the two linear FWGs with a certain intensity distribution, which can be roughly estimated by a simple geometrical calculation (see the text for detail).

When an excitation beam hits a spot $(X,Y)$ on the planar FWG, as depicted in Fig. 12(b), PL photons are generated and some of them enter the linear FWG at $x=L/2$ with a certain intensity distribution $I_{\mathrm{ex}}(y)$. The PL photons also reach the linear FWG at $x=-L/2$ with a different distribution. A simple 2-D model can roughly reproduce these distributions as follows. Let us place an isotropic emitter at $(X,Y)$ in a lossless medium and consider a photon propagating from this point to a narrow section at $(L/2,y)$. Denoting the width of this section as $\mathrm{\Delta }y$, the probability of the photon reaching this section is equal to ${\theta }_d/2\pi$, where ${\theta }_d$ is the angle subtended by this section. Because the distribution $I_{\mathrm{ex}}(y)$ is proportional to this probability, it is expressed as

These PL photons from the planer FWG generate the second PL photons in the linear FWGs. Some of the second PL photons reach the end of the linear FWG and are guided to the spectrometer through the optical fiber. The spectra of the PL photons are recorded for each linear FWG: $S_R(\lambda )$ and $S_L(\lambda )$. To determine the incident spot $(X,Y)$, we define the following two indices. As described in Sec. 2, quantification of the redshift in the PL spectra gives the coordinate $Y$. Here, we adopt the second index for determining the coordinate $Y$ as follows:

3.2.

Experiment

We fabricated a planar FWG with a mixture of Coumarin 6 (Sigma-Aldrich), UV-curable resin (NOA81) and two $50\mathrm{mm}\times 50\mathrm{mm}\times 4\mathrm{mm}$ acrylic plates, according to the method described in Ref. 17. Briefly, we sandwiched the mixture with two rectangular acrylic plates and cured the resin. The thickness of the phosphor layer was of the order of 0.1 mm. Linear FWGs were fabricated with a mixture of Lumogen F Red 305 and the same UV-curable resin by the method described in Sec. 2.2. Note that the PL photons from Coumarin 6 can excite Lumogen F Red 305.^19,20 The concentrations of Coumarin 6 and Lumogen F Red 305 were 0.07 and 0.01 wt. %, respectively. The length of the linear FWGs was about 90 mm. As shown in Fig. 13, the two linear FWGs were coupled to the two edge surfaces of the planar FWG with the UV-curable resin (NOA81). We painted the other two edge surfaces black to minimize light reflection there. The surfaces of the two linear FWGs were also painted black.

Fig. 13

Photograph of the sensor head.

We used the same optical fibers (Ocean Optics, Model P400-21-VIS/NTR) for guiding the PL photons from each linear FWG to a spectrometer (Ocean Optics, USB2000). The end of each linear FWG was butt-coupled to each optical fiber with a mating sleeve (Thorlabs, ADASMAV SMA to SMA mating sleeve). We placed the same laser unit (Z-Laser, ZZ30M18-F-450-pe) emitting at 450 nm with optical power of $3.4\mu \mathrm{W}$ on an $X-Y$ stage (Sigmakoki, TAM-1202SUU). The integration time of the spectrometer was set to 5 s. All the measurements were carried out in a darkroom.

We changed the excitation point $(X,Y)$ in the first quadrant of the planar FWG, as shown in Fig. 12(b). The measured spectra are shown in Fig. 14. For each graph, the coordinate $X$ is fixed, while the coordinate $Y$ is varied. There are a couple of features to be noted here. First, as shown in Fig. 14(c), the intensity of the PL photons in the wavelength range from 600 to 640 nm decreases as $Y$ increases. This redshift in the spectra becomes less evident at $X=0$, as shown in Fig. 14(a). We attribute this observation to the fact that $I_{\mathrm{ex}}(y)$ becomes wider and smaller at a small $X$. Second, the PL intensity at the wavelength $>640\mathrm{nm}$, where there is no self-absorption, decreases as $Y$ increases. This trend is observed consistently, irrespective of $X$. Again, we believe that this is due to the function $I_{\mathrm{ex}}(y)$: the number of the PL photons entering the linear FWGs decreases as $Y$ increases.

Fig. 14

The spectra of the PL photons from the right linear FWG. The excitation laser beam hits each point on the grid. In each plot, $X$ is fixed and $Y$ is varied.

3.3.

Analysis

We calculated the index $L_X$ using Eq. (14) and the measured spectra. As $X$ increases, the index $L_X$ increases monotonically, as shown in Fig. 15. It is strongly dependent on $X$, whereas its dependency on $Y$ is relatively small. For example, we fit $L_X$ as a function of $X$ as follows:

Fig. 15

The index $L_X$ is regarded as a function of the coordinate $X$ only.

The solid curve in Fig. 15 represents the fitting. The experimental data are more or less reproduced by this equation. Hence, we calculate the coordinate $X$ from the index $L_X$ as follows:

Fig. 16

Index $L_Y$ calculated from Eq. (13). It is proportional to $Y$ with the common intercept at $Y_0=4$ and different slope $\frac{\mathrm{d}{L}_Y}{\mathrm{d}Y}$ for each $X$.

Fig. 17

Slope $\mathrm{d}{L}_Y/\mathrm{d}Y$ plotted as a function of the coordinate $X$.

3.4.

Error

Using Eqs. (10) and (13), we estimated the incident position $(X,Y)$. We compare the result with true positions in Fig. 18. The dots and crosses represent the true and the estimated positions, respectively. The discrepancy between them takes its maximum value of 1.5 mm for the incident position $(X,Y)=(\mathrm{0,20})$.

Fig. 18

The true incident positions (dots) and the estimated ones (crosses).