Enhancing sensitivity in absorption spectroscopy using a scattering cavity

Absorption spectroscopy is widely used to detect samples with spectral specificity. Here, we propose and demonstrate a method for enhancing the sensitivity of absorption spectroscopy. Exploiting multiple light scattering generated by a boron nitride (h-BN) scattering cavity, the optical path lengths of light inside a diffusive reflective cavity are significantly increased, resulting in more than ten times enhancement of sensitivity in absorption spectroscopy. We demonstrate highly sensitive spectral measurements of low concentrations of malachite green and crystal violet aqueous solutions. Because this method only requires the addition of a scattering cavity to existing absorption spectroscopy, it is expected to enable immediate and widespread applications in various fields, from analytical chemistry to environmental sciences.

where I 0 and I are the measured intensities in the absence of a sample and in the presence of a sample, respectively, A is the dimensionless absorbance of the sample, ε is the molar attenuation coefficient of the sample, and c is the molar concentration of the solution 9 .
The sensitivity of absorption spectroscopy can be enhanced by increasing l. For instance, multi-path absorption cells with mirrors have been employed [10][11][12][13] . Such systems can significantly amplify the OPL but generally require a bulky system and sophisticated alignment. Attenuated total reflection spectroscopy exploits multiple total internal reflections in a crystal, which creates an evanescent wave 14,15 . However, this method requires a complicated configuration, such as the exact optical contact between a sample and a crystal 16 . The need for a method of using simpler and more compact equipment to increase the OPL has been developed 17 .
Multiple light scattering has been exploited to increase the OPL and overcome the limitations of conventional optical elements 18 , including superlens 19 , temperature 20 , pressure sensing 21 , wavelength meters 22 , fiber-based spectrometers 23 , and non-resonant lasers 24 . The existing approaches employing the multiple scattering regime are represented by an integrating sphere [25][26][27][28] . Absorption spectroscopy using an integrating sphere has the advantage of increasing the OPL without the demand for precise alignment of a beam and optical components 25 .
Recently, Martin et al. 29 suggested multiple scattering for enhancing the sensitivity of absorption spectroscopy. Dielectric microspheres were added to a sample solution to induce multiple scattering, which effectively increased the OPL. However, this method has various limitations: it requires the addition of microspheres for each measurement. Once mixed with microspheres for measurement, the remaining beads prevented the reuse of the sample. In addition, the degree of increase in the OPL varies depending on the quantity and size of the beads, as well as the refractive index (RI) difference between the microspheres and the sample. Thus, the enhancement factor varies according to the experimental environment.
Here, we present a simple but powerful method for increasing the OPL in absorption spectroscopy. By introducing a scattering cavity to existing absorption spectroscopy to enclose a sample, the sensitivity of the measurements is significantly improved, because the light is trapped inside a scattering cavity and interacts with a sample numerous times before exiting. This method does not perturb a sample or require complex instruments. (1) In addition, the method does not require calibration for each measurement and has not interfered with the sample condition. Although there are methods that showed the increase of the OPL using an integrating sphere, our method can be an alternative in the practical perspective because the present scattering cavity is easily combined with an existing commercial cuvette and a spectrometer in the minimal modification. With this regard, we demonstrate that the limit of detection (LOD) can be lowered to what extent with a commercial cuvette.

Materials and methods
In the conventional method, light passes through a cuvette only once. In the proposed method, the diffusive surface of a scattering cavity scatters light, causing the diffusively reflected light to pass through a longer path, and the reflected light is collected several times (Fig. 1a). The experimental setup was composed of a halogen lamp (OSL1-EC, Thorlabs, Inc.), a custom-made scattering cavity, and a spectrometer (HR4000, Ocean Optics, Inc.) (Fig. 1b). Two linear polarizers (LPVISE100-A, Thorlabs, Inc.) were employed as the beam power attenuators. A short-pass filter (under 750 nm, FES0750, Thorlabs, Inc.) was utilized to filter the wavelengths that exceeded the spectral range of the spectrometer. Note that linear polarizers and short-pass filters are not essential components.
The scattering cavity was made of > 99.5% purity hexagonal boron nitride (h-BN). h-BN exhibits minimal absorbance 30,31 , and high diffuse reflectance in the visible region 32 makes h-BN suitable for absorption spectroscopy. Due to its graphite-like atomic structure, h-BN exhibits excellent mechanical properties and exhibits satisfactory machinability [33][34][35][36] . The diffuse reflectance of h-BN was calibrated using a spectrophotometer (Lambda 1050, Perkin Elmer, Inc.) (Fig. 1c). h-BN has a high diffuse reflectance of more than 80% at wavelengths longer than 500 nm. The inverse adding-doubling method 37,38 was used to estimate the absorption and scattering coefficients of h-BN. The estimated absorption coefficient µ a and reduced scattering coefficient µ ′ s were 0.023 mm −1 and 129 mm −1 , respectively, at 532 nm. The front and top views of the scattering cavity are shown in Fig. 1d. To prevent the direct passing of normal incident light, the exit hole was offset from the entrance with a height difference of 10 mm. The height difference makes the light hit the wall of the scattering cavity and multiply-reflected. Generally, the roughness of the surface will change the specular reflection portion of the reflected light. In our cavity geometry, however, the offset between the entrance and exit holes prevents the domination of the direct or few specular reflections, similar to the function of baffles in a conventional integrating sphere.

Results
Measurement of the normalized intensity and absorbance with the scattering cavity. To verify this method, the absorption spectra of malachite green and crystal violet were measured. The differentiation of substances from the absorption spectrum of their mixtures has been a difficult task in absorption spectroscopy, especially when two or more substances have overlapped absorption peaks 39 . We demonstrated the www.nature.com/scientificreports/ proposed method for pure solutions. Malachite green and crystal violet have high water solubility and exhibit maximum absorption at wavelengths of 617 nm and 590 nm, respectively 40,41 . We measured the malachite green aqueous solutions at various concentrations (Fig. 2). It was difficult to discern the malachite green solution with the naked eye when the concentration was below 1 µM (Fig. 2a). The absorption spectra were measured from the sample solution and deionized (DI) water, which correspond to I and I 0 , respectively, in Eq. (1). The normalized spectrum I/I 0 using the conventional method was measured in the same manner. Figure 2b presents the normalized spectra using the proposed and conventional methods for 0.2 µM malachite green aqueous solution. The absorption dip at 617 nm can be clearly observed in the proposed method, whereas the conventional method provides a low signal-to-noise ratio (SNR). The normalized spectra of malachite green and crystal violet aqueous solutions at various concentrations are shown in Fig. 3. For validation, five measurements were acquired from the same sample solution (Fig. 3a,b) and five individual solutions of the same concentration (Fig. 3c,d). We discovered that the absorption dips were consistently observed at 617 nm and 590 nm for malachite green and crystal violet, respectively, which shows an agreement with the known values. In addition, the linear relationship between concentration and absorbance in Eq. (1) is shown with high R-square values in the graphs of the absorbance (Fig. 3a-d). The linearity of the  Enhancement factor for the sensitivity of detection. According to the results using the scattering cavity in Fig. 3, it is possible to see a distinct dip of the normalized intensity. To quantify the enhancement in absorbance (−log(I/I 0 )) of the proposed method, we calculated the ratio of the absorbances between the proposed method and the conventional method (control) using the same sample solution (malachite green and crystal violet, 1 µM) (Fig. 4a,b). The normalized intensity depending on the wavelength contains 25 data for each case. Figure 4c,d show the enhancement factor as a function of the wavelength for both aqueous solutions. For wavelengths near the dips, the enhancement factors were almost constant regardless of the wavelength. The highly variable enhancement in the low-absorbance regimes is due to the near-zero absorbance of the control experiments. The averaged enhancement factors at the wavelengths near the dip were 10.22 times and 10.41 times for malachite green and crystal violet, respectively (Fig. 4e). Because the increment in the OPL is not dependent on the sample, the result of a similar enhancement for the two samples is reasonable.

Limit of detection.
The LOD is the lowest concentration of a sample that discernable with the absence of the sample 42 and can be lower by enhancing the measured absorbance. To determine the LOD of the proposed system, we used highly diluted malachite green solutions (Fig. 5). The LOD was obtained by interpolating the concentration that yields the absorbance criterion μ 0 + 3σ 0 , where μ 0 and σ 0 are the mean and standard deviation, respectively, of the results using pure water (0 µM) 42,43 . The evaluation of the LOD via pure water (blank solution) fundamentally reflects the systematic error of the detection system. Figure 5a shows the absorbance measurements for the LOD calibration. We employed malachite green solutions at concentrations of 0.040 µM and 0.004 µM for the conventional system (control) and proposed system, respectively. Figure 5b,c show the shaded regions in Fig. 5a. The absorbance was calculated from the mean and standard deviation of the 0 µM (pure water) absorbance results. We found that the absorbance criteria were μ 0 + 3σ 0 = 0.01 in both cases. Note that the absorbance criteria should be the same in both cases because the zero fluctuations are solely derived from the sensitivity and precision of the detection system. In the conventional method (control), the linear correlation was maintained up to 0.120 µM, but the deviation increased for concentrations lower than 0.100 µM (Fig. 5b). The calibrated LOD was 0.059 µM, which was consistent with the data observations. In the proposed method, it is noteworthy that the linearity was maintained at substantially lower concentrations (minimum of 0.010 µM) than in the conventional method (Fig. 5c). The calibrated LOD was 0.004 µM, which is lower than 1/10 of the LOD of the control.

Conclusion
In summary, we present a scattering cavity to enhance the sensitivity of absorption spectroscopy via a significant increase in the OPL. The scattering cavity was composed of h-BN and led to diffusive reflection on its surface, achieving an improvement in the absorbance by more than 10 times. Moreover, the LOD was drastically lowered in the scattering cavity, and malachite green could be detected even at 0.004 µM using a commercial cuvette. We expect that a higher diffuse reflectance will further improve the enhancement factor. For example, a commercially available highly reflective surface shows > 99% diffuse reflectance in the visible and near-infrared range 44 ; many common ceramics (such as alumina and zirconia) or synthetic polymers (such as PTFE) with high reflectance can be utilized instead. Furthermore, the proposed method may be improved by optimizing the size of the entrance and the scattering cavity for further enhancement of the OPL 24 .
It should be emphasized that the proposed method using multiple scattering is more robust against misalignment than the methods using specular reflection of a mirror. In addition, the proposed method enables quick and simple measurement of absorbance using a plastic cuvette, which is commonly employed in analytical chemistry and can be readily applicable to existing spectrometers. Due to the effectiveness of the proposed method in detecting trace amounts of a sample mixed in a liquid solvent, the method is expected to widen the detection range for a substance and the wavelength of interest, expanding the research area. We believe that our system can be beneficial for practical applications that require low LOD in water 45 , such as those in the food industry 46 , pathological diagnosis 47 , and biochemical sensing 48,49 .