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Abstract
In this study, we demonstrate a reflective imaging system in which a dual polarizer structure, consisting of a uniform polarizer and a polarizer on the pixel of a polarization image sensor, enables the detection of weak polarization changes. The uniform polarizer can achieve a high extinction ratio and is used to render the amount of polarization change in a condition that is easily detectable by the polarization image sensor. The polarization image sensor uses two types of polarizers arranged in an orthogonal relationship with each other to obtain complementary signals for polarization rotation. This is also used for differential detection to reduce the in-phase noise components. In the prototype system, the signal characteristics were in close agreement with theoretical considerations. Furthermore, as a demonstration of high-sensitivity polarization rotation imaging, the polarization rotation of a menthol solution in a 150-µm-thick channel was detected.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical polarization is one of the most useful means to obtain information, such as the birefringence of materials, molecular orientation, angle of reflected surfaces, and structure, optically and noninvasively [1,2]. Image sensors with a polarizer at each pixel have been proposed as a method for observing such distributions. Various types of polarizers, such as metal wire grids [3–12], dielectric multilayer films in the form of gratings [13], and polymers [14] have been used as on-pixel polarizers. These techniques enable visualization of the distribution of the polarization rotation with removal of the reflection components. The aforementioned examples are techniques for detecting relatively large differences in the polarization angles.
However, methods to measure more subtle changes in polarization have been applied in the fields of materials science and electronics. For example, a method to measure the amount of polarization rotation has been used to detect the concentration of optical isomers. In addition, techniques have been developed to measure the intensity of electric and magnetic fields by converting them into the amount of polarization rotation using electro-optical and magneto-optical effects [15–19]. In these techniques, light with pre-controlled polarization is irradiated , and the amount of polarization change is observed. Therefore, even slight changes in polarization have to be detected with high sensitivity.
Imaging this weak polarization rotation distribution is expected to be applied in various fields. However, the polarization detection performance of a polarizer in a polarization image sensor or pixel array equipped with a polarizer is lower than that of a single component and is unsuitable for weak polarization detection.
The low saturation light intensity of the pixel also makes detection by the image sensor difficult. The polarizer, which acts as an analyzer, converts the slight polarization rotation into a slight light intensity change. The photon shot noise determines the signal-to-noise ratio (SNR) of the photodetector when the light intensity is sufficiently high. As photon shot noise is proportional to the square root of the number of incident photons [20], the ability to detect light at high intensities is advantageous for high-SNR detection. However, individual pixels in a typical image sensor have low saturation light intensity. Therefore, the signal to be observed is buried in the photon shot noise.
To overcome this problem, we proposed a method for detecting weak polarization changes by combining a polarization image sensor with a uniform polarizer [21–23]. This method takes advantage of the high extinction ratio of the uniform polarizer and the high sensitivity and resolution of the polarization image sensor. Although the light intensity is reduced, the amount of polarization rotation is large in this method. Hence, the image sensor can measure the distribution of weak polarization changes.
In this study, we theoretically examine the sensitivity improvement of the proposed polarization measurement method and evaluate it by analyzing the characteristics of an actual prototype device. We also constructed a reflective optical system for polarization rotation measurement and demonstrated polarization rotation measurement in a flow channel.
2. Dual polarizer configuration for high-sensitivity polarized light imaging
2.1 Basic polarization rotation detection method with single polarizer
In the basic experimental configuration for polarization rotation detection, a polarizer, which serves as a detector, and a photodetector are used. By rotating the angle of the polarizer with respect to the linearly polarized incident light, the transmittance changes and polarization information is converted into light intensity. The change in the transmittance follows a sinusoidal curve. In other words, the intensity change per angle is not constant. If the angle between the direction of the polarization of the incident light and the transmission axis of the polarizer is $\theta$, the maximum is obtained when $\theta$ is $\pm \pi /4$ rad. In other words, the polarization rotation is most efficiently converted into an intensity change under these conditions.
Signals in opposite phases can be obtained using polarizers with $\theta$ of $+\pi /4$ rad and $-\pi /4$ rad. This characteristic reduces in-phase noise, such as light source intensity variations, by subtracting signals using a differential amplifier circuit [24–26].
The extinction ratio is an important property that indicates the performance of a polarizer. This is represented by the ratio of the maximum and minimum transmittance. When the extinction ratio is $ER$, the sensitivity coefficient $\eta$ is given by
The sensitivity of the polarization rotation improves as the extinction ratio increases. However, the improvement rate owing to the extinction ratio decreases gradually.
2.2 Proposed method
A limitation of the aforementioned method is that only half of the incident light is transmitted and requires a high optical saturation limit, which is difficult to achieve with image sensor pixels. In this study, we resolve this by using two types of polarizers: a uniform external polarizer and an on-pixel polarizer. Using a polarizer-equipped pixel array and an external polarizer in superposition, allows high-sensitivity polarization imaging by enhancing the polarization rotation angle and performing differential detection.
In this study, we constructed a highly sensitive reflective polarization rotation measurement system consisting of a polarization image sensor with a polarizer on each pixel and a polarization beam splitter (PBS) as an external polarizer, as shown in Fig. 1.
The incident light is linearly polarized, and the PBS is positioned to reflect the linear incident polarization. The reflected polarization is transmitted through the object of observation and is reflected by a mirror positioned below. If the polarization does not change and the PBS is an ideal polarizer, the light returns to the light source and does not reach the sensor positioned above. However, a small amount of light is transmitted in an actual PBS. In this method, a slightly transmitted component is used. The PBS reflects most of the incident polarized light back to the incident light source. However, the component generated by the polarization rotation of the observed object is almost completely transmitted. As a result, polarization rotation enhancement is realized. The polarizer on the pixel detects this enhancement. The reduction in the incident polarization component by the uniform polarizer considerably reduces the light intensity while increasing the rotation angle. This translates to conditions that facilitate measurement even with low- resolution detectors. Image sensor pixels have high sensitivity, low pixel saturation limits, and low SNR owing to their low pixel capacitance. The aforementioned conversion makes the conditions suitable for detection using the image sensor pixels. Here, a relatively low extinction ratio is sufficient for the polarizer performance on the pixel because a region with $\theta$ of $\pi /4$ rad is used. This is also convenient for polarized image sensors.
Figure 2 illustrates the relationship between the incident polarization and the output. The length of each arrow corresponds to the amplitude of the optical field. In the figure, linearly polarized light with amplitude $A_0$ is the incident light to the object of observation. When it passes through a detector positioned at $\pi /4$ rad, its Jones vector $\boldsymbol {a_1}$ is
If the polarization is rotated by $\theta$, the vector $\boldsymbol {a_1'}$ is given by
Here, $\theta$ is assumed to be sufficiently small.
The intensity transmittance of the uniform polarizer in a cross-nicol arrangement is defined as $T_\bot$. That is, the amplitude transmittance is $\sqrt {T_\bot }$. The polarization vector of the detected light without any polarization rotation is given by
When the polarization of the incident light is rotated by $\theta$, it becomes approximately
The second polarizer, the on-pixel polarizer used as a detector on the pixel, is positioned at an angle $\pi /4$ rad to the incident polarization, as in the basic polarization detection method. As depicted on the right side of the figure, the projection component is measured using a photodetector.
Figure 3 shows the relationship between the extinction ratio of the polarizer on the pixel and relative sensitivity. It is normalized when the extinction ratio of the polarizer on the pixel is infinite without using a uniform polarizer. As mentioned earlier, the sensitivity improvement effect of increasing the extinction ratio became increasingly smaller. Although achieving a high extinction ratio with on-pixel polarizers is difficult, as with a uniform polarizer, this method reduces the requirement for a high extinction ratio. However, if the extinction ratio of the uniform polarizer is increased, the relative sensitivity can be significantly improved. This occurs only when the light-receiving amount is assumed to be constant. The method is effective when the upper limit of the light-receiving amount is low, as in the case of image sensor pixels.
The intensity change obtained by the slight polarization rotation is
when there is no uniformt polarizer. In contrast, in the proposed method, which is reduced by the amplitude transmission of the first polarizer. However, when performing optical measurements with a sufficiently low-noise detection system, the photon shot noise is given by the square root of the incident light intensity. In other words, because the light intensity is $1/T_\bot$ in the proposed method, the photon shot noise is $1/\sqrt {T_\bot }$. When both methods are compared when performing measurements under photon-shot noise limit conditions, the SNRs are comparable.The output of a pixel with the proposed dual-polarizer arrangement is shown in Fig. 4(a). The extinction ratios are set to approximately 900 (uniform polarizer) and 3 (on-pixel polarizers). These values are set at the same level as the on-pixel polarizers of the PBS and the polarized image sensor used in the experimental system described below. $0^\circ$ in the figure corresponds to the polarization angle of the crossed-Nicole, and is the point at which the transmittance of the uniform polarizer is minimal. The minimum point is shifted by transmission through the polarizer on the pixel. The direction of the shift is opposite to each other with a polarizer of $\pm \pi /4$rad to the external polarizer. When performing polarization measurements, the difference between the two is considered. The results are shown in Fig. 4(b). In this observation range of $\pm 2^\circ$, the difference is almost linear with respect to the angular change. In other words, a value proportional to the amount of polarization rotation is obtained from the intensity difference.
Fig. 4. (a) Calculated transmittance of the dual polarizer with respect to the angle of incident polarization. (b) Output difference of $\pm \pi /4$-rad pixels. Extinction ratios of the uniform and on-pixel polarizers are assumed to be 900 and 3, respectively. .
If the pixel pitch is sufficiently fine to observe the pattern and the intensities at two adjacent points are approximately the same, the in-phase noise caused by changes in light source intensity can be reduced, as described in the previous section. In other words, a simple difference calculation can be used to estimate the polarization rotation angle and reduce the SNR.
Our proposed method can be realized by combining a commercially available polarization image sensor with an external polarizer. The method uses polarization pixels with transmission axes of $\pm \pi /4$ rad. However, general polarization image sensors are equipped with polarizers supporting four directions that differ by $\pi /4$ rad, resulting in unnecessary pixels. Therefore, we use a polarization image sensor designed in our laboratory, as described in the next section.
3. Measurement system
3.1 Polarization image sensor
A polarization image sensor was designed in our laboratory. A 0.35-µm 2-poly 4-metal standard CMOS process was used for fabrication. We also developed a software system for reading images from the image sensor. The specifications are listed in Table 1. Figure 5 shows the chip micrograph. The pixel pitch was 30 µm and the photodiode was a 15-µm square. The on-chip polarizer in the polarization image sensor is a wire-grid polarizer that uses a CMOS process wiring layer. The polarizer has a grating structure with line/space = 0.7 µm / 0.7 µm; the same layout overlaps the second and third layers of the wiring. The extinction ratio can be improved using multiple layers. Although the direction of the polarizers can be designed arbitrarily, two types of polarizers, one for the horizontal (x-polarizer) and the other for the vertical (y-polarizer) direction of the pixel array, are mounted alternately in each row to obtain complementary characteristics with respect to polarization rotation. The extinction ratio of the pixels was approximately 3.3 at a wavelength of 780 nm.
Fig. 5. (a) Micrograph of the polarization image sensor. (b) Schematic of on-pixel polarizer structure.
Table 1. Specifications of the image sensor
3.2 System characteristics
We conducted a measurement experiment on polarization rotation detection performance using the prototype system. A schematic of the measurement system is shown in Fig. 6. A superluminescent diode (SLD) with a center wavelength of 770 nm was used as the light source. A fiber-type polarization controller was used to control the incident polarization of the PBS. The extinction ratio of PBS was measured to be approximately 900. A quarter-wave plate was used to rotate the polarization. As the light passes through the quarter-wave plate twice, the optical system, provides a phase difference of half a wavelength. In other words, the amount of polarization rotation was twice that of the quarter-wave plate.
The measured pixel outputs for each polarizer are presented in Fig. 7(a). As predicted by theory, the minima have shifted. However, as the transmittance of the polarizer on the pixel differs between the $x$-polarizer and the $y$-polarizer. This may be due to slight differences in the fabrication process of the on-pixel polarizers. We observed similar outputs between adjacent $x$- and $y$-polarizer pixels throughout the chip. The difference was corrected by normalization, as shown in Fig. 7(b). Figure 7(c) is the result of taking the difference between the two. The linear response characteristics were obtained for the amount of polarization rotation, as in the theoretical study.
Fig. 7. (a)Measured outputs of polarization image sensor pixels as functions of incident polarization angle. (b) Corrected result of (a). (c) Difference of $x$- and $y$-polarizer outputs.
Another advantage of the proposed method is that it can achieve differential detection. For images acquired at a frame rate of 30 fps, the signal differences of $50\times 50$ pixels ($25\times 50$ for different polarizer pairs) were averaged to verify the variation in the output values. The 30 frames were moving averaged and Fourier transformed by the fast Fourier transform, and the results are shown in Fig. 8. From this result, the noise is observed to be reduced by taking the difference. The standard deviation of the estimated detection angle during the measurement period of 60 s was $2.8 \times 10^{-4\circ }$.
Fig. 9. (a) Schematic of the experimental setup with a fluidic plate. (b) Optical image of the fluidic channel.
3.3 Imaging demonstration
A 1.38-mm wide and 150-µm deep channel was fabricated and placed between the PBS and quarter-wave plate of the reflective optics shown in Fig. 1. An image of the channel portion observed using the polarization image sensor is shown in Fig. 9(a). Ethanol, in which the optical isomers L- and D-menthol were dissolved, was poured into the flow channel, and a polarization change was observed. The concentration of the solutions prepared was approximately 0.5 g/ml.
As the menthol solution exhibits natural optical rotation, the direction of polarization rotation is determined based on the direction of light travel. Therefore, when the polarization rotated light is reflected by a mirror and transmitted again on the return path, the polarization direction returns to the original direction. A quarter wave plate was placed between the sample and the mirror to avoid this. As the light is transmitted back and forth twice, it functions as a half-wave plate. If the fast axis (or slow axis) coincides with the direction of polarization when there is no polarization rotation by the menthol solution, the direction of polarization is reversed with respect to the axis, and the menthol solution is transmitted again. If the menthol solution is transmitted through the flow path again, it will be polarization-rotated again, resulting in a double polarization rotation for the round trip.
Observations were made by sequentially flowing the prepared menthol solutions through the channels. Initially, pure ethanol was flowed, followed by L-menthol solution for 2 min, washing with pure ethanol for 1 min, and D-menthol solution for 2 min. Finally, the pure ethanol was allowed to flow again. Ten frame averages of 36 $\times$ 15 pairs of the flow channel section were obtained, and the estimated polarization rotation angles are plotted in Fig. 10. The polarization rotation angles of L- and D-menthol were opposite to each other and almost the same. Figure 11 shows the images observed at times (a)62 sec, (b)188 sec and (c)369 sec shown in Fig. 10. Although the estimated refractive index in the channel was less uniform with the flow of the menthol solution, the spatial average of the polarization rotation was in accordance with the characteristics of the solution.
4. Discussion
The experimental results with the proposed dual-polarizer structure are consistent with the theory. A relatively simple optical system was developed using a polarization image sensor. Further improvement of the polarization change detection performance can be achieved by improving the polarizer on the pixels of the polarization image sensor. The extinction ratio of the pixels in the polarization image sensor is approximately 3, which is approximately 50% of the sensitivity when the extinction ratio is infinite. The extinction ratio could be improved to approximately 100 by creating a finer grating structure. In this case, Eq. (1) shows that the extinction ratio is approximately 98% of the limit that can be improved by on-chip polarizers.
For the external uniform polarizer, a PBS was used as a reflective optical system, which enabled the light source and sensor to be placed on the same side with respect to the object being observed. The extinction ratio of the PBS was approximately $10^3$. Theoretically, it is possible to increase the polarization rotation angle further by improving the extinction ratio of the uniform polarizer. However, if the extinction ratio is very high, the intensity of the signal component may be weak, making it susceptible to stray light and other influences. In addition, the range of detectable polarization angle changes became narrower. The SNR does not depend on the extinction ratio of the uniform polarizer if the observation can be made under conditions where photon shot noise becomes dominant. Thus, the optimal extinction ratio is the minimum value at which the image sensor does not saturate the pixels. The intensity of the light source and the pixel saturation limit of the image sensor determines the required extinction ratio.
In the flow channel measurement, the 150-µm-thick channel structure was insufficient to obtain sufficient sensitivity in single-point measurements. However, because it is an image sensor, detecting polarization rotation is possible by specifying the region of interest from the measurement image. In addition, the transmission of bubbles can be detected through continuous measurement; the noise due to the bubbles can be reduced by image processing. In Figs. 11(b) and 11(c), the polarization distributions in the channel are not uniform. The patterns did not change much over time when the solution in the channel was completely replaced by menthol solution. Also, stripe patterns are observed near the channel boundaries. Although a more detailed study is needed, it seems that the observed image was slightly affected by the refractive index differences between the high-concentration menthol solution and pure ethanol.
5. Conclusion
In this study, we theoretically derive the polarization detection characteristics of a highly sensitive polarization change imaging method based on a dual polarizer configuration consisting of a polarization image sensor and a uniform polarizer. This configuration reduces the amount of light and increases the amount of polarization change due to the observed object. In addition, depending on the direction of the polarizer on the pixel of the polarization image sensor, the signal change is inverted and differentiated, showing a linear characteristic with the polarization rotation angle. When compared under photon shot noise limit conditions, a photodetector with a low-saturation light level, such as an image sensor pixel in the proposed system , can achieve an SNR equivalent to that of a photodetector with a high-saturation light level and a single polarizer.
Funding
Ministry of Internal Affairs and Communications/SCOPE (JP225007001).
Acknowledgment
The authors would like to thank the activities of the d-lab. VDEC, University of Tokyo, in collaboration with Cadence Design Systems and Mentor Graphics.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable requests.
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