Polarization Navigation Research Articles

An Extended Polarization Sensor Model Considering the Influence of Obliquely Incident Direct Sunlight

The polarization sensor model plays a key role in bioinspired polarization navigation. Existing models consider the linearly polarized light and vertically incident unpolarized light. The performance of the polarization sensor, however, will be degraded due to the effect of obliquely incident direct sunlight. To account for the influence of obliquely incident direct sunlight and improve the conventional model, we established an extended polarization sensor model. In the proposed model, the transmitted intensity of direct sunlight obliquely passing through the polarizer is analyzed, and the influence of obliquely incident direct sunlight on the polarization sensor is characterized. Then, the extended polarization model is established considering the linearly polarized light and vertically incident unpolarized light, as well as the obliquely incident direct sunlight. Based on the proposed model, the secant Levenberg–Marquardt (LM) least-squares algorithm is used to estimate the polarization parameters of interest, such as Degree of Polarization (DoP) and Angle of Polarization (AoP). Finally, the effectiveness of the proposed polarization sensor model is verified via simulation, indoor, and outdoor experiments. The results show that the root mean square of AoP error can be narrowed to 0.67° even under the obliquely incident direct sunlight environment.

Ultraviolet-visible light compass method based on local atmospheric polarization characteristics in adverse weather conditions

Bionic polarization navigation has attracted extensive attention because of its strong anti-interference performance and no accumulation of errors over time. However, very few studies have fully considered the influence of adverse weather conditions such as cloudy and overcast weather, which play a key role in navigation accuracy. Therefore, we propose an adaptive ultraviolet-visible light compass method based on local atmospheric polarization characteristics applicable to various weather conditions. The proposed method transforms the heading determination problem into a multiclassification problem by using a weather recognition technique. Ultraviolet detection is used to weaken the depolarization effect of cloud particles and to obtain more accurate skylight polarization patterns. Then, on the basis of screening effective data, the sun direction vector is calculated by using the electric vector direction and is finally combined with the astronomical calendar to achieve navigation. The experimental results confirm that, compared to the other methods, the designed algorithm can suppress the interference of clouds better and adapt to complex weather conditions. Under cloudy and overcast conditions, the heading angle error is reduced to less than 2°.

A bio-inspired polarization navigation sensor based on artificial compound eyes

Insect compound eyes are optical systems with small volume and a compact structure. The ommatidia in the dorsal rim area of some insects have polarized vision, which can perceive the polarization pattern of the sky and provide them with navigation information. In this paper, inspired by the polarization-sensitive compound eyes of insects, a bio-inspired polarization navigation sensor based on artificial compound eyes is designed. The sensor consists of an artificial compound eye, an integrated polarization detector and an integrated circuit. The optical path of the sensor uses the lens defocus method, which can ensure that the sensor obtains redundant polarization information. The integrated polarization detector is used to obtain the polarization information of the incident light, and the integrated circuit is responsible for the calculation. To extract effective information from images, we propose a multi-threshold segmentation method to filter and classify effective pixels. We use the least squares method to fit the inherent error of the sensor and then compensate it. The indoor calibration accuracy of the sensor is ±0.3°, and the outdoor calibration accuracy is ±0.5°. The sensor can provide accurate direction information for general smart mobile devices. The size of the sensor is 4 × 4 × 2 cm, and the weight is only 15 g. The key components of the sensor can be mass-produced, and it is a miniaturized and low-cost polarization navigation sensor.

An approach for fabrication of multi-directional polarizer array by picosecond laser micro-processing

A method for preparing a multi-directional polarization filter by using one-dimensional nano-grating polarizers is proposed. A picosecond laser is employed to precisely ablate aluminum film on TAC (Triacetate Cellulose) substrate to form grating pixels. The effects of the key laser processing parameters (power density I, line spacing b, number of repetitions σ) on the ablation morphology and optical transmittance are studied. A three-layer polarization filter is aligned and stacked together with the directions of 0°, 45°, and 90°, respectively to obtain the Stokes parameters. The Rigorous Coupled Wave Analysis (RCWA) theory is deployed to calculate the polarization properties of one-dimensional metal gratings. The polarization performance of the three-dimensional subwavelength metal aluminum polarizer is experimentally evaluated. Results show that the transmittance of the laser-ablated area increases to more than 96 % from the original 84 % at the wavelength of 550 nm. The polarization filter prepared in our study is applied to the polarization angle measurement. The original error of the polarization angle is measured to be less than ± 0.3°, which indicates a high degree of measurement accuracy. The proposed method is flexible, cost-effective, maskless, no-need-of stringent cleanroom environment, and of high speed. It has the potential for applications in the field of polarization navigation, image processing, and polarization imaging.

A 3D Attitude Estimation Method Based on Attitude Angular Partial Feedback for Polarization-Based Integrated Navigation System.

Polarization (POL) navigation is inspired by insects’ behavior of precepting celestial polarization patterns to orient themselves. It has the advantages of being autonomous and having no accumulative error, which allows it to be used to correct the errors of the inertial navigation system (INS). The integrated navigation system of the POL-based solar vector with INS is capable of 3D attitude determination. However, the commonly used POL-based integrated navigation system generally implements the attitude update procedure without considering the performance difference with different magnitudes of the angles between the solar-vector and body-axes of the platform (S-B angles). When one of the S-B angles is small enough, the estimated accuracy of the attitude angle by the INS/POL is worse than that of the strapdown inertial navigation system. To minimize the negative impact of POL in this situation, an attitude angular adaptive partial feedback method is proposed. The S-B angles are used to construct a partial feedback factor matrix to adaptively adjust the degree of error correction for INS. The results of simulation and real-world experiments demonstrate that the proposed method can improve the accuracy of 3D attitude estimation compared with the conventional all-feedback method for small S-B angles especially for yaw angle estimation.

Algorithms for calculating polarization direction based on spatial modulation of vector optical field

Polarization is an important property of electromagnetic waves, and measuring their polarization properties fast and precisely is a very important issue in many applications, such as skylight polarization navigation, optical activity measurement, imaging polarimetry, spectroscopic ellipsometry, and fluorescence polarization immunoassay . The polarization measurement method based on vector optical field modulation and image processing is a new type of spatial modulation polarization detection technology. The key step of this technique moving to practical application is determined by effective polarization measuring algorithms with high speed and accuracy. In order to find out the method of fast and precisely calculating polarization direction, the principle of polarization direction measurement based on vector optical field and spatial modulation is introduced briefly, and the basic characteristics of the spatially modulated intensity distribution images are analyzed. According to the properties of spatially modulated image, we propose and implement four different polarization direction calculation methods, which are the Radon transform, intensity modulation curve detection, radial integration, and image correlation detection, and also introduce their working principles and physical thoughts elaborately. To compare the detailed performances of these four algorithms, an experimental setup is constructed to collect the images and perform the algorithm verification, and the stabilities, speeds and accuracies of the four algorithms are compared. The research results indicate that all the four methods can achieve their stable and reliable polarization direction detections. The three methods, intensity modulation curve detection, radial integration and image correlation detection, can achieve the polarization direction measuring accuracy better than 0.01° . The intensity modulation curve detection and radial integration have relatively fast calculation speed and the best comprehensive performances , and are the most promising methods to realize real-time and high-precision polarization measurement.

Research on Algorithms for Calculating Polarization Direction Based on Spatial Modulation of Vector Optical Field

Polarization is an important property of electromagnetic waves, and measuring their polarization properties fast and precisely is a very important issue in many applications, such as skylight polarization navigation, optical activity measurement, imaging polarimetry, spectroscopic ellipsometry, fluorescence polarization immunoassay and so on. The polarization measurement method based on vector optical field modulation and image processing is a new type of spatial modulation polarization detection technology. The key step of this technique moving to practical application is determined by the effective polarization measuring algorithms with high speed and accuracy. In order to find out the fast and high precision polarization direction calculation methods, the principle of polarization direction measurement based on vector optical field and spatial modulation is introduced briefly, and the basic characteristics of the spatially modulated intensity distribution images are analyzed. According to the properties of spatially modulated image, we have designed and implemented four different polarization direction calculation methods, which are the Radon transform, intensity modulation curve detection, radial integration and image correlation detection, and their working principles and physical thoughts are introduced elaborately. To compare the detailed performance of these four algorithms, an experimental setup has been constructed to collect the images and perform the algorithm verification, and the stability, speed and accuracy of the four algorithms are compared respectively. The research results indicate that all the four methods can achieve stable and reliable polarization direction detection. The three methods of intensity modulation curve detection, radial integration and image correlation detection, can obtain the measurement accuracy of polarization direction better than 0.01 degrees. The intensity modulation curve detection and radial integration own the fast calculation speed relatively, and their overall performances are the best, and they are the most promising methods for realizing real-time and high-precision polarization measurement.

Measurement error model of the bio-inspired polarization imaging orientation sensor.

This article studies the measurement error model and calibration method of the bio-inspired polarization imaging orientation sensor (BPIOS), which has important engineering significance for promoting bio-inspired polarization navigation. Firstly, we systematically analyzed the measurement errors in the imaging process of polarized skylight and accurately established an error model of BPIOS based on Stokes vector. Secondly, using the simulated Rayleigh skylight as the incident surface light source, the influence of multi-source factors on the measurement accuracy of BPIOS is quantitatively given for the first time. These simulation results can guide the later calibration of BPIOS. We then proposed a calibration method of BPIOS based on geometric parameters and the Mueller matrix of the optical system and conducted an indoor calibration experiment. Experimental results show that the measurement accuracy of the calibrated BPIOS can reach 0.136°. Finally, the outdoor performance of BPIOS is studied. Outdoor dynamic performance test and field compensation were performed. Outdoor results show that the heading accuracy of BPIOS is 0.667°.

Skylight polarization patterns under urban obscurations and a navigation method adapted to urban environments

Owing to preferable anti-interference and anti-cumulative-error capabilities, polarized skylight navigation technology has been developed. However, in urban environments with extensive demand, the sky is usually partially obscured by buildings and trees. Urban landscape obscurations with polarization patterns that have not been sufficiently studied can greatly influence navigation accuracy. In this paper, we study the polarization patterns generated by obscurations and summarize the impacts of obscured urban sky scenes on the navigation results. We also propose a full-sky polarization imaging navigation method adapted to urban environments. A compact full-sky polarimeter is established, and a specific pattern inpainting algorithm based on convolution operation is proposed to amend the navigation errors caused by obscurations. Among 174 sets of comparative experiments, 90.2% of the extraction results are improved after inpainting, which verifies the effectiveness and robustness of the method. Discussions on the optimization of parameters in the algorithm and the recommended values are also provided. This work offers a novel approach to overcome the impacts of obscurations for urban polarization navigation.

Error Analysis and Optimization of a Sky Full-Polarization Imaging Detection System

An accurate sky polarization field map is a prerequisite for polarization navigation applications. In this article, a detector for sky full-polarization imaging detection is described, the major error-influencing factors (MEIFS ) are obtained, and the error propagation is modeled and analyzed. We reveal the relationship between the error of the inversed Stokes vector and the condition number of the detector matrix, which shows that the error of the inversed Stokes vector is affected by the Stokes vector of the incident light itself and the MEIFS together, with the MEIFS playing a decisive role. With the MEIFS optimized, the impact of detector error on the inversed Stokes vector is attenuated. A control equation for system calibration is also deduced which can establish the connection between the detector matrix design and calibration process. The work in this article provides a reference for optimization and calibration of sky full-polarization imaging detectors.

Solar-tracking methodology based on refraction-polarization in Snell's window for underwater navigation

Underwater navigation system is an indispensable part for autonomous underwater vehicles. Due to the indiscernibility of satellite signal, however, the underwater navigation problem is quite challenging, and a satellite-free navigation scheme should be looked for. Polarization navigation, inspired by insects’ capability of autonomous homing and foraging, is an alternative solution to satellite navigation with great application potential. Underwater polarization provides an indirect sun compass to animals for orientation determination. However, it is difficult to apply terrestrial solar-tracking methodologies in underwater situations due to the refraction of polarized skylight at the air–water interface. To resolve this issue, an underwater solar-tracking algorithm is developed based on the underwater refraction-polarization pattern inside the Snell's window. By employing Snell's law and Fresnel refraction formula to decouple the refractive ray bending and polarization deflection, the celestial polarization pattern is obtained based on underwater measurement. To further improve the accuracy, the degree of polarization is employed as a weight factor for E-vector. A long-lasting underwater experiment was conducted to validate the effectiveness of the proposed approach, and the results showed the root-mean-square errors of solar zenith and azimuth employing this algorithm were 0.3° and 1.3°, respectively. Our experimental results show that the refraction-polarization pattern inside the Snell's window exhibits immense potential to improve the solar-tracking accuracy for underwater navigation.

Bioinspired polarized light compass in moonlit sky for heading determination based on probability density estimation

Bioinspired polarized skylight navigation, which can be used in unfamiliar territories, is an important alternative autonomous navigation technique in the absence of Global Navigation Satellite System (GNSS). However, the polarization pattern in night environment with noise effects and model uncertainties is a less explored area. Although several decades have passed since the first publication about the polarization of the moonlit night sky, the usefulness of nocturnal polarization navigation is only sporadic in previous researches. This study demonstrates that the nocturnal polarized light is capable of providing accurate and stable navigation information in dim light outdoor environment. Based on the statistical characteristics of Angle of Polarization (AoP) error, a probability density estimation method is proposed for heading determination. To illustrate the application potentials, the simulation and outdoor experiments are performed. Resultingly, the proposed method robustly models the distribution of AoP error and gives accurate heading estimation evaluated by Standard Deviation (STD) which is 0.32° in a clear night sky and 0.47° in a cloudy night sky.

Simulation and measurement of the effect of various factors on underwater polarization patterns

To realize the underwater polarization navigation, the study of underwater polarization patterns is necessary. The current method is mainly numerical simulation because of detection equipment and experimental environment limitations. In the paper, we establish the model to simulate the underwater polarization patterns under different conditions and design the experiment to study the effect of various factors on the underwater polarization patterns. The consistency between the simulation and measurement illustrates the correctness of the model and predictability of the patterns. By discussing the influence of wavelength, water turbidity, water composition, and particle size on underwater polarization patterns, underwater polarization navigation technology can be applied better by avoiding negative effects. Through comparison and analysis, it is demonstrated that underwater polarization navigation is feasible to varying conditions.

Calibration and region extraction of polarization sensor for navigation

Polarization navigation is an autonomous navigation method that relies on stable polarization patterns in the sky. The polarization sensor for navigation is composed of a CMOS image sensor (CIS) and four-direction metal nanograting. The optical conversion deviation of the CIS and the transmittance deviation of metal nanograting are the main factors affecting the angle measurement accuracy of the polarization sensor. A full-parameter calibration method that can accurately calculate the performance parameters in the Mueller matrix of all pixels is proposed. To reduce the error of the sensor, a mode-based region extraction algorithm that can extract the effective region of the sensor according to the statistical law of these performance parameters is proposed. The experimental results demonstrate that the proposed algorithm can effectively improve the angle measurement accuracy of the sensor. Compared with the single-parameter calibration and the region selection method based on the light intensity graph, the proposed method reduces the angle measurement error by 27.89% and significantly improves the robustness.

CONSTRUCTION AND TEST OF BIO-INSPIRED IMAGING POLARIZATION NAVIGATION PROTOTYPE

Abstract. Bio-inspired polarization navigation is a promising navigation method inspired by insects’ autonomous foraging and homing behaviour. Many insects acquire their spatial orientation by sensing the polarization pattern of the skylight. We propose utilization of solar meridian in the polarized skylight as an orientation cue because of its significant features. Using its features, we then design and construct an imaging polarization navigation prototype. The prototype consists of a field-division polarization imaging sensor, the corresponding software, an interface, and the solar-meridian recognizing and measurement algorithm. The field-division polarization imaging sensor is the core component of the prototype and acquires polarized intensity images. To adapt to the demand of real-time on navigation system, we then propose an optimized real-time polarization image processing and pattern recognition algorithm based on Hough transform. The azimuth measurement accuracy of the sensor is then calibrated using a facility that is able to get higher azimuth accuracy by measurement of the star light. To verify the navigation capability of the developed system, we use a dynamic experiment, where the prototype is installed on the top of a vehicle and its navigation performance is compared with GNSS.

Sensor Modeling and Calibration Method Based on Extinction Ratio Error for Camera-Based Polarization Navigation Sensor.

The performance of camera-based polarization sensors largely depends on the estimated model parameters obtained through calibration. Limited by manufacturing processes, the low extinction ratio and inconsistency of the polarizer can reduce the measurement accuracy of the sensor. To account for the challenges, one extinction ratio coefficient was introduced into the calibration model to unify the light intensity of two orthogonal channels. Since the introduced extinction ratio coefficient is associated with degree of polarization (DOP), a new calibration method considering both azimuth of polarization (AOP) error and DOP error for the bionic camera-based polarization sensor was proposed to improve the accuracy of the calibration model parameter estimation. To evaluate the performance of the proposed camera-based polarization calibration model using the new calibration method, both indoor and outdoor calibration experiments were carried out. It was found that the new calibration method for the proposed calibration model could achieve desirable performance in terms of stability and robustness of the calculated AOP and DOP values.

An equivalent incident light model for multiple scattering and polarization neutral point of skylight

The symmetry breaking in the skylight polarization pattern is caused by the shape of the atmosphere and multi-scattering. We analyzed the physical processes of multi-scattering and found out that when neutral points split from two into four there should be an altitude shift of the center of polarization pattern. The altitude shift could be positively related to the split angle of the neutral point, which would reduce the accuracy of polarization navigation based on the single scattering model. To quantify the positive relationship which is useful for error correction in navigation, the Monte-Carlo method was used to simulate the multiple scattering processes of sunlight. The simulation results show that the split angle of the neutral point is in direct proportion to the altitude shift angle. Experimental data from Horvath also show the proportional relation. According to the simulation results and experimental data, an equivalent incident light model was established to explain the proportional relation which could be used in sunlight navigation.

Polarization Navigation Simulation System and Skylight Compass Method Design Based upon Moment of Inertia

Unpolarized sunlight becomes polarized by atmospheric scattering and produces a skylight polarization pattern in the sky, which is detected for navigation by several species of insects. Inspired by these insects, a growing number of research studies have been conducted on how to effectively determine a heading angle from polarization patterns of skylight. However, few research studies have considered that the pixels of a pixelated polarization camera can be easily disturbed by noise and numerical values among adjacent pixels are discontinuous caused by crosstalk. So, this paper proposes a skylight compass method based upon the moment of inertia (MOI). Inspired by rigid body dynamics, the MOI of a rigid body with uniform mass distribution reaches the extreme values when the rigid body rotates on its symmetry axes. So, a whole polarization image is regarded as a rigid body. Then, orientation determination is transformed into solving the extreme value of MOI. This method makes full use of the polarization information of a whole polarization image and accordingly reduces the influence of the numerical discontinuity among adjacent pixels and measurement noise. In addition, this has been verified by numerical simulation and experiment. And the compass error of the MOI method is less than 0.44° for an actual polarization image.

Study on displacement estimation in low illumination environment through polarized contrast-enhanced optical flow method for polarization navigation applications

Polarization navigation techniques become more and more significant for a wide range of researches and applications. However, most of the polarization navigation sensors can only output the navigation angle information of a carrier based on the angle of polarization (AoP) from the skylight in the daytime; they cannot provide the displacement information in day and night. In this paper, a polarized contrast-enhanced (PCE) optical flow method is proposed to improve the accuracy of displacement estimation and reduce the influence of the ambient brightness. We acquire the degree of linear polarization (DoLP) images during the motion of the carrier in low illumination environment, and the hypothesis of the DoLP continuity is used for the theoretical foundation of this PCE optical flow method under the conditions of parallel light source and small displacements. The displacement calibration on the experimental platform is obtained by using a laser interferometer and spectrometer, and the contrast of the polarimetric image and the calculated polarized optical flow value are used as the validation criteria. Under 0.7198Lx illumination intensity, the cumulative error of the displacement obtained by the PCE method is less than 8 mm and the accuracy of the displacement estimation is almost 2 times higher than that of the traditional Lucas-Kanade(LK) optical flow method. Our experimental results have also shown that under 10°, 10−1, or even 10-2 levels of the standard illumination, the displacement values from the PCE optical flow method are in good agreement with the theoretical values.

Self-adaptive robust algorithm applied on compact real-time polarization sensor for navigation

Celestial navigation has remarkable performance in autonomous navigation without error accumulation. For supplying orientation information to a portable vehicle in real time, a compact polarization sensor with high precision and strong robustness was constructed in this study based on the mechanism of insect polarization-opponent neurons structure. The sensor, composed of polarization-dependent module and microcontroller unit, could supply heading angle for real-time navigation. To enhance the robustness of sensor in a complex environment, a self-adaptive algorithm based on information entropy theory was proposed. The algorithm could eliminate the effect of random obstacles in the sensor field under constantly changing light conditions. The laboratory and outdoor tests indicated that the sensor, with ±0.1 deg measured error and ±0.4 deg fluctuation under natural obstacle, had potential application prospects in polarization navigation.