Angle algorithm based on Hough transform for imaging polarization navigation sensor

Underwater biomimetic orientation method using imaging polarization sensor based on direct sunlight compensation

This paper addresses the challenge of significant interference caused by direct sunlight, which adversely affects the orientation accuracy of underwater imaging polarization sensors (IPS). A novel underwater polarization orientation method is proposed based on direct sunlight compensation. Firstly, based on the polarization transmission model at the water-air interface, the interference mechanism of the underwater direct sunlight polarization detection model was analyzed. The underwater IPS detection model based on direct sunlight compensation is constructed, which uses the weight coefficient of underwater direct sunlight to compensate for the interference on the polarization channel and improve the accuracy of underwater polarization detection models. Furthermore, the analytical solution method for the polarization state information of underwater IPS is proposed, employing the augmented Stokes vectors to construct a linear equation for solving the weight coefficients of direct sunlight and improving the computational efficiency. Finally, an underwater polarization orientation experimental platform is established, and both simulation and actual underwater experiments are conducted. Compared with the traditional methods, the proposed method reduces heading error by an average of 92.53% at different solar altitudes.

An Improved Bio-Orientation Method Based on Direct Sunlight Compensation for Imaging Polarization Sensor

Direct sunlight in complex environmental conditions severely interferes with the light intensity response for imaging Polarization Sensor (PS), leading to a reduction in polarization orientation accuracy. Addressing this issue, this article analyzes the impact mechanism of direct sunlight on polarization sensor detection in a complex environment. The direct sunlight interference factor is introduced into the intensity response model of imaging polarization detection, enhancing the accuracy of the polarization detection model. Furthermore, a polarization state information analytical solution model based on direct sunlight compensation is constructed to improve the accuracy and real-time performance of the polarization state information solution. On this basis, an improved bio-orientation method based on direct sunlight compensation for imaging polarization sensor is proposed. The outdoor dynamic reorientation experiment platform is established to validate the effectiveness of the proposed method. Compared with the traditional methods, the experimental results demonstrate a 23% to 47% improvement in the polarization orientation accuracy under various solar zenith angles.

Image-registration-based solar meridian detection for accurate and robust polarization navigation

Skylight polarization, inspired by the foraging behavior of insects, has been widely used for navigation for various platforms, such as robots, unmanned aerial vehicles, and others, owing to its stability and non-error-accumulation. Among the characteristics of skylight-polarized patterns, the angle of polarization (AOP) and the degree of polarization (DOP) are two of the most significant characteristics that provide abundant information regarding the position of the sun. In this study, we propose an accurate method for detecting the solar meridian for real-time bioinspired navigation through image registration. This method uses the AOP pattern to detect the solar meridian and eliminates the ambiguity between anti-solar meridian and solar meridian using the DOP pattern, resulting in an accurate heading of the observer. Simulation experiments demonstrated the superior performance of the proposed method compared to the alternative approaches. Field experiments demonstrate that the proposed method achieves real-time, robust, and accurate performance under different weather conditions with a root mean square error of 0.1° under a clear sky, 0.18° under an overcast sky with a thin layer of clouds, and 0.32° under an isolated thick cloud cover. Our findings suggest that the proposed method can be potentially used in skylight polarization for real-time and accurate navigation in GPS-denied environments.

Measurement Modeling and Performance Analysis of a Bionic Polarimetric Imaging Navigation Sensor Using Rayleigh Scattering to Generate Scattered Sunlight

The bionic polarimetric imaging navigation sensor (BPINS) is a navigation sensor that provides absolute heading, and it is of practical engineering significance to model the measurement error of BPINS. The existing BPINSs are still modeled using photodiode-based measurements rather than imaging measurements and are not modeled systematically enough. This paper proposes a measurement performance analysis method of BPINS that takes into account the geometric and polarization errors of the optical system. Firstly, the key error factors affecting the overall measurement performance of BPINS are investigated, and the Stokes vector-based measurement error model of BPINS is introduced. Secondly, based on its measurement error model, the effect of the error source on the measurement performance of BPINS is quantitatively analyzed using Rayleigh scattering to generate scattered sunlight as a known incident light source. The numerical results show that in angle of E-vector (AoE) measurement, the coordinate deviation of the principal point has a greater impact, followed by grayscale response inconsistency of CMOS and integration angle error of micro-polarization array, and finally lens attenuation; in degree of linear polarization (DoLP) measurement, the grayscale response inconsistency of CMOS has a more significant impact. This finding can accurately guide the subsequent calibration of BPINS, and the quantitative results provide an important theoretical reference for its optimal design.

Compact all-dielectric metasurface for full polarization detection at the long-wavelength infrared region

Metasurfaces have been extensively demonstrated in engineering and detection of polarization of light from the visible to terahertz regions. However, most of the previous metasurfaces for polarization detection are spatially divided into different parts, and each of the parts focuses on different polarization components, resulting in large metasurface size and hindering their integration development. In this paper, a compact all-dielectric metasurface is proposed and numerically demonstrated to achieve full polarization detection at the long-wavelength infrared region (LIR). First, we design the metasurface at a wavelength of 10 µm, which can converge incident beams to specific positions corresponding to different polarization states. In this design, the metasurface is based on an oblique alternant double-phase modulation method, which arranges meta-atoms with the ability to control as many as possible different polarizations in a limited region, ensuring the high efficiency of polarization detection while giving more freedom and flexibility to the metasurface. Second, the intensity distributions of the electric field of different polarization components are simulated at wavelengths of 9.4 µm and 10.5 µm, verifying the broadband performance of the proposed metasurface. The proposed method has potential applications in integrated multifunctional devices and multispectral polarization imaging.

Modeling the celestial distribution of skylight polarization patterns by incorporating the influence of both the sun and the moon through an analytical model

The orientation of many polarization-sensitive animals and the hypothetical sky-polarimetric Viking navigation both rely on the polarization pattern of skylight. For 40 years, scientists have attempted to construct various models to simulate this pattern. However, existing theoretical models have only analyzed the polarization pattern of skylight that is influenced separately by the sun or the moon and have built their modeling frameworks based on the position of one light source. This approach fails to account for the combined influence of the sun and the moon on the distribution of skylight polarization patterns at certain times. In fact, ignoring the influence of the moon during the dawn and dusk periods in clear weather conditions may lead to significant errors in the simulation results compared to the measured data. In this paper, we present an analytical model that considers various factors, including skylight intensity, horizon correction factor, atmospheric turbidity condition, and combined influence of both the sun and moon on the distribution of polarized skylight. We believe our model demonstrates enhanced agreement with measured data and will further our understanding of how animals use the celestial polarization pattern for navigation, particularly when both the sun and the moon appear in the sky. Moreover, the findings of this study may facilitate the advancement of bio-inspired navigation systems.

High-similarity analytical model of skylight polarization pattern based on position variations of neutral points

The skylight polarization pattern contains rich information for navigation, meteorological monitoring, and remote sensing. In this paper, we propose a high-similarity analytical model by considering the influence of the solar altitude angle on the neutral point position variations for the distribution pattern of the polarized skylight. A novel function is built to determine the relationship between the neutral point position and solar elevation angle based on a large number of measured data. The experimental results show that the proposed analytical model achieves a higher similarity to measured data compared with existing models. Furthermore, data from several consecutive months verifies the universality, effectiveness, and accuracy of this model.

Polarized light compass decoding

The brains of some insects can encode and decode polarization information and obtain heading angle information. Referring to the encoding ability of insects, exponential function encoding is designed to improve the stability of the polarized light compass artificial neural network. However, in the decoding process, only neurons with the largest activation degree are used for decoding (maximum value decoding), so the heading information contained in other neurons is not used. Therefore, average value decoding (AVD) and weighted AVD are proposed to use the heading information contained in multiple neurons to determine the heading. In addition, concerning the phenomenon of threshold activation of insect neurons, threshold value decoding (TVD) and weighted TVD are proposed, which can effectively eliminate the interference of neurons with low activation. Moreover, this paper proposes to improve the heading determination accuracy of the artificial neural network through pre-training. The simulation and experimental results show that the new, to the best of our knowledge, decoding methods and pre-training can effectively improve the heading determination accuracy of the artificial neural network.

Biomimetic navigation system using a polarization sensor and a binocular camera

With the vigorous development of vision techniques, simultaneous localization and mapping (SLAM) has shown the capability of navigating autonomous robots in global-navigation-satellite-system-denied environments. However, the long-term robust navigation of lightweight autonomous robots in outdoor environments with complex interferences, such as illumination change, dynamic objects, and electromagnetic interference, is still a great challenge. In this paper, a polarization sensor-aided SLAM (POL-SLAM) that can provide absolute heading constraints for pure SLAM is proposed. POL-SLAM is a lightweight, tightly coupled system consisting of a polarization sensor and binocular camera. By means of an initialization that uses a polarization sensor, an absolute heading angle for the entire map is designed. Additionally, an algorithm to eliminate mismatching points using the matching point vector is proposed. The objective function of bundle adjustment is then deduced according to the re-projection error and polarization sensor. The vehicle test shows that the yaw and trajectory accuracies of POL-SLAM are significantly improved compared to pure SLAM. The yaw and trajectory accuracies are increased by 43.1% and 36.6%, respectively. These results indicate that the proposed POL-SLAM can improve the reliability and robustness of pure SLAM and can be used in lightweight autonomous robots in outdoor environments.

Polarized light sun position determination artificial neural network

Our previous work has constructed a polarized light orientation determination (PLOD) artificial neural network. Although a PLOD network can determine the solar azimuth angle, it cannot determine the solar elevation angle. Therefore, this paper proposes an artificial neural network for polarized light solar position determination (PLSPD), which has two branches: the solar azimuth angle determination branch and the solar elevation angle determination branch. Since the solar elevation angle has no cyclic characteristics, and the angle range of the solar elevation angle is different from that of the solar azimuth angle, the solar elevation angle exponential function encoding is redesigned. In addition, compared with the PLOD, the PLSPD deletes a local full connection layer to simplify the network structure. The experimental results show that the PLSPD can determine not only the solar azimuth angle but also the solar elevation angle, and the solar azimuth angle determination accuracy of the PLSPD is higher than that of the PLOD.

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°.

Adaptive method for estimating information from a polarized skylight

The acquisition and processing of skylight polarization information forms the cornerstone in modern navigation systems that are developed by imitating certain biological mechanisms. The accuracy of skylight polarization mode information plays a major part in improving the accuracy of polarized light navigation. This paper mainly focuses on developing a methodology that can avoid the error caused by the inaccurate rotation of the polarizer and manual readings from non-electrical equipment, when the time-sequence polarization measurement system is used to obtain the skylight polarization mode information. We propose an adaptive algorithm that can obtain the pictures of angle of polarization and degree of polarization with sets of random rotation angles with no need for precise readings for the rotation angle of the polarizer. By allocating initial random values to rotation angles, a simple iterative estimation method like the Gaussian-Newton method can be used to converge calculated angle of polarization and degree of polarization values to their respective real values. The experiment results show that the proposed method can be used to estimate polarization information with high accuracy and universality under various experiment settings including both sunny and cloudy weathers. Meanwhile, the time efficiency of the proposed method is comparable to traditional methods.

Neutral point detection using the AOP of polarized skylight patterns

The neutral points are one of the most significant characteristics of the polarized skylight pattern in the whole sky. At present, detection of the neutral points mostly utilizes ellipse fitting of the degree of polarization. However, because the degree of polarization distribution characteristics of a polarized skylight pattern is easily affected by the environment, the robustness of the detection is unstable. Aiming at the problem, we analyzed the angle of polarization distribution characteristics of polarized skylight patterns in the region around the neutral point by measurement experiments. Based on this, we proposed an automatic detection method of neutral points using the angle of polarization of the polarized skylight pattern. The experimental results of different times in a continuous period of time show that compared with ellipse fitting of the degree of polarization, the detection accuracy of the proposed method is almost the same, but the robustness is better. It provides a novel method for the position detecting of the neutral point, which is in favor of the measurement applications of polarization technology.

Limitation of Rayleigh sky model for bioinspired polarized skylight navigation in three-dimensional attitude determination

Insects such as desert ants and drosophilae can sense polarized skylight for navigation. Inspired by insects, many researchers have begun to study how to use skylight polarization patterns for attitude determination. The Rayleigh sky model has become the most widely used skylight polarization model for bioinspired polarized skylight navigation due to its simplicity and practicality. However, this is an ideal model considering only single Rayleigh scatter events, and the limitation of this model in bio-inspired attitude determination has not been paid much attention and lacks strict inference proof. To address this problem, the rotational and plane symmetry of the Rayleigh sky model are analyzed in detail, and it is theoretically proved that this model contains only single solar vector information, which contains only two independent scalar pieces of attitude information, so it is impossible to determine three Euler angles simultaneously in real-time. To further verify this conclusion, based on a designed hypothetical polarization camera, we discuss what conditions different three-dimensional attitudes must satisfy so that the polarization images taken at different 3D attitudes are the same; this indicates that multiple solutions will appear when only using the Rayleigh sky model to determine 3D attitude. In conclusion, due to its single solar vector information and the existence of multiple solutions, it is fully proved that 3D attitude cannot be determined in real time based only upon the Rayleigh sky model. Code is available at: https://github.com/HuajuLiang/HypotheticalPolarizationCamera.

Bio-inspired attitude measurement method using a polarization skylight and a gravitational field

High precision and reliability attitude measurement play an important role in autonomous unmanned navigation. Finding inspiration from desert ants, known as highly efficient navigators who can find their way after foraging for hundreds of meters from their home in hostile environments, we propose an attitude measurement method using polarization skylight and gravitational field. Contrary to the previous method, we utilize three-dimensional polarization vectors and any one-dimensional output of the accelerometers to calculate attitudes. In addition, we designed an accelerometer component selection algorithm, which is to select the one-dimensional component with the minimum motion acceleration from the output of the three-dimensional accelerometer. With this method, even if the carriers remain in a maneuvering state, the motion acceleration of the vehicle will have less impact on the accuracy of attitude measurement. To evaluate the performance of our method, the outdoor experiment was carried out to compare our method with existing traditional methods. Comparison results show that our method has higher measurement accuracy than others and is still applicable in the case of carriers maneuvering in practice under a clear sky.

Polarized skylight compass based on a soft-margin support vector machine working in cloudy conditions

The skylight polarization pattern, which is a result of the scattering of unpolarized sunlight by particles in the atmosphere, can be used by many insects for navigation. Inspired by insects, several polarization navigation sensors have been designed and combined with various heading determination methods in recent years. However, up until now, few of these studies have fully considered the influences of different meteorological conditions, which play key roles in navigation accuracy, especially in cloudy weather. Therefore, this study makes a major contribution to the study on bio-inspired heading determination by designing a skylight compass method to suppress cloud disturbances. The proposed method transforms the heading determination problem into a binary classification problem by segmentation, connected component detection, and inversion. Considering the influences of noise and meteorological conditions, the binary classification problem is solved by the soft-margin support vector machine. In addition, to verify this method, a pixelated polarization compass platform is constructed that can take polarization images at four different orientations simultaneously in real time. Finally, field experimental results show that the designed method can more effectively suppress the interference of clouds compared with other methods.

A Bio-Inspired Polarization Sensor with High Outdoor Accuracy and Central-Symmetry Calibration Method with Integrating Sphere

A bio-inspired polarization sensor with lenses for navigation was evaluated in this study. Two new calibration methods are introduced, referred to as "central-symmetry calibration" (with an integrating sphere) and "noncontinuous calibration". A comparison between the indoor calibration results obtained from different calibration methods shows that the two proposed calibration methods are more effective. The central-symmetry calibration method optimized the nonconstant calibration voltage deviations, caused by the off-axis feature of the integrating sphere, to be constant values which can be calibrated easily. The section algorithm proposed previously showed no experimental advantages until the central-symmetry calibration method was proposed. The outdoor experimental results indicated that the indoor calibration parameters did not perform very well in practice outdoor conditions. To establish the reason, four types of calibration parameters were analyzed using the replacement method. It can be concluded that three types can be easily calibrated or affect the sensor accuracy slightly. However, before the sensor is used outdoors every time, the last type must be replaced with the corresponding outdoor parameter, and the calculation needs a precise rotary table. This parameter, which is mainly affected by the spectrum of incident light, is the main factor determining the sensor accuracy. After calibration, the sensor reaches an indoor accuracy of ±0.009° and a static outdoor accuracy of ±0.05° under clear sky conditions. The dynamic outdoor experiment shows a ±0.5° heading deviation between the polarization sensor and the inertial navigation system with a ±0.06° angular accuracy.

Bio-inspired orientation using the polarization pattern in the sky based on artificial neural networks

Many insects use the pattern of polarized light in the sky as a navigational cue. In this study, we use this sensory ability as a source of inspiration to create a computational orientation model based on an artificial neural network (POL-ANN). After a training phase using numerically generated sky polarization patterns, stable and convergent networks are obtained. We undertook a series of verification tests using four typical but different sky conditions and showed that the post-trained networks were able to make an accurate prediction of the direction of the sun. Comparisons between the proposed models and models based on the convolutional neural network (CNN) structure revealed the merits of the bio-inspired architecture. We further investigated the accuracy of the models based on two different (locust-like, broader; Drosophila-like, narrower) visual fields of the sky. We find that the accuracy of the computations depends on the overhead visual scene, specifically that wider fields of view perform better when information about the overhead polarization pattern is missing.

Polarization patterns under different sky conditions and a navigation method based on the symmetry of the AOP map of skylight

The polarization states of a skylight can be used for navigation by a lot of insects as well as by human beings. However, the polarization patterns of skylight are greatly influenced by the atmospheric conditions. This paper studied the polarization patterns of skylight under different sky conditions by polarized imaging measurements, in which the AOT (Aerosol Optical Thickness) and clouds were taken into account. The results showed that both the aerosol and cloud disturbed the polarization patterns of the skylight, but the patterns of AOP (Angle of Polarization) showed great robustness. The symmetry of the AOP images was found to be quite steady under most of the sky conditions. We proposed a navigation method by finding out the solar meridian according to the symmetry of an AOP map. The results showed that the solar meridian can be identified accurately under different situations. The calculation errors slightly fluctuated along with the aerosol and cloud.

Efficient polarization direction measurement by utilizing the polarization axis finder and digital image processing

We report a new quantitative measurement method of polarization direction based on the polarization axis finder (PAF) and digital image processing. The PAF acts as an azimuthal analyzer to determine the polarization direction of linearly polarized light and form an "hourglass" intensity pattern, and a digital camera is employed to record the pattern, and then the lightwave's polarization direction is obtained accurately by analyzing the pattern with a specially designed digital image processing algorithm. The quantitative measuring experiments have been carried out by validating the standard quartz plates with known rotation angles, and the measurement accuracy has reached 0.01°.

Global positioning method based on polarized light compass system

This paper presents a global positioning method based on a polarized light compass system. A main limitation of polarization positioning is the environment such as weak and locally destroyed polarization environments, and the solution to the positioning problem is given in this paper which is polarization image de-noising and segmentation. Therefore, the pulse coupled neural network is employed for enhancing positioning performance. The prominent advantages of the present positioning technique are as follows: (i) compared to the existing position method based on polarized light, better sun tracking accuracy can be achieved and (ii) the robustness and accuracy of positioning under weak and locally destroyed polarization environments, such as cloudy or building shielding, are improved significantly. Finally, some field experiments are given to demonstrate the effectiveness and applicability of the proposed global positioning technique. The experiments have shown that our proposed method outperforms the conventional polarization positioning method, the real time longitude and latitude with accuracy up to 0.0461° and 0.0911°, respectively.

Real-time polarization imaging algorithm for camera-based polarization navigation sensors

Biologically inspired polarization navigation is a promising approach due to its autonomous nature, high precision, and robustness. Many researchers have built point source-based and camera-based polarization navigation prototypes in recent years. Camera-based prototypes can benefit from their high spatial resolution but incur a heavy computation load. The pattern recognition algorithm in most polarization imaging algorithms involves several nonlinear calculations that impose a significant computation burden. In this paper, the polarization imaging and pattern recognition algorithms are optimized through reduction to several linear calculations by exploiting the orthogonality of the Stokes parameters without affecting precision according to the features of the solar meridian and the patterns of the polarized skylight. The algorithm contains a pattern recognition algorithm with a Hough transform as well as orientation measurement algorithms. The algorithm was loaded and run on a digital signal processing system to test its computational complexity. The test showed that the running time decreased to several tens of milliseconds from several thousand milliseconds. Through simulations and experiments, it was found that the algorithm can measure orientation without reducing precision. It can hence satisfy the practical demands of low computational load and high precision for use in embedded systems.

Angle of sky light polarization derived from digital images of the sky under various conditions

Skylight polarization is used for navigation by some birds and insects. Skylight polarization also has potential for human navigation applications. Its advantages include relative immunity from interference and the absence of error accumulation over time. However, there are presently few examples of practical applications for polarization navigation technology. The main reason is its weak robustness during cloudy weather conditions. In this paper, the real-time measurement of the sky light polarization pattern across the sky has been achieved with a wide field of view camera. The images were processed under a new reference coordinate system to clearly display the symmetrical distribution of angle of polarization with respect to the solar meridian. A new algorithm for the extraction of the image axis of symmetry is proposed, in which the real-time azimuth angle between the camera and the solar meridian is accurately calculated. Our experimental results under different weather conditions show that polarization navigation has high accuracy, is strongly robust, and performs well during fog and haze, clouds, and strong sunlight.

Polarized skylight navigation

Vehicle state estimation is an essential prerequisite for navigation. The present approach seeks to use skylight polarization to facilitate state estimation under autonomous unconstrained flight conditions. Atmospheric scattering polarizes incident sunlight such that solar position is mathematically encoded in the resulting skylight polarization pattern. Indeed, several species of insects are able to sense skylight polarization and are believed to navigate polarimetrically. Sun-finding methodologies for polarized skylight navigation (PSN) have been proposed in the literature but typically rely on calibration updates to account for changing atmospheric conditions and/or are limited to 2D operation. To address this technology gap, a gradient-based PSN solution is developed based upon the Rayleigh sky model. The solution is validated in simulation, and effects of measurement error and changing atmospheric conditions are investigated. Finally, an experimental effort is described wherein polarimetric imagery is collected, ground-truth is established through independent imager-attitude measurement, the gradient-based PSN solution is applied, and results are analyzed.

Novel robust skylight compass method based on full-sky polarization imaging under harsh conditions

A novel method based on Pulse Coupled Neural Network(PCNN) algorithm for the highly accurate and robust compass information calculation from the polarized skylight imaging is proposed,which showed good accuracy and reliability especially under cloudy weather,surrounding shielding and moon light. The degree of polarization (DOP) combined with the angle of polarization (AOP), calculated from the full sky polarization image, were used for the compass information caculation. Due to the high sensitivity to the environments, DOP was used to judge the destruction of polarized information using the PCNN algorithm. Only areas with high accuracy of AOP were kept after the DOP PCNN filtering, thereby greatly increasing the compass accuracy and robustness. From the experimental results, it was shown that the compass accuracy was 0.1805° under clear weather. This method was also proven to be applicable under conditions of shielding by clouds, trees and buildings, with a compass accuracy better than 1°. With weak polarization information sources, such as moonlight, this method was shown experimentally to have an accuracy of 0.878°.

Real-time Imaging Orientation Determination System to Verify Imaging Polarization Navigation Algorithm

Bio-inspired imaging polarization navigation which can provide navigation information and is capable of sensing polarization information has advantages of high-precision and anti-interference over polarization navigation sensors that use photodiodes. Although all types of imaging polarimeters exist, they may not qualify for the research on the imaging polarization navigation algorithm. To verify the algorithm, a real-time imaging orientation determination system was designed and implemented. Essential calibration procedures for the type of system that contained camera parameter calibration and the inconsistency of complementary metal oxide semiconductor calibration were discussed, designed, and implemented. Calibration results were used to undistort and rectify the multi-camera system. An orientation determination experiment was conducted. The results indicated that the system could acquire and compute the polarized skylight images throughout the calibrations and resolve orientation by the algorithm to verify in real-time. An orientation determination algorithm based on image processing was tested on the system. The performance and properties of the algorithm were evaluated. The rate of the algorithm was over 1 Hz, the error was over 0.313°, and the population standard deviation was 0.148° without any data filter.

Optical implementation of the generalized Hough transform with totally incoherent light

The generalized Hough transform is a well-established technique for detecting complex shapes in images containing noisy or missing data. We present an efficient optical implementation of this transform using an electrical lens with variable focal length and a rotating pupil mask matching the pattern to be found. The proposed setup works under fully (i.e., both spatially and temporally) incoherent illumination and can handle orientation changes or scale variations in the pattern. Validation experiments showing its real-time application are presented.