Optical encoder, method for detecting rotation angle, program, and computer-readable recording medium.

Abstract

By encoding angular information into a high-dimensional space, we provide a robust angle reconstruction technology. [Solution] The optical encoder 100 for detecting the rotation angle comprises a light source 102, a geometric phase element 108 which is rotatably arranged around a predetermined axis and has a geometric phase distribution spatially distributed in a two-dimensional plane, and generates a spatial response that changes two-dimensionally according to the rotation angle in response to incident light from the light source 102, and is configured such that the spatial response includes a plurality of spatial frequency components which are different from each other, an image sensor 114 which receives transmitted light from the geometric phase element 108 and acquires the received signals of a plurality of pixels as a spatial response, and a computer 200 which calculates the rotation angle of the geometric phase element 108 by constructing an observation vector whose components are the received signals of a plurality of pixels and performing estimation processing that integrally uses the received signals of a plurality of pixels based on the correspondence between the observation vector and the rotation angle.

Description

[Technical Field]

[0001] The present invention relates to an optical encoder for detecting a rotation angle, a method for detecting a rotation angle, a program, and a computer-readable recording medium. [Background technology]

[0002] Detecting rotation angle is an essential fundamental technology in industrial robots, machine tools, semiconductor manufacturing equipment, and autonomous driving systems. Conventional optical encoders detect the rotation angle by generating a sinusoidal light intensity signal corresponding to the rotation using a diffraction grating or slit, and then interpolating its phase (see, for example, Patent Document 1). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] International Publication No. 2012 / 114595 [Overview of the project] [Problems that the invention aims to solve]

[0004] However, in conventional detection methods, each detection channel measures a one-dimensional periodic signal of essentially the same single frequency, so the resolution is limited by the signal-to-noise ratio and spatial frequency. As a result, there are limits to both theoretical and practical resolution. Furthermore, in detection methods using rotationally symmetric geometric phase elements (e.g., q-plates), each pixel exhibits an equivalent angular response, so the information dimension does not increase even when using a two-dimensional image sensor. Therefore, if noise, pixel defects, etc. occur, it becomes difficult to detect the rotation angle.

[0005] This invention has been made in view of the above-mentioned problems, and aims to provide a robust angle reconstruction technique by encoding angle information into a high-dimensional space. [Means for solving the problem]

[0006] An optical encoder according to one aspect of the present invention is an optical encoder for detecting a rotation angle, comprising: a light source; a geometric phase element rotatably arranged around a predetermined axis and having a geometric phase distribution spatially distributed in a two-dimensional plane, the geometric phase element generating a spatial response that changes two-dimensionally according to the rotation angle in response to incident light from the light source, and configured such that the spatial response includes a plurality of spatial frequency components that are different from each other; an image sensor that receives transmitted or reflected light from the geometric phase element and acquires the received signals of a plurality of pixels as a spatial response; and a processor that constructs an observation vector with the received signals of a plurality of pixels acquired by the image sensor as components, and calculates the rotation angle of the geometric phase element by performing estimation processing that integrally uses the received signals of a plurality of pixels based on the correspondence between the whole observation vector and the rotation angle.

[0007] A method for detecting a rotation angle according to one aspect of the present invention is a method for detecting a rotation angle using an optical encoder, comprising the steps of: generating a two-dimensional spatial response including a plurality of spatially different spatial frequency components according to the rotation angle by irradiating a geometric phase element, which is rotatably arranged around a predetermined axis and has a geometric phase distribution spatially distributed in a two-dimensional plane, with light from a light source; receiving transmitted or reflected light from the geometric phase element with an image sensor and acquiring received signals of a plurality of pixels as a two-dimensional spatial response; constructing an observation vector using the received signals of a plurality of pixels as components with a processor; and calculating the rotation angle of the geometric phase element by performing estimation processing using the received signals of a plurality of pixels in an integrated manner based on the correspondence between the entire observation vector and the rotation angle with the processor.

[0008] A program according to one aspect of the present invention is a program for estimating the rotation angle of a geometric phase element based on the received signals of a plurality of pixels corresponding to transmitted or reflected light from a geometric phase element that is rotatably arranged around a predetermined axis and has a geometric phase distribution spatially distributed in a two-dimensional plane, and causes a computer to perform the steps of: acquiring a two-dimensional spatial response containing a plurality of different spatial frequency components generated according to the rotation angle of the geometric phase element as received signals of a plurality of pixels, and constructing an observation vector with the received signals of the plurality of pixels as components; and calculating the rotation angle of the geometric phase element by performing an estimation process that integrally uses the received signals of the plurality of pixels based on the correspondence between the whole observation vector and the rotation angle.

[0009] A computer-readable recording medium according to one aspect of the present invention is a non-temporary computer-readable recording medium on which the above-mentioned program is recorded. [Effects of the Invention]

[0010] According to the present invention, the rotation angle of a geometric phase element is encoded as a two-dimensional spatial response containing multiple distinct spatial frequency components, and treated as an observation vector whose components are the light-receiving signals of multiple pixels. This redundantly distributes the angle information across multiple pixels, enabling robust angle estimation. [Brief explanation of the drawing]

[0011] [Figure 1] This is a schematic diagram showing the basic configuration of the optical encoder according to this embodiment. [Figure 2] A block diagram showing the hardware configuration of a computer. [Figure 3] This is an example of a phase pattern for a geometric phase element. [Figure 4] This figure shows the Fisher information distribution obtained based on the phase pattern shown in Figure 3. [Figure 5A] This graph shows an example of a single-pixel angular response signal generated in response to the rotation of a geometric phase element. [Figure 5B] A graph representing the Fourier spectrum of the angular response signal shown in FIG. 5A. [Figure 6A] A graph representing two angular response signals shifted in the angular direction for a single pixel. [Figure 6B] A graph representing the angular restoration result obtained by global correlation integrating the angular response signals of all pixels.

Embodiments for Carrying Out the Invention

[0012] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0013] In a conventional optical encoder, the rotation angle φ is detected by optically reading a periodic pattern on a code disk. The signal I ij (φ) is expressed as a one-dimensional sine wave response with respect to the rotation angle φ as shown in Equation (1). Here, I0 is the average light intensity, A is the amplitude, N is the number of lines per disk rotation, and φ0 represents the initial phase.

Equation

[0014] Equation (1) means that the rotation angle φ is encoded as the phase of a periodic signal. Conventionally, improvement in resolution has mainly been achieved by increasing the amplitude A and the number of lines N and reducing noise.

[0015] In such one-dimensional periodic observation, the angular estimation φ est The theoretical limit of is given by Equation (2) by the Cramer-Rao Lower Bound (CRLB). Here, σ 2 is the variance of the additive noise.

Equation

[0016] Equation (2) shows that the resolution is determined by the signal amplitude and period, and that the lower the noise and the shorter the period, the more accurate the estimation. On the other hand, this evaluation assumes that a sinusoidal signal can be acquired stably.

[0017] In the implementation environment, waveform distortion and amplitude reduction occur due to factors such as dirt, partial shielding, eccentricity, temperature fluctuations, and aging, leading to nonlinear observations. In this case, the performance limit is governed not by noise dispersion, but by the instability and ambiguity of phase estimation based on periodicity. Furthermore, even when using multiple pixels, the angular response of the same waveform is observed at all pixels, so increasing the number of pixels does not increase the amount of information. As a result, there was a bottleneck where angle estimation easily failed when localized signal loss or degradation occurred.

[0018] From the above, it can be seen that the practical limitations of conventional optical encoders stem not from resolution or theoretical accuracy itself, but from the observation structure that relies on a one-dimensional periodic signal. To overcome this limitation, the observation structure itself needs to be redesigned.

[0019] Therefore, the optical encoder of this embodiment does not directly detect the rotation angle from a single periodic signal, but encodes the rotation angle as a light intensity pattern distributed in a two-dimensional space. In other words, even though the angle itself is one-dimensional, the information representation can be high-dimensional, so as described later, each pixel and each frequency component is used as an independent channel, and the rotation angle is redundantly encoded in a high-dimensional space.

[0020] <Basic Configuration of an Optical Encoder> Figure 1 shows the basic configuration of the optical encoder 100 according to this embodiment. The optical encoder 100 comprises a light source 102, a collimating lens 104, a polarizer 106, a geometric phase element 108, an analyzer 110, an imaging lens 112, an image sensor 114, and a computer 200.

[0021] The light source 102 is a light source for irradiating light onto the geometric phase element 108. An example of the light source 102 is a light-emitting diode (LED).

[0022] The collimating lens 104 converts the light emitted from the light source 102 into collimated light. The polarizer 106 allows linearly polarized light with a specific polarization direction to pass through from the collimated light converted by the collimating lens 104. The linearly polarized light from the polarizer 106 is shone onto the geometric phase element 108.

[0023] The geometric phase element 108 is a planar optical element that spatially modulates the geometric phase of light. The plane is positioned perpendicular to the optical axis of the light source 102 and is rotatable by a motor around a predetermined axis (for example, the optical axis of the light source 102). The geometric phase element 108 is composed of a liquid crystal element, a metasurface, a dielectric nanostructure, a diffractive optical element, a subwavelength grating, or an anisotropic structure containing these.

[0024] The geometric phase element 108 has a geometric phase distribution defined in a two-dimensional plane, and when light is irradiated from the light source 102, it spatially modulates the geometric phase of the light so as to generate a two-dimensional spatial response that changes according to the rotation angle. Here, the two-dimensional spatial response refers to the intensity distribution or its electrical signal formed on the image sensor 114 by the action of the geometric phase element 108, which changes according to the rotation angle and includes multiple spatial frequency components that are different from each other.

[0025] The geometric phase distribution of the geometric phase element 108 may, but is not limited to, be configured as a superposition of multiple spatial frequency components. Furthermore, the two-dimensional spatial response may be configured to include spatial frequency components that are different from each other in at least one of the circumferential and radial directions.

[0026] In this embodiment, Pancharatnam-Berry (PB) phase elements are mainly used as the geometric phase element 108. A PB phase element is an optical element that imparts a geometric phase (PB phase) according to the polarization state of incident light based on the spatially changing optical axis orientation. A birefringent film is an example of a PB phase element. The PB phase refers to a phase component that is controlled in particular by the spatial distribution of the optical axis orientation, based on the relationship between the polarization direction of incident light and the optical axis orientation.

[0027] When observing a rotating PB phase element with a fixed imaging optical system, the rotation angle appears as a sequential sampling of different spatial structures. The PB phase element is designed to generate spatially different responses depending on the rotation, thus breaking rotational symmetry. This constructs a higher-dimensional observation structure.

[0028] Note that while Figure 1 shows an example where the planar shape of the geometric phase element 108 is circular, its shape is not limited to this.

[0029] Light transmitted through the geometric phase element 108 is incident on the analyzer 110. In this embodiment, a crossed nicol observation method is employed, and the transmission axis of the analyzer 110 is designed to be perpendicular to the transmission axis of the polarizer 106.

[0030] The imaging lens 112 forms an image on the image sensor 114 of the light incident from the geometric phase element 108 via the analyzer 110.

[0031] The image sensor 114 is an image sensor in which multiple pixels are arranged in a matrix. It receives transmitted light from the geometric phase element 108 and acquires the received signals of multiple pixels. Specifically, the image sensor 114 detects the intensity of the transmitted light from the geometric phase element 108 and converts the detected light intensity into an electrical signal (received signal). The received signals of multiple pixels represent a two-dimensional spatial response that changes according to the rotation of the geometric phase element 108, and each pixel has a different rotation angle dependence. In this embodiment, such received signals are sometimes called angular response signals. The generation of angular response signals will be described in detail later.

[0032] Examples of the image sensor 114 include a Complementary Metal Oxide Semiconductor (CMOS) image sensor and a Charge Coupled Device (CCD) image sensor. The image sensor 114 is connected to the computer 200, and the angle response signal acquired by the image sensor 114 is output to the computer 200.

[0033] Figure 2 shows the hardware configuration of computer 200. Computer 200 comprises a processor 202, an input device 204, a display 206, memory 208, a database (DB) 210, and an I / F 212.

[0034] The processor 202 acquires light reception signals (angle response signals) from multiple pixels of the image sensor 114 and performs rotation angle estimation processing, which will be described later, according to the program stored in the memory 208. The rotation angle estimation processing will be described in detail later.

[0035] The input device 204 includes, for example, a keyboard, mouse, touch panel, touchpad, pointing device, etc. The display 206 displays data input by the input device 204, the results of processing performed by the processor 202, etc.

[0036] Memory 208 has a non-temporary computer-readable recording medium and stores a program to be executed by the processor 202, as well as data and various parameters necessary for the execution of that program. Examples of computer-readable recording media include memory devices such as hard disk drives (HDDs), solid state drives (SSDs), and optical discs.

[0037] Alternatively, the program executed by processor 202 may be stored on another computer connected via a network, and processor 202 may read the program from the other computer via I / F212.

[0038] DB210 stores the data necessary for the estimation process performed by processor 202 (for example, the reference data described later).

[0039] I / F212 is an interface for connecting computer 200 to a network such as a Local Area Network (LAN), Wide Area Network (WAN), and / or the Internet.

[0040] Figure 1 illustrates a system for detecting transmitted light from the geometric phase element 108, but a system for detecting reflected light from the geometric phase element 108 may also be used. Furthermore, the optical encoder 100 may be configured such that the geometric phase element 108 is fixed and other optical elements (for example, one or both of the polarizer 106 and analyzer 110) are rotated. In other words, as long as the relative rotation angle between the geometric phase element 108 and the other optical elements can be estimated, the configuration of the optical encoder 100 is not limited regardless of which element is the primary rotating element.

[0041] <Generation of angular response signals> This section explains the method for generating angular response signals, focusing on the physics of rotational transformation using a PB phase element.

[0042] Figure 3 shows an example of the phase pattern of a PB phase element. The PB phase element is designed to generate different non-sinusoidal and multi-frequency angular responses for each pixel (i.e., responses containing multiple frequency components that cannot be approximated by a single-frequency sine wave) as each pixel rotates, by mixing components with different directions and periods. In this embodiment, the rotation of the PB phase element appears not as a simple addition of phases, but as a nonlinear remapping of the phase distribution.

[0043] The PB phase is described by the local optical axis azimuth angle θ(x, y) on a two-dimensional plane (xy-plane). If the rotation angle of the PB phase element is φ, the local optical axis azimuth angle observed at the coordinates (x, y) of the image sensor 114 after rotation is expressed as a value read out by transforming the coordinates of the pattern θ(x, y) before rotation. Local optical axis azimuth angle θ after rotation φ φ (x, y) can be expressed as shown in equation (3).

number

[0044] In equation (3), R -φ This represents a coordinate transformation (rotational transfer) that rotates a point (x, y) on a two-dimensional plane by -φ, and is defined as shown in equation (4).

number

[0045] Equations (3) and (4) mean that the value of θ is not uniformly added by the rotation angle φ, but rather the phase pattern is spatially rearranged. Because of this property, the changes associated with rotation do not generally result in a simple one-dimensional response like a sine wave, but rather appear as pixel-wise structured angle responses that reflect the structure of the two-dimensional distribution θ(x,y).

[0046] From the above, it can be seen that by using the phase pattern of the PB phase element, a physical operation of rotation can be utilized as a spatially non-linear phase conversion. Through this phase conversion, the angular information is encoded not as a single periodic signal, but as a distributed response containing multiple frequency components, as described below.

[0047] The response waveform I of the rotation angle φ at the pixel index (i, j) ij (φ) is represented by a Fourier series as shown in Equation (5) and contains a number of harmonic components. Here, k is the frequency index, a 0,ij 、a k,ij 、b k,ij (k = 1,..., K; K is an integer greater than or equal to 1) are Fourier coefficients.

Equation

[0048] I ij (φ) is composed of the received light signals of multiple pixels of the image sensor 114 as components. Specifically, I ij (φ) consists of a spatial component (i, j) and a frequency component k, and is represented as a high-dimensional observation vector that redundantly contains angular information distributed among multiple pixels.

[0049] Figure 5A shows an example of the angular response signal of a single pixel generated in response to the rotation of the PB phase element, and Figure 5B shows the Fourier spectrum of the angular response signal in Figure 5A. The angular response signal shown in Figure 5A shows a non-sinusoidal waveform that is significantly different from a sine wave and contains a number of sharp changes. The angular response signal and its Fourier spectrum are different for each pixel, and I ij (φ) and its Fourier spectrum represented by Equation (5) become the minimum unit of high-dimensional coding.

[0050] <Increase in Fisher information amount due to channel diversification> Figure 4 shows the Fisher information amount distribution obtained based on the phase pattern in Figure 3. Figure 4 shows that due to non-linear remapping, the angular sensitivity (∂I ijThis visualizes how / ∂φ) is spatially rearranged and how the Fisher information is designed to be distributed on a two-dimensional plane.

[0051] Fischer information I related to the rotation angle φ PB (φ) is the independent Gaussian noise dispersion σ 2 Assuming this, it is defined as shown in equation (6). Equation (6) shows that the greater the sensitivity of the channel to the rotation angle φ, the greater its contribution to the Fisher information.

number

[0052] I PB When (φ) is averaged with respect to the rotation angle φ, the Fisher information is expressed as shown in equation (7). Equation (7) shows that the Fisher information is added together with a weighting equal to the square of the frequency.

number

[0053] As can be seen from the Fourier spectrum shown in Figure 5B, the angular response of a single pixel contains numerous harmonic components in addition to the fundamental frequency component. As shown in equation (7), these harmonic components are k 2 The weight of this factor contributes significantly to the Fisher information.

[0054] Furthermore, in the phase pattern of the PB phase element, the angular response waveform differs for each pixel, so as shown in Figure 4, the Fisher information is distributed across the entire two-dimensional plane. In other words, the channels are diversified in the form of pixel × frequency, and the Fisher information increases almost proportionally to the number of pixels and the number of frequency components. This eliminates the conventional bottleneck where the same angular response waveform is observed for all pixels, resulting in no increase in information.

[0055] <Rotation angle estimation process> The angular response waveform of each pixel is random, and it is not possible to uniquely determine the rotation angle from a single pixel. In this embodiment, instead of treating the angular response waveform of each pixel individually, a method is adopted to decode the rotation angle using global correlation, which treats all pixels simultaneously.

[0056] Reference pattern I is an observed vector used as a reference value. ij ref (φ) and the observed vector as the measured value, which is observation pattern I ij meas The angular correlation between (φ) and all pixels (i, j) is simultaneously evaluated using the global correlation function defined in equation (8). Equation (8) shows that the angular cross-correlation (periodic correlation / annular correlation) is calculated for each pixel and then added together over all pixels.

number

[0057] I ij ref The (φ) data is stored in DB210 as reference data with a predefined correspondence between the observed vector and the rotation angle. In other words, DB210 stores data in which the angular response signal of each pixel is recorded for one rotation (0 to 2π).

[0058] Equation (8) is used to evaluate the degree of agreement between the reference pattern for each pixel and the observed pattern of all pixels acquired at a given moment. Specifically, as shown in Figure 6A, the degree of agreement when the reference pattern is rotated by an unknown angle Δφ in the angular direction is calculated simultaneously and in parallel for all pixels. Here, Δφ is not a physical quantity associated with the actual rotation, but a parameter (virtual shift amount) used to perform omnidirectional search on the computer.

[0059] At the true Δφ, the degree of agreement between the reference pattern and the observed pattern is maximized. Therefore, in the global correlation, a sharp single peak appears prominently at the position corresponding to the true rotation angle, as shown in Figure 6B. By extracting the Δφ that gives the maximum correlation, the rotation angle can be calculated. In this way, the rotation angle can be decoded by statistical estimation called correlation calculation.

[0060] In implementation, to calculate C(Δφ) in equation (8), convolution is performed on the angular axis using the Fast Fourier Transform (FFT). Specifically, multiplication is performed in the frequency domain using the FFT, followed by an inverse FFT. This makes it possible to evaluate all angular axes simultaneously and quickly.

[0061] Thus, the angle estimation in this embodiment is an estimation that coherently integrates information encoded in a distributed high-dimensional observation space (i.e., estimation that comprehensively uses the received signals of multiple pixels). This means that the spatial design of the Fisher information quantity described above is actually effectively utilized in the decoding process. As a result, the effects of noise and local defects in some pixels are canceled out by the correlation contribution of all pixels, enabling extremely robust and high-speed angle measurement.

[0062] <Performance Verification> To verify the performance of the optical encoder 100, numerical simulations were used to compare it with CRLB, which represents the theoretical limit of estimation accuracy, and to evaluate its robustness to pixel defects in a simulated implementation environment.

[0063] When the root mean square (RMS) error was expressed as a function of the standard deviation σ of the additive noise, and √CRLB was compared with the RMS error, it was found that in the mid-noise range, the RMS error was close to √CRLB, achieving extremely high estimation accuracy.

[0064] Furthermore, by introducing random pixel loss into the observed images and analyzing the peak discriminability using global correlation, high robustness was demonstrated, showing that angle estimation is possible even when many pixels (for example, 90% of all pixels) are lost.

[0065] These verification results are a direct effect obtained by acquiring angular information as a high-dimensional observation vector and performing statistical estimation, and represent characteristics that cannot be achieved with conventional one-dimensional periodic signal models. These results indicate that the factor defining the performance limit of the optical encoder 100 has shifted from conventional additive noise to probability theory.

[0066] <Angle reconstruction using learning process> A learning process can also be used to estimate the rotation angle. In the learning process, a model is used that has been pre-trained to acquire the correspondence between the observation vector and the rotation angle for each pixel.

[0067] For example, a regression model may be trained that outputs a rotation angle, using multiple observation vectors corresponding to known rotation angles as training data. This regression model may be a neural network, Gaussian process regression, support vector regression, or an equivalent learning model. The training data is stored in a predetermined area of ​​memory 208 or in DB 210.

[0068] After training, the rotation angle can be directly estimated by providing an observed vector for an unknown rotation angle as input. Furthermore, the training process may be performed offline, or it may be executed as online training with sequential updates during operation. The trained model is also stored in a predetermined area of ​​memory 208 or in DB210.

[0069] By using this type of learning process, characteristic variations caused by manufacturing variability, changes in optical elements over time, temperature fluctuations, etc., can be absorbed through learning, enabling further improvement in the accuracy of angle estimation.

[0070] Furthermore, instead of the statistical estimation and learning processes described above, optimization processes may be used to estimate the rotation angle, or a combination of these processes may be used.

[0071] <Correction of imaging system errors> The correction of errors in the imaging system of the optical encoder 100 will be described below. In this specification, the term "error in the imaging system" refers to a concept that includes image degradation, characteristic variations, non-uniformity, and other deviations in imaging characteristics that occur due to the imaging optical system or the image sensor 114.

[0072] The imaging optical system of the optical encoder 100 inevitably contains aberrations, and the received signal acquired by the image sensor 114 contains distortion, blur, field of view dependence, etc. These are not merely image quality degradations, but have two fundamentally different effects on correlation-based phase decoding. Specifically, the effect caused by the spread of the point image distribution function manifests as a decrease in the amplitude of the spatial frequency component (a decrease in the modulation transfer function (MTF)), increasing the variance of phase estimation and dominating the resolution and accuracy limits. On the other hand, distortion, asymmetric aberrations, field of view dependent aberrations, etc., add an additional phase term to the frequency component, appearing as a systematic phase bias in the estimation result.

[0073] Processor 202 functions as an image signal processor (ISP) found in smartphones and digital cameras, performing preprocessing such as distortion correction, flat-field correction, shading correction, and phase calibration. This restores the coordinate system and phase reference for which circular correlation calculations are valid. This preprocessing is not merely for improving image quality, but is fundamental processing for enabling decoding based on multi-frequency phase structures.

[0074] Furthermore, the processor 202 may use machine learning to compensate for errors caused by aberrations, temperature fluctuations, individual differences, nonlinearities, etc., that remain after preprocessing. In this case, machine learning does not learn the entire imaging optical system as a black box, but rather functions to compensate for residual components that cannot be fully represented by the physical model and preprocessing.

[0075] Therefore, the processor 202 corrects the errors in the imaging system through preprocessing, and further compensates for any remaining errors after preprocessing using machine learning. This makes it possible to realize a highly accurate and stable optical encoder 100.

[0076] <Effects and Effects> In this embodiment, the rotation angle of the geometric phase element 108 is encoded as a two-dimensional spatial response and treated as an observation vector whose components are the received signals of multiple pixels, thus redundantly distributing the angle information across the pixel group. This redundancy averages out the effects of additive noise, and allows the rotation angle to be estimated even if some pixels are missing or there are variations in sensitivity. By applying statistical estimation, learning, etc., as estimation processes, a higher effective angular resolution can be achieved compared to conventional methods that directly detect the rotation angle from a single periodic signal.

[0077] <Variation> As the geometric phase element 108, it is not limited to a PB phase element using liquid crystal, but a metasurface, dielectric nanostructure, diffractive optical element, etc. may be used to form a geometric phase distribution equivalent to that of a PB phase element. Furthermore, in designing the geometric phase distribution, it is not necessarily limited to a specific combination of spatial frequency components, but a frequency distribution including randomness or a geometric phase distribution that changes adaptively depending on the angle may be adopted.

[0078] For the reconstruction of the rotation angle, methods other than cross-correlation may be used, such as maximum likelihood estimation, Bayesian estimation, machine learning, or other estimation processes.

[0079] Furthermore, the technical concept of this embodiment is not limited to the detection of a single rotation angle, but can be extended and applied to the estimation of the state of a multi-degree-of-freedom mechanism having multiple rotational and / or translational degrees of freedom.

[0080] For example, in a robot joint mechanism, a configuration may be used in which a two-dimensional spatial response generated by multiple geometric phase elements or combinations thereof, arranged to correspond to multiple rotation axes or translation axes, is simultaneously acquired, and state quantities corresponding to multiple degrees of freedom are simultaneously estimated based on a high-dimensional observation vector whose components are said to be the spatial response. In such a configuration, the information corresponding to each degree of freedom is treated as an observation problem in which spatially or frequencywise superimposed information, and it becomes possible to reconstruct the multi-degree-of-freedom state all at once by statistical estimation or learning processing.

[0081] Furthermore, the estimation of a multi-degree-of-freedom state is not limited to a configuration in which each degree of freedom is estimated individually; it may also be a configuration in which multiple degrees of freedom are estimated simultaneously based on the same observation vector.

[0082] Therefore, the technical concept of this embodiment can also be applied to state detection of multi-degree-of-freedom systems, including robot joint control, posture estimation, and dynamic state estimation.

[0083] It should be noted that the present invention is not limited to the embodiments and modifications described above, and various modifications are possible without departing from the spirit of the invention. Other embodiments and modifications made by those skilled in the art are also included in the present invention. [Explanation of Symbols]

[0084] 100 Optical Encoders 102 Light source 104 Collimating Lens 106 Polarizer 108 geometric phase elements 110 Analyzer 112 Imaging lens 114 Image Sensors 200 Computers 202 processors 204 Input Devices 206 displays 208 memory 210 Databases 212 I / F

Claims

1. An optical encoder for detecting rotation angle, Light source and A geometric phase element is rotatably arranged around a predetermined axis and has a geometric phase distribution spatially distributed in a two-dimensional plane, wherein it generates a spatial response that changes two-dimensionally according to the rotation angle in response to incident light from a light source, and the geometric phase element is configured such that the spatial response includes a plurality of spatial frequency components that are different from each other. An image sensor that receives transmitted or reflected light from the geometric phase element and acquires the received signals of multiple pixels as the spatial response, A processor that calculates the rotation angle of the geometric phase element by constructing an observation vector using the received signals of the plurality of pixels acquired by the image sensor as components, and performing estimation processing that integrally uses the received signals of the plurality of pixels based on the correspondence between the whole observation vector and the rotation angle, An optical encoder equipped with [a specific feature].

2. The optical encoder according to claim 1, wherein the processor uses statistical estimation as the estimation process.

3. The system further includes a database that stores reference data in which the correspondence between the observed vector and the rotation angle is defined in advance. The optical encoder according to claim 2, wherein the processor performs a correlation calculation between the reference data and the observed vector in the statistical estimation.

4. The optical encoder according to claim 3, wherein the processor performs convolution on the angular axis using the Fast Fourier Transform in the correlation operation.

5. The optical encoder according to claim 1, wherein the processor uses a model in which the correspondence between the observed vector and the rotation angle has been previously acquired by a learning process as the estimation process.

6. The optical encoder according to claim 1, wherein the geometric phase distribution is defined in the two-dimensional plane as a superposition of the plurality of spatial frequency components.

7. The optical encoder according to claim 1, wherein the spatial response includes the plurality of spatial frequency components in at least one of the circumferential and radial directions.

8. The optical encoder according to claim 1, wherein the geometric phase element includes a Pancratanum Berry phase element that imparts a geometric phase according to the polarization state of the incident light.

9. The system further comprises a polarizer that allows linearly polarized light with a specific polarization direction to pass through from the light emitted from the aforementioned light source. The optical encoder according to claim 8, wherein the Pancratanum Berry phase element is irradiated with the linearly polarized light.

10. A method for detecting a rotation angle using an optical encoder, A process of generating a two-dimensional spatial response containing multiple spatial frequency components that differ from each other depending on the rotation angle, by irradiating a geometric phase element, which is rotatably arranged around a predetermined axis and has a geometric phase distribution spatially distributed in a two-dimensional plane, with light from a light source, The process involves receiving transmitted or reflected light from the geometric phase element using an image sensor and acquiring the received signals of multiple pixels as the two-dimensional spatial response, A process of using a processor to construct an observation vector whose components are the light-receiving signals of the plurality of pixels, The process of calculating the rotation angle of the geometric phase element by performing estimation processing using the light-receiving signals of the plurality of pixels in an integrated manner, based on the correspondence between the entire observation vector and the rotation angle, using the processor, Methods that include...

11. A program for estimating the rotation angle of a geometric phase element based on the light reception signals of multiple pixels corresponding to transmitted or reflected light from a geometric phase element that is rotatably arranged around a predetermined axis and has a geometric phase distribution spatially distributed in a two-dimensional plane, On the computer, A step of acquiring a two-dimensional spatial response, which includes a plurality of different spatial frequency components generated according to the rotation angle of the geometric phase element, as the light-receiving signal of the plurality of pixels, and constructing an observation vector whose components are the light-receiving signals of the plurality of pixels, A step of calculating the rotation angle of the geometric phase element by performing an estimation process that integrates the light-receiving signals of the plurality of pixels based on the correspondence between the entire observed vector and the rotation angle, A program to execute.

12. A non-temporary computer-readable recording medium on which the program described in claim 11 is recorded.

Images