231 results about "Autocollimation" patented technology

The invention discloses an autocollimation method of a carrier aircraft rotating type strapdown inertial navigation system under a shaking base, and belongs to the field of navigation. The autocollimation method comprises the following steps of: firstly obtaining the longitude and latitude of the position of a carrier, secondly collecting output signals of a fiber-optic gyro and a quartz flexible accelerometer in an inertia measurement unit, and then carrying out automatic compensation on a constant error of an inertia device by adopting a double-shaft rotating table rotatory IMU (inertial measurement unit) to form a rotating type strapdown inertial navigation system; and then calculating a rough initial posture array by utilizing gravity acceleration in an inertial coordinate system as a reference vector, establishing a state equation and a measuring equation again of the system, designing a vanishing adaptation Kalman filter to accurately estimate a misalignment angle of the carrier, and correcting a strapdown posture matrix by utilizing the misalignment angle to finish initial alignment and enter a navigation state. The method isolates the influence of shake of a vessel to initial alignment of a carrier aircraft, and dynamic random disturbance in measured noise is restrained through estimating the initial posture array of the system via the vanishing adaptation Kalman filter method, so that rapid autocollimation of the carrier aircraft rotating type strapdown inertial navigation system is realized.

The invention discloses a two-dimensional photoelectric auto-collimation method and device for polarized light pyramid target common-path compensation, belonging to the technical field of precision instrument manufacture and precision measurement. According to the invention, high-precision photoelectric autocollimation angle measurement is realized for solving the defects in the existing method and device. The method comprises: a common-path shift quantity monitoring separating device based on a pyramid combined target can be used for curing a polarizing light splitter, a pyramid reflector and a measurement reflector to form the pyramid combined target, and separating a reference light beam which has a feature identical to that of a measurement light beam and is in common-path transmission with the measurement light beam while obtaining a two-dimensional angle variation by using the linear polarization feature of the laser; a controller is used for controlling a two-dimensional light beam deflection device in real time according to the shift quantity reflected by the reference light beam so as to inhibit the shift quantity coupled in the measurement light beam, thus the precision measurement on the two-dimensional angle variation is realized. The device for realizing the method comprises a two-dimensional photoelectric auto-collimation tube, the common-path shift quantity monitoring separating device based on the pyramid combined target, the controller and the two-dimensional light beam deflection device.

The invention relates to a device and a method for measuring lens focal length as well as a method for evaluating optical quality, wherein the device for measuring the lens focal length is composed of a plane mirror, a lens to be measured, a point light source, a vertical incision, a one-dimensional precise flat movable guide rail, a laser distance measuring instrument, a CCD detector and a display, and the method for measuring the lens focal length is as follows: (1) adjusting the autocollimation of the point light source and the lens to be measured; (2) adjusting the plane mirror to make the transflective convergent beam enter the CCD detector; (3) measuring the focal depth of the lens to be measured; (4) measuring the distance L from the point light source to the geometric main plane of the lens to be measured; (5) calculating the focal length f = L + d of the lens to be measured, and the d is the distance between the geometric main plane of the lens and the optical main plane. The optical processing quality of the lens to be measured is qualitatively evaluated through the observation of shape of the far-field focal spot. The device and the method are applied to the measurement and evaluation of the small-bore short-focus and large-bore long-focus lens, and have the advantages of the intuitionism, the high measuring precision and the simple mechanism.

The invention relates to an attitude testing apparatus and method based on an autocollimator. The apparatus mainly comprises the autocollimator, an optical hexahedron, a double-shaft electronic level meter and a pedestal with a leveling function. The method comprises the following steps: putting the attitude testing apparatus on a firm base, allowing the autocollimator to collimate a reflecting surface of an object, then collimating the optical hexahedron with an autocollimation gyro theodolite and measuring the included angle between the apparatus and a true north azimuth reference; starting the autocollimator for recording and retrieving of continuous data of the attitude of the reflecting surface of the object and starting the double-shaft electronic level meter for recording and retrieving of continuous data of horizontal attitude; and after completion of recording and retrieving of the data, processing the data of the autocollimator and the double-shaft electronic level meter by using a data processing method for the attitude testing apparatus so as to eventually obtain continuous changes of the attitude of the reflecting surface of the object in a geographic coordinate system, thereby meeting demands of continuous absolute measurement.

The invention discloses a collimation measurement system for attitudes and angles among spacecraft devices based on the combination between a robot and a theodolite. The system herein includes a robot, a laser tracker, a laser tracking target (T-MAC), a robot terminal tool, and the like. The system searches a to-be-tested datum cube mirror which is disposed on a spacecraft device by conducting mode identification, and computes the relations of phase position and direction of the datum cube mirror with respect to the theodolite. The laser tracker is intended for calibrating the relative direction relation in a coordinate system of respective spacecraft devices and integrating the measurement results of the theodolite at different measurement positions to the same coordinate system. Based onthe calibration relation and the relative relation, the laser tracker is guided to real-timely track the robot terminal tool and establish the relative relation between the laser track and the robotterminal tool. And eventually, the attitude relation matrix of the spacecraft is computed. According to the invention, the automatic measurement of the attitude relation among different devices is realized, the measurement efficiency can reach one time per half-minute, the measurement precision can be higher than 30'', on-site measurement flexibility is higher, and construction and measurement indifferent places can be much easier.

The invention discloses precise assembling and adjusting device and method for a detector chip of an imaging system. The assembling and adjusting device comprises a movement control system, a detection system, an accessory structure and a computer; the movement control system is composed of a translation stage, a revolving stage and a tilting table and used for adjusting the spatial positions of a device to be detected and the detection system; the detection system is composed of an autocollimation and a telecentric digital microimaging system and used for measuring the angle and positional deviation of the device to be detected; and the compute is able to control the movement of the translation stage and record the position coordinates and can also be used for acquiring an image of the device to be detected from the telecentric digital microimaging system and analyzing and calculating. The assembling and adjusting method includes the assembling and adjusting of a reference mirror, the transmission of the angle and position of the detector chip, and the assembling and adjusting of the detector chip; the measurement precision of the angle and position respectively reaches second level and micro dimension during the assembling and adjusting; and the deviation of angle and position of the detector chip can be respectively less than 1 and 0.02mm after the assembling and adjusting.

Machine tools can be accurately measured and positioned on manufacturing machines within very small tolerances by use of an autocollimator on a 3-axis mount on a manufacturing machine and positioned so as to focus on a reference tooling ball or a machine tool, a digital camera connected to the viewing end of the autocollimator, and a marker and measure generator for receiving digital images from the camera, then displaying or measuring distances between the projection reticle and the reference reticle on the monitoring screen, and relating the distances to the actual position of the autocollimator relative to the reference tooling ball. The images and measurements are used to set the position of the machine tool and to measure the size and shape of the machine tool tip, and examine cutting edge wear. patent

The invention relates to a dynamic angle measurement error detector used in a photo-electric axial angle encoder. A fixation part of a to-be-tested encoder is arranged on a base of the detector, a rotary part of the to-be-tested encoder is connected with a revolving shaft by a coupling joint, a polyhedron is fixed on the revolving shaft of the detector, a dynamic signaling autocollimation aims at a reflecting surface of the polyhedron, and a rotator of a torque motor is connected with the revolving shaft. During the detection, the torque motor is controlled by a computer to continuously rotate at a certain speed, and the revolving shaft, the rotary part of the to-be-tested encoder and the polyhedron are driven to rotate by the torque motor. When one operating angle of the polyhedron is turned, and the operating surface of the polyhedron is perpendicular to an optical axis, a trigger circuit sends out trigger impulses. Encoder values can be sampled after a data acquisition system probes trigger impulse signals. After the rotary part of the to-be-tested encoder rotates a circle, a group of sampling values can be obtained, and dynamic angle measurement errors of the to-be-tested encoder can be calculated by a data-processing system of the computer. The dynamic angle measurement error detector can be used for detecting the dynamic errors of the photo-electric axial angle encoder and has higher precision.

A mammographic imaging system is optimized for use with a single fixed size flat panel digital image receptor. It accommodates compression devices (paddles) of varying sizes, and positions them properly in the field of view of the image receptor. When a compression paddle with size smaller than the field of view of the image receptor is used, the compression paddle can be shifted laterally in the direction parallel to the chest wall, so as to facilitate different views of different size breasts, and permit the image receptor to image as much of the desired tissue as possible. An automatic x-ray collimator restricts the x-ray illumination of the breast in accordance with compression paddle size and location in the field of view. An anti-scatter grid, mounted inside the image receptor enclosure, just below the top cover of the enclosure, can be retracted out of the field of view of the image receptor for use in magnification imaging.

The present invention belongs to the technical field of optoelectronic equipment calibration, and particularly relates to a star sensor reference cube-prism installation error calibration apparatus. According to the present invention, a photoelectric autocollimator and a single star simulator are respectively placed on two orthogonal axes of a reference plane, a detected star senor is placed at the intersection point position of the two axes so as to make the normal lines of the two orthogonal light reflection surfaces of the detected star senor reference prism be respectively parallel to the two orthogonal axes, the optical axes of the photoelectric autocollimator and the single star simulator are respectively adjusted to parallel to the reference plane through a theodolite, the star sensor is installed on a star sensor three-dimensional adjustment reference base, the input optical axis of the star sensor and the output optical axis of the single star simulator are adjusted to achieve a parallel state through the star sensor three-dimensional adjustment reference base, a detected reference cube-prism is arranged on the upper surface of the housing of the detected star senor, the installation angle error of the reference cube-prism round the X-axis and the Y-axis is measured by using photoelectric autocollimation, the star sensor three-dimensional adjustment reference base rotates 90 DEG, and the installation angle error of the reference cube-prism round the Z-axis is measured.

The invention discloses a two-dimensional photoelectric auto-collimation method and device of polarized light plane mirror reference common-path compensation, and the method and device provided by the invention belong to the technical field of precision instrument manufacture and precision measurement. According to the invention, high-precision photoelectric autocollimation angle measurement is realized for solving the defects in the existing method and device. The method comprises: a plane mirror reference common-path shift quantity monitoring separating device can be used for separating a reference light beam with the feature identical to the that of a measurement light beam, especially the reference light beam which is in the common-path transmission with the measurement light beam, while obtaining measurement light beam in a two-dimensional angle variation by using the polarization feature of the laser and using a polarizing beam splitter and a reference plane reflector; and a controller can be used for controlling a two-dimensional light beam deflection device in real time according to the shift quantity reflected by the reference light beam so as to inhibit the shift quantity coupled in the measurement light beam, thus the precision measurement on the two-dimensional angle variation is realized. The device for realizing the method comprises a two-dimensional photoelectric auto-collimation tube, the plane mirror reference common-path shift quantity monitoring separating device, the controller and the two-dimensional light beam deflection device.

An automatic collimation surveying apparatus is provided with a collimation camera optical system (47) of a high magnification ratio; a wide-angle CCD camera optical system (89) having a wide field of view; a touch-panel display (64) for displaying an image picked up by both CCD camera optical systems; an image processing unit (60) for discriminating points of measurement from the above-described image; a touch-pen for pointing out points of measurement on the above-described image; and an automatic collimation unit (69) for automatically collimating the pointed-out points of measurement. In addition, illumination light from light source (80) is concurrently used as collimation light and is aligned so as to be emitted along the collimation axis (O) of a collimation camera optical system. The surveying apparatus can be remotely controlled from a measurement controller such as a peripheral personal computer. The surveying apparatus allows a number of point-of-measurement positions to be efficiently measured on a large-scaled structure by a single operator.

The invention provides an adjusting and correcting method of a light path of a photoelectric system tracking-pointing precision measuring device. The measuring device is mainly composed of an opticalplatform, a laser light source, ground glass, a small-hole diaphragm, a beam splitter, a parallel light pipe collimating mirror, a high-frame-frequency CCD camera and the like, wherein the laser lightsource, the ground glass, the small-hole diaphragm, the beam splitter, the parallel light pipe collimating mirror, the high-frame-frequency CCD camera and the like are installed on the optical platform. By the adoption of a plane mirror, an optical autocollimation, a pentaprism and a theodolite, the positions of the laser light source, the small hole diaphragm and the high-frame-frequency CCD camera of the photoelectric system tracking-pointing precision measuring device are adjusted and corrected, the adjusting and correcting method has the advantages of being high in precision, easy to operate, convenient and visual, the problem of adjusting and correcting the light path of the photoelectric system tracking-pointing precision measuring device is solved, and not only is technological guarantee provided for the development of a space laser communication tracking-pointing technology, but also a reference basis is provided for designing a space laser communication system tracking-pointing precision measuring device.

A laser radar optical path autocollimation method and collimator are disclosed that comprise reflector, laser, signal detecting element, receiving telescope and computer. It's characterized in that it includes mirror bracket, a fixed plate is mounted on the mirror bracket, a movable plate is mounted on the fixed plate, the fixed plate is connected with the movable plate via springs, the reflector is located on the movable plate, two sets of slide blocks / micrometer mechanism and driven step motor are mounted in the mirror bracket, there are push-rods on the slide blocks which extend from the hole on top of the bracket and the fixed plate to the underside of the movable plate. The slide blocks and the push-rods are motivated upwards by the rotation of the driven step motor, the movable plate is adjusted to rotate along the X, Y axis, and the target position of the reflector is fixed at last with high accuracy. The application prospect: atmosphere scientific experiment measuring apparatus and measuring means can be used in various laser radar systems.

The invention provides a method for measuring an installation error coefficient of a strap-down inertial navigation system and an alignment prism. Hardware facilities comprise a two-axis turntable, a strap-down inertial navigation system, an alignment prism, an autocollimation theodolite, a main control computer, a display, a keyboard and the like. The method comprises the following steps: changing collimation positions of the strap-down inertial navigation table, the alignment prism and the autocollimation theodolite by rotating the two-axis turntable twice, recording CCD (Charge Coupled Device) misalignment angle reading and horizontal plate reading beta of the autocollimation theodolite, inside and outside frame coded disc reading alpha of the two-axis turntable and strap-down inertial navigation output parameters twice by the main control computer, and resolving the installation error coefficient between the alignment prism and the inertial navigation system after an initial alignment manner of the alignment prism to the strap-down inertial navigation system is changed into a vertical installation manner.

Combination of polarized laser source, polarized beam splitter mirror and quarter Lambda wave plate is adopted in the 2D photoelectric autocollimation tube, which uses characteristic of polarization to avoid that measuring light beam feeds back laser source so as to prevent further angle drift of the measuring light. Obtaining measurement signal of 2D variance in small angle, beam splitter type target detector also obtains angle drift component of separated and fed back light beam. The said component is identical to inherent component of laser source. Monitoring device monitors quantity of angle drift. Based on quantity of angle drift obtained, computer control 2D optical beam deflection device in real time to adjust the measuring light beam according to direction opposite to quantity of angle drift. The invention restrains and eliminates quantity of angle drift coupled in measuring light beam in propagation path of the measuring light beam.

The invention discloses an automatic guide method for collimation measurement of a cubic mirror based on machine vision. The method comprises the following steps: rotating an industrial camera together with a theodolite, keeping the relative position relationship unchanged, controlling the camera to collect an image of a cubic mirror to be measured, identifying the cubic mirror by image processing, extracting corner points of the cubic mirror, and obtaining the coordinate values of the corner points under an image coordinate system; establishing a mathematical model of a camera coordinate system, a cubic mirror coordinate system and a theodolite coordinate system, performing coordinate transformation and calculating the position of an intersection of a normal line of a mirror surface to be measured of the cubic mirror and a movement plane of the theodolite under the mathematical model, controlling the theodolite to move to the position of the intersection, and adjusting the posture of the theodolite according to the normal direction of the mirror surface to be measured of the cubic mirror, so that the normal direction of the mirror surface to be measured of the cubic mirror moves into the range of field of view of the theodolite, and the automatic collimation of the cubic mirror is implemented on the basis of the automatic theodolite collimation step for image identification.

The invention provides a large-diameter paraboloidal mirror detecting system, comprising a Fizeau interferometer, a high precision plane reflector, a detected paraboloidal mirror, an electrically controlled translation platform and a computer control system, wherein, the plane deflector realizes autocollimation detection to the central part of the paraboloidal mirror, and then the plane deflector is removed; the electrically controlled translation platform is controlled through the computer to move the Fizeau interferometer, so that reference spheric wave fronts of different curvature radiuses generated by a standard lens can be matched with a corresponding annular region outside the diameter of the plane deflector of a detected paraboloid, and phase data corresponding to resolvable interference fringes can be extracted through Fizeau interferometer data processing software on the computer system; acquired sub-aperture test data can be processed by the annular sub-aperture 'stitching' algorithm, and data acquired from the autocollimation detection of the plane deflector undergoes a full aperture wave front reconstruction to acquire surface shape information of the detected paraboloid. The large-diameter paraboloidal mirror detecting system provides an effective detecting means for the development of a large-diameter paraboloidal mirror and an ultra-large-diameter paraboloidal mirror, and has higher application value.

The invention relates to method and device for measuring an optical axis and a gap of a lens group by a differential confocal internal focusing method, belonging to the technical field of optical precision measurement. The method comprises the following steps of: firstly accurately regulating the optical axis of the measured lens group by combining an internal focusing objective with an autocollimation method; then realizing the high-accuracy positioning of each surface of the measured lens group by utilizing a differential confocal focus-fixing principle, and acquiring a numerical aperture angle of a differential confocal light cone positioned on each positioning point; finally sequentially calculating each gap of the measured lens group by utilizing a ray tracing recursion formula, and also leading an annular optical pupil into a measuring optical path to form a hollow measuring light cone so as to reduce the influence of astigmation on a measurement result. The invention combines a differential confocal technology with an internal focusing technology, has high measurement accuracy, high speed, simple system structure, long working distance, no need for disassembling the measured lens group in a measuring process, and the like and can be used for the non-contact high-accuracy measurement of the optical axis and the gap of the lens group.

A method and apparatus for detecting objects has a sensor with a light source, a light receiver, and a light retroreflector between them. Light from the source is transmitted to the detector along a light transmission path from the source to the retroreflector and is reflected back to the detector along a light reflection path that substantially corresponds to the transmission path. A single lens or a pair of adjacent lenses shapes the respective light beams from both light emitted by the source and light reflected by the retroreflector in accordance with either the auto collimation principle or the double-eye principle, respectively. A polarizer and a beam splitter are arranged in the light transmission path for light from the source, and a polarization filter is arranged in the light reflection path so that light reflected by the retroreflector passes through the beam splitter and the polarization filter before it reaches the light receiver. A control unit recognizes an interruption of at least one of the light beams as the detection of an object in the light transmission and / or light reflection paths. The beam splitter is a dielectricum which has differing transmission and reflection characteristics for p-polarized light and s-polarized light.

The invention relates to a method for forming a photo composition; a mold plate layer is formed on a neutral polymer layer, and self-assembling segmented copolymer material is applied and automatically assembled; the mold plate layer comprises a first linear portion, a second linear portion shorter than the first linear portion, and a block-shaped mold plate structure with the width bigger than the second linear portion; in a zone far away from a portion extending in the width direction, the self-assembling segmented copolymer material is arranged in an alternate thin layer through phase separation; the block-shaped mold plate structure disturbs the thin layer and causes the thin layer to stop; when the copolymer segmented content is selectively removed, a cavity parallel to the first and second linear portions is formed, and the cavity can stop with the block-shaped mole plate structure in an autocollimation manner; the graph of the cavity can be reverted and transferred to the material layer so as to form fins with different lengths.

The invention belongs to the field of inertial navigation system performance assessment and relates to a co-base installation-based transfer alignment accuracy quantitative evaluation method aiming at strapdown inertial navitation system transfer alignment accuracy. The method comprises installing slave and main inertial navigation devices sharing a base on an aluminum plate, constructing slave and main inertial navigation device orientation installation misalignment angles, putting the aluminum plate with the slave and main inertial navigation devices on a high precision rotary table, guiding the y axis of the main inertial navigation device to point to the true north direction through an optical sighting telescope, measuring slave and main inertial navigation device y axis orientation installation error angles as orientation installation error angle reference values through a laser tracker and starting the main inertial navigation device to carry out autocollimation. The method can acquire alignment accuracy evaluation reference before transfer alignment and through comparison between the reference value and the evaluation value, alignment accuracy quantitative evaluation is realized. The method is free of slave inertial navigation device navigation calculation and smooth calculation after alignment, greatly reduces computation complexity and data storage demands and realizes repeated tests in short time.

The invention discloses a measuring method of eccentricity. A detected lens (S3) is set at a preset rotating angle, and transversal line (P1,P2)(S4) crosses with image ordinate of reticule, and ordinate (Q1,Q2)(S5) crosses with image transversal line of reticule, and the peak position A, B of light intensity on the transversal line (P1,P2) and the peak position C, D of light intensity on the ordinate (Q1,Q2) is specified. The cross ordinate for connecting A and B is determined and the cross transversal line (S8,S9) for connecting C and D is also determined. Then, the crossing point of the cross ordinate and cross transversal line is specified to be as center R(S11) of reticule image. Each center R is based on multi rotating positions, the image center tracking circle (S14) is calculated and the radius of the image center tracking circle is used as eccentricity Ec(S15) of the detected surface. Therefore, in the measuring method of eccentricity using autocollimation method, the measurement precision is greatly raised in simple structure.

The invention relates to a system and method of measuring an off-axis amount and an off-axis angle of an off-axis paraboloid main reflector. The system comprises an optical axis mark post A, an optical axis mark post B, an autocollimation theodolite A, an autocollimation theodolite B, an autocollimation theodolite C, an interferometer, a planar mirror and a small flat mirror. The autocollimation theodolite A, the optical axis mark post A, the optical axis mark post B and the autocollimation theodolite B are sequentially located on the same optical axis. The autocollimation theodolite B and the autocollimation theodolite C are located on the same optical axis. An off-axis reflector to be detected is placed between the autocollimation theodolite B and the autocollimation theodolite C. The small flat mirror is attached to the off-axis reflector to be detected. The focus of the interferometer and the focus of the off-axis reflector to be detected coincide. Spherical waves emitted by the interferometer are reflected by the off-axis reflector to be detected to form reflected light. The planar mirror is placed on the optical path where the reflected light resides. The invention provides the system and method of precisely measuring the off-axis amount and the off-axis angle of the off-axis reflector.

The invention relates to a system capable of solving an inclination problem of a narrow field of view lens in a wave aberration detection process and a method thereof. The system comprises a laser interferometer, a pentagonal prism, an autocollimation theodolite, a planar mirror and an optical axis directional tool which is in common optical axis with a narrow field of view lens to be detected. The laser interferometer, the pentagonal prism, the optical axis directional tool and the planar mirror are provided on a same optical path in order. The pentagonal prism is provided on an emitting optical path of the autocollimation theodolite. The system capable of solving the inclination problem of the narrow field of view lens in wave aberration detection and the method thereof have the characteristics of high detection precision, a short detection period and good repeatability.

Photoelectric autocollimation methods and apparatuses based on beam drift compensation are provided. The methods and apparatuses can be used to achieve a high autocollimation angle measurement accuracy. The apparatuses includes an autocollimator, a measurement mirror (12a), a beam drift monitoring and separating unit, a beam steering device (8), and a data processing controller (7). The beam drift monitoring and separating unit generate a reference beam with the same drift as the measurement beam. The measurement beam carries both angular deflection information of the measurement mirror and the angular beam drift information, while the reference beam carries only the angular beam drift information. The data processing controller gives out a signal to the beam steering device in real-time according to the magnitude of drift of the reference beam, to compensate the drift of the measurement beam.

The invention relates to a system and method for detecting the orthogonality of a precision shafting. The detection system comprises a four-dimension adjustable reticle, a television interior focusing autocollimator, and a detection platform. The four-dimension adjustable reticle is mounted on a rotating link of a pitch component of a to-be-detected precision orthogonal shafting. The detection platform is used for supporting the to-be-detected precision orthogonal shafting. The television interior focusing autocollimator is used for working with the four-dimension adjustable reticle to detect the orthogonality of the shafting through autocollimation and collimation. The four-dimension adjustable reticle is mounted on the rotating link of a shafting, the mirror surface of the reticle is adjusted to be perpendicular to the axis, the reticle center is on the axis, and the axis is simulated with the aid of the center of the reticle in the detection process rather than the center of a process hole. The limitations and defects of the prior art are overcome. After one adjustment, both the verticality and the intersection deviation can be obtained. The system and the method of the invention are based on the optical principle. The detection accuracy and efficiency are high. The method is simple. No requirement is put on the machining precision of a process hole in a bearing sleeve. The system and the method are easy to implement.

A magnetic field measuring device includes: a first cell and a second cell in which alkali metal atoms are entrapped and which are disposed in this order in a sensing direction of a magnetic field; a first reflective mirror, a second reflective mirror, and an autocollimator as an optical axis detector. Beam light as second polarized light and beam light as fourth polarized light, which are detected by the autocollimator, have orientations of optical axes in the same direction.