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En este trabajo se presenta la interfaz gráfica de usuario y se explica el modelo de detección de líneas diseñado en Python para la misma. Luego de los resultados de la calibración del instrumento electrónico se procedió a crear la interfaz gráfica de usuario en python en base al prototipo de la GUI construida en Matlab para lo cual se tuvo que escribir el algoritmo de detección en el mismo lenguaje. El instrumento electrónico está construido con un autocolimador analógico comercial, Nikon 6D, y una interfaz visual ad hoc.

A photoelectric autocollimator with high accuracy and extended measurement range based on the quadrangular pyramid is proposed, and the corresponding algorithms are also deduced. A new image processing algorithm has been proposed to improve the accuracy, and the corresponding errors are also estimated, the error does not exceed half a pixel when the distance between the marks more than two radii. The experimental results have verified that the measurement range of the proposed two-dimensional (2D) quadrangular pyramid photoelectric autocollimator can be increased $$\sqrt{2}$$ times than that of the flat mirror photoelectric autocollimator from 10′ to 15′. The accuracy is better than 1″ when the deflection is less than 15′.

For the purpose of realizing the dynamic angle measurement and calibration of the inertial equipment (such as rotary table), a dynamic angle measurement system based on the autocollimator and the fiber optic gyroscope (FOG), which can be used as an angle standard device, is designed in this paper. In this system, the scale factor of the FOG can be calibrated in the field application based on the autocollimator with the precision of $1^{\prime \prime }$ in the range of ±0.05°. Furthermore, the angle measurement deviation between the FOG and the rotary table can be limited in $\pm 3^{\prime \prime }$ when the scale factor of the FOG is calibrated by the autocollimator when necessary. This research can guarantee the long-term accuracy of the scale factor of the FOG in the field application and it will greatly promote the applications of the FOG as an angle standard device in the field of dynamic angle measurement.

In this study, we proposed an autocollimator for the angular measurement of rough surfaces. A mid-infrared laser having a wavelength of 2.8 μm was employed as the light source because it possesses high specular reflectivity on rough surfaces. Although a conventional autocollimator using a visible laser has a high resolution of angular measurement, it can only be used to measure mirror surfaces because the intensity distribution of the reflected light from a rough surface changes significantly due to the influence of diffused reflection. The suitability of a mid-infrared laser in an autocollimator for the angular measurement of rough surfaces (sub-micrometer level) was verified through simulations using reflection models. Therefore, a continuous-wave mode fluoride glass fiber based mid-infrared laser was developed for the autocollimator. Furthermore, an autocollimation unit was designed and constructed for detecting the angular displacement of mid-infrared laser light reflected from a target surface. The capability of the developed autocollimator for the angular measurement of rough surfaces was demonstrated through experiments.

A major modification has been made to the conventional mode-locked femtosecond laser autocollimator so that the apex angle of a small prism, which is a transparent object difficult to be measured by the conventional optical methods, can be measured. In the oblique-incidence optical setup, a collimated mode-locked femtosecond laser is at first made incident to a target prism, and the laser beam reflected from the prism surface is then projected onto a reflective-type grating for angle measurement based on the principle of the femtosecond laser autocollimator. With the robust signal processing technique in the femtosecond laser autocollimator where the spectrum of the first-order diffracted beams emanated from the grating is captured by the fiber detector, high-precision angle measurement can be realized even on a surface having a small area for measurement and/or on a surface having low reflectivity. An oblique-incidence femtosecond laser autocollimator with a fiber-based femtosecond laser source is developed, and its basic characteristics are then evaluated in experiments. An experimental setup composed of the oblique-incidence femtosecond laser autocollimator and a high-precision rotary table is also constructed for prism angle measurement. To avoid the influence of the internally reflected beam in a prism, a method employing the characteristic of Brewster's angle is newly proposed, and its feasibility is verified through experiments. The uncertainty analysis on the measurement of the prism apex angle by the oblique-incidence mode-locked femtosecond laser is also carried out based on GUM.

We present a new method to realize a vector magnetometer that has been optically referenced to an external coordinate system. The vector magnetometer is made up of three Hall sensors attached to the orthogonal faces of a glass cube. When placed in a homogeneous magnetic field, rotating the vector magnetometer around two axes allows the orientation of each sensor to be determined with respect to the glass cube. The orientation of the glass cube is detected by an autocollimator and optically referenced to an external coordinate system. A direction uncertainty below $130~\mu $ rad (which is traceable to angle standards) is achieved.

We present a simple autocollimator with sub-microradian sensitivity. To demonstrate the capabilities of our autocollimator, we study the simple harmonic motion of a cantilever beam and apply an external force to affect the cantilever's resonant frequency in the context of dynamic force microscopy. Our setup is ideal for the advanced undergraduate instructional laboratory and allows a variety of high-precision, tabletop experiments.

We present a dispersive interferometry of optical frequency comb for simultaneous measuring absolute distance and angle. The reconfigured Michelson interferometer can emit two parallel measured beams and one reference beam. The three pulse beams interfere with each other, and the interference spectrum is sampled by a spectrometer. It is simultaneously modulated by the three optical path differences, which contains the information of absolute distance and angle and can be demodulated by a Fourier transform. By making an angle measurement comparison with a calibrated turntable, the proposed method shows that the obtained mutual agreement is better than 3 arcsec in the range of ± 5°. The commercial interferometer and autocollimator are used to verify the feasibility of the proposed method for precision distance and angle measurement.

Optical levers for precision angle measurement have the advantage of exerting only a negligible force on the object being measured. Also, in autocollimating configuration, optical levers are insensitive to longitudinal movements of the target mirror. In this article, a reference-beam multi-slit autocollimator with variable number of slits, built from cost-effective off-the-shelf components, is presented. Further, an optimized algorithm for data processing is introduced, reducing computational effort for repeated Gaussian peak fitting. In the described setup, by adjusting the number of slits, the measurement range can be increased at the cost of sensitivity, and vice versa. In the tested configuration with 28 slits, the device has a measurement range of 12 mrad, and a sensitivity in the order of nrad/Hz starting at frequencies of 0.1 Hz, with increased sensitivity compared to other recently described autocollimators at frequencies over 1 Hz.

The structure design scheme of U-type tracking frame was put forward for a 700 mm aperture horizontal telescope. The double row dense ball bearings were used for azimuth shafting, and the bearing was designed as double row of axial thrust steel balls and double row of radial steel balls. The dense of the ball could ensure the high rotation accuracy of the shafting. First, the pitching shafting was designed as a structure with one end fixed and one end floating to compensate the effect of mechanical error and thermal deformation on the rotation accuracy. Then, the finite element model of tracking frame was established, and the first order resonance frequency could reach to 47.6 Hz, which showed that it had good modal characteristics. Finally, the electronic level and digital autocollimator were used to measure the pitch axis and azimuth axis respectively. The shaking of azimuth axis shafting was better than 1.3″, and the shaking of pitching axis shafting was better than 1.8″. The test results show that the designed telescope tracking frame structure has high stiffness and high rotation accuracy, which provides some reference value for the structure design of similar tracking frames.

Space technology is the core competitiveness of a powerful country. Space maintenance technology has just started in our country. The biggest innovation of this article is to design a set of interface system, which is suitable for on-orbit maintenance of space science instruments. It represents that this technology from scratch in our country. A new measuring method is proposed. According to the homogeneous coordinate transformation, the mathematical models of the relationships between fit clearances of interface system and the six-degree of freedom change of the maintenance module are derived. According to the index requirements, the corresponding fit clearance and repeat positioning accuracy are determined. Set up an experimental platform, and use autocollimator and laser tracker to measure the repeated positioning accuracy of the module. Based on the theory of small displacement, the least square method is used to deduce the rotation angle and translation amount of the module through the change of the characteristic point coordinates. The experiment proves that the interface meets the requirement of on-orbit maintainable operation, and the experimental data proves that the theoretical equation is correct. Providing engineering reference for other space maintenance scientific instruments.

It is known that linear motion errors for linear guides can be measured by the autocollimation method. In this case, it is necessary to install a mirror on the measurement target. On the other hand, if a light with a wavelength sufficiently longer than that of the surface roughness of the measurement target is used, the need for a mirror is eliminated. We have proposed an autocollimation method using a mid-infrared laser. In the original prototype of mid-infrared autocollimator, the angle of laser irradiation is 45° to the measurement target. However, this method does not allow us to obtain a long measurement range. Therefore, we construct a system in which the laser irradiation angle is set to 0° by controlling the polarization of light. By using this method, autocollimation is applied to a sample with a root mean square roughness Rq of 0.2 μm, and an angular resolution of 1.1 arc-second is obtained.

In the present study, we proposed a new type of autocollimator for high-accuracy angular measurement within a large angle range. The new system comprises a traditional autocollimator and Risley prisms, and it employs the normal tracing method to measure the angle. By rotating the Risley prisms, the outgoing beam of the autocollimator can be deflected close to the normal direction of the reflecting mirror and then reflected back to the system by the mirror along the near normal direction to realize normal tracing. Based on the angle measured by the autocollimator and the rotation angles of Risley prisms, we can calculate the tilt angle of the mirror. Since the beam returns to the system close to the original path, the angle error caused by aberration, optical component processing defects, nonuniform refractive index, and so on, can be ignored. Due to the normal tracing measurement method, theoretically, the angle error is not affected by the working distance. ZEMAX non-sequential simulation shows that the angle error caused by aberration in the new system can be significantly reduced.

Torsional properties of single fibers have considerable effects on the performance of fabrics. A new torsion tester with high resolution is developed based on the torsion-balance method and the autocollimation principle for measuring the torsional properties of single fibers. The tester can measure the torque accurately using the torsion wire of known torsional rigidity. The angular displacement of the torsion wire is measured by a non-contact electronic autocollimator. The calibration results show that the maximum torque capability is around 6 × 10−6 N m with a theoretical resolution of about 8 × 10−11 N m. The instrument’s validity is verified by comparing the measurement result with that obtained by a torsion pendulum. Torsion tests on four industrially microfibers, including glass fiber, polyimide fiber, carbon fiber, and gold wire, are performed with the tester, which gives shear moduli 71.0 ± 0.4, 5.6 ± 0.1, 22.6 ± 3.1, and 34.3 ± 0.5 GPa, respectively. Young’s moduli of these fibers are also provided. It is demonstrated that these fibers have a high anisotropy in mechanical properties.

In this paper, a self-compensation method for improving the accuracy of roll angle measurement of a linear stage caused by the non-parallelism of dual-beam due to time-dependent mechanical deformation of the support is proposed and integrated into a 5-DOF sensor to verify the feasibility. The non-parallelism between two laser beams is online real-time monitored by a pair of small autocollimator units. Through the ray-tracing analysis, the method to separate the roll angle of the moving stage and non-parallelism induced roll error is determined. A series of experiments under different supporting forces and ambient conditions have been carried out. The compensated P-V values of the roll angles are all within ±4 arc-sec, no matter how bad the originally measured value of the linear stage is. The average improvement of about 95% is significant. The effectiveness and robustness of the proposed measurement system in the changing environment are verified.

Currently, high-resolution X-ray telescope mirrors, such as for the Lynx X-Ray Observatory concept, are measured using a Fizeau interferometer with a cylindrical null corrector. Uncertainties in the null wavefront directly couple into the surface measurement uncertainty, including the axial figure and cone angle variation. We extend the absolute surface metrology method of lateral shift mapping for measuring X-ray telescope mirror segments. Lateral shift mapping involves laterally shifting the surface under test relative to the null to multiple positions. The null wavefront can be extracted from the difference between these shifted measurements, leaving only the surface under test. Accurately extracting quadratic terms of the surface under test requires measuring its tilt during shifting. We will show surface metrology results of optical flats measured by Fizeau-based lateral shift mapping with the required angle measured using an autocollimator and compare these results against a three-flat test. We will show how we plan to extend this method to conical X-ray telescope mirror metrology. The lateral shift mapping method reduces the uncertainty introduced by the cylindrical null, a critical step toward making high-resolution X-ray telescope mirrors.

The improved autocollimator for measuring angular and shift deformations of the large constructions as mirrors of the rotatable radiotelescopes are analyzed. Two types of the measuring scheme for autocollimator are researched. The first type of the autocollimator scheme uses three cube-corner reflectors which are set in 3 points of the counter reflector of the radiotelescope. This type of the autocollimator measures the angular and line shifts in a large range. The counter reflector is set on the SEMS moving platform and the range of its line and angular shifts is 3 arc degree and 100 mm respectively. The second type of autocollimator scheme uses a tetrahedral reflector. This autocollimator is used for the measuring pitch and yaw angular deviations and line shifts of the section boards of the main mirror of the radiotelescope. The range of section board line and angular shifts is 30 arc minutes and 10 mm respectively. The changing one measuring scheme to another is made by switching the radiation marks of the autocollimator. The technical characteristics of the suggested autocollimator and algorithms of measuring line and angular shifts are discussed.

Optical glass is the most widely used optical material. It is necessary to measure its geometric characteristic quickly and reliably to meet the quality of optical glass. A vision measuring system combining photoelectric autocollimation system with high-precision rotary stage is designed to measure the parallelism and angle of optical glass plane. A novel method is proposed to overcome the difficulty of measuring parallelism of optical glass. The model of parallelism and angle measurement is established and the feasibility is analyzed. The image processing algorithm combining Steger algorithm with the least square method is selected. The uncertainty of angle measurement system for angle measurement is 3.0″. The system can solve the problem of measuring the angle of optical glass with high precision and has important significance for optical system. Keywords: Optical glass, Plane angle, Parallelism, Photoelectric autocollimation system

A resolution-enhanced roll-angle measurement system based on a transmission grating autocollimator is proposed. The measurement principle is analyzed in detail. The system uses a transmission grating and a mirror group to produce a pair of central symmetric differential measurement beams that enable the measurement of roll angle. Because the measurement beams transmit through the rotating grating twice, the resolution is enhanced compared to conventional grating autocollimation methods with the same device. The roll-angle resolution reached 0.1 arcsec. Additionally, the effect of laser beam drift on the stability of angular measurement is effectively suppressed by using differential measurement method, the stability of the proposed grating autocollimator after the differential measurement is 0.11 arcsec.

This paper proposes a new geometric error model and compensation algorithm for the three-axis machine tools. First, the relative motion matrix to the coordinate system is constructed by the homogenous transformation matrix (HTM). Next, the geometric error model is deduced based on homogenous transformations. Then, an error compensation algorithm is developed by means of the computer numerical control (CNC) program reconstruction by using the geometric error model. Finally, the simulation is implemented on a virtual machine tool established in the VERICUT software to validate the efficiency of the model and the compensation algorithm. An autocollimator is used to measure the yaw errors and an experiment is implemented on a real machine tool. The results simulation and experiment indicate that the error modele and compensation algorithm can significantly improve the machining precision.

Autocollimator is an important optical detection instrument, which is mainly used to measure small angle, and plays an important role in the field of optical equipment manufacturing and debugging. For many years, the autocollimation accuracy of collimator has been one of the factors affecting its performance. In order to improve the autocollimation accuracy of collimator optical axis, an auxiliary calibration method based on image recognition is proposed in this paper. And the concrete realization idea of this method is given. The accuracy of this method to detect and identify the optical axis eccentricity error can reach 0.1 pixel. Taking the detection data as reference to adjust the optical axis, the autocollimation accuracy of collimator optical axis can be greatly improved.

We have demonstrated a simple method to measure high-precision absolute angular displacement using an optical frequency comb (OFC). The dispersive interferometry with parallel configuration can take advantage of its large non-ambiguity range and achieve absolute angular measurement in a large range. The influence factors of the angle accuracy, including the accuracy of optical path difference, the determination of absolute zero position and the correction of sine arm have been analyzed in detail. The angle comparison is performed with the autocollimator and multi-tooth indexing table. The angle accuracy can reach ±2 arcsec (k=2) in the range of 5°, which represents a good agreement with the Monte Carlo simulation. The proposed approach has potential to be extended to multi-degree-of-freedom measurement with a simple structure in future.

A high-precision error measurement method of angular displacements based on the biaxial of the reciprocal roll angles (RRA) is presented. The resolution and precision of the angular displacement measurement systems are guaranteed using the principle of small-angle measurements, along with a photoelectric autocollimator and reflector. Based on the method of the biaxial RRA and the principle of full-circle closure, a displacement measurement system covering the full circumferential range is built. The displacement measurement system can recognize the reference angle error elimination, the calibration angle error, and mutual compensation. The total error model of the angular displacement error measurement and the biaxial turntable is established, and the main error terms are analyzed using the total error model of the turntable and the components. The traditional “Fourier harmonic analysis” and sparse decomposition methods are used to correct the system error components. The simulation accuracy of the corrected turntable is similar to that of the error-free term, and the analysis results are used in the system-optimized configuration, including precision distribution. The experiment verifies the feasibility and effectiveness of the proposed high precision, angular displacement, and error measurement method.

Null-indicator (NI) is an optical device setting up a reference direction in space for high-precision angle measurements by means of dynamic goniometry. During continuous rotation of the optical object under test (e.g. optical polygon or gauge) together with the angular scale the NI registers moments when reflecting faces of the object are normal to the optical axis of the NI. At these moments NI yields electronic logical pulse which triggers the readout from the angular scale. Conventionally interferometric null-indicators were considered as the most accurate, though they have few significant drawbacks. The interferometric NI is very sensitive to the quality of the reflecting surface and other factors that may bring aberrations to the NI emitted wavefront. This makes the interferometric NI suitable only for laboratory applications with test objects of high quality. Recent development has shown that autocollimating NI with digital signal processing can reach the same level of random error as the interferometric one. But during testing of the experimental model of the autocollimating NI authors have encountered systematic error that needed additional study. The encountered error was related to the adjustment of certain element of the NI optical scheme and the object under test relatively to the axis of rotation. The report presents theoretical and experimental study of the influence of aforementioned factors on the accuracy of setting the reference direction by the autocollimating NI. Also authors give recommendations on the adjustment procedure of the dynamic goniometer utilizing autocollimating NI in order to reach required measurement accuracy.

The article describes methods for calibrating angular encoders. The descriptions of calibration methods based on the use of autocollimator, laser interferometer and precision angular encoder are presented. The minimum step of measurements of the controlled positions was determined during the calibration of angular encoders by various methods. A comparative analysis of the number of measured positions in the calibration of angular encoders is carried out. The main sources of error of angular encoders are presented. A description of the experiment of calibrating angular encoders using a precision rotary table is given. The influence of eccentricity and inclination of the mounting shaft on the readings of the calibrated encoder was revealed. The concept of building a stand for calibrating angular encoders is demonstrated. The method of leveling the error of the angular displacement transducer caused by the eccentricity and inclination during its installation in the stand is shown.

A practical instrumentation configuration for measuring focal length of cell-phone camera lenses is presented that uses a custom autocollimator, a grating, an autostigmatic microscope, and a precision stage. Uncertainty in LED wavelength is reduced by using a white LED and a set of narrow-band filters. The autocollimator is designed to allow for rapid focus adjustment at each test wavelength. Examples of the measurement technique and an error analysis are provided.

We present experimental, analytical, and numerical methods developed for reconstruction (deconvolution) of one-dimensional (1D) surface slope profiles over the spatial frequency range where the raw data are significantly perturbed due to the limited resolution of the measurement instrument. We characterize the spatial resolution properties of a profiler with the instrument's transfer function (ITF). To precisely measure the ITF, we apply a recently developed method utilizing test surfaces with 1D linear chirped height profiles of constant slope amplitude. Based on the results of the ITF calibration, we determine parameters of an analytical model for the ITF that is used in the original reconstruction software. Here, we treat surface slope metrology data obtained with the Optical Surface Measuring System (OSMS), using as a sensor an electronic autocollimator (AC) ELCOMAT-3000. The spatial resolution of the OSMS is limited by the size of the AC light-beam-collimating aperture. For the purposes of this investigation, the OSMS is equipped with a circular aperture with a diameter of 2.5 mm. This is a typical arrangement of most AC-based slope profilers developed for surface slope metrology of state-of-the-art x-ray mirrors. Using the example of surface slope metrology of two state-of-the-art elliptically shaped x-ray focusing mirrors, we demonstrate that the developed data reconstruction procedure allows us to significantly improve the accuracy of surface slope metrology with the OSMS over the spatial wavelength range from ∼1.6 mm to 7 mm. Thus, the amplitude of the quasi-periodic error characteristic of the deterministic polishing process used appears to be higher by a factor of ∼2 than is apparent from the rough metrology data. Underestimation of the surface slope errors in this spatial wavelength range can lead to serious errors in the expected performance of x-ray mirrors in synchrotron beamlines, especially at modern light sources utilizing coherent x rays, where the perturbations can lead to increased speckle-like intensity variation.

Autokolimatori su mjerni instrumenti za mjerenje malih kuteva, umjeravanje drugih mjernih uređaja i očitavanje određenih geometrijskih značajki mjerenog predmeta poput pravocrtnosti ili ravnosti. Ovdje opisan postupak utvrđivanja svojstava autokolimatora i ishod tog postupka popraćeni su teorijskim osnovama o mjerenju i o autokolimatorima kao mjernim uređajima. Opisan je laboratorijski postav za mjerenje najvažnijih značajki digitalnog autokolimatora i svi mjerni uređaji upotrijebljeni u ispitivanjima. Navedeni su ključni dijelovi autokolimatora te optičke značajke tih dijelova i izrazi po kojima se tražene značajke autokolimatora izračunavaju. Na kraju su opisana provedena ispitivanja i predstavljeni njihovi ishodi. Autocollimators are measuring instruments for measuring fine angles, calibrating other measuring devices and reading certain geometric features of the measured object, for example, straightness or flatness. The described procedure for determining the properties of the autocollimator and its results are backed up by theoretical foundations on measurement and on autocollimators as measuring devices. The laboratory setup for measuring the required digital autocollimator characteristics and all measuring devices used in the tests are described here. The key parts of the autocollimator, the optical characteristics of those parts and the equations used to calculate said characteristics are listed, as well. The performed tests and their outcomes are described at the close of the thesis.

The inaccurate deflection behavior of the probing system degrades the performance of the diameter-measuring machines. In this experiment, the probing is improved, applying an autocollimator and an angular positioning datum. We have devised this datum using a liquid wedge. A ring gauge is chosen as a workpiece to evaluate the deflection behavior of the probing system. The improved uncertainty of the probing is found as low as 40 nm. Subsequently, the inner diameter of the ring gauge is measured on this experimental setup. By employing a simulation, we aligned the workpiece. The deflections of the stylus are optimized to achieve zero deflection error at the zenith points. Consequently, the swing of the probe at the zenith points is combined with the rectilinear displacement of the workpiece to estimate the inner diameter. The uncertainty of the measurement of the ring gauge is improved up to 140 nm.

The measurement accuracy of the precision instruments that contain rotation joints is influenced significantly by the rotary encoders that are installed in the rotation joints. Apart from the imperfect manufacturing and installation of the rotary encoder, the variations of ambient temperature could cause the angle measurement error of the rotary encoder. According to the characteristics of the 2&pi, periodicity of the angle measurement at the stationary temperature and the complexity of the effects of ambient temperature changes, the method based on the Fourier expansion-back propagation (BP) neural network optimized by genetic algorithm (FE-GABPNN) is proposed to improve the angle measurement accuracy of the rotary encoder. The proposed method, which innovatively integrates the characteristics of Fourier expansion, the BP neural network and genetic algorithm, has good fitting performance. The rotary encoder that is installed in the rotation joint of the articulated coordinate measuring machine (ACMM) is calibrated by using an autocollimator and a regular optical polygon at ambient temperature ranging from 10 to 40 &deg, C. The contrastive analysis is carried out. The experimental results show that the angle measurement errors decrease remarkably, from 110.2&Prime, to 2.7&Prime, after compensation. The mean root mean square error (RMSE) of the residual errors is 0.85&Prime

High precision reducer is the core component of industrial robot. Its performance test is the key to improve product quality and ensure the accuracy of robot operation. One of the basic geometric parameters in performance test is the angle, which refers to the angular displacement of the input or output of the tested reducer. Based on a vertical instrument, angular measurement systems are designed in this article. In order to ensure the precision of results, the angle encoder is as close as possible to the measured object, which shortens the measurement chain and reduces the number of error sources. A cylindrical and disk structure improves the structural stiffness, ensures regular deformation patterns, and minimizes the angular errors caused by weak stiffness supports in the conventional instrument. Another system consisting of an autocollimator and a regular polyhedron, whose output is taken as angular standard, calibrates absolute circular gratings in the instrument. The model based on back propagation neural network can compensate the errors over the whole circumference, and finally get the angular displacement of input and output of the tested reducer in the drive process accurately. After compensation, the angular measurement errors of the instrument are within ±2 arc seconds.

The accuracy of the circular grating is the key point for control precision of the single gimbal control moment gyroscope servo system used in civilian micro-agile satellites. Instead of using the multi reading heads to eliminate eccentricity errors, an algorithm compensation method based on a calibration experiment using a single reading head was proposed to realize a low-cost and high accuracy angular position measurement. Moreover, the traditional hardware compensation method using double reading heads was also developed for comparison. Firstly, the single gimbal control moment gyroscope system of satellites was introduced. Then, the errors caused by the installation of the reading head were studied and the mathematic models of these errors were developed. In order to construct the compensation function, a calibration experiment using the autocollimator and 24-sided prism was performed. Comparison of angle error compensation using the algorithm and hardware method was presented, and results showed that the algorithm compensation method proposed by this paper achieved the same accuracy level as the hardware method. Finally, the proposed method was further verified through a control system simulation.

International audience; This paper outlines a complete methodology for designing a control system that reshapes the dynamic response of the flexible structure to robustly match the dynamics of a given adaptable reference model. The procedure was experimentally verified on a setup developed at the European Space Agency, consisting of a cantilevered flexible plate actuated by two shakers. Angular displacements at the free tip of the plate were measured with sub-microradian resolution using a laser autocollimator. Following a comprehensive system identification phase, mathematical models of the uncertain plant were extracted. The models reliably fit the experimental data and were used to synthesize a low order and high bandwidth structured Linear Parameter Varying controller. The controller was designed by taking into account the limits of achievable performance and the closed loop effectively constrained the flexible structure to behave like it was made out of an adaptable material. The robust stability and worst case performances were assessed by means of a structured singular value analysis and excellent agreement between theoretical predictions and experimental results was observed.

Any Light Particle Search II (ALPS II) is a light-shining-through-a-wall experiment seeking axion-like particles. ALPS II will feature two 120 m long linear optical cavities that are separated by a wall and support the same photon mode. The central optical bench at the core of the experiment will be equipped with a light-tight shutter and two planar mirrors for the cavities. We show that the mounting concept for ALPS II provides sufficient angular stability and verify that a simple autocollimator assisted alignment procedure for crucial components of the ALPS II optical cavities can lead to the required overlap of the cavity eigenmodes. Furthermore, we show that mounted quadrant photodiodes added to the optical bench can have sufficient stability to maintain this overlap even without a clear line of sight between the two optical cavities. © 2020 Optical Society of America

Autocollimators are versatile devices for angle metrology used in a wide range of applications in engineering and manufacturing. A modern electronic autocollimator generally features two measuring axes and can thus fully determine the surface normal of an optical surface relative to it in space. Until recently, however, the calibration capabilities of the National Metrology Institutes were limited to plane angles. Although it was possible to calibrate both measuring axes independently of each other, it was not feasible to determine their crosstalk if angular deflections were present in both axes simultaneously. To expand autocollimator calibrations from plane angles to spatial angles, PTB and VTT MIKES have created dedicated calibration devices which are based on different measurement principles and accomplish the task of metrological traceability in different ways. Comparing calibrations of a transfer standard makes it possible to detect systematic measurement errors of the two devices and to evaluate the validity of their uncertainty budgets. The uncertainty levels of the devices are comparable to each other, with an expanded uncertainty U = 0.014 arcsecond (95.5% coverage probability) over a measuring range of ±1000 arcsecond in the case of PTB and U = 0.015 arcsecond over a range of ±500 arcsecond and U = 0.020 arcsecond over ±1000 arcsecond in the case of VTT MIKES. Over a range of ±1000 arcsecond with regards to both measuring axis of an Elcomat 3000 autocollimator as a transfer standard, no statistically significant differences between the calibrations were detected. The results thus confirm the calibration capabilities of PTB and VTT MIKES as stated in the calibration and measuring capability database of Bureau International des Poids et Mesures.

Laser autocollimation is innovated for absolute angular position measurement based on an optical frequency comb. The conventional laser autocollimation can only make relative angle measurement due to the unknown angular distance between the incident laser beam and the axis of the autocollimation unit. In the proposed absolute laser autocollimation employed with the femtosecond laser autocollimator, in which a femtosecond laser and a diffraction grating are employed as the measurement light source and the reflector, respectively, a new method is proposed for accurate identification of the angular distance through taking use of first-order diffracted beams from the reflector associated with the optical frequency comb of the femtosecond laser source. With the identified angular distance, the absolute angular position of the grating reflector, which is defined by the angle between the normal axis of the reflector surface and the incident laser beam, can be determined from the information of optical frequencies of the first-order diffracted beams based on the fact that each of the first-order diffracted beams from the grating reflector has a deterministic angular position corresponding to the optical frequency of each comb mode of the femtosecond laser. Principle of the proposed absolute laser autocollimation and an experimental setup as well as experimental results demonstrating the effectiveness and potentiality of the proposed method are presented.

Angle detection technology in the field of precision measurement has important significance. The angle measurement compares the measured angle with the standard angle to obtain the actual value or deviation value of the measured angle. At present, China’s angle measurement technology has achieved productization, but there are still obvious defects in some special measurement fields. The angle measuring instrument based on the auto-collimation principle has a large volume and has high requirements for the measurement environment. Nowadays, with the development of optoelectronic technology, it is necessary to develop high-precision, portable and automated angle measuring instruments. The autocollimation is a very important measuring instrument for small angle measurements. It is often used to compare or measure small angles. Widely used due to its high accuracy and measurement resolution. In order to study the effect of the magnetic field in space on the bending degree of the extension rod of the star sensor, it is necessary to carry out the precise measurement of the three-dimensional small angle. Due to the small installation and measurement space of the satellite and the strong electromagnetic interference and temperature changes in the measurement environment, the existing three-dimensional angle measurement method cannot measure the three-dimensional bending small angle of the star-sensitive sensor extension rod with high precision, and even damage the instrument. In order to achieve the high precision measurement of three-dimensional small angle in small space conditions, this paper develops a three-dimensional small angle measurement system based on embedded system for data acquisition and data processing. And the algorithm based on the principle of auto-collimation is studied. Firstly, this paper introduces the hardware structure and measurement principle of the angle measurement system, and briefly describes the design of the optical amplification system. According to the working principle of the optical autocollimation and the two-dimensional PSD, a optical auto-collimation system is designed. Secondly, the application of auto-collimation principle in three dimensional angle measurement is introduced. Finally, based on the synthesis and decomposition of the spatial three dimensional angle, a three-dimensional angle measurement algorithm is proposed and taking the theoretical parameters as an example to analyze the theoretical error of the optical autocollimator system and the installation error of reflector. The focal length, resolution and magnification of the optical system are calculated based on the design objectives. On the basis of this, the optical devices are selected and the optical auto-collimation system is designed. Finally, the experimental results were analyzed by data obtained from several experiments, and a passive non-contact three-dimensional angle measurement method was proposed. The experimental results show that the proposed three-dimensional angle measuring instrument has the advantages of anti-interference and high precision, and its working accuracy is 0.23 arc seconds. The method is mainly applied in the narrow and strong electromagnetic interference three-dimensional angle measurement field, and it meets the requirements of stable and reliable, high precision and strong anti-interference ability of the three-dimensional angle measurement under the condition of small space. It solves the problem of three-dimensional angle measurement under small space conditions to a certain extent.

In this paper, we present a methodology which identifies and characterizes the sources of uncertainty associated with the operation of an electronic autocollimator. It was developed based on a commercial autocollimator—Nikon 6B model—with the addition of a visual interface and its respective image processing software. The visual interface allows the optical instrument’s performance to be surpassed, thus increasing the resolution and accuracy with respect to the original equipment. The development allows for an improvement in the measurement capacity of the laboratories when calibrating electronic levels, reference planes, and angular patterns, among others. On the other hand, fundamental information is provided for the new instrument’s last stage of design through a detailed evaluation of the measurement system’s mathematical model. This allows us to determine the relative impact of each uncertainty component in order to identify those of greater weight and minimize them by correction.

Precise geometric parameters are essential to ensure the positioning accuracy for space optical cameras. However, state-of-the-art onorbit calibration method inevitably suffers from long update cycle and poor timeliness performance. To this end, in this paper we exploit the optical auto-collimation principle and propose a real-time onboard calibration scheme for monitoring key geometric parameters. Specifically, in the proposed scheme, auto-collimation devices are first designed by installing collimated light sources, area-array CCDs, and prisms inside the satellite payload system. Through utilizing those devices, the changes in the geometric parameters are elegantly converted into changes in the spot image positions. The variation of geometric parameters can be derived via extracting and processing the spot images. An experimental platform is then set up to verify the feasibility and analyze the precision index of the proposed scheme. The experiment results demonstrate that it is feasible to apply the optical auto-collimation principle for real-time onboard monitoring.

To satisfy the requirements of precision angle measurement and machine leveling, a high-sensitivity dual-axis optoelectronic level using double-layer liquid refraction is proposed in this paper. Silicone oil, with a constant horizontal surface, is used as a reference. A double-layer liquid refraction principle is used to improve the level's sensitivity. An autocollimator is used as a detector of two-dimensional angle. Parallel-light paths are adopted to avoid interference from reflected light. When the level has a tilt angle, the light spot on the quadrant photodiode of the autocollimator is bound to shift. The sensitivity model of the level was established, and the level was designed and tested. Experimental results revealed that the level has a resolution of 0.05 arcsec, a range of ± 150 arcsec, a repeatability of 0.4 arcsec, and a stability of ± 0.2 arcsec. It can be used to measure tilt with a high-precision requirement.

Interferometers are widely used to measure large aspheric surfaces because of their high accuracy and high efficiency. However, they cannot be used for aspheric surfaces with large curvature and asphericity. In this paper, we propose a method for measuring aspheric surfaces using scanning deflectometry with an autocollimator. A rotary stage is used to enlarge the measurement range of the autocollimator, so that aspheric surfaces with large slope changes can be measured. Three-dimensional error analysis is performed. We use an autocollimator with a measurement range of 21500 μrad (4500 arcsec) to measure a spherical surface with a curvature radius of 400 mm to perform the experiment. Experimental results showed that the average root-mean-square error was approximately 100 nm.

An installation for measuring the angles of polyhedral prisms is considered, in which autocollimators with digital registration of the coordinates of the optical mark are applied. Algorithms for solving systems of equations for the determination of angles by the method of aggregate measurements with the help of two and three autocollimators are described. The errors in the measurements are calculated and compared with the results of experimental measurements of the angles of polyhedral prisms.

The paper describes the alignment technique developed for the wavefront error measurement of ellipsoidal mirrors presenting a central hole. The achievement of a good alignment with a classic setup at the finite conjugates when mirrors are uncoated cannot be based on the identification and materialization at naked eye of the retro-reflected spot by the mirror under test as the intensity of the retro-reflected spot results to be ≈1E−3 of the intensity of the injected laser beam of the interferometer. We present the technique developed for the achievement of an accurate alignment in the setup at the finite conjugate even in condition of low intensity based on the use of an autocollimator adjustable in focus position and a small polished flat surface on the rear side of the mirror. The technique for the alignment has successfully been used for the optical test of the concave ellipsoidal mirrors of the METIS coronagraph of the ESA Solar Orbiter mission. The presented method results to be advantageous in terms of precision and of time saving also when the mirrors are reflective coated and integrated into their mechanical hardware.

Small angle generators are simple devices for providing small angles traceable to the definition of the SI-unit radian. The most accurate ones use a laser interferometer for measurement of angular displacement. Small angle generators used for autocollimator calibration usually create angles around a single axis. A two-directional angle generator would be preferable, as it could more efficiently reveal artefacts related to angular displacement across both axes, such as orthogonality of the autocollimator's measuring axes. Characterizing errors depending on one axis only would also be easier, as the setup needs to be aligned only once for studying both axes of the autocollimator. We describe a novel interferometric two-directional small angle generator which we have built and tested for autocollimator calibration. The range is ±1000'' for both axes. The estimated standard uncertainty for full range is 0.0036'' for the horizontal and 0.0053'' for the vertical direction.

We demonstrate the use of a high‐precision ground‐rotation sensor to subtract wind‐induced tilt noise in a horizontal broadband seismometer at frequencies above 10 mHz. The measurement was carried out at the LIGO Hanford Observatory using a low‐frequency flexure‐beam‐balance with an autocollimator readout and a T240 seismometer, located in close proximity to each other. Along their common horizontal axis, the two instruments show significant coherence below 100 mHz, which increases as a function of wind speed due to floor tilt induced by wind pressure on the walls of the building and the ground outside. Under wind speeds of 10–15 m/s, correcting the seismometer for measured ground rotation lowered the signal by a factor of ∼10, between 10 and 100 mHz. This article describes the instruments used, shows representative data for low and high wind speeds, and discusses the tilt subtraction and possible limitations.