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Deflectometric profilometers are used to precisely measure the form of beam shaping optics of synchrotrons and X-ray free-electron lasers. They often utilize autocollimators which measure slope by evaluating the displacement of a reticle image on a detector. Based on our privileged access to the raw image data of an autocollimator, novel strategies to reduce the systematic measurement errors by using a set of overlapping images of the reticle obtained at different positions on the detector are discussed. It is demonstrated that imaging properties such as, for example, geometrical distortions and vignetting, can be extracted from this redundant set of images without recourse to external calibration facilities. This approach is based on the fact that the properties of the reticle itself do not change - all changes in the reticle image are due to the imaging process. Firstly, by combining interpolation and correlation, it is possible to determine the shift of a reticle image relative to a reference image with minimal error propagation. Secondly, the intensity of the reticle image is analysed as a function of its position on the CCD and a vignetting correction is calculated. Thirdly, the size of the reticle image is analysed as a function of its position and an imaging distortion correction is derived. It is demonstrated that, for different measurement ranges and aperture diameters of the autocollimator, reductions in the systematic errors of up to a factor of four to five can be achieved without recourse to external measurements.

Deflectometric profilometers are used to precisely measure the form of beam shaping optics of synchrotrons and X-ray free-electron lasers. They often utilize autocollimators which measure slope by evaluating the displacement of a reticle image on a detector. Based on our privileged access to the raw image data of an autocollimator, novel strategies to reduce the systematic measurement errors by using a set of overlapping images of the reticle obtained at different positions on the detector are discussed. It is demonstrated that imaging properties such as, for example, geometrical distortions and vignetting, can be extracted from this redundant set of images without recourse to external calibration facilities. This approach is based on the fact that the properties of the reticle itself do not change – all changes in the reticle image are due to the imaging process. Firstly, by combining interpolation and correlation, it is possible to determine the shift of a reticle image relative to a reference image with minimal error propagation. Secondly, the intensity of the reticle image is analysed as a function of its position on the CCD and a vignetting correction is calculated. Thirdly, the size of the reticle image is analysed as a function of its position and an imaging distortion correction is derived. It is demonstrated that, for different measurement ranges and aperture diameters of the autocollimator, reductions in the systematic errors of up to a factor of four to five can be achieved without recourse to external measurements.

During non-landing measurements of a theodolite, the accuracy of the goniometric readings can be compromised by wobble errors induced by various factors such as wind loads, theodolite driving torque, and the stiffness of the supporting structure. To achieve high-precision non-landing measurements, it is essential to accurately determine and correct the platform wobble errors affecting the azimuth and pitch pointing angles. In this paper, a non-contact optical measurement method is proposed for quantifying platform wobble errors. The method establishes an auto-alignment optical path between an autocollimator and a reflector in the measuring device. By detecting the deviation angle of the CCD image point as the optical path changes, precise measurements of the platform wobble errors can be obtained. Experimental results demonstrate that the measuring device can achieve an auto-alignment optical path within 5 minutes, significantly improving measurement efficiency. Furthermore, after measuring the platform wobble error and applying data correction, the average error in the azimuth pointing angle is reduced from 31.5″ to 9.8″, and the average error in the pitch pointing angle is reduced from 21″ to 9.2″. These results highlight the substantial correction effect achieved by the proposed method.

The significance of an autocollimator in angular metrology cannot be overestimated: in many countries, it is either included as part of the primary plane angle standard or is involved in transferring the unit of plane angle from this standard to less accurate measuring instruments. This paper presents a historical overview of the problems encountered when using an autocollimator in angular metrology, as well as of proposed solutions. Not for the first time, the problem of the theoretical definition of the angle being measured between surfaces that are not perfectly flat is raised. In addition, the authors attempt to compile a complete list of factors affecting angular measurements using an autocollimator and to build a model that allows some of these factors to be taken into account for a subsequent algorithmic compensation of their influence. To assess the level of accuracy of angular measurements at which the use of the proposed model is reasonable, a simplified simulation example is presented. In an attempt to confirm the validity of the proposed model, a corresponding analysis of experimental data is provided. The applicability and limitations of the proposed model are discussed in the conclusion. [ABSTRACT FROM AUTHOR]

The paper proposes a modified method for measuring the refractive index of a triangular prism using an autocollimation angle measuring system designed to measure angles formed by flat surfaces of objects. The method involves using a fixed mirror to reflect the refracted beam, measurement of the angles of incidence of the beam on the face of the prism corresponding to the autocollimation positions and calculating the refractive index of the prism material using the solution of a system of equations. The paper presents the experimental study results for a triangular prism made of K8 optical glass using the proposed method, and a comparison of the results with the readings obtained using the State Primary Standard of the Refractive Index Unit GET 138-2021. The proposed method makes it possible to simplify the process of measuring the refractive index since there is no need to measure the angle of deviation of the beam.

The significance of an autocollimator in angular metrology cannot be overestimated: in many countries, it is either included as part of the primary plane angle standard or is involved in transferring the unit of plane angle from this standard to less accurate measuring instruments. This paper presents a historical overview of the problems encountered when using an autocollimator in angular metrology, as well as of proposed solutions. Not for the first time, the problem of the theoretical definition of the angle being measured between surfaces that are not perfectly flat is raised. In addition, the authors attempt to compile a complete list of factors affecting angular measurements using an autocollimator and to build a model that allows some of these factors to be taken into account for a subsequent algorithmic compensation of their influence. To assess the level of accuracy of angular measurements at which the use of the proposed model is reasonable, a simplified simulation example is presented. In an attempt to confirm the validity of the proposed model, a corresponding analysis of experimental data is provided. The applicability and limitations of the proposed model are discussed in the conclusion.

The increasing demands of highly precise industrial products lead to continuous seeking for the improvements in cabapility of manufacturing machines, i.e., machine tools. Machine tools include different types of manufacturing machines, i.e., turning, lathe, drilling, and milling machines whatever computerized numerical control (CNC) type or manual type. The cabaplity improvement in machine tools requires a real understanding of their productivity, accuracy, and operating parameters, i.e., their geometrical errors. These errors can be accurately identified through measurements with highly accurate measuring instruments. These machine errors have different error sources. The angular errors, horizontal and vertical straightness errors, paralleism errors, and squarness errors are clear examples for these sources. In this work, a comparative study for the determination of machine tools errors is carried out. Two main instruments of laser interferometer system and autocollimator system are used. The geometric errors are identified, measured, and analyzed. [ABSTRACT FROM AUTHOR]

Abstract—A procedure for measuring the systematic error in angular positioning of a rate table platform based on goniometrical method is described. The method has been tested on a three-axis rate table STA-10. Possible error sources have been detected. The positioning error has been compensated and greatly reduced. Instability of rate table axes rotation rate has been studied, and nonortogonality of its axes has been measured. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

• A novel technique extends the benefit of the closure and reversal techniques to calibrate the angle gauges. • The pitch angle of the angle gauges is found by solving the modelled measurement equations. • An improved uncertainty of angle gauge measurement is estimated as 0.32″. • The proposed method is experimental validated. • The analysis of results assured the elimination of influence of the RIT errors. • Simultaneous measurement of two angle blocks with quick check quality assurance. Artefact standards, viz. polygons, angle gauges and indexed rotary tables, realize the geometric plane angle. The construction of the standard angle gauges restricts the pitch angle calibration using the closure technique. The angle gauges are traditionally calibrated using an autocollimator with an indexed rotary table. The positional errors in the angular scale of the rotary stage affect the measurement accuracy. A novel technique is devised to extend the benefit of the closure and the reversal techniques to calibrate the angle gauges. Eleven measurements are made on three angle gauge blocks, one reference angle block, and two angle stacks. These measurements are modelled using a set of equations. The pitch angle of the angle gauges is found by solving these equations. The uncertainty of angle gauge measurement is estimated as 0.32″. The proposed method is experimentally validated. The analysis of results ensured the elimination of the influence of the reference-indexed rotary table. [ABSTRACT FROM AUTHOR]

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.

A collaboration, including all DOE synchrotron labs, industrial vendors of x-ray optics, and with active participation of the HBZ-BESSY-II optics group has been established to work together on a new slope measuring profiler -- the optical slope measuring system (OSMS). The slope measurement accuracy of the instrument is expected to be

We overview the results of a broad US collaboration, including all DOE synchrotron labs (ALS, APS, BNL, NSLS-II, LLNL, LCLS), major industrial vendors of x-ray optics (InSync, Inc., SSG Precision Optronics-Tinsley, Inc., Optimax Systems, Inc.), and with active participation of HBZ-BESSY-II optics group, on development of a new generation slope measuring profiler -- the optical slope measuring system (OSMS). The desired surface slope measurement accuracy of the instrument is

A new low budget slope measuring instrument, the Developmental Long Trace Profiler (DLTP), was recently brought to operation at the ALS Optical Metrology Laboratory. The design, instrumental control and data acquisition system, initial alignment and calibration procedures, as well as the developed experimental precautions and procedures are described in detail. The capability of the DLTP to achieve sub-microradian surface slope metrology is verified via cross-comparison measurements with other high performance slope measuring instruments when measuring the same high quality test optics. The directions of future work to develop a surface slope measuring profiler with nano-radian performance are also discussed.

We present the results of research of the angle measurement system for direction measurements. Development of the system is based on the dynamic goniometer, whose operation is defined by continuous rotation of the platform with the autocollimating null-indicator. The measurements of angles between mirrors are provided by the null-indicator and optical encoder. The results of the system calibration with the use of standard optical polygon are presented. The computer simulation of the calibration process was carried out, and requirements to optical elements alignment accuracy were estimated. [ABSTRACT FROM AUTHOR]

Deflectometric profilometers based on industrial electronic autocollimators (ACs), as the ELCOMAT-3000, have become indispensable tools for precision form measurements of optical surfaces. A growing number of labs at synchrotron and free electron laser x-ray facilities are going for BESSY-II NOM-like versions of the AC-based profilometers. These tools have proven capable of characterizing state-of-the-art aspherical x-ray optics with an accuracy on the level of 100 nrad (root-mean-square) over the spatial frequency range limited by the size of the aperture used in the profilometer. Typically, a round aperture with a diameter of about 2.5 mm is used. Previous investigations have shown that with the optimally aligned 2.5-mm aperture, the spatial resolution of a NOM-like profilometer corresponding to the first zero-crossing of the optical transform function (OTF) is ∼1.2 mm. In this paper, we investigate the performance of an AC ELCOMAT-3000 for a slope profilometer with different aperture sizes and shapes. The results of angular calibration of the AC equipped with circular and rectangular apertures placed at different distances from the AC are discussed. The calibration was performed at the Physikalisch-Technische Bundesanstalt using the original experimental arrangements, also discussed in the paper. The OTF measurements with the specially developed test sample with chirped surface slope profiles were performed at the Advanced Light Source X-Ray Optics Laboratory (XROL) in application to a new optical surface measuring system under development at the XROL. In the OTF measurements, we have shown that application of a rectangular aperture with dimensions of 1.5 mm × 3 mm improves the spatial resolution in the tangential direction by a factor of ∼1.4 compared to that of the standard circular aperture of 2.5-mm diameter. We believe that the results of our investigations are crucial for reaching fundamental metrological limits in deflectometric profilometry utilizing state-of-the-art electronic autocollimators. [ABSTRACT FROM AUTHOR]

To ensure the high performance of beamlines in Taiwan Photon Source, the metrology of the beamline optical components is essential to realize the theoretical optical simulation. The design and performance of a long-trace profiler (LTP) with moving optical head is described. A LTP is used as a metrological tool for the assembly and correction of optical components at the beamline. For a water-cooled mirror, a LTP serves to optimize the surface profile to a slope error of 0.1 µrad (rms) and adequate thermal conductance. To correct a bendable cooling mirror in a twisted condition, the sagittal slope is decreased by a screw adjustment through the LTP measurement. For the double-crystal monochromator (DCM) with flow-induced vibrations, we proposed an approach to stiffen the bellows hose partially inside the vacuum chamber. From an investigation of the vibrational spectra of the DCM before and after the treatment with the aid of the autocollimator, the current approach is confirmed to be an effective solution for suppression of vibration. [ABSTRACT FROM AUTHOR]

Deflectometric profilometers are indispensable tools for the precision form measurement of beam-shaping optics of synchrotrons and x-ray free electron lasers. They are used in metrology labs for x-ray optics worldwide and are crucial for providing measurement accuracy dictated by the form tolerances for modern state-of-the-art x-ray optics. Deflectometric profilometers use surface slope (angle) to assess form, and they utilize commercial autocollimators for the contactless slope measurement. In this contribution, we discuss the influences of environmental parameters, such as temperature and air pressure, including their gradients, on high-accuracy metrology with autocollimators in profilometers. They can cause substantial systematic errors in form measurement, especially in the case of large and strongly curved optical surfaces of high dynamic range. Relative angle and form measuring errors of the order of 10−4 are to be expected. We characterize environmental influences by extended theoretical and experimental investigations and derive strategies for correcting them. We also discuss the possibility to minimize the contributions of some errors by the application of sophisticated experimental arrangements and methods. This work aims at approaching fundamental limits in autocollimator-based slope and form metrology. [ABSTRACT FROM AUTHOR]

Subject of Research. The paper deals with application of quaternions for optimization of reflector parameters at autocollimation measurements in comparison with a matrix method. Computer-based results on the quaternionic models are presented that have given the possibility to determine conditions of measurement error reduction in view of apriori information on the rotation axis position. The practical synthesis technique for tetrahedron reflector parameters using found ratios is considered. Method. Originally, received conditions for reduction of autocollimation system measurement error are determined with the use of a matrix method for definition of an angular object position as a set of three equivalent consecutive turns about coordinate axes. At realization of these conditions the numerous recalculation of orientation parameters between various systems of coordinates is necessary that increases complexity and reduces resulting accuracy of autocollimation system at practical measurements. The method of quaternions gives the possibility to analyze the change of an absolute angular position in space, thus, there are conditions of accuracy increase regardless of the used systems of coordinates. Main Results. Researches on the mathematical model have shown, that the orthogonal arrangement of two basic constant directions for autocollimator tetrahedron reflector is optimal with respect to criterion of measurement error reduction at bisection arrangement of actual turn axis against them. Practical Relevance. On the basis of the found ratios between tetrahedron reflector angles and angles of its initial orientation parameters we have developed a practical method of reflector synthesis for autocollimation measurements in case of apriori information on an actual turn axis at monitoring measurements of the shaft or pipelines deformations.

Abstract 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. Highlights • Laser autocollimation is innovated for absolute angle measurement. • An optical frequency comb is employed for absolute angle measurement. • A scale grating is employed to generate first-order diffracted beams. • The first-order diffracted beams have deterministic unique angular positions. • It is the first time to establish the absolute laser autocollimation. [ABSTRACT FROM AUTHOR]

An improved k-means algorithm is proposed to enhance the stability and dynamic measurement accuracy of high-frequency small angle measurement using a dynamic autocollimator. The improved algorithm incorporating an optimized initialization scheme is used to determine the accurate position of the light spot for angle calculation. Simulations executed on different datasets demonstrate the effectiveness of the algorithm. Experimental results indicate that the 30-min stability of 0.58 and 0.69 arc sec at the measurement frequencies of 5 and 10 kHz can be achieved by the improved algorithm, respectively. Also, the dynamic measurement accuracy of 0.99 and 1.25 arc sec under the rotation speeds of 1 and 20 deg/s, respectively, at the measurement frequency of 10 kHz can be obtained. It is confirmed that the improved algorithm is necessary and effective for the autocollimator. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A unified approach to the management of measurements in optical digital measurement systems with 2D sensor is considered. The proposed approach is based on exhaustive use of information redundancy, that is, the use of coordinate information about the object distributed over the entire field of the image. The efficiency of the approach is demonstrated for the case of autocollimators. Results of simulation and experiment that confirm that the precision of devices may be increased through the use of a multi-element mark and coordinate information over the entire information field are presented. The basic problems that arise in the development and introduction of the approach are formulated. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]