Method for absolute measurement of flat surface.

Angular displacement sensor plays an indispensable role in high-precision angular measurement and position feedback. With the development of sensing technology, some traditional incremental measurement methods have been unable to meet the requirements such as anti-interference ability, lossless of power-off data information and other factors that are susceptible to environment and mechanical system changes. Therefore, this paper has proposed a method based on combined measurement for absolute measurement of time-grating angular displacement sensor, which is mainly assembling two time-grating sensors that use different pole pair in a co-prime relationship on the axis. By this method, it can build high-precision and high-resolution sensor that meets vernier-subdivision principle in the form of a combination of sensor and fine sensor. The sensor model and simulation experiment results are introduced by Inventor 2016 and ANSYS Maxwell 16.0, respectively. Then, the absolute position measurement method is validated by analyzing the initial phase of the induced electromotive force of the simulation experiment results with the mathematical method. Experiment results show the absolute measurement method is feasible.

Most of the commercial available sub-aperture stitching interferometers measure the surface with a standard lens that produces a reference wavefront, and the precision of the interferometer is generally limited by the standard lens. The test accuracy can be achieved by removing the error of reference surface by the absolute testing method. When the testing accuracy (repeatability and reproducibility) is close to 1nm, in addition to the reference surface, other factors will also affect the measuring accuracy such as environment, zoom magnification, stitching precision, tooling and fixture, the characteristics of optical materials and so on. We establish a stitching system in the thousand level cleanroom. The stitching system is including the Zygo interferometer, the motion system with Bilz active isolation system at level VC-F. We review the traditional absolute flat testing methods and emphasize the method of rotation-shift functions. According to the rotation-shift method we get the profile of the reference lens and the testing lens. The problem of the rotation-shift method is the tilt error. In the motion system, we control the tilt error no more than 4 second to reduce the error. In order to obtain higher testing accuracy, we analyze the influence surface shape measurement accuracy by recording the environment error with the fluke testing equipment.

This paper proposes a new shearing approach to eliminate the systematic errors in phase measuring deflectometry (PMD). Besides a normal measurement using PMD, another three measurements are taken when the test surfaces are translated and rotated with an amount of known magnitude in our proposed method. The four measurements give three sheared wavefronts, and then the difference Zernike polynomial fitting and a least squares algorithm are proposed to reconstruct the true test surface figure. The proposed method is demonstrated and verified through computer simulation and experimental results. The error propagation when the sheared wavefronts include random noise and the introduced errors due to the incorrect shearing values are both analyzed.

In an interferometer which uses a reference surface, the measured surface heights correspond to the difference between the test and reference surfaces. To accurately determine the rms roughness of supersmooth surfaces, the effects of the reference surface roughness need to be removed. One technique for doing this involves averaging a number of uncorrelated measurements of a mirror to generate a reference surface profile which can then be subtracted from subsequent measurements so that they do not contain errors due to the reference surface. The other technique provides an accurate rms roughness of the surface by taking two uncorrelated measurements of the surface. These two techniques for measurement of supersmooth surfaces are described in detail, and results of the measurement of a 0.7-A rms roughness mirror are presented. The expected error in the rms roughness measurement of a supersmooth mirror due to instrument noise is 0.02 A.

Objectives:To compare the diagnostic reliability of optic nerve sheath diameter (ONSD) ultrasonography with a transcranial Doppler (TCD)-based absolute intracranial pressure (ICP) value measurement method for detection of elevated ICP in neurological patients. The ONSD method has been only tested previously on neurosurgical patients.Methods:A prospective clinical study of a non-invasive ICP estimation method based on ONSD correlation with ICP and an absolute ICP value measurement method based on a two-depth TCD technology has recruited 108 neurological patients. Ninety-two of these patients have been enrolled in the final analysis of the diagnostic reliability of ONSD ultrasonography and 85 patients using the absolute ICP value measurement method. All non-invasive ICP measurements were compared with ‘Gold Standard’ invasive cerebrospinal fluid (CSF) pressure measurements obtained by lumbar puncture. Receiver-operating characteristic (ROC) analysis has been used to investigate the diagnostic value of these two methods.Results:The diagnostic sensitivity, specificity, and the area under the ROC curve (AUC) of the ONSD method for detecting elevated intracranial pressure (ICP >14·7 mmHg) were calculated using a cutoff point of ONSD at 5·0 mm and found to be 37·0%, 58·5%, and 0·57, respectively. The diagnostic sensitivity, specificity, and AUC for the non-invasive absolute ICP measurement method were calculated at the same ICP cutoff point of 14·7 mmHg and were determined to be 68·0%, 84·3%, and 0·87, respectively.Conclusions:The non-invasive ICP measurement method based on two-depth TCD technology has a better diagnostic reliability on neurological patients than the ONSD method when expressed by the sensitivity and specificity for detecting elevated ICP >14·7 mmHg.

Novel absolute phase measurement method with few-patterns

Absolute distance measurement plays an important role in many areas, such as aerospace and scientific research. Traditional measurement methods generally cannot meet requirements for long-range and high-precision at the same time. In this paper, an absolute distance measurement method based on alternately oscillating optoelectronic oscillator is proposed. This method places the distance to be measured in the loop of optoelectronic oscillator and takes advantage of accumulative magnification effect to achieve high accuracy. The measurement and the reference optoelectronic oscillators are established and selected by an optical switch, and a microwave switch is used to choose the high-order or low-order oscillating frequency. The high-order frequency and low-order oscillating frequency of the measurement and reference optoelectronic oscillators are measured in turn by frequency counter to calculate the loop lengths of two optoelectronic oscillators. The low-order frequencies are used to measure the fundamental frequency roughly and the high-order frequencies are used to calculate loop length precisely. Although the mode hopping occurs in the measurement process, it does not affect the loop length calculation by substituting the corresponding oscillating mode number. Note that the loop length measurement moments of two optoelectronic oscillators are different due to the switching order of optical switch and microwave switch. In order to calculate the absolute distance, which is the length difference between two optoelectronic oscillators at the same moment, the measured loop lengths should be averaged.In this way, systematic error accumulation caused by slow drift of environment can be eliminated, and this method does not need to control the length of reference optoelectronic oscillator. Meanwhile, the measurement system is simple. In the experiment, 1 km, 5 km and 8 km fibers are placed in a common part of the measurement and reference optoelectronic oscillators to simulate different long-range distances in space. A high-resolution optical delay line is placed in the measurement optoelectronic oscillator to verify the performance of the measurement system. The experimental results show that the measurement error is 3.5 μm with a 3.5 μm maximum standard deviation of each measurement distance at an emulated round trip distance of 6 km. The relative measurement accuracy reaches 5.8 × 10<sup>－10</sup>. This method provides a feasible idea for solving the technical problems of long-range and high-precision absolute distance measurement.

This paper presents a non-nulling absolute interferometric method for fast and full-area measurement of aspheric surfaces without the necessity of any mechanical movement. Several single frequency laser diodes with some degree of laser tunability are used to achieve an absolute interferometric measurement. The virtual interconnection of three different wavelengths makes it possible to accurately measure the geometrical path difference between the measured aspheric surface and the reference Fizeau surface independently for each pixel of the camera sensor. It is thus possible to measure even in undersampled areas of the high fringe density interferogram. After measuring the geometrical path difference, the retrace error associated with the non-nulling mode of the interferometer is compensated for using a calibrated numerical model (numerical twin) of the interferometer. A height map representing the normal deviation of the aspheric surface from its nominal shape is obtained. The principle of absolute interferometric measurement and numerical error compensation are described in this paper. The method was experimentally verified by measuring an aspheric surface with a measurement uncertainty of λ/20, and the results were in good agreement with the results of a single-point scanning interferometer.

In this study, the shift-rotation absolute testing method is extended to weakly aspheric surfaces, providing a direct, null-compensator-free solution for subnanometer figure testing. A key limitation of existing shift-rotation methods, namely the tradeoff between high-resolution and low-noise propagation, is addressed. Accordingly, a pixel-level-resolution absolute testing method based on multiple rotations and two orthogonal lateral shifts is proposed. Rotationally asymmetric errors are calibrated via rotation averaging, while rotationally symmetric errors are reconstructed by dividing shift-induced differential wavefronts into subapertures for least-squares fitting and stitching. These components are then fused to achieve pixel-level absolute surface figure reconstruction. The proposed method preserves high-frequency surface information while maintaining a low noise-propagation ratio, thereby achieving subnanometer accuracy. Numerical simulations and absolute testing experiments on a weakly aspheric surface validate the effectiveness and reliability of the proposed method for high-precision optical surface testing.

Based on reflection arrangement, two antenna polarization measurement techniques, the absolute polarization measurement method and the polarization‐transfer measurement method are presented with experimental results. In the absolute polarization measurement method or the system calibration, the polarization characteristics of transmitting and receiving dual‐polarization antennas used in the measurement system are determined using the two polarization‐isolated scattering calibrators. In the polarization‐transfer measurement method, the antenna being tested operates in either transmitting mode or receiving mode. Since the transmitting and receiving antennas are located side by side in the measurement system, the phase reference signal between two antennas can be implemented with a short cable.

In the solar reflective band, the on-board calibration method based on a solar diffuser (SD) is the mainstream calibration method. However, the calibration accuracy is limited by the measurement accuracy of the SD bidirectional reflectance distribution function (BRDF) in the laboratory. The limitations of the light sources and detectors hinder accurate BRDF measurements in the short-wave infrared band, particularly beyond 1700 nm. In this study, the angle integration-band crossing transfer (AIBCT) method is proposed for SD BRDF measurement to avoid the influence of the Fourier spectrometer's signal processing and detector nonlinearity in the absolute measurement. The method utilized the relationship between the BRDF and directional-hemispherical reflectance, and calculated the spectral distribution of the SD BRDF at the standard in-plane geometry with an 0° incidence zenith angle and a 45° reflection zenith angle (0:45) by integration. The absolute measurement result of the 0:45 SD BRDF at 1150 nm was used as the standard for transfer to the short-wave infrared band. The SD BRDF at 0:45 was generalized to other geometries through relative measurements based on the reciprocity theorem. The mean relative error of the results of the AIBCT and absolute measurement methods was less than 0.3 % in the range of 1100 nm to 1600 nm. Analysis of the results showed that the AIBCT method’s measurement uncertainty (coverage factor k = 2) of the 0:45 SD BRDF is better than 0.84 % at 1100 nm to 2300 nm and 1.05 % at 2300 nm to 2500 nm. Furthermore, the AIBCT method was found suitable for the ultraviolet band.

Turbines or pumps in hydropower plants achieve peak efficiencies of far more than 90% depending on the specific speed and the type of machine. Based on model tests or numerical simulations, the efficiency of a prototype machine has to be guaranteed and measured with the best measurement technique available. The choice of the appropriate efficiency measurement method does not only depend on the expected measurement uncertainties and tolerances set in a contract, it is also a question of the effort required for such a measuring campaign and of technical challenges, e.g., limitations imposed by plant operating conditions as draining of the system or constant load operation. Concerning hydraulic turbomachines, modern measuring technology offers different methods for efficiency measurements at a turbine unit. Primarily through the development of real-time capable data acquisition systems, it is possible to perform high-precision measurements rather quickly, whereby minimal downtimes can be achieved. In the first part, the specific measurement methods available in different standards are presented in an overview, and then in the second part, the achieved accuracies of a very complex thermodynamic measurement are compared with a low-cost clamp-on acoustic Doppler measurement using a concrete example.

Compared with conventional high-end optical systems, application of freeform optics offers many advantages. Their widespread use, however, is held back by the lack of a suitable measurement method.The NANOMEFOS project aims at realizing a universal freeform measurement machine to fill that void.The principle of operation of this machine requires a novel sensor for surface distance measurement, the development and realization of which is the objective of the work presented in this thesis. The sensor must enable non-contact, absolute distance measurement of surfaces with reflectivities from 3.5% to 99% over 5 mm range, with 1 nm resolution and a 2s measurement uncertainty of 10 nm for surfaces perpendicular to the measurement direction and 35 nm for surfaces with tilts up to 5°. To meet these requirements, a dual-stage design is proposed: a primary measurement system tracks the surface under test by translating its object lens, while the secondary measurement system measures the displacement of this object lens. After an assessment of various measurement principles through comparison of characteristics inherent to their principle of operation and the possibilities for adaptation, the differential confocal measurement has been selected as the primary measurement method. Interferometry is used as secondary measurement method. To allow for correction of tilt dependent error through calibration, a third measurement system has been added, which measures through which part of the aperture the light returns. An analytical model of the differential confocal measurement principle has been derived to enable optimization. To gain experience with differential confocal measurement, a demonstrator has been built, which has resulted in insights and design rules for prototype development. The models show satisfactory agreement with the experimental results generated using the demonstrator, thus building confidence that the models can be applied as design and optimization tools. Various properties that characterize the performance of a differential confocal measurement system have been identified. Their dependence on the design parameters has been studied through simulations based on the models. The results of this study are applied to optimize the sensor for use in NANOMEFOS. An optical system has been designed in which the interferometer and the differential confocal systems are integrated in a compact design. The optical path of the differential confocal system has been folded using prisms and mirrors so that it can be realized within the allotted volume envelope. For the same reason, many components are adapted from commercially available parts or are custom made. An optomechanical and mechatronic design has been made around the optical system. A custom focusing unit has been designed that comprises a guidance mechanism and actuator to enable tracking of the surface. To achieve a low measurement uncertainty, it aims at accurate motion, high bandwidth and low dissipation. The lateral position of the guidance reproduces within 20 nm and from the frequency response, it is expected that a control bandwidth of at least 800 Hz can be realized. Power dissipation depends on the form of the freeform surface and is a few mW for most expected trajectories. Partly custom electronics are used for signal processing, and to drive the laser and the focusing unit. Control strategies for interferometer nulling, focus locking and surface tracking have been developed, implemented and tested. Various tests have been performed on the system to evaluate the performance. Calibrations must be carried out to achieve the required measurement uncertainty. One calibration is based on a new method to measure tilt dependency of distance sensors. The sensor realized has 5 mm measurement range, -2.5 µm to 1.5 µm tracking range, sub-nanometer resolution, and a small-signal bandwidth of 150 kHz. Using the test results, the 2s measurement uncertainty after calibration is estimated to be 4.2 nm for measurement of rotationally symmetric surfaces, 21 nm for measurement of medium freeform surfaces and 34 nm for measurement of heavily freeform surfaces. To test the performance of the machine with the sensor integrated, measurements of a tilted flat have been carried out. In these measurements, a tilted flat serves as a reference freeform with known surface form. The measurements demonstrate the reduction of tilt dependent error using the new calibration method. A tilt robust, single point distance sensor with millimeter range and nanometer uncertainty has been developed, realized and tested. It is installed in the freeform measurement machine for which it has been developed and is currently used for the measurement of optical surfaces.

The accuracy of surface measurement determines the manufacturing quality of membrane mirrors. Thus, an efficient and accurate measuring method is critical in membrane mirror fabrication. This paper formulates this measurement issue as a surface reconstruction problem and employs two-stage trained Zernike polynomials as an inline measuring tool to solve the optical surface measurement problem in the membrane mirror manufacturing process. First, all terms of the Zernike polynomial are generated and projected to a non-circular region as the candidate model pool. The training data are calculated according to the measured values of distance sensors and the geometrical relationship between the ideal surface and the installed sensors. Then the terms are selected by minimizing the cost function each time successively. To avoid the problem of ill-conditioned matrix inversion by the least squares method, the coefficient of each model term is achieved by modified elitist teaching–learning-based optimization. Subsequently, the measurement precision is further improved by a second stage of model refinement. Finally, every point on the membrane surface can be measured according to this model, providing more the subtle feedback information needed for the precise control of membrane mirror fabrication. Experimental results confirm that the proposed method is effective in a membrane mirror manufacturing system driven by negative pressure, and the measurement accuracy can achieve 15 µm.

Micro absolute distance measurement (MADM) is widely used in industrial and military fields. To achieve high accuracy and frequency response, a polarized low-coherence interferometry (PLCI)-based method for MADM is proposed. The nearly linear relationship between the envelope center and m-order PLCI fringe (PLCIF) peak center is found and verified. Dispersion compensation is achieved by fringe peak position estimation and polynomial fitting to get rid of the dependence on an a priori model and birefringence parameters, and make this method very robust. Meanwhile, the zero-order PLCIF center is estimated and located to demodulate the measured displacement. Then, the measurement accuracy is raised by polynomial fittings. In comparison to conventional methods, the proposed method can effectively avoid jump errors and has a higher accuracy. Experimental results indicate that the measurement accuracy is higher than 19.51 nm, the resolution is better than 2 nm, and its processing data rate can reach 35 kHz.