In the high-precision-long-stroke manufacturing system, precise servo control of a motor determines the machining accuracy during manufacturing. Moreover, the value of the motor subposition is an important signal in the motor feedback control system, which determines the control precision of the linear motor servo system. Therefore, analyzing the position measurement algorithm for a high-precision-long-stroke linear electric motor is crucial. Currently, the linear electromotor measurement based on a digital image is mostly a short-stroke measurement and cannot achieve long-stroke precision measurement. However, with the continuous improvement of precision manufacturing requirements, the need for the accurate measurement of the displacement of long-stroke linear electric motor becomes extremely urgent. Moreover, unlike the two-frame image measurement system in short-stroke measurement, long-stroke measurement comprises a multi-frame image measurement system. The number of frames increases as the measurement distance increases, resulting in problems related to error accumulation. The cumulative measurement error is the most important factor that affects the measurement accuracy of rectilinear distance displacement. Hence, to address the issue of error accumulation owing to the displacement superposition of multiple frames during the measurement of the linear electromotor subposition, an error reduction algorithm based on machine vision with a threshold transform reference map was proposed herein.

In this study, the phase correlation algorithm is used to obtain the whole pixel offset between two frames rapidly, and the corresponding distance of the registration image is translated to decrease the displacement deviation between the registration image and reference frame to <1 pixel. The gray gradient algorithm is used to measure the subpixel displacement of the translated image in a small range. To improve the measurement accuracy and range of adjacent frames, then, the reference map is set, and the displacement images at different moments are registered to obtain the displacement value at specific moments. When the displacement between the registration map and reference map exceeds the maximum measured displacement between two frames, the transformation threshold is set to dynamically adjust the reference map. Based on the number of threshold transformations, the dynamic–real-time position is obtained using displacement superposition. Compared with the method of stacking adjacent frame displacements to obtain long-stroke displacement values, the proposed method can effectively reduce the displacement stacking time and cumulative error.

First, a one-dimensional image measurement system is designed based on the one-dimensional rigid body translation of the linear motor, and one-dimensional target images are generated and optimized to improve the accuracy of the measurement system, as shown in Figs. (1) and (3). The measurement range of the adjacent frame image measurement algorithm is optimized, and the measuring distance of displacement between two frames is extended, which lays a foundation for reducing the cumulative error. As shown in Fig. (6), the measurement range of the improved algorithm increases from 1 pixel to 189.54 pixel. Finally, the cumulative error reduction approach for a self-adjusting reference graph is proposed, which can reduce the cumulative error by ensuring high-resolution feedback from all positions through the changes in the reference graph, as seen in Fig. (7). The feasibility of the proposed method is verified via the experimental data in Figs. (10), (11), and (12). Fig. (11) verifies the feasibility of the proposed method, and demonstrates that its measurement accuracy is higher than the other methods. Fig. (12) verifies the robustness of the proposed method, which maintains a high level of measurement accuracy under low illumination conditions.

In this study, by improving the measurement accuracy of adjacent frames and decreasing the cumulative error, the long-stroke measurement of linear electromotor displacement with high precision is realized. First, image registration is divided into two parts: whole pixel translation and subpixel high-precision measurement. The accuracy and range of the algorithm in adjacent frame displacement image measurements are improved via step calculation. Then, to reduce the cumulative error in the displacement measurement process of long-stroke electromotor subunits, a threshold transform reference graph is added to reduce the cumulative times of displacement. The feasibility and effectiveness of the proposed method were verified via simulation and platform experiments. Experimental results show that compared with the traditional algorithm, the proposed method can effectively reduce the cumulative error by >80% and exhibit better cumulative error reduction under different illumination conditions. Therefore, the algorithm proposed herein can effectively reduce the cumulative error in the long-stroke measurement, which is conducive to the realization of high-precision measurement of the long-stroke linear electromotor displacement.

There are two primary three-dimensional (3D) measurement error sources of structural light based on the phase shift method: phase shift error and nonlinear error. With the development of a digital projector, the computer can produce standard sinusoidal stripes to eliminate the phase shift error. However, the nonlinear error of the projector and camera will cause the stripe to lose particular sinusoidal properties, affecting the measurement accuracy and effect. To reduce the nonlinear error of the system, global scholars have put forward various solutions, among which the binary stripe method is the most widely studied. The binary stripe is not affected by nonlinearity because it has only two gray values. The projection speed can be significantly improved by a digital projector projecting 1-bit binary stripes. In the study of many binary stripes, the binary coded stripe method uses multiple binary stripes to generate a sinusoidal stripe, which avoids defocusing projection, effectively reduces the nonlinear effect of the system, and improves measurement accuracy and projection efficiency. Based on the binary coded stripe method, this paper proposes a method of reusing weighted binary coded stripes, which significantly reduces the number of binary stripes weighted with a sinusoidal stripe and further improves the projection efficiency.

This paper proposes a method of reusing weighted binary coded stripes. The binary coded stripe method samples the gray value of sinusoidal stripes uniformly to obtain the discrete decimal gray values of a sinusoidal stripe. The gray values are then processed by binary coding, and all of the code words with the same level of binary code words are combined to generate binary stripes. After sequential projection by a digital projector, the collected stripe images are weighted in binary to generate a sinusoidal stripe modulated by object depth information. In the implementation process of binary coded stripes, a certain number of repeated binary stripes will appear under a specific gray-value sampling number. After comparison, 12 gray values are uniformly sampled within a sinusoidal period, and the binary coding generates binary stripes. After unique processing, the same binary stripes only need to be projected once, and repeated weighting is performed in the calculation process. As a result, only four binary stripes are required to generate a sinusoidal stripe. Finally, the method is combined with the three-step phase shift technique. The complementary gray code method is also used to carry out the phase unwrapping, which can realize an efficient 3D measurement with 20 binary stripes in the state of constant focus.

This paper uses the proposed method, three-step phase shift method, and the four-step phase shift method to measure different objects and carry out comparison experiments of different gray values, and the comparison experiment with the traditional methods aims to verify the superiority of the method of reusing weighted binary coded stripes. In the first experiment, through the measurement of a standard sphere, the average distance difference between local point cloud data obtained by different gray values and fitted standard sphere is small. The average distance obtained by the three-step phase shift optimization method is 0.0153 mm, and that by the four-step phase shift optimization method is 0.0107 mm (Fig. 6 and Table 3). As shown in Fig. 7, the actual item is measured, and the reconstructed results are comparable, which verifies that the proposed method of reusing weighted binary coded stripes can still maintain high accuracy and measurement impact after reducing the number of projections. In the comparison experiment with the traditional methods, sinusoidal fitting is carried out on the sinusoidal stripe obtained by the traditional methods and the proposed method. The root-mean-square error (RMSE) of the sinusoidal fitting is 3.6082 and 3.3125, and the sum of squared errors (SSE) is 3529.3 and 3028.4 (Fig. 8 and Table 4). Linear fitting is performed on the measurement results of the high-precision plane. The RMSE is 0.0415 and 0.0388 mm, respectively, and the SSE is 0.4804 and 0.4493 mm (Fig. 9 and Table 5). As demonstrated in Fig. 10 and Table 6, after measuring the standard sphere, the average distance between the local point cloud and the fitted standard sphere is reduced by 72.3% when compared with that by the traditional three-step phase shift method. For the measurement of the plaster head, whose surface depth varies greatly, the traditional three-step and four-step phase shift methods have strip-like systematic errors due to the nonlinear effects of the system. However, the surface reconstruction effect of the proposed method is better (Fig. 11).

This paper proposes a method of reusing weighted binary coded stripes. A better sampling scheme is designed by further studying the principle of the binary coded stripe method. After the unique processing of binary coding and binary stripes, the method of reusing weighted binary coded stripes generates sinusoidal stripes to reduce the actual projection number of binary stripes. In order to generate a sinusoidal stripe, eight weighted binary stripes are reduced to four binary stripes. As a result, only 20 binary stripes are required to complete the 3D measurement by the three-step phase shift method and the complementary gray code phase unwrapping method. The results of comparison experiments show that the proposed method will not reduce the measurement accuracy and effect while significantly reducing the projection number by the binary coded stripe method. Compared with the traditional phase shift method, the proposed method can significantly reduce the nonlinear effect of the system and further improve the projection rate of the DLP projector. In conclusion, the proposed method effectively reduces the projection number required by the binary coded stripe method and provides technical support for high-speed 3D measurement based on phase shift stripe analysis.

For an aero-engine in operation, the pressure distribution of the exhaust jet flow field is the main parameter of flow characteristics and temperature field. Therefore, the accurate measurement of the exhaust jet flow field pressure of the aero-engine is of great significance to study the state of the aero-engine in operation. As traditional speed and pressure measurement tools, sensors such as pitot tubes fail to be directly applied to high-temperature and high-speed complex flow fields such as combustion due to their shortcomings of destructive flow fields, single point measurement, and low temporal and spatial resolutions. With the development of visual measurement and image processing technologies, optical measurement methods have been gradually applied to measure the physical parameters of the flow fields. As a typical optical diagnosis method, the pressure field reconstruction method based on particle image velocimetry (PIV) is only applicable to the pressure field reconstruction of incompressible fluid. As a flow field visualization measurement technology, the schlieren method has the characteristics of a large measurement range, fast response speed, and simple test equipment. It is an effective method for real-time measurement of flow field parameters. By applying the schlieren method to reconstruct the pressure field of the jet flow field of the aero-engine, the real non-contact measurement can be realized, and the accuracy of measurement can be improved.

This paper proposes a method of reconstructing the pressure field distribution of high-speed airflow by using the schlieren method to decouple the velocity and density fields, so as to realize the real-time measurement and reconstruction of the density field, velocity field, and pressure field of the high-speed airflow. First, the relationship between the brightness of schlieren images and the light shift is calibrated by using the calibrated schlieren method. After obtaining the calibration curve, the light shift can be obtained according to the light and dark changes in the schlieren images, and then the density distribution of the flow field will be indirectly obtained. Meanwhile, the velocity distribution can be obtained by using an optical flow velocimetry algorithm through the schlieren images of continuous frames. Finally, the static and dynamic pressure distributions of the flow field can be obtained through a numerical calculation by using the obtained velocity and density information, and then the total pressure distribution can be obtained.

The density field (Fig. 11) and velocity field (Fig. 13) of the micro vortex jet wake field are reconstructed by the schlieren method, and the density field of the micro vortex jet wake field is reconstructed by using the obtained density and velocity information. In order to verify the feasibility and accuracy of the experimental method, the measured pressure at five points near the nozzle is selected and compared with the reconstructed pressure field (Fig. 18). The results show that the two results are close within the error range, and the maximum error is not more than 5%. The following factors are considered to determine error sources: when the density field of the flow field is measured, the model of the flow field is regarded as axisymmetric, and there is a certain error; when the pressure gradient distribution is calculated, the numerical calculation method is used, which has some errors; since the measurement time of pitot tubes and schlieren velocity-density field coupling reconstruction method is different, there will be some errors in the measurement results although the interval time is short. However, these errors are within the allowable range of measurement. Therefore, the reconstruction method of the high-speed airflow pressure field by using the schlieren method to decouple the velocity and density fields is feasible.

In this paper, the schlieren optical flow method is used to synchronously reconstruct the density and velocity fields of the axisymmetric flow field, which not only overcomes the shortcomings of the traditional single point measurement of pressure sensors, contact measurement, poor spatial and temporal resolutions but also compensates for the disadvantages of the PIV-based pressure field reconstruction technology. The technology requires the distribution of tracer particles and can only reconstruct the pressure field of incompressible fluid. Therefore, the proposed method is effective in accurately reconstructing the pressure distribution of high-speed flow fields, and it can extend the application scope of the schlieren method in the quantitative measurement of flow fields.

Corrosion has a great impact on the strength and durability of steel materials (such as rebar and steel plate). Research reveals the absorption resonance of some iron oxides produced during steel material corrosion with terahertz (THz) electromagnetic waves. Moreover, THz waves can penetrate common coating materials. Therefore, THz spectroscopy has application potential in non-destructive testing of the early corrosion of steel materials. To investigate the optical parameters of the corrosion products of steel materials and identify the characteristics of the products, we measured the THz transmission signals of different kinds of corrosion product samples and the main component crystals Fe₃O₄, Fe₂O₃, and α-FeOOH in the samples with a THz time-domain spectroscopy (THz-TDS) system. The experimental results show that in the effective frequency range of 0-1.2 THz, the refractive indexes of the mixture samples of different corrosion products are in the range of 2.7-3.4, and those of the component crystals Fe₃O₄, Fe₂O₃,_{and α-FeOOH are 4.0, 2.7, and 2.2, respectively. The content of Fe3O4 in the corrosion product mixture has a substantial influence on the optical parameters, such as absorption coefficient and refractive index. Then, we built an ultra-wideband THz-TDS system based on the two-color field to further extend the effective THz measurement range to 0-10 THz. The results indicate that within 0-10 THz, no characteristic absorption peaks of Fe3O4 are observed. In contrast, the characteristic absorption peaks of Fe2O3 are located at 3.4 THz, 4.2 THz, 4.85 THz, and 5.8 THz, respectively, and those of α-FeOOH are located at 3.6 THz, 4.05 THz, 5 THz, and 5.45 THz, respectively. In addition, this THz method can identify the characteristics of Fe2O3 and α-FeOOH from the THz absorption spectra of the samples of different corrosion products. Suggesting that the occurrence of steel material corrosion can be determined according to the characteristic absorption peaks of Fe2O3 and α-FeOOH, the experimental results in this paper lay a foundation for the application of THz spectroscopy in non-destructive testing of steel material corrosion.}

First of all, we used a Terapulse 4000 instrument to determine the transmission signals of samples of different kinds of corrosion products and the main component crystals Fe₃O₄, Fe₂O₃, and α-FeOOH. Then, we built an ultra-wideband THz-TDS system to extend the effective THz measurement range to 0-10 THz. Afterwards, this ultra-wideband THz system was employed to identify the locations of the characteristic absorption peaks of Fe₂O₃ and α-FeOOH. Finally, samples of different corrosion products were measured to identify the characteristics of Fe₂O₃ and α-FeOOH in the mixtures.

To investigate the optical parameters of corrosion product samples, we measured samples of different kinds of corrosion products and the main component crystals Fe₃O₄, Fe₂O₃, and α-FeOOH (Figs. 2-4). The experimental results show that the refractive indexes of the samples of the corrosion product mixtures are in the range of 2.7-3.4, and those of the component crystals Fe₃O₄, Fe₂O₃, and α-FeOOH are 4.0, 2.7, and 2.2, respectively. The content of Fe₃O₄ in the corrosion product mixture has a great influence on the optical parameters. Using the ultra-wideband THz system, we identified the locations of the characteristic absorption peaks of Fe₂O₃ and α?FeOOH. The characteristic absorption peaks of Fe₂O₃ are located at 3.4 THz, 4.2 THz, 4.85 THz, and 5.8 THz, respectively, while those of α-FeOOH are located at 3.6 THz, 4.05 THz, 5 THz, and 5.45 THz, respectively (Fig. 5). Furthermore, the characteristic absorption peaks of the Fe₂O₃ and α-FeOOH in the mixture samples were detected (Fig. 6), demonstrating that the mixture state of corrosion products does not affect the identification of the characteristics of Fe₂O₃ and α-FeOOH by THz spectroscopy.

We mainly studied the optical parameters of corrosion products and locates the characteristic absorption peaks of Fe₂O₃ and α?FeOOH. Since the components of the mixture samples of different corrosion products have different relative contents, the refractive indexes of the samples are in the range of 2.7-3.4. Moreover, the content of Fe₃O₄ has a great influence on the optical parameters of corrosion product mixtures. An ultra-wideband THz-TDS system based on the two-color field was built to extend the effective THz measurement range to 0-10 THz. The experimental results reveal that in the range of 0-10 THz, Fe₃O₄ has no characteristic absorption peaks; the characteristic absorption peaks of Fe₂O₃ are located at 3.4 THz, 4.2 THz, 4.85 THz, and 5.8 THz, respectively, and those of α?FeOOH are located at 3.6 THz, 4.05 THz, 5 THz, and 5.45 THz, respectively. The ultra-wideband THz waves can identify the characteristic absorption peaks of the Fe₂O₃ and α?FeOOH in the corrosion product mixtures. The characteristic absorption peaks of the two corrosion products Fe₂O₃ and α?FeOOH can be used as identification marks to determine the occurrence of corrosion. The experimental results in this paper lay a foundation for the application of THz spectroscopy to the non-destructive testing of the early corrosion of steel materials.

The reflected light field information of a rough surface includes the reflected light angle and intensity, which can be used to retrieve the reflection and morphology characteristics of the surface. Therefore, accurate measurement of the reflected light field has high research value and practical applications in the fields of target detection and recognition, in-orbit radiation calibration, material property analysis, optical device stray light analysis, etc. Presently, the traditional "scanning" method uses a mechanical mechanism to achieve point-by-point scanning measurement of the spatial reflected light field information of the target sample; however, there are problems such as slow measurement efficiency, numerous measurement error links, and poor repeatability. Furthermore, given the influence of incident light wavelength and energy fluctuation on the measured data during the scanning process, the weight gradually increases with increasing time, which may lead to distortion of full-space BRDF fusion information. In contrast, the emerging "photographic" measurement method based on optical imaging techniques only measures the reflected light field in a small angle range. In this study, to overcome the low efficiency of the "scanning" reflected light field measurement system and the small measuring angle range of the "photographic" reflected light field measurement system, a rough surface reflected light field measurement method based on ultrawide-angle imaging is proposed. This method realizes the measurement of multidirectional angle reflected light field information over a large angle range, enriches measurement means of rough surface reflected light fields and is suitable for measuring optical reflection characteristics and damage of material surface. Here, the simulation and reconstruction provide a research basis and technical support.

Based on the principle of reflected light field measurement, this paper first determined the overall structure of the reflected light field measurement system, which comprises a light source, sample plate to be measured, a hemispherical reflecting ball screen, and a refractive reflecting ultrawide-angle imaging optical system. Next, the catadioptric ultrawide-angle imaging optical system was optimized and the best resolution angle in the optical system's field of view was simulated and analyzed. Subsequently, a calibration method for the reflected light field measurement system was studied to realize off-axis spatial position calibration and light field intensity calibration. Finally, the reflected light field measurement results were simulated and analyzed using a Labsphere Permaflect-80 diffuse reflector, WhiteOptics-DF60 diffuse reflector, and American ACA specular aluminum plate, proving the feasibility of the proposed surface reflected light field measurement method.

The best resolution angle of the designed reflected light field measurement system is 2° in the range of 0°-54° zenith angle and 15° in the range of 0°-360° azimuth angle (Fig. 9). The coordinate distribution of the feature points after calibration was obtained using the off-axis spatial position mapping relationship (Fig. 11); the relative error of light field measurement increases with increasing zenith angle. The maximum relative error in the range of the measuring field of view is 4.12% at the zenith angle of 54° and azimuth angle of 255°. The maximum average relative error is 2.06% and the average relative error is less than 1% within the range of 0°-36° zenith angle (Fig. 14). The measurement results were obtained using the Labsphere Permaflect-80 diffuse reflective plate, WhiteOptics-DF60 diffuse reflective plate, and ACA specular aluminum plate of the United States under conditions of uniform illumination using a 550-nm incident beam with a zenith angle of 40° and azimuth angle of 270°(Fig.16). The results show that the surface of specular aluminum material with rough surfaces have strong specular reflection characteristics, which is consistent with the reflection characteristics of the material itself (Fig.17).

Based on the principle of ultrawide-angle imaging, a reflective light field measurement system has been successfully designed here that achieves a best angle resolution of 15° in the azimuth range of 0°–360° and a best angle resolution of 2° in the zenith range of 0°-54°. After calibration, the maximum average relative error of the circumference under each zenith angle is 2.06%. These results support that the "photographic" method of measuring a reflected light field can also be used to measure a reflected light field in a large angle range using a reasonable optical system design.