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The spatial distribution of elevated particulate matter (PM) concentrations represents a public health concern due to its association with adverse health effects. In this study, a city-wide spatial variability of PM (PM

Structured-lighting projection methods are the important parts of the optical three-dimensional (3D) measurement. Phase-shifting profilometry has a higher accuracy,however it requires multiple phase-shifting sinusoidal patterns’ projection,it can only be used for static measurement. The 3D shape measurement of dynamic objects is a challenging issue and attracts many scholars’ attention. The single frame 3D reconstruction technique (such as the Fourier transform, color-encoded or composite coded grating method and single frame Moire retrieval method) can meet the requirements of dynamic measurement well since only one-frame deformed pattern is required to obtain the 3D information of the object, but there are still issues in the stability and accuracy when using these methods. Recently, Wang et. al. [26] presented a high-speed Moire-based phase retrieval method. However, it is used only to measure the thin objects. Inspired by reference 27, we combined phase-shifting, moire algorithm and reconstruction algorithm of complex Fast Fourier Transform (FFT), proposed a dynamic three-dimensional (3D) measurement based on four-step phase-shifting Moire algorithm. Only one fringe pattern of the object was required to reconstruct the 3D shape of the tested object after the four fringe patterns with a π /2 phase shift of the reference plane were captured in advance. Only a single Fourier transform of a complex fringe composed of two multiplexed fringe patterns is calculated,the calculation time of the inverse 2D FFT is decreased due to the smaller calculated data matrix. First, four sinusoidal fringe patterns with a π/2 phase-shift are projected on the reference plane and acquired four deformed fringe patterns of the reference plane. Then single-shot deformed fringe pattern of the tested object is captured in measurement process. Four Moire fringe patterns can be obtained by numerical multiplication between the the AC component of the object pattern and the alternating components(AC) of the reference patterns respectively. The four low-frequency components corresponding to the Moire fringe patterns are calculated by the complex encoding FT (Fourier transform) ,spectrum filtering and inverse FT. Thus the four phase-shifting Moire fringe patterns can be retrieved. Then the wrapped phase of the object can be determined in the tangent form from the four phase shifting Moire fringe patterns using the four-step phase shifting algorithm.The continuous phase distribution can be obtained by the phase unwrapping algorithm.The 3D shape distribution can be reconstructed according to the phase-to height mapping relation after the calibration of the system. Finally, experiments are conducted to prove the validity of the proposed method. The results demonstrate that our method not only can expand the measurement scope, but also can improve accuracy and speed.

Low-cost sensors have become an increasingly important supplement to air quality monitoring networks at the ground level, yet their performances have not been evaluated at high-elevation areas, where the weather conditions are complex and characterized by low air pressure, low temperatures, and high wind speed. To address this research gap, a seven-month-long inter-comparison campaign was carried out at Mt. Tai (1534 m a.s.l.) from 20 April to 30 November 2018, covering a wide range of air temperatures, relative humidities (RHs), and wind speeds. The performance of three commonly used sensors for carbon monoxide (CO), ozone (O3), and particulate matter (PM2.5) was evaluated against the reference instruments. Strong positive linear relationships between sensors and the reference data were found for CO (r = 0.83) and O3 (r = 0.79), while the PM2.5 sensor tended to overestimate PM2.5 under high RH conditions. When the data at RH &gt, 95% were removed, a strong non-linear relationship could be well fitted for PM2.5 between the sensor and reference data (r = 0.91). The impacts of temperature, RH, wind speed, and pressure on the sensor measurements were comprehensively assessed. Temperature showed a positive effect on the CO and O3 sensors, RH showed a positive effect on the PM sensor, and the influence of wind speed and air pressure on all three sensors was relatively minor. Two methods, namely a multiple linear regression model and a random forest model, were adopted to minimize the influence of meteorological factors on the sensor data. The multi-linear regression (MLR) model showed a better performance than the random forest (RF) model in correcting the sensors&rsquo, data, especially for O3 and PM2.5. Our results demonstrate the capability and potential of the low-cost sensors for the measurement of trace gases and aerosols at high mountain sites with complex weather conditions.

In this paper, we develop a novel dual-frequency pattern which not only releases the restriction of conventional two-frequency phase-shifting algorithm that at least six fringe patterns are needed, but reduces the noise impact by decreasing the frequency ratio between the high- and low-components. To decrease the number of necessary patterns to five, a novel composite dual-frequency pattern scheme combining together a high- with a low-frequency pattern is employed. To make the algorithm less sensitivity to noise, the low-frequency component is with more than one period fringes, which is relatively prone to recover the continuous result by simple spatial phase unwrapping approach. Besides, the restriction of special phase shifts between two-frequency components in conventional methods is released by the generalized phase-shifting algorithm. Simulations and experiments are conducted to demonstrate that in addition to maintaining the minimum number of patterns, the proposed method reveals higher accu...

Conventional dual-frequency fringe projection algorithm often suffers from phase unwrapping failure when the frequency ratio between the high frequency and the low one is too large. Zhang et.al. proposed an enhanced two-frequency phase-shifting method to use geometric constraints of digital fringe projection(DFP) to reduce the noise impact due to the large frequency ratio. However, this method needs to calibrate the DFP system and calculate the minimum phase map at the nearest position from the camera perspective, these procedures are are relatively complex and more time-cosuming. In this paper, we proposed an improved method, which eliminates the system calibration and determination in Zhang's method,meanwhile does not need to use the low frequency fringe pattern. In the proposed method,we only need a set of high frequency fringe patterns to measure the object after the high frequency is directly estimated by the experiment. Thus the proposed method can simplify the procedure and improve the speed. Finally, the experimental evaluation is conducted to prove the validity of the proposed method.The results demonstrate that the proposed method can overcome the main disadvantages encountered by Zhang's method., Comment: 15 pages, 11 figures

Phase unwrapping is one of the key steps of optical interferogram analysis.However,implementing phase-unwrapping algorithm(PUA) can be challenging,and the accuracy may be low when it is used to handle fringe patterns containing complicated singularities, such as noise, shadow, shears and surface discontinuity. When weighted least-squares unwrapping approach is adopted to unwrap the phase,the weighting coefficients are designed and defined to distinguish the singularities regions and normal regions in wrapped phase patterns.The weighting coefficients corresponding to the singularities are given zero-weighted, the singularities will not affect the unwrapping.But weighted least-squares unwrapping approach has the smooth effect on the final phase map.In view of this problem, a Robust Weighted leastsquares phase-unwrapping algorithm is proposed in this paper, which is based on combining the phase correction operation and weighted least-squares(WLS) method.In our method, Two partial derivatives of the wrapped phase are obtained from the fringe patterns. The phase singularities are determined using reliability, and the weighting coefficient is obtained from the binary mask from the reliability mask generated by thresholding method. The Weighted leastsquares phase-unwrapping was solved using the preconditioned conjugate gradient (PCG) method,The result of WLS is used to estimate the fringe order directly.The spatial phase unwrapping algorithm is applied to correct the phase with residual wraps by. Experiments are conducted to prove the validity of the proposed method. Results are analyzed and compared with the other least-squares methods, The experimental results demonstrate that the performance of proposed method.

With the development of the air pollution control, the low-cost sensors are widely used in air quality monitoring, while the data quality of these sensors is always the most concern for users. In this study, data from nine air monitoring stations with standard PM instruments were used as reference and compared with the data of mobile and fixed PM sensors in Jinan, the capital city of Shandong Province, China. Data quality of PM sensors was checked by the cross-comparison among standard method, fixed and mobile sensors. And the impacts of relative humidity and size distribution (PM2.5/PM10) on the performance of PM sensors were evaluated as well. To optimize the calibration method for both fixed and mobile PM sensors, a two-step model was designed, in which the RH and PM2.5/PM10 ratio were both used as input parameters. We firstly calibrated the sensors with five independent models, and then all the calibrated data were linearly fitted by the LR-final model. In comparison with standard instruments, the LR-final model increased the R2 values of the PM2.5 and PM10 measured by fixed sensors from 0.89 and 0.79 to 0.98 and 0.97, respectively. The R2 values of PM2.5 and PM10 measured by the mobile sensors both increased to 0.99 from 0.79 and 0.62. Overall, the two-step calibration model appeared to be a promising approach to solve the poor performance of low-cost sensors.

In phase unwrapping, the locations and densities of the residues are indicative of the severity of the unwrapping problem. Gdeisat et al. proposed an algorithm to increase the number of residues in a wrapped phase map to improve the results of phase unwrapping. The method proposed, though, is extremely time-consuming involving the computation of a Fourier transform along with the selection and shift of its spectral components. Moreover, there is no theoretical analysis on the reasons why the frequency shift should be able to increase the number of residues. In an attempt to address these problems, we propose a simple algorithm to increase the number of residues in a wrapped phase map. The algorithm uses a simple multiply operation in spatial domain to realize the frequency shift exploiting the frequency shift property of Fourier transform. We also discuss the relationship between the number of residues and frequency shift. Experimental results have demonstrated that the proposed method can speed u...

Although temporal phase unwrapping method can be applied to solve some problems to measure an object with steep shapes, isolated parts or fringe undersampling in three-dimensional (3D) shape measurement, it needs to acquire and process a sequence of fringe pattern images which would take much time. Servin et al. proposed a 2-step temporal phase unwrapping algorithm, which only needs the 2 extreme phase-maps to achieve exactly the same results as standard temporal unwrapping method. But this method is only validated by computer simulation, shortage of experimental demonstration, its sensitivity coefficient G is limited, and it cannot be used when the G value is larger. We proposed an iterative two-step temporal phase-unwrapping algorithm which is an extension of Servin׳s method. First, add a fringe pattern with an intermediate sensitivity, project the fringe patterns of different sensitivity onto the tested object’s surface, and collect deformed fringe patterns with a CCD camera. Then we obtain the unwrapped phase with larger sensitivity coefficient G by cascading the sensitivity coefficients. And we derive the initial phase conditions of the 2-step temporal phase unwrapping algorithm. Finally, the experimental evaluation is conducted to prove the validity of the proposed method. The results are analyzed and compared with Servin׳s method. The experimental results show that the proposed method can achieve higher sensitivity and more accurate measurement, and it can overcome the main disadvantages encountered by Servin׳s method.

Digital holography is a powerful tool for non-contact quantitative phase imaging. Off-axis configuration remains a popular choice among the digital holography systems due to its ability to separate the dc and cross-terms in the recorded hologram in Fourier spectral space.However, compensating the off-axis tilt of the reference wave is one of the open challenges in the off-axis digital holography.Deng et al. proposed an off-axis tilt compensation method based on hologram rotation [DENG et.al. Opt. Let., 2017]. The off-axis tilt is removed by subtracting the phase of the digital reference hologram obtained by rotating the original specimen’s hologram from the retrieved phase corresponding to the original hologram. Nonetheless, Deng’s method is extremely time consuming due to the computation of Fourier transform,inverse Fourier transform and phase unwrapping for many times. In this paper, we propose a simple algorithm to compensate the off-axis tilt . Firstly, apply Fourier transform to the original off-axis hologram, filter out the first-order spectrum by band filter, then determine directly the spectrum of digital reference hologram from the spectrum of the original hologram, then filter out the first-order spectrum from the spectrum of digital reference hologram, apply inverse Fourier transform to the two first-order spectra to obtain two complex fields, then retrieve directly the phase difference from the two complex fields using the direct phase difference algorithm, then unwrap the wrapped phase map by the phase unwrapping algorithm. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with those of Deng’s method, demonstrating that our method not only can speed up by more than 50% the calculation time, but also can improve measurement accuracy.

In order to avoid frequency aliasing,improve the spatial resolution of the phase map in Fourier transform Profilometry(FTP),an approach based on the digital time-multiplexing technique is proposed to remove the background component from the deformed fringe pattern. Firstly, a sinusoidal fringe pattern is projected onto the tested object by digital-light-processing( DLP) projector, the fringe pattern modulated by the object’s surface is captured by a CCD camera.Secondly, apply Fourier transform to the captured fringe pattern to obtain the spectrum. Thirdly, rotate the specimen’s fringe pattern 90-deg to obtain the rotated fringe pattern , then obtain the new spectrum corresponding to the rotated fringe pattern.Fourthly,the new spectrum is subtracted from the original spectrum ,clip the negative going values in the resultant spectrum by digital manipulation.Fifthly, filter out the first-order spectrum from the resultant spectrum by the band filter,apply inverse Fourier transform to the selected spectrum to obtain complex fields,then retrieve the phase, unwrap the wrapped phase map by the phase unwrapping algorithm.Finally, the simulation and experimental evaluations are conducted to prove the validity and performance of the proposed method. The results are analyzed and compared with those of the conventional method.The effectiveness and superiority of the proposed method have been demonstrated and verified.

Phase unwrapping is a complex step in three-dimensional (3D) surface measurement. To simplify the computation process, Martino et al. proposed a differential algorithm. However, it will result in large error when the orthogonal fringes are not in horizontal or vertical direction. To solve this problem, the relationship between projector׳s and camera׳s coordinate systems is introduced. With the data obtained from coordinate transformation, the improved differential algorithm can be used for orthogonal fringes in any direction. Besides that, taking advantage of Fourier differentiation theorem makes operation and calculation simpler. By contrast, the results of experiments show that the proposed method is applicable to the patterns with orthogonal fringes in every direction. In addition, Fourier differentiation theorem effectively increases the speed of differential process.

An improved phase unwrapping method is proposed to reduce the projection fringes in three-dimensional (3D) surface measurement. Color fringe patterns are generated by encoding with sinusoidal fringe and stair phase fringe patterns in red and blue channels. These color fringe patterns are projected onto the tested objects and then captured by a color CCD camera. The recorded fringe patterns are separated into their RGB components. Two groups of four-step phase-shifting fringe patterns are obtained. One group of the stripes are four sinusoidal patterns, which are used to determine the wrapped phase. The other group of stripes are four sinusoidal patterns with the codeword embedded into stair phase, whose stair changes are perfectly aligned with the 2π discontinuities of sinusoidal fringe phase, which are used to determine the fringe order for the phase unwrapping. The experimental results are analyzed and compared with those of the method in Zheng and Da (2012. Opt Express 20(22):24139–24150). The results show that the proposed method needs only four fringe patterns while having less error. It can effectively reduce the number of projection fringes and improve the measuring speed.

One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et. al [H Yun, B Li, S Zhang. 2017] proposed a dual-frequency method based on the Fourier transform profilometry (FTP), yet the low frequency lobes are close to each other for accurate band-pass filtering. In light of this problem, a novel dual-frequency pattern based on the spatial-temporal fringes (STF) method is developed in this paper. Three fringe patterns with two different frequency are required. The low frequency phase is obtained from two low frequency fringe patterns by the STF method, so the signal lobes can be extracted accurately as they are far away from each other. The high frequency phase is retrieved from another fringe pattern without the impact of the DC component. Simulations and experiments are conducted to demonstrate the excellent precision of the proposed method., 24 pages,39 figures

Phase retrieval is one of the most challenging processes in many interferometry techniques. To promote the phase retrieval, Xu et. al [X. Xu, Y. Wang, Y. Xu, W. Jin. 2016] proposed a method based on dual-wavelength interferometry. However, the phase-difference brings large noise due to its low sensitivity and signal-to-noise ratio (SNR). Beside, special phase shifts are required in Xu's method. In the light of these problems, an extended depth-range dual-wavelength phase-shifting interferometry is proposed. Firstly, the least squares algorithm is utilized to retrieve the single-wavelength phase from a sequence of N-frame simultaneous phase-shifting dual-wavelength interferograms (SPSDWI) with random phase shifts. Then the phase-difference and phase-sum are calculated from the wrapped phases of single wavelength, and the iterative two-step temporal phase-unwrapping is introduced to unwrap the phase-sum, which can extend the depth-range and improve the sensitivity. Finally, the height of objects is achieved. Simulated experiments are conducted to demonstrate the superb precision and overall performance of the proposed method., 21 pages, 19 figures

OPTICA APPLICATA; 02/2017; ISSN 1429-7507

For many profilometry techniques, phase unwrapping is one of the most challenging process. In order to sidestep the phase unwrapping process, Perciante et. al [Appl Opt 2015; 54(10):3018-23] proposed a wrapping-free method based on the direct integration of the spatial derivatives of the patterns to retrieve the phase. But it is only applicable for the case of the phase continuity for the tested object, which means it may fail to handle fringe patterns containing complicated singularities, such as noise, shadow, shears and surface discontinuity. In view of this problems, a robust wrapping-free phase retrieval method is proposed in this paper, which is based on combined Perciante's method and weighted least-squares method. Two partial derivatives of the desired phase is obtained from the fringe patterns, meanwhile the carrier is eliminated using direct phase difference method. The phase singularities are determined using derivative variance correlation map (DVCM), and the weighting coefficient is obtained from the binary mask of the reverse DVCM. Simulations and experiments are conducted to prove the validity of the proposed method. Results are analyzed and compared with those of Perciante's method, demonstrating that the proposed method can be available for measuring objects with some kinds of singularities sources., Comment: 12 pages, 20 figures

An algorithm based on the principal component analysis (PCA) is proposed to measure transparent surface topography. First, many frames of random phase shifted fringe patterns are captured. Second, the first and second principal components are extracted from the phase shifted fringe patterns by PCA. Then, the phase is calculated from principal components. Finally, the correct global phase sign is determined by the clustering method considering local fringe phase monotonicity. The experimental results show that the proposed method can directly extract the three-dimensional (3D) shape, which does not need to determine the amount of phase shift, without precise phase shifter. It reduces the experimental hardware requirements and improves its adaptability in profilometry.

It is a challenge for Phase Measurement Profilometry (PMP) to measure objects with a large range of reflectivity variation across the surface. Saturated or dark pixels in the deformed fringe patterns captured by the camera will lead to phase fluctuations and errors. Jiang et al. proposed a high dynamic range real-time 3D shape measurement method without changing camera exposures. Three inverted phase-shifted fringe patterns are used to complement three regular phase-shifted fringe patterns for phase retrieval when any of the regular fringe patterns are saturated. But Jiang's method still has some drawbacks: (1) The phases in saturated pixels are respectively estimated by different formulas for different cases. It is shortage of an universal formula; (2) it cannot be extended to four-step phase-shifting algorithm because inverted fringe patterns are the repetition of regular fringe patterns; (3) only three unsaturated intensity values at every pixel of fringe patterns are chosen for phase demodulation, lying idle the other unsaturated ones. We proposed a method for enhanced high dynamic range 3D shape measurement based on generalized phase-shifting algorithm, which combines the complementary technique of inverted and regular fringe patterns with generalized phase-shifting algorithm. Firstly, two sets of complementary phase-shifted fringe patterns, namely regular and inverted fringe patterns are projected and collected. Then all unsaturated intensity values at the same camera pixel from two sets of fringe patterns are selected, and employed to retrieve the phase by generalized phase-shifting algorithm. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results are analyzed and compared with Jiang's method, which demonstrate that the proposed method not only expands the scope of Jiang's method, but also improves the measurement accuracy., Comment: 18 pages, 22 figures

The number of phase wraps in 2D wrapped phase map can be completely eliminated, or greatly reduced by frequency shifting. But the wraps usually cannot be optimally reduced using the conventional fast Fourier transform (FFT) because the spectrum can be shifted only by an integer number in the frequency domain. In order to completely eliminate the phase wraps or achieve a significant phase wrap reduction, in this paper, we propose a fast and precise two-step method for phase wraps reduction, which uses the iterative local discrete Fourier transform (DFT) to determine the sub-pixel spectral peak location and the frequency shifting algorithm that operates in spatial domain to reduce the number of phase wraps. Firstly, an initial estimate of the frequency peak is obtain by FFT, then the sub-pixel spectral peak with high resolution is determined by iteratively upsampling the local DFT around the initial spectral peak location, further the non-integer frequency shifting in spatial domain is realized to eliminate or reduce the number of phase wraps. Finally, simulations and experiments are conducted to prove the validity of the proposed method. The results demonstrate the proposed method's superb computing efficiency, high resolution and overall performance., Comment: 12 pages,27 figures

In order to get continuous and one-point-width of edge line, a method for noise-supprssion in accordance with rough extent of image is presented. After getting the edge lineby way of wavelets transform, a suit of improvements for edge line is established and adopted. Finally, a satisfied result is obtained with piece grain image segmented successfully.

In 3D projecting grating profilometry, we are often persecuted by some disgusted phenomenon of images, such as reflecting flare, overlapping of grating and other noise. All these can bring a bigger error in image processing. The intention of this paper is to propose some special filter and other methods of image processing. The technique we applied is based on peculiarity of projecting grating profilometry image, which has obvious directionality. We used the nonsymmetrical multi band-pass filters to reject the high frequency noise along the grating and other component except base frequency part. The result obtained from the processed image by multi band-pass filter is much better than that from primary image. The method is propitious to measure some smooth surfaces.

The shift step must be an accurate value in the traditional algorithm of phase-measuring profilometry technology, the result error is found in unequal step-shifting in which one or more step is not the accurate value. So the phase shifter is expensive to meet the high precision. In this paper, the software is made to give a chart of error phase in any unequal step phase-shifting, and a calibration algorithm is presented to give the correct phase based on this error-phase chart. With the help of computer emulator written by us, the calibration algorihtm based on checking proved to be correct. So the precise request of phase shifter is reduced greatly.

The surface profile is presented various, that forming cause of the specific trace is different. The specific trace is distributed as two types, from its criterion. First, the criterion of the specific trace is large, surpass a millimeter, is called grand specific trace; Second, the criterion is small, more or less the same length micron, is called micron specific trace. Using projection, contracting beam micrography, two-dimensions adusting image mode exchange, low-pass filter off noise, wavelet, and intelligent mode phase reconstruction, the surface profile of recognizing specific trace is given exactly and rapidly, that is a new optical image processing technology in recognition and diagnosis. This paper introduces the speciality above the technology and gave typical examples.

This paper described principle of some projection technologies, attached importance to some measurement technologies in engineering and measurement in complicated profile of fine-micro body. The optoelectronical system and the image processing system are supplied. The typical measurement result are obtained. It is proven that the projection technology is a composite technology, which has extensive applications in many ways.