Phase Error Compensation Method Research Articles

Generic exponential fringe model for alleviating phase error in phase measuring profilometry

Phase measuring profilometry (PMP) is susceptible to phase error caused by gamma distortion that leads to the captured fringe patterns deviating from ideal sinusoidal waveforms. Existing phase-error compensation methods are generally complex and require significant computational resources for implementation. This paper proposes a generic exponential fringe model expressed as an exponential function of the generated fringe patterns. Based on this model, a straightforward gamma correction method is presented to alleviate phase error without the need for any estimation of nonlinear coefficients or complex calibration. Experimental results demonstrate that the proposed method improves the quality of measurements by suppressing phase error.

Phase error compensation and accuracy analysis for phase measurement profilometry

A phase error compensation method is proposed for phase measurement profilometry. The gamma nonlinearity of a projector–camera pair can induce higher-order harmonics in a deformed pattern, resulting in periodic phase errors in the unwrapped phase map. To reduce the phase error caused by gamma nonlinearity, a model relating the phase error and practical wrapped phase is established, and a phase matrix for compensation is obtained based on the model instead of solving the gamma value of the projector–camera pair (γ). In addition, the compensation accuracy theoretically decreases with the ratio of the third-harmonic coefficient to the fundamental frequency components of the deformed pattern (β). The simulated measurement shows that the root-mean-square (RMS) before and after compensation is 0.0052 and 2.6840 × 10 − 4 rad when β is 0.0063, respectively, and it is 0.0755 and 0.0175 rad when β is 0.0880, respectively. The experimental results indicate that the RMS of the unwrapped phase in a uniform plane before and after compensation is 0.0639 and 0.0156 rad, respectively, when β is ∼0.09 using the proposed method. The periodic phase error caused by gamma nonlinearity decreases dramatically using the proposed method.

Full-field phase error compensation method based on relationship between unwrapped phase and phase error

ABSTRACTThe three-dimensional reconstruction in phase-measuring profilometry (PMP) usually involves the phase error caused by the gamma effect of the projector. In this study, the relationship between the unwrapped phase and the phase error of every pixel is analysed, and an effective full-field phase error compensation method based on this relationship is proposed for the reduction of every pixel error. In our optimized PMP system, the full-field phase error can be detected by directly fitting the unwrapped phase of the reference plane. In addition, the relationship between the unwrapped phase and the phase error can be established by creating a phase-error lookup table for the phase error compensation of every pixel. The experimental results demonstrate the effectiveness of the proposed method in practical PMP, and the measurement errors can be reduced by a factor of least 10.

Recent Progress on Aberration Compensation and Coherent Noise Suppression in Digital Holography

Digital holographic microscopy (DHM) is a topographic measurement technique that permits full-field, nondestructive, dynamic, quantitative amplitude, and phase-contrast imaging. The technique may realize the lateral resolution with submicron scale and the longitudinal resolution with subnanometer scale, respectively. Improving imaging quality has always been the research focus in DHM since it has a direct effect on the precise topographic measurement. In this paper, the recent progress on phase aberration compensation and coherent noise suppression is reviewed. Included in this review are the hologram spectrum’s centering judgment methods of side band in tilt phase error compensation, the physical and numerical compensation methods in phase aberration compensation, and the single-shot digital process methods in coherent noise suppression. The summaries and analyses for these approaches can contribute to improving the imaging quality and reducing the measurement error of DHM, which will further promote the wider applications of DHM in the topographic measurement fields, such as biology and micro-electro mechanical systems.

Force tracking control of an electro-hydraulic control loading system on a flight simulator using inverse model control and a damping compensator

The electro-hydraulic control loading system (EHCLS) of a flight simulator is mainly used to simulate the force feel of flying a real airplane. A double-loop model, including control and hydraulic mechanism of the EHCLS, is established and its force–displacement impedance is analysed to evaluate force tracking performances and its stability. An approximated feed-forward inverse model controller is designed using a zero phase error compensation method for expanding the frequency bandwidth of the inner loop because the identified force closed-loop model is a nonminimum phase system and its direct inverse model is unstable. Modelling error between the designed feed-forward inverse model and the actual plant is discussed and a damping compensator is presented to increase stability of the EHCLS. Theoretical analysis, simulation and experimental results show that the control methods presented are feasible and can effectively improve force feel fidelity and stability of the EHCLS.

Phase error compensation methods for high-accuracy profile measurement

In a phase-shifting algorithm-based fringe projection profilometry, the nonlinear intensity response, called the gamma effect, of the projector-camera setup is a major source of error in phase retrieval. This paper proposes two novel, accurate approaches to realize both active and passive phase error compensation based on a universal phase error model which is suitable for a arbitrary phase-shifting step. The experimental results on phase error compensation and profile measurement of standard components verified the validity and accuracy of the two proposed approaches which are robust when faced with changeable measurement conditions.

Flexible phase error compensation based on Hilbert transform in phase shifting profilometry.

This paper makes use of Hilbert transform to analyze and compensate the phase error caused by the nonlinear effect in phase shifting profilometry (PSP). The characteristics of the phase error distribution in Hilbert transform domain was analyzed and compared with spatial domain. A simple and flexible phase error compensation method was proposed to directly process the phase-shifting fringe images without any auxiliary conditions or complicated computation. Experimental results demonstrated that the phase error can be reduced by about 80% in three-step PSP, and more than 95% in four or more step PSP, which verified the effectiveness, flexibility, robustness and automation of the proposed phase error compensation method.

Real-time phase error compensation in phase sensitive scanning near-field optical microscopy.

Phase measurements are critical for investigations on the optical properties of surface plasmon polariton (SPP) nanostructures. In this paper, a real-time phase error compensation method based on a phase sensitive scanning near-field optical microscopy (SNOM) measurement system is proposed. The method adopts the common optical path configuration and CMR (common-mode rejection) principle. It can be seen that the phase error compensation is real-time and mainly relies on optical devices, therefore neither post processing nor previous knowledge of environmental effects is required. The causes of the phase drift errors are discussed. We demonstrate experimentally the effectiveness of this method by measuring a SPP focusing device. Regardless of the drift velocity, degree of linearity, or phase accuracy, the compensation method shows great improvement compared to the previous phase sensitive SNOMs. All the measured distributions are in good agreement with theoretical simulations obtained by the finite-different time-domain (FDTD) method.

Full-field phase error detection and compensation method for digital phase-shifting fringe projection profilometry

Digital fringe projection profilometry is one of the most widely utilized non-contact three-dimensional (3D) profile measurement techniques. The phase error caused by nonlinear gamma of digital projectors and cameras eventually reduces the 3D measurement accuracy. This kind of phase error still cannot be detected directly at present. A novel method is present in this paper not only to measure the phase error straightforwardly but also to extract the full-field error distributions. With the aid of the detected phase error distributions, the full-field look-up tables (LUTs) can be obtained to correct the phase measurement result. A set of experiments to validate our methods has been performed. Experimental results well prove that the full-field phase error distributions have been detected successfully, and after utilizing our phase correction method the phase accuracy is obviously improved.

A novel three-dimensional shape measurement method based on a look-up table

Fringe projection profilometry is widely used for three-dimensional shape measurement. In an oblique-angle projection, the fringe cycle is broadened on the reference plane. Phase errors are mainly caused by the nonlinear gamma of the projector and fringe cycle broadening. This study describes a phase error compensation method to eliminate these phase errors. A look-up table that stores phase errors is constructed for phase error compensation. Based on it, a new height equation is proposed. The experimental results show that the proposed method can compensate for the phase errors of the fringe projection profilometry, thereby improving the measurement accuracy significantly.

Phase error analysis and compensation considering ambient light for phase measuring profilometry

The accuracy of phase measuring profilometry (PMP) system based on phase-shifting method is susceptible to gamma non-linearity of the projector–camera pair and uncertain ambient light inevitably. Although many researches on gamma model and phase error compensation methods have been implemented, the effect of ambient light is not explicit all along. In this paper, we perform theoretical analysis and experiments of phase error compensation taking account of both gamma non-linearity and uncertain ambient light. First of all, a mathematical phase error model is proposed to illustrate the reason of phase error generation in detail. We propose that the phase error is related not only to the gamma non-linearity of the projector–camera pair, but also to the ratio of intensity modulation to average intensity in the fringe patterns captured by the camera which is affected by the ambient light. Subsequently, an accurate phase error compensation algorithm is proposed based on the mathematical model, where the relationship between phase error and ambient light is illustrated. Experimental results with four-step phase-shifting PMP system show that the proposed algorithm can alleviate the phase error effectively even though the ambient light is considered.

FFT를 이용한 주파수 영역의 RVDT 센서 오차 보상

본 논문에서는 FFT 영역을 이용한 새로운 RVDT 인코더의 위상 오차 보상 방법을 제시하였다. 최소 개수의 보상 저항의 조합으로 오차를 측정하고 FFT 변환 후 1차 하모닉 성분의 저항에 따른 계수의 변화를 구하였다. 또한 삽입 저항과 계수의 크기가 반비례 관계에 있음을 알아냈다. 이 방법은 기존의 시간 영역에서의 보상에 비해 테이블을 구하는데 드는 시간이 단축되고 테이블의 크기를 획기적으로 줄일 수 있었다. 또한 축변환을 통해 보상 저항의 위치도 정확히 찾을 수 있었으며 첨두간 위상 오차값을 0.57도 정도로 2배 가까이 개선하였다. This paper proposes new phase error compensation method of RVDT encoder in the FFT domain. Phase errors are measured with a small combination of compensation resistors and the changes of first order coefficients of FFT for each resistor are obtained. It is found that the coefficient change is inversely proportional to the inserted resistor. The proposed method takes less time and the size of the table is smaller than previous time domain approaches. In addition, the location of the compensation resistor can be found through axis transformation of the coefficients. Finally, the peak-to-peak phase error was improved to 0.57 which is two times better than previous one.

Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry

In fast phase-measuring profilometry, phase error caused by gamma distortion is the dominant error source. Previous phase-error compensation or gamma correction methods require the projector to be focused for best performance. However, in practice, as digital projectors are built with large apertures, they cannot project ideal focused fringe images. In this Letter, a thorough theoretical model of the gamma-distorted fringe image is derived from an optical perspective, and a highly accurate and easy to implement gamma correction method is presented to reduce the obstinate phase error. With the proposed method, high measuring accuracy can be achieved with the conventional three-step phase-shifting algorithm. The validity of the technique is verified by experiments.

Phase error compensation method using smoothing spline approximation for a three-dimensional shape measurement system based on gray-code and phase-shift light projection

A novel phase error compensation method is presented for the reduction of phase error and shape waviness for a three-dimensional shape measurement system based on gray-code and phase-shift light projection. The phase error is mainly caused by the nonsinusoidality of projected phase-shift patterns. According to the system's phase-distribution properties, the proposed method adopts smoothing spline approximation to precisely extract the specific system phase error from the reference phase. This specific system phase error can be used to compensate the object phase during measures. The experimental results show that this compensation can reduce the shape waviness by 70%. In addition the residual object phase error is reduced by a smoothing procedure based on smoothing spline approximation. This procedure shows a 65% reduction in the residual shape waviness.

레졸버 기반의 절대위치 검출 센서 드라이버의 FPGA 구현

Absolute position detector which is one of the major equipment in the field of factory automation, not only perceives the absolute position of the rotary machine but also outputs switch data according to the given angle. Absolute position detector is composed of sensor module and its controller. In this paper, a sensor driver is implemented using FPGA with VHDL. This chip has a less form factor than conventional circuit. A test shows reliable precision within THD(total harmonic distortion) of 0.2% which can be applicable commercially. Also, FPGA-based phase error compensation methods were newly discussed. In the future, more research will be conducted to enhance the precision by the introduction of 3-phase transformer.

Phase error compensation for a 3-D shape measurement system based on the phase-shifting method

This paper describes a novel phase error compensation method for reducing the measurement error caused by nonsinusoidal waveforms in phase-shifting methods. For 3-D shape measurement systems using commercial video projectors, the nonsinusoidal waveform of the projected fringe patterns as a result of the nonlinear gamma of projectors causes significant phase measurement error and therefore shape measurement error. The proposed phase error compensation method is based on our finding that the phase error due to the nonsinusoidal waveform depends only on the nonlinearity of the projector's gamma. Therefore, if the projector's gamma is calibrated and the phase error due to the nonlinearity of the gamma is calculated, a lookup table that stores the phase error can be constructed for error compensation. Our experimental results demonstrate that by using the proposed method, the measurement error can be reduced by 10 times. In addition to phase error compensation, a similar method is also proposed to correct the nonsinusoidality of the fringe patterns for the purpose of generating a more accurate flat image of the object for texture mapping. While not relevant to applications in metrology, texture mapping is important for applications in computer vision and computer graphics.

An accurate three-dimensional scanning system with a new phase error compensation method

An accurate three-dimensional scanning system based on fringe projection and active triangulation is presented. The structured light projection is implemented by using a special grating element fabricated by electron beam lithography which ensures the phase-shifting accuracy and continuous intensity. The phase error caused by non-sinusoidal phase-shifting patterns is reduced significantly by a new compensation method, and an average 62.5% improvement of the vibration error is revealed. The experimental results indicate that the measurement error of the system is lower than 0.04 mm, with a variability of about 0.03 mm. The registration of multi-view test results indicates registration standard deviation can be lower than 0.1 mm. The system promises a favourable future for industrial application, especially in reverse engineering of free form surfaces.