Sinusoidal Fringe Patterns Research Articles

一种改进的消零频三维面形测量方法

为了提高傅里叶变换轮廓术的测量精度，降低频谱混叠对傅里叶变换轮廓测定术的影响，提出了一种便捷的抑制零频分量的方法。通过采集一幅正弦条纹图，在投影仪前方添加一固定厚度的平行平板，利用折射得到新的条纹图，将采集的两幅变形条纹图进行处理得到消零频的条纹差图。对条纹差图进行适当的快速傅里叶变换以后，对频谱进行滤波并提取基频成分。相比于安装精密相移装置，测量系统更加简单，高速。理论和实验证明了本方法的可行性。 In order to improve the accuracy of Fourier transform profilometry and reduce the influence of frequency aliasing. A convenient method to suppress the zero frequency components is proposed. By collecting a sinusoidal fringe pattern and adding a fixed thickness parallel plate to the front of the projector, a new fringe pattern is obtained by refraction. The two deformed fringe patterns are processed to get the stripe pattern of zero frequency elimination. After the proper fast Fourier transform of the fringe pattern, the spectrum is filtered and the fundamental frequency components are extracted. The measurement system is simple and high-speed compared to the installation of precision phase shifting devices. The feasibility of this method is proved by theory and experiment.

An improved error-diffusion algorithm for projector defocusing profilometry

To improve the sinusoidal feature of binarized sinusoidal fringe pattern, a new error-diffusion method based on Floyd-Steinberg error-diffusion dithering algorithm in traditional halftoning is proposed. Firstly, the error-diffusion kernel is expanded to reduce quantization error of the binarized sinusoidal fringe pattern and restrain the unsymmetrical texture. And then the error-diffusion coefficients are distributed linearly to smooth the fringe pattern and enhance the dispersion. The simulations and experiments indicate that, the proposed method smoothes the fringe pattern and reduces the phase error of 3D measurement compared with traditional Floyd-Steinberg dithering algorithm.

Accurate and fast 3D surface measurement with temporal-spatial binary encoding structured illumination.

Balancing the accuracy and speed for 3D surface measurement of object is crucial in many important applications. Binary encoding pattern utilizing the high-speed image switching rate of digital mirror device (DMD)-based projector could be used as the candidate for fast even high-speed 3D measurement, but current most schemes only enable the measurement speed, which limit their application scopes. In this paper, we present a binary encoding method and develop an experimental system aiming to solve such a situation. Our approach encodes one computer-generated standard 8 bit sinusoidal fringe pattern into multiple binary patterns (sequence) with designed temporal-spatial binary encoding tactics. The binary pattern sequence is then high-speed and in-focus projected onto the surface of tested object, and then captured by means of temporal-integration imaging to form one sinusoidal fringe image. Further the combination of phase-shifting technique and temporal phase unwrapping algorithm leads to fast and accurate 3D measurement. The systematic accuracy better than 0.08mm is achievable. The measurement results with mask and palm are given to confirm the feasibility.

Multi-subzone algorithm for absolute phase retrieval in digital fringe projection profilometry.

Codewords are important in encoded absolute phase retrieval techniques such as two-frequency, gray-code, and phase-coding. Each sinusoidal fringe is marked by a unique codeword so that an absolute fringe order can be determined by decoding the codeword. However, due to the limited number of unique codewords, sinusoidal fringe patterns do not contain high-frequency fringes without the use of additional patterns. A multi-subzone coding and decoding algorithm is thus proposed to overcome this limitation. Three multi-subzone coding methods based on two-frequency, gray-code, and phase-coding techniques are presented. The coding creates multiple subzones of unique codewords and the decoding enables it to use non-unique codewords to identify absolute fringe order. Specifically, the range of fringe order is estimated by the use of a wrapped phase map and the absolute fringe order is identified by a codeword. Experimental studies demonstrate the advantages of the proposed algorithm over existing coding methods. The proposed algorithm is suitable to measure objects with large step-height surface discontinuities.

Three-dimensional profilometry with mixed binary defocusing technique

The existing binary defocusing techniques have excellent performance in the measurement speed, while the measurement precision is not high. We propose a mixed binary defocusing method, which combines the respective advantage of one-dimensional modulation defocusing techniques and two-dimensional modulation defocusing techniques. The mixed binary defocusing method adopts the frequency-dependent property of these two kinds of methods to approach the sinusoidal fringe patterns. The optimized pulse width modulation technique is selected to produce high-frequency binary patterns, and the improved error diffusion dithering technique is selected to generate low-frequency patterns. Then the phase-shifting method is adopted to obtain the wrapped phase from the defocused pattern, and the absolute phase is obtained with a multiple-wavelength phase unwrapping method from these wrapped phases at different frequencies. With the standard of the root mean square error of the wrapped phase, different defocusing methods are compared in the simulation. The measurement surfaces are compared in the real object measurement. The results verify the frequency-dependent property of these two kinds of methods and the proposed method has a greater performance than any one binary defocusing technique.

Removing harmonic distortion of measurements of a defocusing three-step phase-shifting digital fringe projection system

Binary defocusing method was adopted in 3D profilometry as it allows real-time measurement and does not need to handle the luminance nonlinearity of a projector. Current patch-based binary fringe patterns are periodic and carry strong harmonic distortion as compared with the ideal sinusoidal fringe patterns, which affects the measuring performance remarkably. In this paper, we propose a framework for generating aperiodic fringe patterns based on optimized patches. The produced fringe patterns can significantly lower the noise floor and suppress the harmonic distortion in the constructed phase map. Accordingly, the achieved depth measuring performance can be significantly improved. Special care is also taken during the optimization of the patches in our framework such that the depth measuring performance is robust to fringe period and defocusing extent.

Improved least-squares method for phase-to-height relationship in fringe projection profilometry

The height estimating function is very important for three-dimensional (3-D) measurement systems based on a digital light processing (DLP) projector and a camera. Sinusoidal fringe patterns of the projector are projected onto an object, and the phase of the measuring point is calculated from the camera image. Generally, the least-squares method (LSM) and look-up table(LUT) method are typically used to obtain the phase-to-height relationship. The merit of LSM is that one equation is obtained from geometric analysis, but it has difficulty incorporating lens distortion. The LUT method can obtain an exact model that includes lens distortion, but the amount of memory needed increases with the number of pixels because each model is obtained at each pixel. This paper compares for these two methods and proposes an improved LSM using LUT. The proposed method has one equation like the case of LSM, but the modeling result is better than LSM because lens distortion is fully considered.

Time-encoded structured illumination microscopy: toward ultrafast superresolution imaging.

An imaging strategy based on optical time-encoded structured illumination microscopy (TE-SIM) opens the way toward ultrafast superresolution imaging. A proof-of-principle experiment is conducted and the introduced TE-SIM accelerates the generation rate of sinusoidal fringe patterns to an unprecedented speed (dozens of megahertz). At such a high speed, superresolution imaging that surpasses the diffraction limit by a factor of 1.4 is demonstrated. This imaging strategy with high temporal and spatial resolution has great potential in many exciting applications, such as dynamic live cell imaging or high-throughput screening.

Absolute phase recovery in structured light illumination systems: Sinusoidal vs. intensity discrete patterns

Structured light illumination is a well-established technology for noncontact 3D surface measurements. A common challenge in those systems is to obtain the absolute surface information using few measurement frames. This work discusses techniques based on the projection of multiple sinusoidal fringe patterns with different fringe period, as well as the projection of intensity discrete Gray Code and grey-level coded patterns. The use of sinusoidal multi-frequency techniques has been since years an on-going area of research, where various algorithms have been developed based on beats, look-up tables, or number-theoretical approaches. This work shows that a related technique, the so-called algebraic reconstruction technique that is borrowed from the area of multi-wavelength interferometry can be used for this purpose. This approach provides a robust analytical solution to the phase-unwrapping problem. However, this work argues that despite these advances, the acquisition of additional phase maps obtained with different fringe periods requires too many measurement frames, and hence is inefficient. Motivated by that, this work proposes a new grey level coding scheme that uses only few measurement frames, overcomes typical defocus errors, and has an error detecting feature. The latter feature makes the need of separate error detecting algorithms obsolete. This so-called closed-loop space filling curve can be implemented with an arbitrary number of N grey-levels enabling to code up to (2N) code-words. The performance of this so-called closed-loop space filling curve is demonstrated using experimental data.

High-speed three-dimensional shape measurement using GOBO projection

A projector which uses a rotating slide structure to project aperiodic sinusoidal fringe patterns at high frame rates and with high radiant flux is introduced. It is used in an optical three-dimensional (3D) sensor based on coded-light projection, thus allowing the analysis of fast processes. Measurements of an inflating airbag, a rope skipper, and a soccer ball kick at a 3D frame rate of more than 1300 independent point clouds per second are presented.

Piston and tilt interferometry for segmented wavefront sensing.

We present a novel interferometric technique dedicated to the measurement of relative phase differences (pistons) and tilts of a periodically segmented wavefront. Potential applications include co-phasing of segmented mirrors of Keck-like telescopes as well as coherent laser beam combining. The setup only requires a holes mask selecting the center part of each element, a diffracting component, and a camera. Recorded interferogram is made of many subareas with sinusoidal fringe pattern. From each pattern, piston is extracted from fringe shift and tilts from fringe frequency and orientation. The pattern analysis is simple enough to enable kilohertz rate operation. The λ ambiguities are solved by a two-wavelength measurement. This technique is compatible with a very high number of elements and can be operated in the presence of atmospheric turbulence.

A real-time, full-field, and low-cost velocity sensing approach for linear motion using fringe projection techniques

A velocity sensing approach using the fringe projection technique is presented. The moving object is projected with a sinusoidal fringe pattern. A CCD camera located at a different view angle observes the projected fringes on the dynamic object. The long exposure time of the CCD camera makes the fringes blurred by linear motion. The blurred fringes provide additional information to describe the depth displacement, and therefore the velocity vector can be identified. There is no need to take multiple-shot measurements to address the change in 3D positions at a sequence of time. Only one-shot measurement is required. Consequently, there is no need to perform image registration. The full-field approach also makes it possible to simultaneously inspect several objects.

Measuring the 3D shape of high temperature objects using blue sinusoidal structured light

The visible light radiated by some high temperature objects (less than 1200 °C) almost lies in the red and infrared waves. It will interfere with structured light projected on a forging surface if phase measurement profilometry (PMP) is used to measure the shapes of objects. In order to obtain a clear deformed pattern image, a 3D measurement method based on blue sinusoidal structured light is proposed in this present work. Moreover, a method for filtering deformed pattern images is presented for correction of the unwrapping phase. Blue sinusoidal phase-shifting fringe pattern images are projected on the surface by a digital light processing (DLP) projector, and then the deformed patterns are captured by a 3-CCD camera. The deformed pattern images are separated into R, G and B color components by the software. The B color images filtered by a low-pass filter are used to calculate the fringe order. Consequently, the 3D shape of a high temperature object is obtained by the unwrapping phase and the calibration parameter matrixes of the DLP projector and 3-CCD camera. The experimental results show that the unwrapping phase is completely corrected with the filtering method by removing the high frequency noise from the first harmonic of the B color images. The measurement system can complete the measurement in a few seconds with a relative error of less than 1 : 1000.

An improved two-step phase-shifting profilometry

An improved two-step phase-shifting profilometry is put forward in three-dimensional (3D) shape measurement. Firstly, two phase-shifted randomly sinusoidal fringe patterns are projected onto the tested object by digital-light-processing (DLP) projector. The fringe patterns modulated with the object's surface are captured by a CCD camera. Secondly, the background and modulation components are obtained by parameter estimation using the least square method; fringe normalization is accomplished by the background bias removal and modulation normalization of a given deformed fringe. Then based on the statics characteristics of fringe gray, the phase step between two phase-shifted randomly sinusoidal fringe patterns is determined by using the inverse cosine function. Then, the phase is extracted from the two frame's normalized patterns and the step value. Finally, the experimental evaluation is conducted to prove the validity and performance of the proposed method. The experimental result is analyzed and compared with that of the method by reference 16. The effectiveness and superiority of the proposed method has been demonstrated.

Composited color-coded sinusoidal fringe pattern for absolute phase measurement

A novel color-coded sinusoidal fringe pattern for absolute phase measurement is proposed in this letter. We used composited color sinusoidal fringe to calculate the wrapped phases and fringe orders without other assistant gratings. A novel algorithm was used to map wrapped phase to absolute phase. Three different colors were employed to mark to fringe orders, and then 27 fringes could be encoded by 4-bits codeword in three gratings with a phase shift of 2π/3. Gray values of the color-coded sinusoidal fringe are employed to calculate the wrapped phases by phase shift method, and then we used wrapped phases to obtain the lowest bit of codewords. Color information were used to decide three high bits of codewords. With codewords of 4 bits, the fringe orders can be found from a lookup table, and then the wrapped phased could be mapped to absolute phase. Moreover, shortcomings of channels coupling in color grating measurement are also circumvented. The experimental results showed the validity of our algorithm.

Iterative optimization calibration method for stereo deflectometry.

An accurate system calibration method is presented in this paper to calibrate stereo deflectometry. A corresponding iterative optimization algorithm is also proposed to improve the system calibration accuracy. This merges CCD parameters and geometrical relation between CCDs and the LCD into one cost function. In this calibration technique, an optical flat acts as a reference mirror and simultaneously reflect sinusoidal fringe patterns into the two CCDs. The normal vector of the reference mirror is used as an intermediate variable to implement this iterative optimization algorithm until the root mean square of the reprojection errors converge to a minimum. The experiment demonstrates that this method can optimize all the calibration parameters and can effectively reduce reprojection error, which correspondingly improves the final reconstruction accuracy.

Filter Dependence on the Phase Error of Fourier Transform Profilometry

In phase measuring fringe reflection Fourier transform profilometry, it gets the captured image data from the projected sinusoidal fringe patterns by using the CCD cameras. Added white noise in captured fringe images and its low contrast levels affect the accuracy of three-dimensional surface profile measurements induced the phase errors. In this work, we present a phase error reduction method using the low pass spatial image filter and median filter. Experimental results have shown to validate the low pass filter and median filter. Although the effect of the filter is to be smoothed the fringe, white noise included in the pattern was able to remove effectively. In case of the median filter, it showed negative influence to the phase error, but the low-pass filter evidently reduced the phase error about 30%.

Pixel-to-pixel correspondence alignment method of a 2CCD camera by using absolute phase map

An alignment method of a 2CCD camera to build pixel-to-pixel correspondence between the infrared (IR) CCD sensor and the visible CCD sensor by using the absolute phase data is presented. Vertical and horizontal sinusoidal fringe patterns are generated by software and displayed on a liquid crystal display screen. The displayed fringe patterns are captured simultaneously by the IR sensor and the visible sensor of the 2CCD camera. The absolute phase values of each pixel at IR and visible channels are calculated from the captured fringe pattern images by using Fourier transform and the optimum three-fringe number selection method. The accurate pixel corresponding relationship between the two sensors can be determined along the vertical and the horizontal directions by comparing the obtained absolute phase data in IR and visible channels. Experimental results show the high accuracy, effectiveness, and validity of the proposed 2CCD alignment method. By using the continuous absolute phase information, this method can determine the pixel-to-pixel correspondence with high resolution.

Temporal-spatial encoding binary fringes toward three-dimensional shape measurement without projector nonlinearity

Projector nonlinearity is a common problem for digital structured light-based three-dimensional (3-D) shape measurement techniques. A temporal-spatial binary encoding method is presented for the purpose of eluding it. We build a 3-D shape measurement scheme by combining our proposed method with phase measurement profiling. A standard sinusoidal fringe pattern is divided into more than two binary fringe patterns using specially designed temporal and spatial binary encoding rule based on intensity hierarchic quantification, and then are in-focus projected onto the measured object at a time sequence to reconstruct a frame phase-shifting fringe image. On account of the projected binary fringe pattern strictly consisting of zeros and ones, the influence of the projector nonlinearity on the measurement result can be effectively ruled out and simultaneously enables high-quality sinusoidality. In-depth investigations by theoretical analysis and experiments are conducted to demonstrate the performance of this method.

Comparative study on passive and active projector nonlinear gamma calibration

This paper compares the active and passive projector nonlinear gamma compensation methods for phase error reduction. The active method modifies fringe patterns before their projection to ensure sinusoidality; the passive method, in contrast, compensates for the phase error after capturing those distorted sinusoidal fringe patterns. Our study finds that the active method tends to provide more consistent high-quality fringe patterns regardless of the amount of projectors defocusing; yet the effectiveness of the passive method is diminished if the measurement condition deviates from the calibration condition. Experimental results will be presented to demonstrate the differences between these two nonlinear gamma compensation methods.