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Uncertainty evaluation of fringe projection based on linear systems theory
Abstract
Fringe projection techniques offer fast, non-contact measurements of the surface form of manufactured parts. Fringe projection has seen successful implementation in the automotive, aerospace and medical industries. Recently, advances in fringe projection have reduced the sensitivity of the measurement system to effects such as multiple surface reflections and projector defocus. Typically, the measurement method is altered to optimise the system for specific measurement conditions, without any regard for quantifying the effects of influence factors. Furthermore, there is no standardised calibration framework for fringe projection systems and uncertainty evaluation of surface measurements is rarely carried out in practice, which places some restrictions on the use of this technique in manufacturing industry. Fringe projection systems detect the intensity of a projected fringe pattern that is reflected from the surface to be measured. Any process that alters the intensity of this pattern received by the camera will change the measurement outcome. Therefore, fringe projection systems typically have many influence factors that affect the measurement outcome, including the surface characteristics (e.g. optical properties and topography), imaging optics (e.g. defocus and aberrations) and external factors (e.g. ambient light intensity level, mechanical vibration and temperature). The complexity of the measurement model makes current calibration methods given in ISO 15530 (for contact coordinate measuring machines) unsuitable for fringe projection. Additionally, it is unclear how to apply the calibration method in ISO 25178 for areal surface topography measuring instruments. A calibration framework for estimating spatial frequency dependent measurement uncertainty built on solid theoretical foundations is required. To move towards a traceable surface measurement using fringe projection techniques, we are developing a measurement model to accurately predict the captured image and include all major uncertainty contributors. The first step of the model is to describe the optical field distribution within the projection volume of the projector by considering its point spread function in three dimensions. The optical field distribution is sampled at surface locations, using a ray tracing algorithm to map intensity values to corresponding camera pixels. The results are validated by comparing to an experimental fringe projection system with carefully controlled parameters. The intention is to use this simulation within a Monte-Carlo framework to create an uncertainty map of the phase image that can be used to estimate the uncertainty at each point-cloud data point. Additionally, the model will give insights into the relationships between influence factors, allowing the implementation of improvements to fringe projection systems.
... For this reason, ISO Technical Committee 213 working group 10 have developed a number of strategies for uncertainty estimation, at least for contact CMS [13]. Strategies for non-contact CMSs remain an open research area, although there has been some recent work highlighting the issues [5,[14][15][16][17]. ...
... It is relatively simple to understand and model the physical interaction of a contact probe tip with a surface, but it not so simple to model the equivalent optical interaction, and this is a significant part of the uncertainty problem [24]. There has been some recent activity on modelling optical systems with virtual instruments in mind [16,17,25], but there is still a lot to do and the issues are not yet under development in ISO Technical Committee 213 Working Group 10. Most current technologies for the inspection and verification of form are centred around the measurement and manipulation of point cloud surface data. ...
In this work an approach to investigate measurement uncertainty in coordinate metrology is presented, based on fitting Gaussian random fields to high-density point clouds produced by measurement repeats. The fitted field delivers a depiction of the spatial distribution of random measurement error over a part geometry, and can incorporate local bias information through further measurement or with the use of an external model to obtain a complete, spatial uncertainty map. The statistical model also allows the application of Monte Carlo simulation to investigate how error propagates through the data processing pipeline ultimately affecting the determination of features of size and the verification of conformance to specifications. The proposed approach is validated through application to simulated test cases involving known measurement error, and then applied to a real part, measured with optical and contact technologies. The results indicate the usefulness of the approach to estimate measurement uncertainty and to investigate performance and behaviour of measurement solutions applied to the inspection and verification of industrial parts. The approach paves the way for the implementation of automated measurement systems capable of self-assessment of measurement performance.
... See Fig. 1 Researchers have reported some preliminary work implementing FPP for LPBF process monitoring, but without fully considering the unique LPBF process characteristics (e.g., surface reflectance and build location effect) or with limited measurement performance [17,18]. Moreover, few literature studies specifically focused on FPP measurement's uncertainty analysis for LPBF [19][20][21]. As shown in Table 1, the state of art work by Zhang et al. [22] and Liu et al. [23] have implemented a FPP system in LPBF for metal AM, which, however, could not attain a desired combination of wide field of view, high vertical resolution, and height measurement range. ...
Fringe Projection Profilometry (FPP) is a cost-effective and non-invasive technology that has been shown to measure finer features. In this work, we developed an in-situ FPP method to measure the dynamic topography of powder bed and printed layer during Laser Powder Bed Fusion (LPBF) additive manufacturing (AM) process. A systematic study towards developing a comprehensive framework of LPBF-specific FPP is demonstrated to enhance and evaluate the performance of applying FPP for in-situ LPBF monitoring, including 1) a modified sensor model with localized correction; 2) improved phase unwrapping with FFT filtering 3) quantitative uncertainty analysis; and 4) experimental validation with ex-situ characterization. The developed LPBF-specific FPP system and methods are implemented on a commercial LPBF-AM machine, achieving better accuracy, more robustness, and increased field of view while maintaining sufficient measurement range and decent resolution, in contrast to literature methods. The established FPP framework will facilitate the development of closed-loop control strategies for advancing LPBF based AM.
Large-scale surfaces are prevalent in advanced manufacturing industries, and 3D profilometry of these surfaces plays a pivotal role for quality control. This paper proposes a novel and flexible large-scale 3D scanning system assembled by combining a robot, a binocular structured light scanner and a laser tracker. The measurement principle and system construction of the integrated system are introduced. A mathematical model is established for the global data fusion. Subsequently, a robust method is introduced for the establishment of the end coordinate system. As for hand-eye calibration, the calibration ball is observed by the scanner and the laser tracker simultaneously. With this data, the hand-eye relationship is solved, and then an algorithm is built to get the transformation matrix between the end coordinate system and the world coordinate system. A validation experiment is designed to verify the proposed algorithms. Firstly, a hand-eye calibration experiment is implemented and the computation of the transformation matrix is done. Then a car body rear is measured 22 times in order to verify the global data fusion algorithm. The 3D shape of the rear is reconstructed successfully. To evaluate the precision of the proposed method, a metric tool is built and the results are presented.
This article examines the influence of incident angle, object colour and measurement distance on the computer numerically
controlled laser scanning process. To determine the physical background of these influences, the operation of the triangulation
sensor, the surface reflection and the colour properties of the measured object were analysed. The various influences and
their physical background are explained by using a test-measurement setup, which makes it possible to investigate a specific
influencing factor. The article concludes with several guidelines that should be followed in order to obtain better measurement
results.
KeywordsLaser scanner-Accuracy-3D scanning-Surface acquisition-Point cloud-Reverse engineering
High-speed 3D shape measurement (or imaging) has seen tremendous growths over the past decades, especially the past few years due to the improved speed of computing devices and reduced costs of hardware components. 3D shape measurement technologies have started penetrating more into our daily lives than ever before with the recent release of iPhone X that has an built-in 3D sensor for Face ID, along with prior commercial success of inexpensive commercial sensors (e.g., Microsoft Kinect). This paper overviews the primary state-of-the-art 3D shape measurement techniques based on structured light methods, especially those that could achieve high measurement speed and accuracy. The fundamental principles behind those technologies will be elucidated, experimental results will be presented to demonstrate capabilities and/or limitations for those popular techniques, and finally present our perspectives on those remaining challenges to be conquered to make advanced 3D shape measurement techniques ubiquitous.
Anti-spoof touchless imaging of human ear has strong potential to be a useful alternative to traditional biometric sensors. The features in a human ear are more reliable than other physical traits like fingerprint, face, palm print, etc. In this paper, we propose an efficient ear pattern sensor by introducing a new imaging technique that is capable of simultaneous retrieval of the topographic details as well as its liveliness information. In the proposed technique, a collimated laser beam is made incident on a sinusoidal grating, and the resultant structured pattern is projected towards the ear specimen. For detection of topographic information and liveliness, time series bio-speckled fringe sequences are recorded using a CCD camera. For noise removal and shape reconstruction from the acquired information, a combination of windowed Fourier filtering and low pass filtering is used. Discrete cosine transform based fast biospeckle algorithm is introduced for assessment of genuineness (i.e. to create distinction between real and fake samples) of the specimen. The proposed sensor is simple, compact, full-field and robust against different spoof attacks.
Blade with complex and thin-walled shape is one of the critical parts in an aircraft engine, and its whole 3D shape should be measured to ensure the efficiency and safety of the engines. But there hardly exist an omnipotent blade 3D measurement method that can simultaneously address accuracy, efficiency and ability of measuring high-reflective surface. To this end, a hybrid 3D metrology method integrated by fringe projection profilomety (FPP) and conoscopic holography (CH) is developed, and FPP is responsible for gaining measurement accuracy and efficiency, while CH scans the high-reflective areas that FPP fails to measure. In this integrated system, the key task involved is calibration of rigid transformation between coordinate systems of inhomogeneous 3D sensors, so an accurate calibration method is proposed. It only requires FPP sensor and CH sensor to measure a planar target at several different poses in the measurement volume, and then the measured space planes can be used to compute rigid transformation. In order to enhance its robustness to noise, a non-linear optimization model that considers signal-to-noise ratio (SNR) of CH sensor is establish for obtaining the optimal calibration results. The simulations and real experiments demonstrate that proposed method can achieve accurate and robust calibration of inhomogeneous 3D sensors for measuring the blade.
We investigate the feasibility of using fringe projection to monitor the powder bed of a polyamide 12 polymer laser sintering machine. In particular, we demonstrate the ability of fringe projection to identify a number of defects arising during the printing process by recording the three-dimensional structure of the sintered powder bed after the completion of each layer. The defects identified ranged in size from hundreds of micrometres to hundreds of millimetres. The three-dimensional analysis of the powder bed data has shown the ability to quantify effects, such as curling, powder spreader blade interactions and the consolidation of a sintered layer. It has, therefore, been shown that the use of fringe projection in polymer laser sintering machines can provide deeper understanding and monitoring of the dynamic behaviour during the process. Fringe projection has shown potential to become part of a feedback and control system that interrupts the build and corrects for in-process defects where possible.
When fringe projection profilometry is used for measuring texture on rough surfaces, the measurement resolution is subject to the spatial frequency response of the instrument. The instrument transfer function (ITF) is a good metric to quantify this property. A valid ITF analysis requires the system to be linear. In this paper, we investigate the validity of using ITF to characterize the spatial resolution of a fringe projection system. Approximate linearity is shown through a mathematical analysis and simulation. We also demonstrate a practical method for measuring ITF using a stepped surface. The measured ITF is compared with an ITF prediction, which is simulated with a theoretical model.
A new fibre optic Lloyd’s mirror method is developed for extracting 3-D height distribution of various objects at the micron scale with a resolution of 4 µm. The fibre optic assembly is elegantly integrated to an optical microscope and a CCD camera. It is demonstrated that the proposed technique is quite suitable and practical to produce an interference pattern with an adjustable frequency. By increasing the distance between the fibre and the mirror with a micrometre stage in the Lloyd’s mirror assembly, the separation between the two bright fringes is lowered down to the micron scale without using any additional elements as part of the optical projection unit. A fibre optic cable, whose polymer jacket is partially stripped, and a microfluidic channel are used as test objects to extract their surface topographies. Point by point sensitivity of the method is found to be around 8 µm, changing a couple of microns depending on the fringe frequency and the measured height. A straightforward calibration procedure for the phase to height conversion is also introduced by making use of the vertical moving stage of the optical microscope. The phase analysis of the acquired image is carried out by One Dimensional Continuous Wavelet Transform for which the chosen wavelet is the Morlet wavelet and the carrier removal of the projected fringe patterns is achieved by reference subtraction. Furthermore, flexible multi-frequency property of the proposed method allows measuring discontinuous heights where there are phase ambiguities like 2π by lowering the fringe frequency and eliminating the phase ambiguity.
Coherence scanning interferometry (CSI) offers three dimensional (3D) measurement of surface topography with high precision and accuracy. Defocus within the interferometric objective lens, however, is commonly present in CSI measurements, and reduces both the resolving power of the imaging system and the ability to measure tilted surfaces. This paper extends the linear theory of CSI to consider the effects of defocus on the 3D transfer function and the point spread function in an otherwise ideal CSI instrument. The results are compared with measurements of these functions in a real instrument. This work provides further evidence for the validity of the linear systems theory of CSI.
Fringe projection profilometry has been widely applied in many fields. To set up an ideal measuring system, a virtual fringe projection technique has been studied to assist in the design of hardware configurations. However, existing virtual fringe projection systems use parallel illumination and have a fixed optical framework. This paper presents a virtual fringe projection system with nonparallel illumination. Using an iterative method to calculate intersection points between rays and reference planes or object surfaces, the proposed system can simulate projected fringe patterns and captured images. A new explicit calibration method has been presented to validate the precision of the system. Simulated results indicate that the proposed iterative method outperforms previous systems. Our virtual system can be applied to error analysis, algorithm optimization, and help operators to find ideal system parameter settings for actual measurements.
Although coherence scanning interferometry (CSI) is capable of measuring surface form with sub-nanometre precision, it is well known that the performance of measuring instruments depends strongly on the local tilt and curvature of the sample surface. Based on 3D linear systems theory, however, a recent analysis of fringe generation in CSI provides a method to characterise the performance of surface measuring instruments and offers considerable insight into the origins of these errors. Furthermore, from the measurement of a precision sphere, a process to calibrate and partially correct instruments has been proposed. This paper presents, for the first time, a critical look at the calibration and correction process. Computational techniques are used to investigate the effects of radius error and measurement noise introduced during the calibration process for the measurement of spherical and sinusoidal profiles. Care is taken to illustrate the residual tilt and curvature dependent errors in a manner that will allow users to estimate measurement uncertainty. It is shown that by calibrating the instrument correctly and using appropriate methods to extract phase from the resulting fringes (such as frequency domain analysis), CSI is capable of measuring the profile of surfaces with varying tilt with sub-nanometre accuracy.
In transmission microscopy, many objects are three dimensional, that is, they are thicker than the depth of focus of the imaging system. The three-dimensional (3-D) image-intensity distribution consists of a series of two-dimensional images (optical slices) with different parts of the object in focus. First, we deal with the fundamental limitations of 3-D imaging with classical optical systems. Second, a transfer theory of 3-D image formation is derived that relates the 3-D object (complex index of refraction) to the 3-D image intensity distribution in first-order Born approximation. This theory applies to weak objects that do not scatter much light. Since, in a microscope, the illumination is neither coherent nor completely incoherent, a theory for partially coherent light is needed, but in this case the object phase distribution and the absorptive parts of the object play different roles. Finally, some experimental results are presented.
In this paper, we characterize 3D optical imaging techniques as 3D linear shift-invariant filtering operations. From the Helmholtz equation that is the basis of scalar diffraction theory, we show that the scattered field, or indeed a holographic reconstruction of this field, can be considered to be the result of a linear filtering operation applied to a source distribution. We note that if the scattering is weak, the source distribution is independent of the scattered field and a holographic reconstruction (or in fact any far-field optical imaging system) behaves as a 3D linear shift-invariant filter applied to the refractive index contrast (which effectively defines the object). We go on to consider tomographic techniques that synthesize images from recordings of the scattered field using different illumination conditions. In our analysis, we compare the 3D response of monochromatic optical tomography with the 3D imagery offered by confocal microscopy and scanning white light interferometry (using quasi-monochromatic illumination) and explain the circumstances under which these approaches are equivalent. Finally, we consider the 3D response of polychromatic optical tomography and in particular the response of spectral optical coherence tomography and scanning white light interferometry.
This paper aims at giving an overview on the state of the art of vision-based, non-contact 3D measurement systems based on structured light. Such systems are equipped with a camera and a light projector, and are referred to in the literature as active stereo systems. This report is structured into structured light, calibration methods and 3D measurement techniques. Moreover, several selected research works are described in order to illustrate these different topics
Geometrical product specifications (GPS) -Coordinate measuring machines (CMM): Technique for determining the uncertainty of measurement
ISO 15530: Geometrical product specifications (GPS) -Coordinate measuring machines
(CMM): Technique for determining the uncertainty of measurement, 2013