Peter Kühmstedt

3D shape measurement with phase correlation based fringe projection

Here we propose a method for 3D shape measurement by means of phase correlation based fringe projection in a stereo arrangement. The novelty in the approach is characterized by following features. Correlation between phase values of the images of two cameras is used for the co-ordinate calculation. This work stands in contrast to the sole usage of phase values (phasogrammetry) or classical triangulation (phase values and image co-ordinates - camera raster values) for the determination of the co-ordinates. The methods main advantage is the insensitivity of the 3D-coordinates from the absolute phase values. Thus it prevents errors in the determination of the co-ordinates and improves robustness in areas with interreflections artefacts and inhomogeneous regions of intensity. A technical advantage is the fact that the accuracy of the 3D co-ordinates does not depend on the projection resolution. Thus the achievable quality of the 3D co-ordinates can be selectively improved by the use of high quality camera lenses and can participate in improvements in modern camera technologies. The presented new solution of the stereo based fringe projection with phase correlation makes a flexible, errortolerant realization of measuring systems within different applications like quality control, rapid prototyping, design and CAD/CAM possible. In the paper the phase correlation method will be described in detail. Furthermore, different realizations will be shown, i.e. a mobile system for the measurement of large objects and an endoscopic like system for CAD/CAM in dental industry.

A new method for the computer-aided evaluation of three-dimensional changes in gypsum materials

OBJECTIVES The quantitative evaluation of the time- or process-dependent three-dimensional stability of dental materials is a common question in dentistry. An investigation procedure has been developed based on a CAD-surface model of a prepared upper canine, as well as a high-precision physical copy (metal master die). The specific aim of this study was to test this methods reliability. Additionally, the ability of the developed procedure to determine the three-dimensional stability of resin-reinforced gypsum master casts over time was investigated. METHODS Ten duplicate dies of improved dental stone (esthetic-rock, dentona, Germany) were manufactured, and digitized 1, 3, 7, 28 and 56 days after pouring. A three-coordinate optical measuring device was used for the data acquisition. The three-dimensional accuracy of stone dies was determined by comparing the digitized data of the stone dies made from the metal master die to its CAD-surface model (Surfacer) Version 9.0. Imageware Inc., Ann Arbor Michigan, USA). To assess the procedure, test surfaces were created from the digitized data and compared with a reference. RESULTS The mean deviation between the digitized point cloud and the test surface was less than 3 microm. During the 56 day examination period no significant three-dimensional changes in dimensional stability were found. SIGNIFICANCE The procedure for the quantitative three-dimensional evaluation was shown to be suitable. Best-fit registration enabled a reliable alignment of the point cloud to the CAD-surface model. Alteration of three-dimensional accuracy over 6 weeks was insignificant and without clinical relevance.

Array projection of aperiodic sinusoidal fringes for high-speed three-dimensional shape measurement

Abstract. Three-dimensional (3-D) measurement systems based on coded-light techniques are conventionally limited by the projection speed, which is typically in the range of a few 100 Hz, resulting in 3-D frame rates of 1 to 60 Hz. We propose to use an array projector for 3-D shape measurements, which enables much higher projection frame rates of up to the 100-kHz range. In contrast to previous setups, it does not project well-known phase-shifted sinusoidal fringes and Gray code patterns, but aperiodic sinusoidal fringes. This new technique, based on sine-shaped fringes with spatially and temporally varying offset, amplitude, period length, and phase shift, allows accurate 3-D measurement of objects, even with sharp edges, high slope, or varying surface properties, at high speed up to the kilohertz range. This paper explains the 3-D measurement principle and the basic design of an array projector that projects aperiodic sinusoidal fringes. It verifies the consistency between specified and projected patterns and points out the results of the setup’s characterization, e.g., of its high-speed capability. Furthermore, first 3-D shape measurements at a projection frame rate of 3 kHz resulting in a 3-D frame rate of >330  Hz are presented and evaluated.

Theoretical considerations on aperiodic sinusoidal fringes in comparison to phase-shifted sinusoidal fringes for high-speed three-dimensional shape measurement

The demand for optically reconstructing the three-dimensional (3D) surface shape of moving objects or deformation processes makes the development of high-speed projectors necessary. Our 3D sensor containing an array projector can achieve frame rates of several tens of kilohertz and is based on the projection of aperiodic sinusoidal fringes. This approach is compared with phase-shifting fringe projection as probably the most widely used technique. Theoretical considerations as well as extensive simulations are conducted to derive criteria for the design of optimal sequences of aperiodic sinusoidal fringes and to compare the number of patterns of both approaches necessary for comparable accuracies.

Phase unwrapping using geometric constraints for high-speed fringe projection based 3D measurements

A new methodology for 3D surface measurement based on phase shifted fringe pattern projection is presented which enables real-time measurement and high-speed performance of 3D measurements using stereo camera observation. The essence of the new technique is a drastic reduction of the fringe code which makes the process of pattern projection and image recording faster and real-time applicable. The new algorithm allows the complete omission of the typically used Gray code sequence or other additional code to the phase shifted sinusoidal fringe sequence. Its main concept is a special geometric design of the arrangement of the projection unit in relation to one of the involved cameras. The 3D point calculation is performed by triangulation between the two cameras with the help 3D point determination between the projection unit and one of the cameras. Whereas the second mode ensures the uniqueness, mode one realizes the accurate calculation. The realization of the uniqueness of the measurement is obtained by a corresponding arrangement of the parameters projected fringe width, the measurement volume size, the triangulation angle between the principal rays of first camera and the projection unit, and camera constants of second camera and projection unit. First experiments with a 3D measurement systems based on fringe projection technique show the robustness of the new method. Real time measurements can be performed which is the precondition of the supervision or quality check of several dynamic processes.

Intraoral 3D scanner

Here a new set-up of a 3D-scanning system for CAD/CAM in dental industry is proposed. The system is designed for direct scanning of the dental preparations within the mouth. The measuring process is based on phase correlation technique in combination with fast fringe projection in a stereo arrangement. The novelty in the approach is characterized by the following features: A phase correlation between the phase values of the images of two cameras is used for the co-ordinate calculation. This works contrary to the usage of only phase values (phasogrammetry) or classical triangulation (phase values and camera image co-ordinate values) for the determination of the co-ordinates. The main advantage of the method is that the absolute value of the phase at each point does not directly determine the coordinate. Thus errors in the determination of the co-ordinates are prevented. Furthermore, using the epipolar geometry of the stereo-like arrangement the phase unwrapping problem of fringe analysis can be solved. The endoscope like measurement system contains one projection and two camera channels for illumination and observation of the object, respectively. The new system has a measurement field of nearly 25mm × 15mm. The user can measure two or three teeth at one time. So the system can by used for scanning of single tooth up to bridges preparations. In the paper the first realization of the intraoral scanner is described.

Underwater 3D Surface Measurement Using Fringe Projection Based Scanning Devices.

In this work we show the principle of optical 3D surface measurements based on the fringe projection technique for underwater applications. The challenges of underwater use of this technique are shown and discussed in comparison with the classical application. We describe an extended camera model which takes refraction effects into account as well as a proposal of an effective, low-effort calibration procedure for underwater optical stereo scanners. This calibration technique combines a classical air calibration based on the pinhole model with ray-based modeling and requires only a few underwater recordings of an object of known length and a planar surface. We demonstrate a new underwater 3D scanning device based on the fringe projection technique. It has a weight of about 10 kg and the maximal water depth for application of the scanner is 40 m. It covers an underwater measurement volume of 250 mm × 200 mm × 120 mm. The surface of the measurement objects is captured with a lateral resolution of 150 μm in a third of a second. Calibration evaluation results are presented and examples of first underwater measurements are given.

Distance Dependent Lens Distortion Variation in 3D Measuring Systems Using Fringe Projection.

Measuring systems using fringe projection provide the possibility of very accurate touchless measurements. For the measurement of small objects compact devices are possible. However, in the case of very close distances between the optical system and the measuring object there is a considerable influence of the measuring distance to the lens distortion. This will lead to considerable measuring errors if neglected. In typical cases of our measuring systems the amount of the distortion may change by a factor greater than two in the range of a distance difference of a few centimetres. Results of the distance dependence will be given for the lenses of two devices.

On the accuracy of point correspondence methods in three-dimensional measurement systems using fringe projection

Abstract. Different concepts of correspondence findings in contactless optical three-dimensional (3-D) measurement systems using fringe projection are analyzed concerning the accuracy of the 3-D point calculation. These concepts are different concerning the kind of performance of the triangulation procedure in order to calculate the resulting 3-D points and the use of geometric constraints versus second projection sequence. Triangulation may be alternatively performed between camera pixels and the phase origin of the projection, between one camera pixel in the prior camera and the image of the corresponding measured phase value in the second camera, or between the image points of certain raster phase values in the two observation cameras. Additionally, triangulation procedures can be distinguished concerning the use of two perpendicular projection directions of the fringes versus the use of geometric constraints, i.e., epipolar geometry instead of the second projection direction. Advantages and disadvantages of the different techniques are discussed. In addition, a theoretical analysis of the application of synthetic data has been simulated as well as experiments performed on real measurement data. Both simulations and real data experiments confirm the theoretical assumptions concerning the magnitudes of the random errors occurring in 3-D point determination.

High-speed 3D shape measurement using array projection

Measuring the three-dimensional (3D) surface shape of objects in real time has become an important task e.g. in industrial quality management or medical sciences. Stereo vision-based arrangements in connection with pattern projection offer high data acquisition speed and low computation time. However, these coded-light techniques are limited by the projection speed which is conventionally in the range of 200. . .250Hz. In this contribution, we present the concepts and a realized setup of a so-called 3D array projector. It is ultra-slim, but nonetheless able to project fixed patterns with high brightness and depth of focus. Furthermore, frame rates up to the 100 kHz range are achievable without any need of mechanically moving parts since the projection speed is limited mainly by the switching frequency of the used LEDs. According to the measurement requirements, type and structure of the patterns can be chosen almost freely: linear or sinusoidal fringes, binary codes such as the Gray code, square, hexagonal or random patterns and many more. First investigations on the functionality of such a 3D array projector were conducted using a prototype with a combination of Gray codes and phase-shifted sinusoidal fringes. Our contribution proves the high brightness of the proposed projector, its sharpness and the good Michelson contrast of the fringe patterns. We deal with the patterns’ homogeneity and the accuracy of the phase shift between the sinusoidal patterns. Furthermore, we present first measurement results and outline future research which is, inter alia, addressed to the use of other structured light techniques with the help of new purpose-built 3D array projector prototypes.