Characterization and control of threedimensional objects using fringe projection techniques

Spatiotemporal phase unwrapping for the measurement of discontinuous objects in dynamic fringe-projection phase-shifting profilometry

A spatiotemporal phase-unwrapping method is presented that combines the dynamic fringe-projection method and the phase-shifting technique and extends the phase-unwrapping method, which measures two phase maps at different sensitivities. The most important feature of the method is that it makes possible the automatic three-dimensional shape measurement of discontinuous objects with large dynamic range limits and high precision because the effective wavelength of the fringe-projection profilometry can be continuously varied over several orders of magnitude by rotation of the projection grating in its own plane. Only one grating and several steps of rotating the grating are required; therefore the method is inherently simple, fast, and robust. In the experiment, choosing the rotation angle was crucial for optimizing the measurement speed and the measurement accuracy. A criterion is presented for the choice of the minimum number of rotational steps for a given accuracy. The experimental results demonstrate the validity of the proposed method.

Profilometry by phase-shifted Talbot images

We introduce a profilometry sensor that combines phase shifting with a Talbot self-image of a sinusoidal grating as the illumination part of the sensor. Contrast of the Talbot diffraction pattern produced with a sinusoidal grating in a diverging beam is theoretically discussed and verified experimentally. The mathematical relationship that is used to convert the phase measured with this sensor to the corresponding relief of an object is derived in the Appendix. A ceramic former used in the production of lenses was profiled with this sensor, and measurement results are presented.

Optical methods to measure shape and size

A number of methods are available to quantify exterior size and shape of living and non-living objects. Relevant items for dentistry are the exterior of face and skull and the surface of dental casts. To the best of our knowledge, dentitions have not yet been measured in situ. The optical methods using incoherent light are mechanical sensing of casts, visual stereometry (on the subject or on stereophotographic pairs), moire techniques, and optical-sensor morphometry. It will be shown that the three latter systems in fact rely on the same physical principles, although they involve quite different technologies. On the other hand, coherent optical techniques, such as holography and contouring holographic interferometry, are presented.

The basic principles of the different techniques are shown, and their main features in relation to applications to the dental object discussed. Main features include: resolving power, range, time needed for a measurement, requirements for the surface of the object, and ease of selection and collection of data. Examples of methods from the literature and from work by the author are given.

Moire technique by means of digital image processing

Moiré technique by means of projected fringes is a suitable method for full field measurements of out-of-plane deformations and object contouring. One disadvantage in industrial applications has been the photographic process with the involved time-consuming development of the photographic film. This paper presents a new method using a TV camera and a digital image processor whereby real-time measurements of deformations and comparison of object contours are possible. Also the principles and limitations of the projected moiré method are described.

Electronic processing of moiré fringes: application to moiré topography and comparison with photogrammetry

Some elements of comparison are given between projection-type moiré topography and photogrammetry. The basic mathematics of photogrammetry is used to reconstruct the 3-D shape of the object from the moiré pattern. Some particular aspects of the moiré method are discussed, and a general methodology is proposed. In connection with this, an optoelectronic technique is described, which measures the moiré phase with high resolution and sign determination. The experimental results show that this technique is especially suitable for high accuracy automatic reconstruction of 3-D shapes.

Profile measurement using projection of running fringes

A method of profile control or measurement using projected fringes is presented. The fringes are dynamically translated over the object, and the phase of the signal picked up at a selected point on the surface is used to determine the depth or the depth error of the profile at this point. The method has the advantage of being contact-free, fast, accurate, and easily automated.

Scanning moiré method and automatic measurement of 3-D shapes

A new type of moiré and its application to topography are discussed. moiré fringes are generated by observing a grating projected on an object under test with a scanning imaging device. The general equations of the projection-type moiré topography are given. By controlling the phase, the pitch, or the direction of the virtual grating corresponding to the scanning lines of the imaging device, the automatic sign determination of the contour lines is accomplished. By the use of a high precision flying spot scanner with CRT(DD-tube) and a minicomputer system, an experimental measurement system is developed. Very significant is the fact that a contour line system and a sectional shape of the object are automatically reconstructed and displayed on a color TV monitor.

Moiré topography by means of a grating hologram

A new method of moire topography is described. This encompasses two processes: recording of the deformed grating projected onto a 3-D object, and posterior development of contour moire from the record. The development of contour moire is realized by projecting a linear grating onto a photographic print of the record of the deformed grating, using a photographic enlarger. By this new method, a technique for describing a 3-D object by means of the slope of facets composing the object is made possible.