Xianyu Su

Automated Phase-measuring Profilometry Using Defocused Projection of a Ronchi Grating

Abstract A new method is presented for automatic phase measuring profilometry (PMP), in which a defocused image of the projected square-wave Ronchi grating and a phase shifting technique are chosen for the optical phase evaluation. This makes it possible to design all-electronic LCTV-based PMP systems. In this paper a detailed analysis of the applied phase evaluation algorithm as function of the number of steps, N, is given. The alternating feature of the phase measurement precision ϵ(N), which lead to the obvious choice of seven or five steps, is clearly demonstrated. Then an analytical description is presented of the low-pass optical filtering performed by defocused imaging of the projected and video-frame-grabbed Ronchi grating. It is followed by an analytical description of the additional low-pass digital filtering of the same signal due to the inherent properties of the N-step phase shifting algorithm. The figure of merits are estimated in comparison to the simulated perfect imaging of a sinusoidal grating. The results are verified experimentally by a relief determination of a typical object. For this purpose the five accurately shifted defocused projections of the original Ronchi grating, spread over the object, were captured by a CCD based video-digitizing system and evaluated with a PC.

Application of modulation measurement profilometry to objects with surface holes

We present a detailed discussion of how modulation measurement profilometry (MMP) is applied to measuring an object that has holes on its surface. MMP is not based on the conventional three-dimensional profilometry method with structured light triangulation but on modulation measurements; it has the advantage of measuring the surface of a test object by perpendicular projection, that is, the direction of the CCD camera is the same as that of the projecting light, and the wrapped phases need not be calculated. Thus the difficulties from shadows and spatial discontinuities in phase measurement profilometry and Fourier transform profilometry methods do not exist in MMP. Here we measure a wheellike object that is 31.5 mm thick with an outer diameter of 80 mm and an inner diameter of 20 mm. All the object seen with the CCD camera can be measured including the hole. Experimental results prove that this method is useful for three-dimensional profilometry measurement, especially for objects with discontinuous height steps and spatial isolation.

Area modulation grating for sinusoidal structure illumination on phase-measuring profilometry

Sinusoidal structured illumination is used widely in three-dimensional (3-D) sensing and machine vision. Phase algorithms, for example, in phase-measuring profilometry, are inherently free of errors only with perfect sinusoidal fringe projection. But it is difficult to produce a perfect sinusoidal grating. We propose a new concept, area modulation, to improve the sinusoidality of structured illumination. A binary-coded picture is made up of many micrometer units. An aperture is open in every micrometer unit, and its area is determined by the value of the sinusoidal function. When such a grating is projected onto an object surface, the image of the grating becomes sinusoidal because of the convolution function of an optical system. We have designed and manufactured an area modulation grating for sinusoidal structure illumination using a large-scale integration technique. The area modulation grating has been used in the high-precision phase-measuring profilometry system, and the phase errors caused by the area modulation grating are reduced to 0.1%. The grating guaranteed the entire measuring accuracy to a 1% equivalent wavelength. The experimental results proved that area modulation grating would be of significant help in improving the phase-measurement accuracy of the 3-D sensing system.

Improved Fourier-transform profilometry

An improved optical geometry of the projected-fringe profilometry technique, in which the exit pupil of the projecting lens and the entrance pupil of the imaging lens are neither at the same height above the reference plane nor coplanar, is discussed and used in Fourier-transform profilometry. Furthermore, an improved fringe-pattern description and phase-height mapping formula based on the improved geometrical generalization is deduced. Employing the new optical geometry, it is easier for us to obtain the full-field fringe by moving either the projector or the imaging device. Therefore the new method offers a flexible way to obtain reliable height distribution of a measured object.

Automated measurement method for 360° profilometry of 3-D diffuse objects

An automated measurement method for 360 degrees surface topography of 3-D diffuse objects is presented. The method is based on the simple principle of triangulation with structured illumination. The geometric specifications of the structured light module used in the system are analyzed on a computer. Using an advantageous data acquisition schedule, high data acquisition rates and measuring accuracy can be achieved. The system comprises a structured lighting projector, a 2-D detector array, and a microcomputer for control and processing. Experimental results for 3-D objects are offered.

Reliability-guided phase unwrapping in wavelet-transform profilometry

The phase unwrapping algorithm plays a very important role in many noncontact optical profilometries based on triangular measurement theory. Here we focus on discussing how to diminish the phase error caused by incorrect unwrapping path in wavelet transform profilometry. We employ the amplitude value map of wavelet transform coefficients at the wavelet-ridge position to identify the reliability of the phase data and the path of phase unwrapping. This means that the wrapped phase located at the pixel with the highest amplitude value will be selected as the starting point of the phase unwrapping, and that pixels with higher amplitude value will be unwrapped earlier. So the path of phase unwrapping is always in the direction of the pixel with highest amplitude value to the one with lowest amplitude value. Making full use of the amplitude information of wavelet coefficients at the wavelet-ridge position keeps the phase unwrapping error limited to local minimum areas even in the worst case. Computer simulations and experiments verify our theory.

Phase-unwrapping algorithm based on frequency analysis for measurement of a complex object by the phase-measuring-profilometry method

A new phase-unwrapping algorithm based on fringe frequency analysis is presented that will achieve greater automation and precision in measuring complex objects by phase-measuring profilometry (PMP). The new algorithm, which combines digital weighted filtering in the frequency domain and modulation ordering in the spatial domain, can recognize corrupt pixels automatically and produce a better phase-unwrapping path. By frequency weighted filtering, the analysis of fringe frequency is converted into the analysis of fringe modulation. Then, based on a strong correlation between local spatial frequency and the reliability of phase data, ordering of the filtered modulation produces an optimized unwrapping path. Simulation and experiments verify the new algorithm.

New Fourier transform profilometry based on modulation measurement

This article propose a new Fourier transform profilometry based on modulation measurement. We briefly call it FTP based on MM. Its main advantage is that it can measure the surface of a complex object in the same direction of projecting light, so it has no the difficulties due to shadow and spatial discontinuity that exist in conventional FTP and also PMP methods. In the paper, we give the principle of the method, the set-up of measurement system, and some primary experimental results. The results proved that this method is a promising method for acquiring 3D data of complex object.

Fourier transform profilometry based on a projecting-imaging model

In order to obtain the correct height reconstruction of a measured object, a projection lens and a camera lens must be placed at equal heights above the reference plane in the traditional Fourier transform profilometry (FTP) method. We propose an improved phase-height mapping formula based on an improved description of the reference fringe and the deformed fringe in FTP when the projection lens and the camera lens are not placed at equal height. With our method, it is easier to obtain the full-field fringe by moving either the projector or the imaging device. In some cases, where the required parallel condition cannot be met, the proposed method offers a flexible way to calculate the height distribution.

Two-dimensional wavelet transform for reliability-guided phase unwrapping in optical fringe pattern analysis

This paper theoretically discusses modulus of two-dimensional (2D) wavelet transform (WT) coefficients, calculated by using two frequently used 2D daughter wavelet definitions, in an optical fringe pattern analysis. The discussion shows that neither is good enough to represent the reliability of the phase data. The differences between the two frequently used 2D daughter wavelet definitions in the performance of 2D WT also are discussed. We propose a new 2D daughter wavelet definition for reliability-guided phase unwrapping of optical fringe pattern. The modulus of the advanced 2D WT coefficients, obtained by using a daughter wavelet under this new daughter wavelet definition, includes not only modulation information but also local frequency information of the deformed fringe pattern. Therefore, it can be treated as a good parameter that represents the reliability of the retrieved phase data. Computer simulation and experimentation show the validity of the proposed method.