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Understanding how the mechanical properties of cells alter with disease may help with the development of novel diagnostics and treatment regimes. The emergence of tools such as the atomic force microscope (AFM) has enabled us to physically measure the mechanical properties of cells. However, suitable models for the analysis of real experimental data are either absent, or fail to provide a simple analysis tool in which experimental data can be analyzed quickly and reliably. The Hertz model has been widely used to study AFM data on living cells, however it makes assumptions that are untrue for cells, namely that cells behave as linear elastic bodies. This article presents and evaluates an alternative nonlinear Hertz model, which allows the Young's modulus to vary according to a second order polynomial function of indentation depth. Evaluation of the model revealed that prostate cancer cells (PC3) responded more uniformly to force compared to the normal PNT2 cells. Also, more energy (J) was needed to deform the normal prostate cells compared to the prostate cancer cells. Finally, the model described here suggests that overall the normal prostate cells behave in a more linear fashion to applied force compared to the prostate cancer cells.

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The use of a second-order digital phase-locked loop (DPLL) to demodulate fringe patterns is presented. The second-order DPLL has better tracking ability and more noise immunity than the first-order loop. Consequently, the second-order DPLL is capable of demodulating a wider range of fringe patterns than the first-order DPLL. A basic analysis of the first- and the second-order loops is given, and a performance comparison between the first- and the second-order DPLL's in analyzing fringe patterns is presented. The implementation of the second-order loop in real time on a commercial parallel image processing system is described. Fringe patterns are grabbed and processed, and the resultant phase maps are displayed concurrently.

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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.

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Phase unwrapping has been and still is a cumbersome concern that involves the resolution of several different problems. When dealing with two-dimensional phase unwrapping in fringe analysis, the final objective is, in many cases, the realization of that analysis in real time. Many algorithms have been developed to carry out the unwrapping process, with some giving satisfactory results even when high levels of noise are present in the image. However, these algorithms are often time consuming and far removed from the goal of real-time fringe analysis. A new approach to the construction of a simple and fast algorithm for two-dimensional unwrapping that has considerable potential for parallel implementation is presented.

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In the shadow-moiré system, the period of the grating is varied by rotation of the grating, so the phase of the moiré pattern is changed as well. By the selection of suitable rotation angles, three images at different positions of the grating are acquired to obtain the absolute distance from the object to the grating. A theoretical analysis is presented for the method, and some experiments have been done to verify the theoretical analysis. The results show that the method is fast and the accuracy is better than 10 µm. The measurable range is directly proportional to the period of the grating and inversely proportional to the angles at which the grating is rotated.

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We describe a technique termed multichannel Fourier fringe analysis and its application to the problem of automatic phase unwrapping in the presence of surface discontinuities. The technique is especially useful for the analysis of fringe projection contour maps in order to measure surface height distributions. Use is made of multiple fringe patterns that are separated in the frequency space of the Fourier transform by means of a set of bandpass filters. We also describe the design of a special fiber-optic interferometer with features particularly important in the case of this technique: easily adjustable fringe spacing and rotation. Fringe production by the interferometer is analyzed, and the relationship between the fringe phase and the height distribution of an illuminated surface is derived. A method for measuring phase in the case of multichannel Fourier fringe analysis is presented. The application of the technique to automatic phase unwrapping is shown. An example of the technique in operation is given, and a discussion of implementation of the technique is included.

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A technique for the quantitative determination of the changes in surface topography of restorations during wear has been developed. This involves the optical contouring of the surface using a laser, and the generation of contour maps. Several different methods for interpreting these maps are discussed. A computer-aided method is the most consistently accurate and measures wear volume to an accuracy of 2--5%.

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