Phase contrast magnetic resonance velocity imaging is a powerful technique for quantitative in vivo blood flow measurement. Current practice normally involves restricting the sensitivity of the technique so as to avoid the problem of the measured phase being 'wrapped' onto the range -pi to +pi. However, as a result, dynamic range and signal-to-noise ratio are sacrificed. Alternatively, the true phase values can be estimated by a phase unwrapping process which consists of adding integral multiples of 2pi to the measured wrapped phase values. In the presence of noise and data undersampling, the phase unwrapping problem becomes non-trivial. In this paper, we investigate the performance of three different phase unwrapping algorithms when applied to three-dimensional (two spatial axes and one time axis) phase contrast datasets. A simple one-dimensional temporal unwrapping algorithm, a more complex and robust three-dimensional unwrapping algorithm and a novel velocity encoding unwrapping algorithm which involves unwrapping along a fourth dimension (the 'velocity encoding' direction) are discussed, and results from the three are presented and compared. It is shown that compared to the traditional approach, both dynamic range and signal-to-noise ratio can be increased by a factor of up to five times, which demonstrates considerable promise for a possible eventual clinical implementation. The results are also of direct relevance to users of any other technique delivering time-varying two-dimensional phase images, such as dynamic speckle interferometry and synthetic aperture radar.

Determining lubricant film thickness between contacting bodies under elastohydrodynamic (EHD) conditions is often simulated by using a ball/cylinder and transparent disc apparatus together with an interferometry technique. The simulated contact will have a point or elliptic shape and the light used can be white or monochromatic. The interference pattern is normally photographed with a regular camera or a video camera and the pictures are then evaluated by the naked eye of the observer. In most cases, only central or minimum thicknesses are evaluated. In this paper an image processing method for the analysis of film thickness is presented. This method makes it possible to extract considerably more information about film thickness fluctuations than is achievable by the naked eye. The method primarily matches hue (but also saturation and intensity values) from digitized colour interferometric images of the unknown film shapes with calibration values obtained with known geometric shapes. The method is shown to work well in the range from 95 up to 700 nm with white light and makes the results unbiased by the observer. Furthermore, absolute film thickness can be evaluated without prior knowledge about the fringe order in the interferogram.

A hybrid evaluation scheme for EHL film thickness determination is proposed and discussed. The film thickness profile in the contact region is measured using interferograms produced with a novel multi channel interferometry method. Since the refractive index distribution in the contact is pressure-dependent, and the initial film thickness profile will be evaluated assuming atmospheric pressure, a refractive index correction scheme is employed. The correction scheme is based on the Lorenz-Lorentz equation and a pressure-density relation together with a numerical pressure solver taking the initial film thickness measurement as input. The film thickness determination scheme is applied to an interesting phenomenon that can be observed at sliding conditions when the discrepancy occurred in the form of a deep and large dimple in the conjunction. Such a dimple appeared instead of the conventional plateau. The phenomenon was studied under different degrees of sliding. The detailed film thickness maps and pressure distributions for highly loaded EHL conjunctions at high degrees of sliding are produced using a hybrid evaluation scheme. The results are analyzed and discussed. [S0742-4787(00)00301-5]

No abstract

Measurement of the thickness of thin lubricant films separating rotating surfaces in elastohydrodynamic experiments presents some challenging problems. The nature of the experimental apparatus inhibits the use of most commonly applied interferometric phase measurement methods. Also the absolute thickness of the separating film must be determined, as opposed to relative distances that would be sufficient in most other measurement scenarios where interferometry methods are used. In this paper, computer-based analysis of interferograms recorded using an elastohydrodynamic lubrication Fitzeu interferometer (a so-called ball-and-disc apparatus) is discussed, the main objective being to extract the absolute oil-film thickness. Intensity based methods (most importantly, calibration look-up procedures where colour parameters from recorded dynamic interferograms are compared with table values corresponding to known film thicknesses, but also a phase measurement approach based on multi-channel interferometry using trichromatic light) are described. A discussion regarding compensation for measurement errors due to the pressure dependence of the refractive index of the lubricant is also included.