Image Processing and Tomography

The fringe patterns produced by the interferometer need to be converted into records of the fluid temperature. This step requires identifying intensity minima within fringes locating fringe edges determining fringe order, and measuring distances between fringes. Since the image is recorded through a computer, these operations can be performed with computer programs. In most real life experiments, this step is difficult since operations such as locating fringe minima and edges result in ambiguity. One of the factors that causes difficulties in identification is speckle, a form of noise. Elaborate procedures must then be employed to remove speckle from the interferometric images. Examples of cleaning strategies are Fourier-filtering using band-pass filters, histogram specification, and Laplacian smoothing.

Let and be the refractive index and temperature fields, respectively, in the physical domain being studied. Let and be their reference values, as encountered by the reference beam. The interferogram is a fringe pattern arising from the optical path difference

(1)

which in terms of temperature is

(2)

The integral is evaluated along the path of a light ray. Neglecting refraction effects, this path will be a straight line and the integral evaluation is greatly simplified. As a special case, if the flow field is two dimensional then the light beam can be oriented in the z-direction and the equation above reduces to

(3)

where L is the length of the test cell parallel to the direction of the light beam.

In a more general setting, when the temperature field is three-dimensional, recovering from a single image is not possible. This image can, however, be viewed as a projection of the temperature field in the s-direction. If the original field is three-dimensional, its projection is a field in a dimension reduced by unity, i.e., two for the present case. It is theoretically possible to record a very large number of projections of the test fields in many directions, and in the practical problems, it is not possible to record too many projections, either due to limitations of the experimental setup or due to cost. This process of three-dimensional reconstruction from two-dimensional projections is called tomography.

In practical problems, it is not possible to record too many projections, either due to limitations of the experimental setup or due to cost. A new subject has now evolved which is concerned with reconstruction with only a few views and is called limited-view tomography. Some of the popular methods used here are algebraic reconstruction techniques (ART), multiplicative algebric reconsturctive technique (MART), and maximum entropy (MENT). These techniques are iterative in nature and reconstruct the unknown function over a grid.

Scope of the present work

Laser interferometry is a powerful measurement technique to record temperature fields in a fluid medium. Combined with tomographic algorithms, the method can reconstruct three-dimensional temperature fields. The review covers interferometric measurements, image processing operations for enhancement of interferograms, evaluation of fringe patterns, and limited-view tomographic algorithms. Experimental results for a variety of buoyancy-driven flow problems have also been presented. The paper is organized under the following sections: Review of literature, laser interferometry, Image processing, Data reduction, Computerized tomography, and Applications.