In Eqn. (2), the numerator and denominator are proportional to the sine and cosine of the phase change between times t1 and t2, weighted by the square of the intensity modulation. Spatial smoothing can therefore be carried out by convolving the numerator and denominator with a kernel of equal constant values over data from neighbouring pixels, and it can be shown that the implicit weighting results in a phase-difference map with optimal signal-to-noise ratio [9]. Such an approach has been implemented on the pipeline image processor using a 3 by 3 kernel. Eqn. (2) allows ∆Φw(t,0), the total wrapped phase change since the start of the recording process, to be calculated. Temporal phase unwrapping is then carried out to restore the unknown integral multiple of 2π for each value of t. The unwrapped phase change distribution will be denoted ∆Φu(t,0). The number of 2π phase jumps between two successive measurements of the phase change is calculated as follows: d(t) = NINT ∆Φw(t ,0) −∆Φw(t −1,0) [ /2π { ] }, t = 2, 3,..., s, (4) where NINT denotes rounding to the nearest integer. The total number of phase jumps by the time of the tth phase measurement, ( )t ν , is calculated by . (5) ν(t) = d( ′ t ) ′ t =2 t ∑ and the unwrapped phase difference map is obtained as ∆Φu(t,0) =∆Φw(t ,0) −2πν(t ) t = 2, 3,..., s. (6) If the deformation becomes too large, significant speckle decorrelation will occur causing an increase in the noise level of the measured displacement fields. Under such circumstances a new reference state should be chosen at times t = t1, t2, t3, etc. in place of the state t = 0. The total unwrapped phase change after rereferencing κ times will then be ∆Φu(t,0) =∆Φu(t,tκ) + ∆Φu(tk,tk−1) k=2 κ ∑ +∆Φu(t1,0) . (7) IMPLEMENTATION USING PIPELINE PROCESSOR Pipeline processing essentially converts a two-dimensional image consisting of a 2-D array of pixel values into a one-dimensional stream of individual pixels. The pixel stream can be processed one pixel at a time by a series of specialised processing elements, and then transformed back into a 2-D image. At the beginning and end of each 1-D pipeline is a 2-D surface that is stored on a virtual surface image memory (VSIM). Pipeline processing has an important performance advantage over fixed-data-path, general-purpose image processing architectures, which process whole images as discrete frames. This advantage is derived from placing the specialised processing hardware at the particular point in the 1-D stream where it can perform its individual processing task on each pixel, without waiting for the entire frame to be processed. The processing hardware can be assembled in a variety of configurations, each optimised for a particular application, thereby creating an image pipeline.
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