Antecedentes Nacionales, Regionales y Locales

There is a lot of background noise in fig. 8.2e which is a d.c. term in the spatial frequency domain. The SSLR can be improved if this d.c. term is filtered off. This can be achieved by using bipolar representations of the patterns. For a CR of 10:1, the bipolar values (+10,-10) are represented by two binary patterns. The first input pattern holds the usual pattern and the second input pattern is the inverse of the first with pixel values of -10 if previously 10, and -1 for 1 (fig. 8.5). The two input patterns are correlated with the filter pattern in turn. The positive correlation between the first input pattern and the filter gives the same result as before (fig. 8.2e) The correlation between the inverted pattern

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Fig. 8.5 The input and filter patterns for (a) Positive correlation and (b) negative correlation (Positive: Black = 1, White = 10; Negative: Black = -1, White = -10)

(b) (c)

Correlator system : O ptim um system design, analysis, sim ulations and experiments 192 and the filter is shown in fig. 8.6. As expected in this negative correlation, the features of peaks previously, have become troughs and the whole pattern is inverted with a large d.c. correlation term in the middle. Since the number of white pixels in the inverted input pattern is greater than that in the original input, simple subtraction of the two patterns does not give a meaningful result. The correlation peaks must be scaled to the same size before the subtraction operation. The number of white pixels in the correlation pattern is given by the size of the correlation peak. The peak values of the positive and negative correlations are found to be 3978 and 12076 respectively. This means the negative correlation pattern must be scaled down to 33% of its original value. Practically this could be done by reducing the illumination intensity to allow easier subtration. The resultant correlation after the subtraction of the two correlation patterns is given in fig. 8.7.

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Fig. 8.7 (a) The correlation pattern after subtraction and (b) its mesh diagram

The centre of the pattern is largely in the negative region and the rim is about zero. The rim can be removed by placing an aperture at the output plane but this limits the field of view for the recognition. If the aperture is placed as shown in fig. 8.8a, then the SSLR is found to be 2.6:1 while the line scan SSR is 7.1:1 (fig. 8.8b) In each case, there is improvement of the original figures.

This bipolar representation can be implemented spatially or temporally. If the space-bandwidth product is large and speed is paramount, then the pattern and its inverted version are placed side by side in the SLM so that the two correlations proceed in parallel. Otherwise, the patterns can be displayed one after another. The final result is obtained by subtraction in the computer.

a. ‘o I S I 6 0 5 0 4 0 30 20 10 aperture 10 2 0 30 4 0 50 N u m ber o f p ix e ls

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Fig. 8.8 (a) The contour plot of the correlation pattern after subtraction

(b) Line scan crosses the correlation peaks along the dotted line within the aperture (c) Correlation pattern and (d) 3- D mesh pattern within the aperture

Correlator system : O ptim um system design, analysis, sim idations and experim ents 194 8.2.5 Simulation of randomised patterns

The disadvantage of the bipolar technique is that when there is an imbalance o f ‘bright’ and ‘dark’ pixels, the d.c, terms in the middle will not simply cancel each other. This problem can be solved by using either orthogonal or randomised patterns which have the same number of bright and dark pixels. Correlations of orthogonal patterns give better discrimination and lower sidelobes are obtained when using randomised patterns. For example, the pattern which we use in the experiment described later in section 8.4.3 is a resolution target which contains features of many spatial frequencies at various spatially separated locations and can be considered as a special type of ‘random ’ pattern i.e. they have high space bandwidth product..

In this simulation, we use a pattern which is generated by a random number generator in the Matlab program and is then normalised to unity. If the pixel value is above 0.5, it is considered having a value of ‘ 1’ (white pixels), otherwise it takes the value of ‘0 ’ (dark pixels). The subsequent correlation of these patterns after subtraction of the negative from the positive patterns will have a very high SLSR. For example, a 10:1 CR randomised pattern is used for the simulation (fig. 8.9a) and the correlation result after subtraction is given in fig. 8.9b. The SLSR is found to be 10:1 which is same as the contrast ratio of the original patterns.

F ig . 8 .9 (a ) A r a n d o m is e d p a tte rn w it h 10:1 c o n t r a s t ra tio