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The phase maps along with the images generated in the process of obtaining them have been

presented in the following pages. (PATTERN - 1).

Fig.1  –  Original fringe pattern Fig.2  –  After applying HT once Fig.3  –  After applying HT again

Fig.4  –  Figure obtained after negating Fig.5  –  Required phase map got by im-

the image obtained after applying HT plementing the formula

for a second time

 

Clearly from the diagrams presented above it can be seen that the application of HT on the first

instance on the original pattern there is a division line along the horizontal waist line which marks asort of zone reversal (easily noticeable if we focus on the central round fringe in fig.2).Apart fromthis the most obvious difference is the superior quality of the contrasting features incorporated in the

 pattern after the application of HT. Now in order to draw our phase map it is only necessary to apply

the HT only once but I have done it twice to demonstrate a very interesting feature of the entireexercise that is the negated image of the image obtained after applying HT twice on a particularfringe pattern gives us our original pattern in its exactness (the only difference being an improved

contrast). To demonstrate this more clearly I have aligned the two said images side by side below.

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The corresponding images for the other fringe patterns are as follows :-

FRINGE PATTERN –  2 (DIAGRAMS)

Fig.6  –  Original fringe pattern Fig.7  –  After applying HT once Fig.8  –  After applying HT again

Fig.9 –  Figure obtained after negating Fig.10  –  Required phase map got by im-

the image obtained after applying HT plementing the formula

for a second time

 

Comparison of figure-6 and 9 :-

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FRINGE PATTERN –  3 (DIAGRAMS)

Fig.11  –  Original fringe pattern Fig.12  –  After applying HT once Fig.13  –  After applying HT again

Fig.14 –  Figure obtained after negating Fig.15  –  Required phase map got by im-

the image obtained after applying HT plementing the formula

for a second time

 

Comparison of figure –  11 and 14 :-

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FRINGE PATTERN –  4 (DIAGRAMS)

Fig.16  –  Original fringe pattern Fig.17  –  After applying HT once Fig.18  –  After applying HT again

Fig.19 –  Figure obtained after negating Fig.20  –  Required phase map got by im-

the image obtained after applying HT plementing the formula

for a second time

 

Comparison of figure –  16 and 19 :-

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FRINGE PATTERN –  7 (DIAGRAMS)

Fig.21  –  Original fringe pattern Fig.22  –  After applying HT once Fig.23  –  After applying HT again

Fig.24 –  Figure obtained after negating Fig.25  –  Required phase map got by im-

the image obtained after applying HT plementing the formula

for a second time

 

Comparing the figure –  21 and 24 :-

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FRINGE PATTERN –  8 (DIAGRAMS)

Fig.26  –  Original fringe pattern Fig.27  –  After applying HT once Fig.28  –  After applying HT again

Fig.29 –  Figure obtained after negating Fig.30  –  Required phase map got by im-

the image obtained after applying HT plementing the formula

for a second time

 

Comparing figure –  26 and 29 :-

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FRINGE PATTERN –  9 (DIAGRAMS)

Fig.31  –  Original fringe pattern Fig.32  –  After applying HT once Fig.33  –  After applying HT again

Fig.34 –  Figure obtained after negating Fig.35  –  Required phase map got by im-

the image obtained after applying HT plementing the formula

for a second time

 

Comparing figure –  31 and 34 :-

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MATLAB programme used : -

a=imread('Picture1.jpg')

imshow(a) b=hilbert(a)c=imag(b)

imshow(c)d=hilbert(c)

e=imag(d)imshow(e)

neg_e=(-1)*eimshow(neg_e)n1=double(a);

n2=double(c);

d1=rdivide(n2,n1); phase1=atan(d1);imshow(phase1)