M anipulation afF om ier transform im ages using a fibre arrav.

A 2D optical fibre array was used to perform spatial transform s of Fourier Transform Images (FTIs). The FTIs were produced from a

p attern on a Spatial Light M odulator (SLM). The SLM was the

Semetex SIGHT-MOD.

A 2D to ID fibre array was used to transform the 2D FTI to a ID

image and a 2D to a point array was correlated w ith the FTI of a pattern on the SIGHT-MOD. The SIGHT-MOD was illuminated by a collimated beam from a HeNe (633nm) laser. A Im focal length lens

placed beyond the SIGHT-MOD produced the FTI of the device in its back focal plane. An optical fibre array, consisting of 40, Im long, large core fibres (970pm) arranged in a two dim ensional 10 by 4 array, was constructed by mounting the ends of the fibres in epoxy resin. The other ends of the fibres were formed into a one dimensional array with a random relationship between the position in the 2D array and the position in the ID array. Thus, any image on the face of the 2D array was converted to a ID image. The 2D array

was placed in the FT plane of the lens, figure 5.40. The intensity across th e ID array was m easured using a lin ear ccd array connected to an oscilloscope. A sequence of patterns was w ritten, in tu rn , onto the SIGHT-MOD. As the p attern changed the FTI changed and this was detected as a change in the ID image detected by the ccd array. The intensity detected by the ccd array for two patterns is shown in figures 5.41 and 5.42. The position of each fibre in the ID array could have been used to encode information about the spatial frequency content of the FTI, such as the spatial frequency in the FTI plane increasing from left to right in the ID array.

The Fourier transform of one pattern was to be correlated with the 2D fibre array. Fibres from the 10 by 4 array, in positions corresponding to the FTI of the pattern, were selected and positioned in front of a single, large area, photodetector connected to an oscilloscope. This is similar to placing a m ask in the FTI plane whose transmittance is either zero or unity and varies across the mask. A sequence of 10

patterns were w ritten onto the SIGHT-MOD and the correlation of the FTI of each p attern w ith the chosen fibres in the 2D array

m easured by the intensity of light detected by the photodetector.

Figure 5.43 shows the correlation of the FTI of each p attern with the fibres. A peak is seen corresponding to the p attern for which the fibre m ask was designed. Sm aller signals are present where partial correlations have occurred or where the resolution of the fibres in the array was not sufficient to discriminate against slightly different spatial frequencies.

5.7.6 Correlation of linear interference fringes with gratings on the

SIGHT-MOD.

L inear interference fringes w ere produced by shearing a Mach- Zehnder interferom eter illuminated by a collimated beam from a

chopped 0.5mW GreNe (543nm). The interferom eter had close to zero

p ath difference. The SIGHT-MOD was placed a t the output of the interferom eter. One arm of the interferom eter was phase modulated by a rotating glass slide. This caused the interference fringes to appear to scan across the SIGHT-MOD. Any light tran smitted through the SIGHT-MOD was focused into a large core optical fibre placed on the optical axis and the intensity of the light was m easured by a photom ultiplier tube. Any correlation between the fringes and the SIGHT-MOD would be seen as modulation of the transmitted

light in the m anner of Moire fringes, figure 5.44. The spacing of the interference fringes was calculated by expanding the second output from the interferom eter. The SIGHT-MOD was cleared of data and m ade to be fully transmitting. The size of the interference fringes was adjusted until modulation was detected. Two correlations were obtained. The first corresponded to the spacing between pixels and the second to the pixel size. G ratings were now w ritten onto the SIGHT-MOD. They had spatial periodicities of 2, 4, 6 and 8 columns.

C orrelations were obtained w ith linear interference fringes which were found to closely m atch the spatial periodicity of the gratings. The signal obtained when fringes were correlated w ith a grating which had a periodicity of 2 columns is shown in figure 5.45. The square wave is due to the chopped laser beam. The calculated sizes of the linear interference fringes when correlation occurred and the actual periodicity of the SIGHT-MOD are given in the following table.

G rating period G rating period M easured fringe period ₁

i

(colum ns) (micron) (micron)

I 0 0 56 0 0 260 1 2 254 246 1 4 508 504 4 509 162 1

]