3.2 Data reduction
In the ideal case all the nanometric scattering centers have the same effectiveness, also the efficiency of coupling is the same for both sides of the component and do not depend on the position of the zero OPD.
Of course our component is not ideal ! One can see on figure 2
that the surface of the component is polluted and the some nanowires of gold are broken. Nevertheless we have been able to reduce the data in order to rebuild the spectrum of our light source. For the data reduction we need to know exactly:
• the effectiveness of each scattering centers
• the position of each scattering centers
• and the efficiency of coupling
Only the position of each scattering centers was known, the others two informations have been extracted from the data acquired. The position of each scattering centers was known thanks to the process of manufacture. Indeed the nanowires of gold have been deposited with a MEB with en accuracy of a few nm. The distance between two scattering centers is 2.7 μm.
In order to acquire the data we took exposure of 5 s with the camera, for each position of injection. The position of injection is defined as the distance between the outside fiber of the Y junction hold by the nanopositioning system and the entrance of the component. The range of variation of this position was from 5 μm to 8 μm by step of 50 nm, which is less than a sixth of the wavelength. The efficiency of coupling is well described by the following expression:
Figure 6. a) Rebuilt interferogram of a SLED. b) Spectrum of the SLED studied
is the flux of light outgoing from the fiber, d is the diameter of the fiber core, D is the distance between the fiber and the component and NA is the numerical aperture of the fiber. The equation 1 can be simplified as following if d << D:
Also for a monochromatic light the equation of the interferogram is:
where each I is the average value of the intensity (I1 is for one entrance and I2 is for the other) and x is the OPD. So we have been able to correct the variation of efficiency of coupling of the side where the fiber was moving. In order to estimate the factors of this equation we interpolated it thanks a root mean square measure on a plot with a high OPD, i.e. where there is no interference and the only variation of intensity is due to the efficiency of coupling. The effectiveness of each scattering centers has been computed as the average flux of each scattering centers on all the pictures acquired.
Finally the “algorithm” for the data reduction is the following:
• division of all the scattered flux by the effectiveness of each scattering centers
• correction of the efficiency of coupling
• repositioning of each part of the interferogram (see figure 5)