4.4        Reconstruction process

This section presents the treatment applied to the measured OLCR data to reconstruct the grating complex coupling coefficient. We limit the study to the time multiplexing case. The first operation produces the slowly varying complex OLCR response (amplitude and phase). The second step is the Fourier transform and the deconvolution from the interferometer signature to obtain the complex spectral response of the grating. The complex coupling coefficient is then calculated by layer-peeling (chapter 3, §3.3.2).

4.4.1        Complex OLCR signal reconstruction

The OLCR measurement consists of four signals : the low coherence light interference amplitude and phase (A_lc and f_lc) and the laser interference amplitude and phase (A_L and f_L). Only the phase difference Df = f_lc - f_L is important since all interferometer phase drifts are canceled in this signal. The OPLD, x, is determined directly by the translation stage control system with an accuracy of 100 nm and an absolute error after several centimeters bellow 1 mm (stepping-motor encoder error).

The laser signal amplitude is supposed to be constant over the scan range due to the large coherence length of the laser source. Nevertheless, the interference signal shows a parabolic behavior due to the coupling variation with the mirror position in the reference arm. The same variation is also observed for the low coherence signal. To correct this effect, a modified low coherence amplitude A_OLCR is calculated by dividing the low coherence amplitude by a parabolic fit of the laser amplitude A_{L,2nd order}

The slowly varying complex OLCR signal f(x) is then defined as