Effect of the spatial coherence length on the self-reconfiguration of a speckle field

The self-reconfiguration property of a speckle pattern is characterized by having the same autocorrelation profile before and after the obstacle from the point at which the intensity speckle distribution is reestablished; i.e., the speckle pattern becomes homogeneous with no signature of the obstacle. We have presented a theoretical model that gives us in a more detailed way the dependence of this effect with the spatial coherence length of the speckle field. This study shows a linear dependence of the reconfiguration distance with the spatial coherence length of the speckle. Additionally, the experimental data are in good agreement with the theory.

Figure 1

Experimental setup: $L_1$ and $L_2$ are lenses, GGD is a ground-glass disk, and CCD is a charge-coupled device camera.

Figure 2

Speckle patterns measured for various positions of lens $L_1$ and without the obstacle: (a) $d_5$, (b) $d_4$, and (c) $d_2$; (d–f) are the corresponding autocorrelation profiles.

Figure 3

Experimental results for the self-reconfiguration effect: (a) ${\delta }_5=8\mu \mathrm{m}$, (b) ${\delta }_2=24.5\mu \mathrm{m}$, and (c) ${\delta }_1=66.5\mu \mathrm{m}$.

Figure 4

Results of the 1D profiles of the propagated speckle field after the obstacle. (a,d) are experimental; (b,e) are simulations; (c,f) are theoretical results obtained from Eq. (9). In the first row we used $\delta =8\mu \mathrm{m}$ and $\lambda =532\mathrm{nm}$. Second row has the same parameters as the first, but with $\delta =66.5\mu \mathrm{m}$.

Figure 5

Theoretical (black solid squares) and experimental results (red solid circles) showing the variation of the reconfiguration distance with the speckle coherence length.