Measurement of the spatial backscattering impulse-response at short length scales with polarized enhanced backscattering

Abstract

In this Letter, we describe an easy to implement technique to measure the spatial backscattering impulse-response at length scales shorter than a transport mean free path with resolution of better than 10 μm using the enhanced backscattering phenomenon. This technique enables spectroscopic measurements throughout the visible range and sensitivity to all polarization channels. Through a combination of Monte Carlo simulations and experimental measurements of latex microspheres, we explore the various sensitivities of our technique to both intrinsic sample properties and extrinsic instrumental properties. We conclude by demonstrating the extraordinary sensitivity of our technique to the shape of the scattering phase function, including higher order shape parameters than the anisotropy factor (or first moment).

Fig. 1

EBS instrument. Collimating lens L₁ (f = 200 mm), linear polarizer P, mirror M, beam splitter B, quarter wave plate QWP, linear analyzer A, Fourier lens L₂ (f = 100 mm), liquid crystal tunable filter LCTF.

Fig. 2

Polarization sensitivities. (a) Function pc for the 4 measured polarization channels as a function of exit radius. (b) Experimental (symbols) and simulation (lines) p_eff. Sample : 0.65μm diameter sphere with $l_s^{\ast }$ = 205 μm at 633 nm. Spot size = 6000 μm and L_sc = ∞. Simulation scaled by 0.65 to obtain match with experiment.

Fig. 3

Illumination beam spot size sensitivities. (a) s as a function of exit radius for 2 beam spot sizes. (b) Comparison between experiment (symbols) and simulation (lines) for the different beam spot sizes using ++ polarization. Sample : 0.65 μm diameter sphere with $l_s^{\ast }$ = 950 μm at 633 nm. L_sc = ∞. Simulation scaled by 0.65.

Fig. 4

Sensitivities to the spatial coherence of the illumination. (a) Function c for different L_sc. (b) Comparison between experiment (symbols) and simulation (lines) for different L_sc using ++ polarization. Sample : 0.65 μm diameter sphere with $l_s^{\ast }$ = 205 μm at 633 nm. Spot size = 6000 μm and L_sc = ∞. Simulation scaled by 0.65.

Fig. 5

Sensitivity of EBS to the phase function. (a) Phase function for two microsphere samples with the same g but different ka. (b) Corresponding p_eff for ++ polarization shows a large difference in shape at short length-scales. ka ~ 4 : 0.65 μm diameter sphere at 633 nm. ka ~ 16 : 2.1 μm diameter sphere at 558 nm. Spot size = 2000 μm and L_sc = ∞. Simulation scaled by 0.65.