Tandem-pulsed acousto-optics: an analytical framework of modulated high-contrast speckle patterns

Recently we presented acousto-optic (AO) probing of scattering media using addition or subtraction of speckle patterns due to tandem nanosecond pulses. Here we present a theoretical framework for ideal (polarized, noise-free) speckle patterns with unity contrast that links ultrasound-induced optical phase modulation, the fraction of light that is tagged by ultrasound, speckle contrast, mean square difference of speckle patterns and the contrast of the summation of speckle patterns acquired at different ultrasound phases. We derive the important relations from basic assumptions and definitions, and then validate them with simulations. For ultrasound-generated phase modulation angles below 0.7 rad (assuming uniform modulation), we are now able to relate speckle pattern statistics to the acousto-optic phase modulation. Hence our theory allows quantifying speckle observations in terms of ultrasonically tagged fractions of light for near-unity-contrast speckle patterns.