Acousto-optic imaging (AOI) is a hybrid imaging process. By perturbing the to-be-reconstructed tissues with acoustic waves, one introduces the interaction between the acoustic and optical waves, leading to a more stable reconstruction of the optical properties. The mathematical model was described in [25], with the radiative transfer equation serving as the forward model for the optical transport. In this paper we investigate the stability of the reconstruction. In particular, we are interested in how the stability depends on the Knudsen number, Kn, a quantity that measures the intensity of the scattering effect of photon particles in a media. Our analysis shows that as Kn decreases to zero, photons scatter more frequently, and since information is lost, the reconstruction becomes harder. To counter this effect, devices need to be constructed so that laser beam is highly concentrated. We will give a quantitative error bound, and explicitly show that such concentration has an exponential dependence on Kn. Numerical evidence will be provided to verify the proof.

中文翻译：

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声光成像中的漫反射标度

声光成像 (AOI) 是一种混合成像过程。通过用声波扰动待重建的组织，引入了声波和光波之间的相互作用，从而导致更稳定的光学特性重建。在[25]中描述了数学模型，其中辐射传输方程用作光传输的前向模型。在本文中，我们研究了重建的稳定性。特别是，我们对稳定性如何取决于 Knudsen 数 Kn 感兴趣，Kn 是衡量介质中光子粒子散射效应强度的量。我们的分析表明，随着 Kn 减小到零，光子散射得更频繁，并且由于信息丢失，重建变得更加困难。为了对抗这种影响，需要构造的设备使激光束高度集中。我们将给出一个定量误差界限，并明确表明这种浓度对 Kn 具有指数依赖性。将提供数字证据来验证证明。