声光成像中的扩散标度
On diffusive scaling in acousto-optic imaging
摘要：
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，引入声波和光波之间的相互作用，导致光学特性的更稳定的重建。数学模型在[25]中进行了描述，其中辐射传输方程用作光学传输的前向模型。在本文中，我们研究的稳定性的重建。特别是，我们感兴趣的是如何稳定性取决于克努森数，Kn，一个数量，衡量的强度的散射效应的光子粒子在介质中。我们的分析表明，随着Kn减小到零，光子散射更频繁，并且由于信息丢失，重建变得更加困难。为了对抗这种效应，需要构造设备以使激光束高度集中。我们将给出一个定量的误差界，并明确表明，这样的浓度有一个指数依赖于Kn。将提供数字证据来验证证明。
英文摘要：
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.
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