论文标题
在声学成像中的扩散缩放
On diffusive scaling in acousto-optic imaging
论文作者
论文摘要
声学成像（AOI）是一个混合成像过程。通过用声波扰动旨在重建的组织，引入了声波和光波之间的相互作用，从而导致光学特性的更稳定的重建。在[25]中描述了数学模型，辐射传递方程是光传输的正向模型。在本文中，我们研究了重建的稳定性。特别是，我们对稳定性如何依赖于knudsen数字，kN（来测量培养基中光子颗粒的散射效应强度的数量）感兴趣。我们的分析表明，随着KN降低到零，光子散布的频率更高，并且由于信息丢失，重建变得更加困难。为了应对这种效果，需要构造设备，以使激光束高度浓缩。我们将给出定量误差的结合，并明确表明这种浓度对KN具有指数依赖性。将提供数值证据以验证证据。
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.
