Imaging Beyond the Born Approximation: A Physical Approach

这项建议的目的是改进成像技术，利用波与物质的相互作用来重建物体的物理特性。迄今为止，这些技术受到分辨率和成像深度之间的权衡的限制。虽然长波长可以穿透到介质深处，但经典的衍射极限排除了观察亚波长结构的可能性。在过去的二十年里，近场显微镜已经证明，通过将探测传感器带到距离待成像物体表面一个波长的距离内，可以突破衍射极限。现在，近场显微镜的范围已经扩展到从在远场中执行的测量重建亚波长结构，这种方法具有更广泛的应用范围，因为通常要成像的结构是不能直接访问的。亚波长分辨率的关键在于描述波散射的物理模型。传统的成像方法使用玻恩近似，该近似不考虑探测波在穿过待成像介质时的失真，因此忽略了所谓的多次散射。另一方面，多重散射是在远场中编码亚波长信息的关键机制，从而导致潜在的无限分辨率。新的实验证据表明，对于距离探测传感器超过70个波长的物体，可以实现优于四分之一波长的分辨率。这项初步工作已经建立了基本原则，即只要放弃玻恩近似，采用更精确的波-物质相互作用模型，远场测量的亚波长分辨率是可能的。该提案的目的是追求这一新的令人兴奋的想法，并专注于更具体的应用，如医疗诊断和地球物理成像。

The objective of this proposal is to improve imaging techniques which exploit the interaction of waves with matter to reconstruct the physical properties of an object. To date these techniques have been limited by the tradeoff between resolution and imaging depth. While long wavelengths can penetrate deep into a medium, the classical diffraction limit precludes the possibility of observing subwavelength structures. Over the past twenty years, near-field microscopy has demonstrated that the diffraction limit can be broken by bringing a probing sensor within one wavelength distance from the surface of the object to be imaged. Now, the scope of near field microscopy has been extended to the reconstruction of subwavelength structures from measurements performed in the far-field, this approach having a much wider range of applications since often the structure to be imaged is not directly accessible. The key to subwavelength resolution lies in the physical models employed to describe wave scattering. Conventional imaging methods use the Born approximation which does not take into account the distortion of the probing wave as it travels through the medium to be imaged, so neglecting what is known as multiple scattering. On the other hand, multiple scattering is the key mechanism which can encode subwavelength information in the far-field, thus leading to a potentially unlimited resolution. New experimental evidence has shown that a resolution better than a quarter of the wavelength can be achieved for an object more than 70 wavelengths away from the probing sensors. This preliminary work has established the fundamental principle that subwavelength resolution from far-field measurements is possible as long as the Born approximation is abandoned and more accurate models for the wave-matter interaction are adopted. The aim of this proposal is to pursue this new and exciting idea and to focus on more specific applications such as medical diagnostics and geophysical imaging.