Synthetic Aperture Scatter Imaging

Qian Huang, Zhipeng Dong, Gregory Nero, Yuzuru Takashima, Timothy J. Schulz, David J. Brady

Abstract: Diffraction limits the minimum resolvable feature on remotely observed targets to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda R_{c}/A_{c}$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda$</tex-math></inline-formula> is the operating wavelength, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{c}$</tex-math></inline-formula> is the range to the target and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A_{c}$</tex-math></inline-formula> is the diameter of the observing aperture. Resolution is often further reduced by scatter or turbulence. Here we show that analysis of scattered coherent illumination can be used to achieve resolution proportional to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lambda R_{s}/A_{s}$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$R_{s}$</tex-math></inline-formula> is the range between the scatterer and the target and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$A_{s}$</tex-math></inline-formula> is the diameter of the observed scatter. Theoretical analysis suggests that this approach can yield resolution up to 1000× better than the diffraction limit. We present laboratory results demonstrating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;30\times$</tex-math></inline-formula> improvement over direct observation. In field experiments, we use a 23.5 cm aperture telescope at 100 m to resolve 27.78 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> m features, improving on diffraction limited resolution by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;10\times$</tex-math></inline-formula> . The combination of lab and field results demonstrates the potential of scatter analysis to achieve multiple order of magnitude improvements in resolution in applications spanning microscopy and remote sensing.