Quantitative, high-resolution images of weak index structures are important for a wide variety of applications. There are a number of techniques for measuring phase structures, but very few can deal with small structures that are embedded in a volume. This makes it difficult to measure waveguides along their length unless they are surface features. In order to overcome this problem in our system, where we write waveguides into volume photopolymers, we have developed a modified optical diffraction tomography system.

Optical diffraction tomography works by sending a collimated laser beam through the sample. The light travels perpendicular to the waveguide and scatters off of the waveguide. The light that scatters gives us information about the object off of which it scattered. There is a simple relationship between the Fourier transform of the scattered field and the Fourier transform of the index structure that allows us to image the structure. This can be done all in the far field without the use of lenses, but still with very high resolution. the image below graphically demonstrates this process.



For very weak structures, imaging is still difficult because the scattered field is frequently weaker than the background noise. In our research, we demonstrate an optical diffraction tomography system capable of measuring deeply-buried, weak index structures written in a three-dimensional volume. High-fidelity cross sections of these weak index structures are constructed by replicating the structure to be measured to form a diffraction grating. The coherent addition of scattering from each of these objects increases the sensitivity of the imaging system. Our method is capable of quantitative index measurements in cases where traditional forms of tomography would suffer from a low signal-to-noise ratio. We demonstrate a form of tomography that does not require phase information from the scattered fields, which considerably simplifies both experimental and computational implementation.