Imaging of crystal defects with ballistic phonons and their three-dimensional reconstruction using digital image processing

Spatial defects in single crystals were imaged with ballistic phonons by their shadow projections using low-temperature scanning electron microscopy. Digital image recording and processing was applied for a quantitative evaluation of the experimental results. We have investigated sapphire and -quartz samples with laser-drilled holes as special model cases of crystal defects. Computer algorithms have been developed to separate the shadows of the defects from the focusing pattern in the phonon images. We obtained binary images of the structures with a typical resolution of about 20 m. Cross-correlation functions of two images were found to be well suited for image alignment procedures. By this technique and from theoretically calculated phonon intensity distributions the bolometer positions within the experimental phonon images could be determined automatically. Using two phonon detectors at different locations stereoscopical imaging of the defects became possible. From the different views the three-dimensional distribution of the defects could be calculated.