## Tomography Across the Scales:

Quantitative Optical Imaging from Single Molecules to Stars

Technologies which provide insight into the structure of biological/human material repeatedly have led to medical breakthroughs. In 1979, Allan MacLeod Cormack and Godfrey Houndsfield won the Nobel Prize in “Physiology and Medicine” for the first development of a CT-Scanner. The ability to inspect the internal three-dimensional structure of the human body by **tomography** has revolutionized medicine. And also on the microscopic scale recently a revolution took place: In 2014, Eric Betzig, Stefan Hell, and William E. Moerner won the Nobel prize in Chemistry for the development of super-resolution microscopy which enables a detail-resolution that was long believed to be impossible in optical microscopy. Mathematicians, meanwhile, have created the basis for the **computational analysis** of imaging data. 100 years ago, the Austrian mathematician Johann Radon derived the **back-projection formulas** for the Radon transform – as it is nowadays called. In the twentieth century, the Russian mathematician Andrey Nikolayevich Tikhonov contributed the mathematical foundations of **regularization theory**. Most current imaging technologies are based on these seminal scientific achievements.

Today imaging techniques are making progress at a breathtaking speed. **Tomography** pervades scientific disciplines beyond medicine, ranging from biology via medicine to astrophysics. Microscopy resolves biological structures down to the nanoscale, where single molecules become visible. Most importantly, the time to record such images has been reduced dramatically so that **dynamic processes** can be imaged in real-time.These developments call for advancing mathematical concepts that enable to extract from such data sets the essential information using modern computing technology.

This SFB connects three experimental imaging groups and three mathematical groups in order to meet these challenges. The experimental groups contribute imaging techniques and scientific expertise in applied optics, biophysics, biology and medicine. The mathematical groups are proficient in modeling, regularization, and numerical optimization. The mission of this consortium is to enable image analysis of **dynamic processes in nature across the scales**.