One governing principle of the microscopic world is "predictable randomness," where snapshots of a fluctuating process may appear random, but the average outcome of the process is predictable. An exciting frontier in biological physics is evaluating if predictable randomness extends to more complex, multi-component biophysical systems, such as active propulsion or genetic regulation. Taking a statistical physics approach to such complex molecular systems may lead to the discovery of predictive models and new insights into how the rules of life interplay with the laws of physics. One necessary step in discovering underlying physical models of complex, dynamic biophysical systems is advancing the current state of the art in quantifying fluctuations with sufficient time and spatial resolution. 

In this talk, I will introduce the fundamentals of quantitative optical imaging of microscopic fluctuations across spatiotemporal scales and the inverse problem frameworks used to extract physical insight from measured fluctuations. I will discuss our recent results on directly measuring the propulsion efficiency for a biological microscopic helical propeller, the E. coli flagella, by combining a new approach to high-speed 3D fluorescence imaging with the fluctuation-dissipation theorem. I will conclude with our recent efforts in developing "Fourier Synthesis" optical diffraction tomography, a pathway to nanoscale 3D imaging at volume rates above 1 kilohertz.