General defocusing particle tracking: fundamentals and uncertainty assessment

General defocusing particle tracking (GDPT) is a single-camera, three-dimensional particle tracking method that determines the particle depth positions from the defocusing patterns of the corresponding particle images. GDPT relies on a reference set of experimental particle images which is used to predict the depth position of measured particle images of similar shape. While several implementations of the method are possible, its accuracy is ultimately limited by some intrinsic properties of the acquired data, such as the signal-to-noise ratio, the particle concentration, as well as the characteristics of the defocusing patterns. GDPT has been applied in different fields by different research groups; however, a deeper description and analysis of the method fundamentals has hitherto not been available. In this work, we first identity the fundamental elements that characterize a GDPT measurement. Afterward, we present a standardized framework based on synthetic images to assess the performance of GDPT implementations in terms of measurement uncertainty and relative number of measured particles. Finally, we provide guidelines to assess the uncertainty of experimental GDPT measurements, where true values are not accessible and additional image aberrations can lead to bias errors. The data were processed using DefocusTracker, an open-source GDPT software. The datasets were created using the synthetic image generator MicroSIG and have been shared in a freely-accessible repository.