Individualized defocusing particle tracking for dynamic surface profilometry

Abstract Three-dimensional (3D) localization and single-particle tracking (SPT) are powerful techniques for characterizing shape, motion, and deformation of materials. However, these methods often require complex optical setups that demand expert use, limiting their accessibility to the wider scientific community. This paper presents a new technique called individualized defocusing particle tracking (IDPT), which uses intrinsic aberrations in ordinary lab microscopes to perform 3D surface measurements at camera frame rates. The IDPT technique comprises a simple in-situ calibration procedure and 3D localization algorithm that leverages particles’ unique defocusing patterns to enhance measurement sensitivity while compensating for optics-induced bias errors. Our empirical approach implicitly transforms systematic optical effects—including those caused by misalignment or defects of optical elements—into valuable sources of positional information, allowing our method to work with common lab microscopes. We validate the IDPT technique through synthetic and benchtop experiments involving rigid body motion of a planar substrate and the dynamic deformation of elastic discs, demonstrating that our algorithm surpasses comparable SPT algorithms in accuracy and resolution. The IDPT technique is simple yet robust, offering broad applicability for dynamic surface profilometry and deformation analysis.