Theoretical considerations for V(r) analysis from experimental SPT data. (A) Error from uncertainty in particle centroid position (spatial resolution). Radial density distributions, d(r)/d(0), without and with three amounts of centroid position error (left). Effect of centroid position error on the error in potential strength, V0/V0,exact (right). (B) Error from uncertainty in potential center position. d(r)/d(0) for different tracking times, tp (left). Error from finite tracking time on the overestimation of potential strength, V0/V0,exact (right). (C) Error from finite measurement time. d(r)/d(0) for confined diffusion in a spring potential, as well as unconfined Brownian diffusion with different tracking times (left). Symbols and solid lines represent confined diffusion in a spring potential and Brownian diffusion, respectively, with colors representing the tracking time (blue, 0.2tp; green, 0.5tp; orange, tp). Density distribution coefficients, Cd, for confined diffusion in a spring potential (circle) and Brownian diffusion (triangle), for different tracking times (right).