Real-time nonlinear correction of back-focal-plane detection in optical tweezers

Photodiode based detection of laser trapped beads using forward scattered light is a frequently employed technique for position measurement. There is a nonlinear relationship between photodiode outputs and bead position but for small displacements linear approximation holds well. Traditionally, the nonlinearity is compensated by normalizing the photodiode's position signal with the intensity signal and then using a polynomial fit in the range where voltage to position mapping is one to one. In this article, this range is extended by using the intensity signal as an independent input along with the two position signals. A map from the input signals to the actual position values is obtained. This mapping is one-to-one for a larger range that results in an increased detection range. An artificial neural network that facilitates implementation is employed for this purpose. This scheme is implemented on a Field Programmable Gate Array based data acquisition and control hardware with closed loop bandwidth of 50 kHz. Detection of the order of 350 nm from the center of detection laser is demonstrated for a 500 nm diameter bead compared to 180 nm achieved by a polynomial fit.