Suite of MATLAB files for analysis, parameter extraction and simulation of data of trapped particles.

1- common_functions

Contains functions for (beautiful) plotting, spectral density estimation, data importing and other commonly used functions.

2- opt_trap

Optical trap functions (polarizability, mass, dipole force in Gaussian Beam).

3- paul_trap

Paul trap functions (in particular, obtain charge by fitting to a series truncation of Mathieu function). Main function is called labview_paultrap.m, which sequentally calls the others.

4- simulation

Contains code to simulate ODEs and SDEs in MATLAB. Designed to easily import particle, trap, etc. data. It is divided in three folders:

1. ODE: numerical simulation of noise-less ODE. Main function is full_numerical_ode, which can be called as:

    >> full_numerical_ode([0, 1e-4], 1e-7, '2nd_order', [0 0]);
   

The function in the ODE can be changed in the file test_2nd_order.m

2. SDE: numerical simulation of SDE (i.e., ODE + noise). Main function is full_numerical_sde, which can be called as:

    >> full_numerical_sde([0, 1e-4], 1e-7, '2nd_order', [0 0], 'runge_kutta', 100, 'optical_tweezer','plot')
   

The function in the ODE can be changed in the files drift_2n_sde.m and diffusion_2n_sde.m

3. Kalman related: Code to simulate Kalman filters, LQR, LQG. In particular for a harmonic oscillator trap.