Removing the effects of additive noise from TIRM measurements

Total internal reflection microscopy (TIRM) is an optical technique for monitoring Brownian fluctuations in separation between a single microscopic sphere and a flat plate in aqueous medium. The sphere is levitated above the plate by colloidal forces such as double-layer and steric repulsion. Changes in elevation as small as 1 nm can be detected by measuring the light scattered by a single sphere when illuminated by an evanescent wave. From the Boltzmann distribution of elevations sampled by the sphere over a long time, the potential energy (PE) profile can be determined with a resolution of about 0.1 kT. By corrupting clean data (having a mean scattering intensity I(s) and standard deviation sigma(s)) obtained by Brownian dynamics simulations with various levels of white, additive, background noise (having a mean background intensity I(b) and standard deviation sigma(b)), we simulate a noisy signal which is then used to test various schemes for removal of the noise. Merely subtracting I(b) from the measured total intensities before analysis removes the distortion in the PE profile when sigma(b)/sigma(s) is less than 0.15. To remove the distortion under more severe conditions, we used a Butterworth low-pass filter with the cutoff frequency chosen by comparing the power spectral density of the signal with that of the noise. This technique was found to be effective in removing distortion from the PE profile for cases when sigma(b)/sigma(s) is as large as 2.5.