Fundamental limits of optical microrheology

Abstract

We estimate the fundamental limits of different microrheological techniques based on optical detection. It is suggested that particle tracking systems using nondifferential detection have a minimum detectable displacement given by 0.2(λ0/NA)(1/SNR), where λ0 is the wavelength, NA is the numerical aperture of the focusing objective, and SNR is the signal-to-noise ratio of the system. This limit has important consequences in microrheology, since the noise contributes with an apparent diffusion constant of Dl≈0.02(λ0/NA)2(B/SNR), where B is the bandwidth of the detection unit. As the SNR of ordinary microscopes is limited, one should be extra careful when probing soft materials with low diffusion constants. On the other hand, in differential systems based on laser detection, the SNR is considerably increased due to reduced laser noise, and the minimum detectable displacement is given by 0.4(λ0/NA)(1/SNR). One may therefore expect to measure the diffusion constant with higher accuracy if the SNR is large. Finally, we find that total internal reflection microscopy (TIRM) has a minimum detectable displacement given by 0.1λ0/SNR.