Computation for optical trap stiffness versus refractive index of biological cell

In order to study the methods for measuring the refractive index of a biological cell based on optical tweezers technology, a ray-optics model has been used to predict the relationship between the trap stiffness and the refractive index of an ideal cell as a spherically symmetric Rayleigh sphere (radius α = 10μm, refractive indices n = 1.35-1.70) in a single-beam gradient optical trapping (laser wavelength λ = 780 nm, power P = 6 mW, beam waist radii ω(0) = 0.6μm, 0.8μm and 1.0μm). Numerical simulation shows that the envelope of each curve is a cubic polynomial fitted well with the cell refractive indices. Results indicate that the calibration process for parameters of a cubic polynomial must be performed on four standard particles before the cell refractive index is obtained by measuring its trap stiffness.