Complex refractive index measurements based on Fresnel's equations and the uses of a lock-in amplifier

A new method for measuring complex refractive index is presented based on Fresnel's equations and the uses of a lock-in amplifier. A lock-in amplifier is introduced into a common path interferometer to measure the product of the amplitude reflection coefficients of s and p polarizations and their corresponding phase difference of a light beam reflected from a medium with complex refractive index. Then, these data are substituted into the special equations derived from Fresnel's equations, the complex refractive index can be obtained by numerical calculations. The resolution of this method is better than 0.01. It has both merits of a conventional common-path interferometer and a heterodyne interferometer. And its validity is demonstrated.