A sensitive method for optical birefringence measurement is presented. To optimize the signal over the noise ratio, the polarization of the laser beam is modulated exceptionally with a high frequency electro-optical modulator. The specially developed optical apparatus exhibits high sensitivity and accuracy, which were checked by measuring the Cotton-Mouton effect in nitrogen as a function of the pressure. It is able to measure the retardance down to 2x10(-4) rad. This apparatus will be used with the locked optical cavity. The optical cavity will serve as an optical path multiplier for increasing the sensitivity. This proposed set-up will be able to measure the Cotton-Mouton effect in helium, where the birefringence effect is Delta n approximate to 2.4x10(-16).