| The phase of the optical wave-front is one of the main information carriers of light field,and the technology of phase measurement and recovery is a significant issue in adaptive optics,information optics and so on.As a precision measurement technology,the optical interferometry has always been the prime technology in the field.The traditional interferometry usually employs interference between an object wave and a reference wave that encounter different optical path,which makes interferometry suffer from measuring errors due to the environment disturbance.To solve this problem,a common-path interferometry is usually preferred.In this paper we have developed two types of interferometry based on a common-path design.One is the lateral shearing interferometry inspired from the idea of self-interference.We have built up a three-wave shearing interferometer that utilizes a spatial light modulator(SLM)as the shearing and phase-shifting device and proposed a novel phase-shifting scheme suitable for the phase extraction of three-wave shearing interferogram.The other is a common-path interferometry which is designed for an specific optical instrument known as phase-only SLM.This interferometry uses the Pancharatnam phase to realize phase shifting and has a nature of robustness to the environment disturbance.This dissertation is devoted to above topics and can be outlined as follows1.Three-wave lateral shearing interferometry and the phase-shifting schemeLateral shearing interferometry employs interference between an object wave-front and its sheared copy and avoids the need for a reference wave.The shearing interferometry is easily implemented in a common-path system and thus is robust against the environmental disturbance.In this paper,we have developed a novel three-wave shearing interferometry,and proposed a generalized phase-shifting scheme for the three-wave shearing interferogram.The phase-shifting algorithm is derived by an optimal process based on least-squares fitting.With this generalized algorithm,the steps of phase-shifting can be reduced to five,which greatly simplifies the measurement and decreases the burden of computation.Both the numerical simulation and the optical experiment are carried out to demonstrate the adaptability of the method.2.Measurement of phase only SLM based on the Pancharatnam phase-shiftingPhase only SLM is an electrically controlled device that modulates the phase of light only.Owing to its flexibility and dynamic modulation,the phase only SLM is becoming a key device in many applications,such as interferometry,holographic imaging,the generation of vector beam,holographic optical tweezers.However,there is always deviations in the SLM’s phase modulation due to the limitation of manufacturing.The completed knowledge of modulation characteristics is a prerequisite for fixing modulation errors of the SLM.Therefore,prior to the on-demand phase modulation the phase created by the SLM must be accurately measured,and such measurement is usually conducted by interferometry.In this work,we proposed a pixel-wise phase measuring scheme that utilizes the Pancharatnam phase shifting.The Pancharatnam phase is also called as geometrical phase,which refers to an extra phase factor,apart from the dynamical phase factor,acquired in certain evolution of a system.The geometrical phase is decided by the geometric path in parameter space as the system state evolving,for example the polarization state varying on the Poincare sphere,as explained by S.Pancharatnam when he studied the interference between the polarized light waves.For an interferometer built up on polarization elements,a phase shift can be introduced via the Pancharatnam phase change,which is stable against the environmental disturbance.We designed and established a common-path interferometer with the Pancharatnam phase-shifting to measure a phase-only SLM.The modulated phase by the SLM,pixel by pixel,can be accurately measured.The method have been verified by our experiments and compared with other measurement systems,which shows good stability and reliability and is thus helpful for the calibration of the SLM. |
