Synchronous Phase-Shifting Shearing Interferometry Based on Polarization Grating
Objective In the precision polishing stage of optical element processing,optical interference detection methods are often employed to detect the surface shape and transmitted wavefront.Among them,the shearing interference method is a measurement technology that adopts its light wave and copied light wave,and there is a dislocation between the light wave and copied light wave in space,which makes it unnecessary to introduce the reference light wave.At present,the synchronous phase-shifting technology is the interference measurement method with the best anti-vibration effect.It can obtain multiple phase-shifting interferograms spontaneously,and then adopt the phase-shifting algorithm to restore the wavefront information to be measured.The combination of shearing interferometry and synchronous phase-shifting technology can realize the absolute common optical path phase-shifting measurement of the phase to be measured and remove the influence of environmental vibration and air disturbance on the interferometry.The study of synchronous phase-shifting shearing interferometry is significant for detecting transmission wavefront pairs and the surface shape of optical elements.In the wavefront measurement,due to the influence of the surface error of the reference mirror,insufficient utilization of light energy,environmental vibration,and air disturbance on the interference measurement results,we propose a synchronous phase-shifting shearing interferometry method based on polarization grating splitting.This can achieve high-precision detection of transmission wavefront and reflection wavefront.Methods The proposed method is based on polarization grating beam splitting to achieve the wavefront test method of synchronous phase-shifting shearing interference,which can be utilized to test the transmission wavefront.The shearing module is a reflective transverse shearing structure composed of a polarization grating,a plane mirror,and a quarter wave plate.The polarization grating is a diffractive optical element that realizes selective beam splitting based on the polarization state of the incident light.The beams carrying the wavefront to be measured are divided into two orthogonal circularly polarized beams by the polarization grating,and then transverse shearing occurs again after being reflected by the plane mirror via the polarization grating.The orthogonal polarized light with certain transverse shear is formed after passing through a quarter wave plate.The phase-shifting module adopts a synchronous phase-shifting structure composed of a two-dimensional phase grating,a small aperture diaphragm,and a phase delay array.The orthogonal linearly polarized light is diffracted by the two-dimensional phase grating,and the diffracted light of(±1,±1)order is selected by the small aperture diaphragm.Then the phase shifting is generated by the phase delay array,and the interference occurs after passing through the linear polarizer.The vertical phase-shifting shearing interferogram can be obtained by rotating the polarization grating.Meanwhile,via adopting the transformation of the test scheme,the surface wavefront generation module of the optical element is added in front of the shear module,which can detect the surface shape of the optical element.For the shearing interference fringes in x and y directions collected by CCD,the image registration algorithm based on phase correlation,the four-step phase-shifting algorithm,and the phase unwrapping algorithm based on DCT are leveraged to obtain the phase distribution to be measured.Subsequently,the wavefront to be measured is reconstructed by the least square wavefront reconstruction algorithm based on differential Zernike polynomials.Results and Discussions We build a phase-shifting shearing interferometer based on polarization grating on the optical platform of the laboratory,and measure a lens with a diameter of 25.4 mm and a focal length of 50 mm.The PV value of the wavefront to be measured is 0.5366λ and the RMS value is 0.1519λ(Fig.7).The results are compared with the measured results of the SID4 wavefront sensor(Fig.8),which proves the accuracy of this method.The repeatability experiment proves the stability of the measurement results of this method.Then,we construct a measuring device of optical element surface shape based on polarization grating synchronous phase-shifting shearing interferometry on the optical platform of the laboratory.A concave mirror with a diameter of 25.4 mm and a focal length of 50 mm is measured.The PV value of the wavefront to be measured is 0.6044λ and the RMS value is 0.1669λ(Fig.13).The comparison experiment with the measurement results of the SID4 wavefront sensor(Fig.14)and the repeatability experiment are also carried out.This can verify the accuracy and stability of the measurement results of the synchronous phase-shifting shearing interferometry based on polarization grating.Conclusions A phase-shifting shearing interferometry based on polarization grating splitting is studied to detect the transmission wavefront and the surface shape of optical elements.The method employs a reflective shearing structure based on polarization grating splitting,with a compact and flexible optical configuration.Compared with traditional grating,the polarization grating has ultra-high diffraction efficiency,the energy of the two beams is uniform,and the light energy utilization is high.By combining shearing interference with synchronous phase-shifting technology,the quasi common path phase-shifting measurement of the wavefront to be measured is realized,which removes the influence of environmental vibration and air disturbance on the interferometry.The shearing interferograms in X and Y directions are processed by the image registration algorithm based on phase correlation,and the four-step phase-shifting algorithm and phase unwrapping algorithm based on DCT are adopted to obtain the shearing phase distribution.Then the wavefront to be measured is reconstructed by the least square wavefront reconstruction algorithm based on differential Zernike polynomials.The results show that the measurement results of this method are accurate and stable,and can achieve high-precision wavefront dynamic measurement,which is of significance for detecting the surface shape and transmission wavefront of optical elements.
measurementwavefront detectionshearing interferencesynchronous phase-shiftingphase recovery and reconstruction algorithm
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