Improved wavefront reconstruction using difference Zernike polynomials for two double-shearing wavefronts

To realize wavefront reconstruction for two double-shearing wavefronts produced by our studied cross phase grating lateral shearing interferometer(CPGLSI) in x and y directions, improved wavefront reconstruction using difference Zernike polynomials is studied in this paper. Firstly, the x directional double-shearing wavefronts in the x direction produced by shearing of (+1, +1), (-1, +1) orders diffraction beams and that of (+1,-1), (-1,-1) orders diffraction beams are represented respectively by the corresponding difference Zernike polynomials. Then the whole difference wavefront in x direction is represented by the half value of the sum of the above x directional double-shearing wavefronts. Similarly, the double-shearing wavefronts in the y direction produced by shearing of (+1, +1), (+1, -1) orders and that of (-1, +1), (-1,-1) orders are represented respectively by the corresponding difference Zernike polynomials. Then the whole difference wavefront in y direction is also represented by the half value of the sum of the y directional double-shearing wavefronts. Secondly, the least square fitting is used to obtain the whole wavefront. Investigations on reconstruction accuracy and reliability are carried out by numerical experiments, in which influences of different shearing amounts and noises on reconstruction accuracy are evaluated. The simulation results show that the wavefront reconstruction accuracy can all reach to high accuracy corresponding to different shearing amounts and also validate that our wavefront reconstruction technique is robust to noise.