The Free-form Surface Wavefront Reconstruction Algorithm Researching Based On The Fringe Reflection Technique

With the development of modern optical manufacturing technology,free-form optical elements are widely used in optical systems.Compared with the traditional sphere,free-form surface has more superior optical properties,such as large degree of freedom and strong aberration correction ability,which can simplify the system structure,reduce the number of optical elements and make the optical system more miniaturized.However,it is more difficult to detect the free-form surface than that of a sphere due to its non-rotational symmetry and complexity.And interferometers have the following disadvantages: small detection dynamic range,unable to achieve full aperture detection,high requirements for the environment,and so on.Fringe reflection technique is an optical detection method with convenient operation,high detection accuracy and wide detection range,which is suitable for the detection of free-form surface optical elements.The reconstruction algorithm inverts the gradient data detected by the fringe reflection technique to obtain the 3D shape of the surface.The reconstruction accuracy of the algorithm directly affects the detection accuracy of the fringe reflection technique.In view of this,this paper studies a series of wavefront reconstruction algorithms.The application range,reconstruction accuracy,advantages and disadvantages of existing reconstruction algorithms are compared and analyzed.On the basis of the research,a series of improved methods are proposed to make the reconstruction algorithm have better applicability and higher accuracy.The research contents are as follows:The reflector with a diameter of 100 mm and a radius of 1000 mm was used as the surface to be measured.The experimental light path of fringe reflection method was simulated by Matlab,and the detection principle of fringe reflection method was verified.Based on the analysis of the existing wavefront reconstruction algorithm,the R vector polynomial is proposed to solve the problem that the Zernike gradient polynomial will lose its orthogonality when fitting the gradient data of the square domain free surface,resulting in coupling coefficient and noise transmission.The vector polynomials are orthogonalized by Gram-Schmidt method for 2D Legendre gradient polynomials.The numerical results prove that the vector polynomials have good reconstruction accuracy for the free surface gradient data within the square aperture.Considering the diversity of aperture shapes of free-form surfaces,a numerical orthogonal method is proposed.A numerical orthogonal gradient polynomial is constructed for the discrete gradient data,which can be used to fit the gradient data in the aperture of any shape.In order to improve the reconstruction accuracy of the first order digitized orthogonal gradient polynomial to the complex free surface,a hybrid reconstruction algorithm was proposed by combining the first order digitized orthogonal gradient polynomial with the iterative region method.Numerical results show that the hybrid reconstruction algorithm can not only obtain the pattern characteristics of the shape,but also improve the reconstruction accuracy of the complex free surface.