In optical testing, such as the fringe reflection technology and Shack-Hartman wavefront sensor technology, slope of a surface is measured instead, from which the faithful surface of the test optic is obtained. Therefore, a gradient data-based wavefront reconstruction is needed. This paper shows the use of the Gram-Schmidt process for orthonormalizing the gradients of the two-dimensional Legendre polynomials. After a set of orthonormalized vector polynomials is generated in a square region, these polynomials can be used to fit the gradient data in the region. By a simple linear transformation, the fitting coefficients can be derived and transformed to the wavefront description of the two-dimension Legendre polynomials, and the wavefront and primary aberration are then obtained. Based on the zonal method, this can effectively reconstruct the high-frequency component by fitting the difference of the high-frequency error, which cannot be done by polynomial fitting. According to the computer simulation, this algorithm can primely realize the reconstruction of wavefront.
The design and manufacture of Continuous Phase Plates (CPPs) with a large aperture is very significant and useful for kilojoule and megajoule-class laser systems, such as the Inertial Confinement Fusion(ICF) due to it has the advantages of precise control of beam-shape and high energy availability ratio. In order to improve the quality of the focused beam in the Inertial Confinement Fusion (ICF) system and reduce the processing difficulty of components, a theoretical design model of the continuous phase plate based on the Magnetorheological Finishing (MRF) technology was established, and improved the traditional Gerchberg-Saxton (GS) algorithm from the aspects of initial phase selection, phase unwrapping, filtering, and speckle spectrum control. The results show that: Compared with the conventionally designed continuous phase plate (CPP), the improved GS algorithm can control the size of the CPP processing unit, meet the requirements of magnetorheological processing technology, better control the focal spot profile, and reduce the modulation of specific frequency bands.
Large-aperture aspheric mirror is usually transferred to the test axis by rotating and translating when measured by a computer-generated hologram(CGH). This paper focused on the optimal design of CGH, minimizing the line density of CGH, in testing off-axis aspheric mirror with large aperture, off-axis amount and asphericity. The analytics formula of the transferred aspheric is used for deriving the phase function of CGH by geometric computing. And the precision of optical path difference(OPD) is proved reaching nanometer level for aspheric mirror with large asphericity by zemax. The defocus and tilt-carrier amount are two parameters to be optimized for filtering the unwanted orders brought out by CGHs. A merit function consists of the line densities at lower and upper boundaries of CGH to describe the etching difficulty of CGH is proposed. The propagation progress is analyzed while the reflection is amended by considering the saggital height of the reflection point. The separated distance of the given (m,n) orders ray is proved reaching micron degree. The filtering condition is expressed as an inequalities system. The gradient descent method with Karush Kuhn Tucker condition is used for optimal solution of the constrained optimization problem. Finally, design example is presented and the parameter optimization for testing off-axis aspheric mirrors is proved to have a high precision, which providing extensive applicability possibility in designing freeform testing system.