Zernike polynomials fitting method is often applied in the test of optical components and systems, used to represent the wavefront and surface error in circular domain. Zernike polynomials are not orthogonal in rectangular region which results in its unsuitable for the test of optical element with rectangular aperture such as cylinder surface. Applying the Chebyshev polynomials which are orthogonal among the rectangular area as an substitution to the fitting method, can solve the problem. Corresponding to a cylinder surface with diameter of 50 mm and F number of 1/7, a measuring system has been designed in Zemax based on Fizeau Interferometry. The expressions of the two-dimensional Chebyshev polynomials has been given and its relationship with the aberration has been presented. Furthermore, Chebyshev polynomials are used as base items to analyze the rectangular aperture test data. The coefficient of different items are obtained from the test data through the method of least squares. Comparing the Chebyshev spectrum in different misalignment, it show that each misalignment is independence and has a certain relationship with the certain Chebyshev terms. The simulation results show that, through the Legendre polynomials fitting method, it will be a great improvement in the efficient of the detection and adjustment of the cylinder surface test.
The aspherical mirror surface quality testing by using compensation null lens in interferometer is described in this paper. For 310mm, f/0.5 hyperboloid mirror microcrystalline components, based on the theory of aberration compensation, a kind of null lens system which is composed of three pieces of spherical lens is developed. A certain amount of spherical aberration is introduced to the null lens for compensating the deviation of aspheric surface in a normal direction. The design result shows that the primary aberration and the senior aberration are balanced well, the MTF is closed to the diffraction limit and the residual wave aberration (RMS) is less than 0.004λ (λ=0.6328μm). Every indicators of the system meets the requirements of high precision detection of null lens system design. In this paper, the errors caused by the manufacturing, testing and assembling of the null lens system are analyzed. Those errors can be divided into the symmetric error and the asymmetric error. Using the correction method, the influence of the asymmetric error is minimized which seemed bigger than the asymmetric one. Finally, analysis results show that the total residual wave aberration of the system is less than 0.0072λ, which satisfies the requirement of aspheric testing. This null lens system has been applied to aspheric processing.
High precision aspheric surface can be obtained conveniently by using single point diamond turning technology, liquidmagnetic polishing technology and ion beam polishing technology, but the costs of manufacturing is too enormous to be widely used. In fact, in the field of optical processing, the most commonly used technical solution is still making a best fit sphere firstly compared with aspheric equation, and then remove the material on the glass to correct the error between aspheric and best fit sphere by precision grinding and precision polishing. The resolving of the best-fit sphere and the material removal, however, is a very important problem during the fabrications. The two dimensional maps of surface error between the best fit sphere and the corresponding aspheric surface shows W shaped which has the maximum removal at the center and the edge of the workpeace and gradually reduces to zero at the 70.7 percent of the diameter. In the process of deterministic optical manufacturing, the edge effect will arise because of the change of machining conditions when polishing tool locates in edge area, which will lower the surface accuracy of workpiece and debase machining efficiency. W shaped error distribution and the edge effect will make it difficult to remove the error on the edge of the workpiece. Aiming at the situation, an algorithm available for control of edge effect is proposed. Considering the requirement of minimum material removal and the control of edge effect, the radius of the anti-edge effect sphere is calculated by programming. The advantage of the algorithm is shown by the comparison of results derived from new algorithm and empirical equation. At the same time, the application in the off-axis asphere fabrications also proves the correctness of the algorithm. This algorithm is very helpful for the theory and practice of the fabrications of off-axis asphere.
We discuss the depth of subsurface damage (SSD) on different processing conditions. Considering different conditions would produce different depths of SSD, this article seriously studies the depth influenced by different sizes of abrasive particles and different grinding discs. Then the depth of SSD would be detected via Three-Coordinate Measuring Machine (CMM) after traditional polishing. The target of this research is to provide some basic references for the choice of the glass-ceramics grinding machining process.
This paper presents a method for automatic marking of optical components for processing area. Using testing equipment, such as wave surface interferometer or coordinate contour measuring machine, we get the two dimensional maps of surface error. According to the positional relationship between the surface error distribution and the corresponding position on the optical surface, we get the X, Y coordinates of the boundary waiting for further milling, grinding or polishing in the workpiece coordinate system. The workpiece coordinate system of optical element is established and the boundary waiting for further processing is marked with points or line by using three-dimensional coordinate machine, so as to realize marking automatically. Experiments show that the processing method of marking is useful in optical manufacturing, and this method is particularly suitable for marking the optical elements that difficult to mark directly in interference testing.
The Computer-Controlled Optical Surfacing (CCOS) technology is widely used for making aspheric mirrors, because of
its high accuracy, simple process conditions, low cost and other merits. The characteristic of the removal function of a
polishing tool is a fundamental factor in determining convergence rate in CCOS process. The ideal removal function in
CCOS shows a Gaussian-like character which has the maximum removal at the center and gradually reduces to zero with
the radius increasing. In this paper, we present a novel approach to get an ideal removal function by tri-rotors machinery.
According to the Preston equation and time-sharing synthesis, we established mathematical models in the modes of trirotors
movement. Through the simulation based on the emulated material removal function, we get the polishing process
technological parameter. Then the experimental setup and results are given. The practical process proves that the result is
basically equal to the simulation result, which validates the feasibility of this simulation optimization method and has a
certain degree of guiding to practical process.
The technical principle of computer controlled optical surfacing (CCOS) and the common method of optimizing removal
function that is used in CCOS are introduced in this paper. A new optimizing method time-sharing synthesis of removal
function is proposed to solve problems of the removal function being far away from Gaussian type and slow approaching
of the removal function error that encountered in the mode of planet motion or translation-rotation. Detailed time-sharing
synthesis of using six removal functions is discussed. For a given region on the workpiece, six positions are selected as
the centers of the removal function; polishing tool controlled by the executive system of CCOS revolves around each
centre to complete a cycle in proper order. The overall removal function obtained by the time-sharing process is the ratio
of total material removal in six cycles to time duration of the six cycles, which depends on the arrangement and
distribution of the six removal functions. Simulations on the synthesized overall removal functions under two different
modes of motion, i.e., planet motion and translation-rotation are performed from which the optimized combination of
tool parameters and distribution of time-sharing synthesis removal functions are obtained. The evaluation function when
optimizing is determined by an approaching factor which is defined as the ratio of the material removal within the area of
half of the polishing tool coverage from the polishing center to the total material removal within the full polishing tool
coverage area. After optimization, it is found that the optimized removal function obtained by time-sharing synthesis is
closer to the ideal Gaussian type removal function than those by the traditional methods. The time-sharing synthesis
method of the removal function provides an efficient way to increase the convergence speed of the surface error in
CCOS for the fabrication of aspheric optical surfaces, and to reduce the intermediate- and high-frequency error.