Aspheric Optical Surfaces Research Articles

大型非球面形状のナノメートル測定（第5報） 走査法を用いた凹面ミラーの測定における誤差要因の検証

大型非球面形状のナノメートル測定（第5報） 走査法を用いた凹面ミラーの測定における誤差要因の検証

A New Algorithm for Solving the Best-Fit Sphere of Optical Aspherical Surface

To solve the best-fit sphere (BFS) accurately is one of the technological keys for the generating and testing of optical aspherical surfaces. This paper presents a new algorithm for solving the BFS of aspherical surfaces to suppress some deficiencies in the existing BFS algorithms. In the proposed approach, a BFS is constructed, which passes through both sides of endpoints in the section of the aspherical surfaces, the center of the BFS is shifted along the x-axis, and its radius of curvature is automatically computed. The variable step size method is proposed to speed up the convergence of the iteration. Through numerically solving the BFS of conic and cubic surface, the advantages of the proposed approach are verified. The results show that the proposed approach is of rapid convergence, and high accuracy; it is not only suitable for the conic surface, but also for higher order aspheres. The obtained asphericity and material removal function is more suitable for the machining and test.

大型非球面形状のナノメートル測定（第４報）:走査法を用いた凹面ミラーの数値計算と実験

大型非球面形状のナノメートル測定（第４報）:走査法を用いた凹面ミラーの数値計算と実験

Nanometer profile measurement of large aspheric optical surface by scanning deflectometry with rotatable devices: Uncertainty propagation analysis and experiments

Abstract High-accuracy mirrors and lenses with large dimensions are widely used in huge telescopes and other industrial fields. Interferometers are widely used to measure near flat surfaces and spherical optical surfaces because of their high accuracy and high efficiency. Scanning deflectometry is also used for measuring optical near flat surfaces with sub-nanometer uncertainty. However, for measuring an aspheric surface with a large departure from a perfect spherical surface, both of these methods are difficult to use. The key problem for scanning deflectometry is that high-accuracy autocollimators usually have a limited measuring range less than 1000″, so it cannot be used for measuring surfaces having a large slope. We have proposed a new method for measuring large aspheric surfaces with large slopes based on a scanning deflectometry method in which rotatable devices are used to enlarge the measuring range of the autocollimator. We also proposed a method to connect the angle data which is cut by the rotation of the rotatable devices. An analysis of uncertainty propagation in our proposed method was done. The result showed that when measuring a large aspheric surface with a diameter over 300 mm and a slope of 10 arc-deg, the uncertainty was less than 10 nm. For the verification of our proposed method, experimental devices were set up. A spherical optical mirror with a diameter of 35 mm and curvature radius of 5000 mm was measured. The measuring range of the autocollimator was successfully enlarged by our proposed method. Experimental results showed that the average standard deviation of 10 times measurement was about 20 nm.

Controlling Profile Error for Spherical Surface Micro-Lens in Precision Grinding

As the consumer market in the optics, electronics and aerospace industries grows, the profile accuracy demand for ultra-precision flat, spherical and aspheric optical surface micro-lens increases. Previous studies have found that machine system accuracy, tool alignment error and tool radius measurement error impact greatly on the profile accuracy of the machined surface. In this paper, we developed a grinding system based on the ultra-precision diamond lathe, presented a unified mathematical model of effects of all the geometric errors to the shape error by using the multi-body system theory. Aiming at the main source of profile error, the practical mathematical model is derived, and their propagation coefficients to profile error are calculated. By means of simulation analysis and grinding experiments of spherical part of tugnsten carbide, we conclude that the radial tool alignment error is the main influencing factor for the profile error of spherical surface; while tool radius measurement error influence the radius of sphere only.

An improved phase retrieval algorithm for optical aspheric surface measurement

In order to overcome the measurement and calculation difficulty for aspheric surface with phase retrieval technology, an improved phase retrieval algorithm was proposed. Due to significant departure from sphere surface, reflected light from different part of the aspheric surface under test will overlap in some areas in the collected images by CCD with general phase retrieval measurement setup, which will lead to the failure to recover the surface phase. The proposed algorithm will only use those areas without light overlapping in each image in the iteration process and employ several defocused images to recover the whole surface. This algorithm can improve the measurement range for aspheric surface with phase retrieval technology. The experimental system was established and a 180 mm diameter, f/1.6 parabolic mirror and a 180 mm effective diameter, f/1.33 hyperboloid mirror were tested by the proposed method. The experimental results show that the retrieved surface errors are in good consistent with that obtained by interferometer, which confirms the validity of the proposed algorithm.

Profile Measurement of Large Aspheric Optical Surface by Scanning Deflectometry with Rotatable Optical Devices - Error Analysis and Pre-Experiment-

Large aspheric mirrors with diameter over 300 millimeters with high surface accuracy are wildly used in many areas such as astronomical telescopes. Interferometers are widely used in profile measurement of optical flat and sphere. However, standard reference aspheric surface which is necessary for this method is difficult to make. Scanning defletometry based on ESAD (Extended Shear Angle Difference) is used to measure ultra-precise large near-flat and slight curved optical surface with the accuracy of sub-nanometer. However, it is not possible for it to measure aspheric surface because of the limitation of the measuring range of autocollimators. We proposed a new measuring method to scan the surface of a large aspheric optical surface using autocollimator with rotatable optical devices fixed on linear motion stage. To eliminate the influence of the pitching error of the scanning stage, we use two mirrors reflecting laser comes from autocollimator, which have the same effect with a pentaprism used in ESAD. To enlarge the measuring range of the autocollimator, we use a rotatable mirror to fit the changes of the slope of the mirror surface under measurement. The error analysis of the method is done. Measurement of an optical flat mirror and a sphere mirror with diameter of 50 mm and biggest slope of 6000 arc-second are done. The rotatable optical devices that we designed are proved effective on eliminating the pitching error of the moving stage.

Nanometer Profile Measurement of Large Aspheric Optical Surface (2nd report)

Nanometer Profile Measurement of Large Aspheric Optical Surface (2nd report)

Performance evaluation of laser lithographic machine for computer-generated hologram

Computer-generated holograms (CGHs) are often used for testing of aspheric optical surfaces. The precision of CGH mainly depends on the errors of the fabrication machine. We have developed a cylindrical-type direct laser lithographic machine whose working area is up to 360 mm. In this paper, the performance evaluation results of the lithographic machine are given.

Neural network based surface shape modeling of stressed lap optical polishing

It is crucially important to establish an accurate model to represent the relationship between the actuator forces and the lap surface changes when polishing a large and highly aspheric optical surface. To facilitate a computer-controlled optical polishing process, a neural network based stressed lap surface shape model was developed. The developed model reflects the dynamic deformation of a stressed lap. The original data from the microdisplacement sensor matrix were used to train the neural network model. The experimental results show that the proposed model can represent the surface shape of the stressed lap accurately and provide an analytical model to be used to polish the stressed lap control system and the active support system for a large mirror.

Research on High-Precision Measurement Platform for Optical Aspheric Surface and Corresponding Error Compensation

With a hardware and software control scheme which including high-precision linear motors, contacting and non-contacting measurement sensor and a new developed of measuring software, this paper designs and establishes a high-precision measurement platform. This paper not only implements the hardware build, measuring software development, but also discusses corresponding error compensation, for example, probe radius compensation, rough error canceling and so on. The experimental results indicate that the measurement platform is suitable for high-precision measurement for optical aspheric surface.

Compact and robust linear Stokes polarization camera

We present novel applications of Bossa Nova Technologies Linear Stokes polarization camera. The SALSA camera is able to perform live measurement of Linear Stokes parameters, usual polarization parameters (Degree Of Linear Polarization and Angle Of Polarization) and other polarization based parameters (polarized image, depolarized image, virtual polarizer, polarization difference). First a brief description of the SALSA camera and its calibration is given. Then we present and discuss several results of target detection and contrast enhancement experiments. We will also introduce a novel polarization based metrological method of 3D shape measurement for in-line control of optical surfaces and control of highly aspheric optical surfaces. The architecture of the hardware and calibration results is presented. A new algorithm based on polarization imaging leading to the construction of the gradient field is described. Finally experimental results and observations as well as possible further steps are discussed.

大型非球面形状のナノメートル測定（第３報）:走査法を用いた凹面ミラーの測定実験とシミュレーション

大型非球面形状のナノメートル測定（第３報）:走査法を用いた凹面ミラーの測定実験とシミュレーション

Ion beam figuring for lithography optics

Optical lithography is the key technology used for mass manufacturing of today’s semiconductor devices. The tremendous development pressure in the semiconductor industry, both in time-to-market and in design quality is best illustrated by “Moore’s Law” [G.E. Moore, Cramming more components on electronic circuits, Electronics 38 (1965) [1]] according to which the number of transistors that can be inexpensively placed on an integrated circuit is doubling approximately every two years. Today, state-of-the-art microprocessors are produced with smallest structures of 0.045μm width. Picometer tolerance requirements are already reality.Since the resolution of a lithography tool is determined by the performance of the imaging optics, it is obvious that the fabrication of such high-quality optics requires tremendous efforts. The following figure requirements have to be met both for spherical and for aspherical optical surfaces used in optical lithography tools to guarantee aberration control and contrast of the imaging optics: Figure<250 pm rmsMid-Spatial-Frequency Roughness (MSFR)<200 pm rmsHigh-Spatial-Frequency Roughness (HSFR)<100 pm rmsThis contribution focuses on the role of the ion beam figuring (IBF) technology in manufacturing of lens elements for lithography optics. An outline on past, present and future developments will be given.

The use of coordinate-measurement machines to optimize the technology of automatic shaping of optical surfaces

This paper presents examples of the use of coordinate-measurement machines in the technology for automatically shaping precision aspheric optical surfaces. A basis is laid for techniques for processing data and measurements, and practical recommendations are made for applying these techniques.

Evolutionary grinding model for nanometric control of surface roughness for aspheric optical surfaces

A new evolutionary grinding process model has been developed for nanometric control of material removal from an aspheric surface of Zerodur substrate. The model incorporates novel control features such as i) a growing database; ii) an evolving, multi-variable regression equation; and iii) an adaptive correction factor for target surface roughness (Ra) for the next machine run. This process model demonstrated a unique evolutionary controllability of machining performance resulting in the final grinding accuracy (i.e. averaged difference between target and measured surface roughness) of -0.2+/-2.3(sigma) nm Ra over seven trial machine runs for the target surface roughness ranging from 115 nm to 64 nm Ra.

Solution for Best Fitting Spherical Curvature Radius and Asphericity of Off-Axis Aspherics of Optical Aspheric Surface Component

This study aimed to establish the coordinate transformation between the off-axis aspherics coordinate system σ and the axial symmetry aspherics coordinate system σ by transforming coordinates and present the computation models of asphericity in rectangular coordinate system and cylindrical coordinate system respectively. The asphericity expressions in both coordinate systems were applicable to the comparative sphere calculation of Off-axis aspherics with different figures. We selected an Initiation sphere in view of technology, along with equations in a right coordinate system for certain caliber and structure. Then, by numerical computation, we selected the best fitting sphere and simplifed the complex models by choosing a right coordinate system. At last, the solution for asphericity and the best fitting sphere curvature radius of off-axis aspherics were introduced by examples.

Design considerations for the absolute testing approach of aspherics using combined diffractive optical elements

Aspheric optical surfaces are often tested using diffractive optics as null elements. For precise measurements, the errors caused by the diffractive optical element must be calibrated. Recently, we reported first experimental results of a three position quasi-absolute test for rotationally invariant aspherics by using combined-diffractive optical elements (combo-DOEs). Here we investigate the effects of the DOE substrate errors on the proposed calibration procedure and present a set of criteria for designing an optimized combo-DOE. It is demonstrated that this optimized design enhances the overall consistency of the procedure. Furthermore, the rotationally varying part of the surface deviations is compared with the rotationally varying deviations obtained by an N-position averaging procedure and is found to be in good agreement.

A novel definition method of optical asphericity

In view of the fact that methods for calculating asphericity of optical aspheric surface are nonuniform, a novel definition method named least maximal error method is proposed on the basis of an analysis of the common calculating methods. It fully unifies the asphericity calculation for conicoid and high-order aspheric surface. It finds the best-fitting spherical surface, notes the maximum deviation between aspheric surface and the best-fitting spherical surface minimum, and this maximum deviation is defined as the maximal asphericity of aspheric surface. The theory of the definition method and some calculation examples are put forward. The method is suitable for computer programming and its result is accurate.

Fabrication error analysis and experimental demonstration for computer-generated holograms

Aspheric optical surfaces are often tested using computer-generated holograms (CGHs). For precise measurement, the wavefront errors caused by the CGH must be known and characterized. A parametric model relating the wavefront errors to the CGH fabrication errors is introduced. Methods are discussed for measuring the fabrication errors in the CGH substrate, duty cycle, etching depth, and effect of surface roughness. An example analysis of the wavefront errors from fabrication nonuniformities for a phase CGH is given. The calibration of these effects for a CGH null corrector is demonstrated to cause measurement error less than 1 nm.