Metrology Of Freeform Surfaces Research Articles

Freeform surface adaptive interferometry assisted with simulated annealing-hill climbing algorithm

The freeform surface adaptive interferometer (FSAI) recently has been employed to realize the unknown freeform surface metrology. A near null interferogram should be acquired from the initial interferogram with undistinguished fringes even dark areas. The direct optimization object in FSAI is just the interferogram rather than the focusing intensity characterization in traditional wavefront-sensorless (WFS) adaptive systems. The simulated annealing-hill climbing (SA-HC) mixed algorithm is employed in the FSAI, which has much better convergence than the stochastic parallel gradient descent (SPGD) algorithm, almost as much as the geneticalgorithm (GA). At the same time, it is much faster than GA and thus applicable to the test of volume-produced in the optical shop. Simulations and experiments validating the algorithm feasibility are presented.

Nano-imprinted subwavelength gratings as polarizing beamsplitters

Polarizing beamsplitters have numerous applications in optical systems, such as systems for freeform surface metrology. They are classically manufactured from birefringent materials or with stacks of dielectric coatings. We present a binary subwavelength-structured form-birefringent diffraction grating, which acts as a polarizing beamsplitter for a wide range of incidence angles −30∘…+30∘. We refine the general design method for such hybrid gratings. We furthermore demonstrate the manufacturing steps with Soft-UV-Nanoimprint-Lithography, as well as the experimental verification, that the structure reliably acts as a polarizing beamsplitter. The experimental results show a contrast in efficiency for TE- and TM-polarization of up to 1:18 in the first order, and 34:1 in the zeroth order. The grating potentially enables us to realize integrated compact optical measurement systems, such as common-path interferometers.

SPGD and Newton iteration mixed algorithm used in freeform surface metrology

Freeform surfaces are widely used in advanced optical systems. In order to accurately measure freeform surfaces, an adaptive interferometer with deformable mirror (DM) has been developed for the freeform surface metrology. To ensure the efficiency, a stochastic parallel gradient descent (SPGD) and Newton iteration mixed algorithm to drive the DM has been proposed, it can achieve the minimum value of the optimization and is suitable for the different interferograms. The simulation and experimental results verify the correctness and feasibility of the proposed DM driving algorithm.

Precise positioning of the test surface and screen in a coaxial software configurable optical test system

The coaxial software configurable optical test system (SCOTS) is an aspheric and freeform surface metrology method with high accuracy. The positioning accuracy of the test surface and screen seriously affects the measurement accuracy. In this paper, a novel method, PDCMC (positioning with differential computation, calibration board assisted, 3D measurement and component displacement), is proposed for the precise positioning in the coaxial SCOTS. In the proposed method, a flat crystal is used as the initial test mirror. In the initial system, the positioning of the screen is carried out using the differential computation method. Then, the positioning of a calibration board is carried out based on the feature points on the calibration board. The relative position and attitude among the flat crystal, the calibration board and the actual test surface are provided by a 3D coordinate measuring machine. Finally, through coordinate transformation and data processing, the precise positioning of the test surface and screen can be completed in the actual coaxial SCOTS. The proposed method is highly versatile and suitable for almost all kinds of test surfaces. Simulation and experiments demonstrate the feasibility and accuracy of the proposed method. Compared with the existing universal positioning method, the proposed method has the advantages of fewer required components and higher precision.

Investigation on multi-body dynamics based approach to the toolpath generation for ultraprecision machining of freeform surfaces

This article presents an innovative approach to toolpath generation for ultraprecision machining of freeform optic surfaces based on the principle of Automatic Dynamics Analysis of Mechanical Systems. As components with freeform surfaces often have non-rotational symmetry, there are potential challenges facing their ultraprecision machining through single-point diamond turning, such as the projected points in complex large sag surfaces, which likely find it difficult to communicate with the control system and, thus, do not perform successfully. In ultraprecision machining, to achieve the highest performance in freeform surface resolution, the factors of dynamics, material and mechanical stiffness, frictions, tooling and accuracy of the servo component should be considered. The investigation is focused on an integrated approach and the associated scientific understanding of precision engineering design, ultraprecision machining and metrology of freeform surfaces as well as their application perspective. In this approach, the toolpath for very complex freeform surfaces can be generated using the Newton–Raphson method to solve the kinematics and dynamics equations of motion. The effect of friction and contact force are also investigated for accurate toolpath curve generation. Moreover, the Gear stiff (GSTIFF)/ Wielenga stiff (WSTIFF) integrator for solving the non-linear equations of motion is employed, and the result shows the time step size, playing a critical role in generating toolpath curves with a higher accuracy and resolution.

Model-based adaptive non-null interferometry for freeform surface metrology

A model-based adaptive non-null interferometry (MANI) is proposed for steep optical freeform surfaces in situ testing. The deformable mirror (DM) affording the flexible compensation is monitored with the beam in the interferometer by a wavefront sensor. The residual wavefront aberration in the non-null interferogram is eliminated by the multi-configuration ray tracing algorithm based on the system model, especially the DM surface model. The final figure error can be extracted together with the surface misalignment aberration correction. Experiments proving the feasibility of the MANI are shown.

Modeling near-null testing method of a freeform surface with a deformable mirror compensator

We present and analyze a new measurement method of freeform surfaces with a deformable mirror (DM), which functions as a wavefront compensator. We discuss the maximum slope compensation of a DM in the first-order approximation and derive how to calculate the ideal DM form. A constrained optimization procedure is conducted to ensure the actual DM form fits the ideal DM form as closely as possible. To demonstrate the feasibility and understand the measurable range of our method, we evaluate freeform surfaces with a single Zernike term, the first 36 random Zernike terms, and 230 random Zernike terms. A tolerance analysis of the DM position is carried out to show the effect of the tilt and the decenter of the DM on the measurement accuracy. Our studies show that the proposed system is very flexible for freeform surface metrology.

Method of alignment error control in free-form surface metrology with the tilted-wave-interferometer

Method of alignment error control in free-form surface metrology with the tilted-wave-interferometer