Scanning measurement of surface error and thickness variation of the hemispherical resonator.

Hemispherical resonant gyroscopes (HRGs) are solid-state vibration gyroscopes with the highest precision and are widely used in the aerospace field. The core part of the gyroscope is the resonator, which is a thin-walled hemispherical shell. Surface error and thickness variation of a hemispherical shell causes frequency splitting, which degrades the performance of the HRG. In order to guide the mass leveling of hemispherical resonator, this paper presents a new method for scanning measurement of the surface error and thickness variation of hemispherical resonators. First, a multi-axis platform is designed for noncontact sensor scanning measurements along the meridian and latitudinal lines of the hemispherical resonator. Second, the error model of the measurement system is established. The surface error of the standard sphere is measured to calibrate and compensate for the assembly errors of the measuring device. In addition, the identification accuracy of assembly errors and the influence of assembly errors on thickness measurement are simulated by a computer. Finally, the surface error and thickness variation of the hemispherical resonators are measured. The method is experimentally demonstrated and validated with a wavefront interferometry test. The results show that the method can achieve high precision and high repeatability, which is instructive for assessment of the machining error and further evaluation of the hemispherical resonator.

Quasi-absolute interferometric testing of cylinders.

A three-step quasi-absolute testing method for optical cylinders is proposed in this Letter. Three measurements are taken at the so-called cat's eye position and confocal null testing positions with a computer-generated hologram (CGH) rotated around the axis parallel to that of the cylinder. The quasi-absolute surface error of the cylinder is obtained by simple operations including addition/subtraction and flip of the datasets. The uncertainty is traceable to an optical flat. Two different CGHs are used for a convex cylinder and give consistent quasi-absolute testing results of the surface error, which experimentally validates the method.

Misalignment measurement of membrane diffractive telescope segments by means of edge sensors with form closure.

The membrane diffractive telescope is an alternative to future 10-meter class space telescopes due to its possible lower cost of manufacturing and launching. To actively control the misalignment, the edge sensor network is utilized to measure the relative in-plane motions as well as out-of-plane motions of neighboring segments. The measurement is vulnerable to noise and malfunction of sensors. We first model the segment kinematics, which is used to simulate the propagation of sensor error to the segment configuration error. Monte Carlo simulation results show that the sensor error is considerably accumulated in the configuration error, which follows approximately normal distribution. On the other hand, the ring-arranged segments imply the form closure with redundancy of edge sensors. It is employed to judge whether there are abnormal sensor readings and then to identify the malfunctioning sensors. A better estimation can further be obtained as correction to the abnormal readings. Simulation results show that without sensor error, the algorithm in most cases can identify two malfunctioning in-plane sensors and two malfunctioning out-of-plane sensors. While considering the sensor error, only one malfunctioning in-plane sensor and one malfunctioning out-of-plane sensor can be identified with a sufficiently big ratio of abnormal reading to the normal sensor error.

Adaptive wavefront interferometry for unknown free-form surfaces.

The primary problem of conventional wavefront interferometers is limited dynamic range. Unknown free-form surface figure error with large amplitude or slope is not measurable for too dense or invisible fringes. To troubleshoot this problem, we propose adaptive wavefront interferometry (AWI). AWI utilizes a wavefront sensor-less adaptive optics (AO) subsystem to intelligently speculate and compensate the unknown free-form surface figure error. In this subsystem, adaptive null optics is utilized to iteratively generate adaptive wavefronts to compensate the unknown severe surface figure error. The adaptive null optics is close-loop controlled (i.e., wavefront sensor-less optimization algorithms are utilized to control it by real time monitoring the compensation effects to guarantee convergence of the iteration). Ultimately, invisible fringes turn into resolvable ones, and null test is further realized. To demonstrate the feasibility of AWI, we designed one spatial light modulator (SLM) based AWI modality as an example. The system is based on a commercial interferometer and is easy to establish. No other elements are required besides the SLM. Principle, simulation, and experiments for the SLM based AWI are demonstrated.

Stitching test of large flats by using two orthogonally arranged wavefront interferometers.

The most challenging problem in the stitching test of large flats with a small-aperture interferometer is the accumulation effect of the second-order error. As it is approximately enlarged by the square of the ratio of full aperture size to subaperture size, a very small amount of the second-order error in the reference surface of a transmission flat can be accumulated and gets far from negligible when the subaperture is far smaller than the full aperture. We present here a solution by using two orthogonally arranged wavefront interferometers. One is responsible for a subaperture test and the other for the simultaneous measurement of relative tilts. Because the accumulation effect originates from the lateral shift of the second-order error, only the tilt along the subaperture scanning direction needs to be measured accurately. It is no longer determined by stitching optimization instead to avoid the error accumulation. Piston and tilt perpendicular to the scanning direction are still determined by stitching optimization. The method is experimentally verified and compared to the stitching test with the reference surface error calibrated out, both referenced to the full aperture test result obtained with a 24-inch interferometer.

High spatial resolution zonal reconstruction with modified multishear method in frequency domain.

An exact multishear zonal algorithm is proposed to reconstruct two-dimensional wavefronts in frequency domain. The algorithm maintains the advantage of fast Fourier transform and loosens the "natural extension" requirement that the shear amounts must be divisors of sampling points N; therefore, it can be rapidly executed for large data arrays. The effect of tilt errors in multishear interferometry is analyzed and compensated in our method. The presented algorithm is applicable for a general aperture shape by using an iterative method. Application of large shears is allowed, and high resolution of the reconstructed wavefront can be achieved. Results of numerical simulations demonstrate the capability of our method.

Exact recovery of wavefront from multishearing interferograms in spatial domain.

An exact algorithm based on the multishearing interferograms has been proposed to reconstruct a two-dimensional wavefront. It allows large shears and high resolution of the reconstructed wavefront to be achieved. In this paper, we use simultaneous linear equations to express the relationship between difference wavefronts and the unknown original wavefront, and then the least-squares method is applied to reconstruct the wavefront. To solve the memory problem, an improved wavefront reconstruction algorithm based on virtual subaperture stitching was proposed to improve the calculation efficiency. Lastly, numerical simulations are implemented and the proposed algorithm is compared with another modal and zonal method. The results indicate that the proposed algorithm is capable of reconstructing continuous or discontinuous wavefronts exactly with a large grid. Numerical simulation also shows high accuracy recovery capability of the proposed method in the existence of mixed noise.