Hongwei Jing

Simulation and validation of a prototype swing arm profilometer for measuring extremely large telescope mirror-segments

The Extremely Large Telescope (ELT) projects presuppose segmented primary mirrors. The metrology of the off-axis aspherical segments is particularly challenging in terms of global form, mid spatial frequencies and matching of the base-radius and conic constant. We propose to use a swing arm profilometer (SAP) to provide verification independent of interferometry. In this paper we present results of a simulation of the swing arm profilometer as applied to mirror segments, and experimental verification of the simulation using a prototype instrument.

Measurement of influence function using swing arm profilometer and laser tracker

We present a novel method to accurately measure 3D polishing influence functions by using a swing arm profilometer (SAP) and a laser tracker. The laser tracker is used to align the SAP and measure the parameters of the SAP setup before measuring the influence function. The instruments and the measurement method are described, together with measurement uncertainty analysis. An influence function deliberately produced with asymmetric form in order to create a challenging test is measured, and compared with that of a commercial 3D profilometer. The SAP result is 48.2 microm in PV, 7.271 mm(3) in volume. The 3D profilometer result is 48.4 microm in PV, 7.289 mm(3) in volume. The forms of the two results show excellent correlation. This gives confidence of the viability of the SAP method for larger influence functions out of range of the commercial instrument.

Measurement of an off-axis parabolic mirror using coordinates measurement machine and swing arm profilometer during the grinding process

We present the measurement methods for off-axis parabolic mirrors using Coordinates Measurement Machine and Swing Arm Profilometer during the grinding process. An off-axis parabolic mirror with 1200mm in parent focal length, 360mm in off-axis displacement and 410mm in diameter is measured using the methods introduced in this paper. The convergence curves of the surface error are reported, which is reduced from 204.7μm in PV, 55.3μm in rms to 1.1μm in PV, 0.3μm in rms after 39 iterations of grinding. Besides, the measurement methods are able to control the parent focal length and off-axis displacement to less than 0.1mm tolerance. An interferometric result is presented, which validates the measurement methods.

Measurement of large aspherical mirrors using coordinate measurement machine during the grinding process

A new method has been developed to measure large aspherical mirrors accurately, quickly, and economically by using CMM (coordinate measurement machine). By using CMM to get the 3D coordinates of the actual points on the large aspherical mirrors and make bestfitting of actual surface and nominal surface, we can evaluate the surface of the large aspherical mirrors. It costs only 2 hours to measure an aspherical mirror with diameter larger than 1000mm. The results show good agreement with the results measured by Hartmann-Shack interferometer. Using this method, we can supervise the profile error to less than 5 μm PV during the grinding process. All the aspherical mirrors with dimensions within the range of the machine can be measured.

Error separation technique for measuring aspheric surface based on dual probes

In this paper, we present an error separation method based on dual probes for the swing arm profilometer to calibrate the rotary table errors. Two probes and the rotation axis of swinging arm are in a plane. The scanning tracks cross each other as both probes scan the mirror edge to edge. Since the surface heights should ideally be the same at these scanning crossings, this crossings height information can be used to calibrate the rotary table errors. But the crossings height information contains the swing arm air bearing errors and measurement errors of probes. The errors seriously affect the correction accuracy of rotary table errors. The swing arm air bearing errors and measurement errors of probes are randomly distributed, we use least square method to remove these errors. In this paper, we present the geometry of the dual probe swing arm profilometer system, and the profiling pattern made by both probes. We analyze the influence the probe separation has on the measurement results. The algorithm for stitching together the scans into a surface is also presented. The difference of the surface heights at the crossings of the adjacent scans is used to find a transformation that describes the rotary table errors and then to correct for the errors. To prove the error separation method based on a dual probe can successfully calibrate the rotary table errors, we establish SAP error model and simulate the effect of the error separation method based on a dual probe on calibrating the rotary table errors.

Measurement of centering error for probe of swing arm profilometer using a spectral confocal sensor

A spectral confocal sensor was used to measure the centering error for probe of swing arm profilometer (SAP). The feasibility of this technology was proved through simulation and experiment. The final measurement results was also analyzed to evaluate the advantages and disadvantages of this technology.

Calibrating the axes of the swing arm profilometer by the four-based laser trackers

The swing arm profilometer realizes the measurement of the different surface shape by adjusting the axis of the arm bearing and the axis of the workpiece bearing for different spatial positional relationships,so the high precision positional relationship between the axis of the arm bearing and the axis of the workpiece bearing is the premise to obtain accurate result. This paper presents a way using four-based laser trackers to calibrate the axes of the swing arm profilometer,that satisfies the requirement of the high precision and the dynamic calibration. The four-based laser trackers system only uses the precise distances to obtain the coordinates of points. The coordinates of points in the rotate arc of the axes can fit the axes，and the relationship between the axes can be know. The study of the self-calibration of the four-based laser trackers, the arrangement of four-based laser trackers, the design of the calibration method and the processing of measurement data are included in this paper. Finally, the study is validated by the preliminary experiment.

Research on the measurement technology of effective arm length of swing arm profilometer

When the swing arm profilometer(SAP) measuring the mirror, the effective arm length of SAP which haves an obvious influence on the measurement results of the mirror surface shape needs to be measured accurately. It requires the measurement uncertainty of the effective arm length to reach 10μm in order to meet the measurement requirements, in this paper, we present a kind of technology based on laser tracker to measure the effective arm length of SAP. When the swing arm rotates around the shaft axis of swing arm rotary stage, the probe and two laser tracker balls form three sections of circular arc around the shaft axis of swing arm rotary stage in space. Laser tracker tracks and measures the circular arcs of two laser tracker balls, the center coordinates of the circular plane of circular arc can be calculated by data processing. The linear equation that passes through the two center coordinates is the equation of the shaft axis of rotary stage, the vertical distance from the probe to the shaft axis of rotary stage which can be calculated refer to the equation from the point to the line is the effective arm length. After Matlab simulation, this measurement method can meet the measurement accuracy.

Focal length measurement of microlens-array by the clarity function of digital image

In this paper, a method for the focal length measurement of Microlens-array (MLA) is introduced. The measuring setup is composed by monochromatic, condenser, collimator, MLA, microscope and CCD sensor. An experiment was performed using a MLA whose focal length is about 8 mm and a GUI based on Matlab software was developed to analyze the image gathered at the vertex and the focus by the clarity of digital image processing technology. The measuring uncertainty of this method is about 0.8% and this method introduced in this paper can finish tens of microlens array measurement at a single shot. Compared with traditional technology for MLA measuring, this method not only has a preferable precision but also super efficiency.

Experimental study on absolute measurement of spherical surfaces with shift-rotation method based on Zernike polynomials

Absolute testing methods have been widely employed in the accurate metrology of optical surface deviation. As a general method, the shift-rotation method requires several rotations and translations of the surface under test. And the surface deviation of the reference and the surface under test can be both calculated in terms of Zernike polynomials. The validity of the shift and rotation procedure was proved through experiments. Two different transmission spheres (with the same F number but different quality of the reference surfaces) were used to test the same spherical surface under test. The test results of the spherical surface under test are in good agreement.