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Overview: Stressed polishing technology was firstly proposed by Jerry E.Nelson in 1980, considered as an effective method of aspheric fabrication. According to the calculated results of elastic mechanics, this method exerts an external force on the mirror to form a deformation which opposite to the desired deformation from spherical surface to off-axis aspheric surface. Under the state of deformation, the mirror is polished into sphere surface. After removing the external force, the required off-axis aspheric surface can be obtained. Because aspheric fabrication is converted to spherical fabrication, tools with large diameter can be used and efficiency is greatly improved.
The key to achieve high precision of stressed polishing is to test the deformation of mirror with high precision. However, the main methods of surface measurement nowadays are interferometer and CMM. If interferometer is used, its dynamic range can only support the detection below micron deformation. If CMM is used, probe may scratch the mirror surface, and the detection tempo is very slow. Furthermore, interferometer and CMM are both expensive and complex equipments.
So, aimed at stressed polishing above micron deformation, stereoscopic phase measuring deflectometry was used to test its surface topography and deformation. It is low cost and convenient technique and only screen, camera, and computer were needed when implemented. More importantly, characteristics such as high dynamic range, full-field three-dimensional measurement and excellent performance in medium and high frequency were brought in, which are very suitable for the test of stressed mirror.
When measuring, firstly calculating the unwrapped phase distribution through CCD cameras, then calculating the height of a specific point on the measured surface using normal consistency constraint, and finally the full-field height distribution was obtained by Southwell gradient integral algorithm. To improve the measuring accuracy, composition of systematic errors were simulated, proved that it mainly includes low-order non-rotational symmetry items. According to simulating results, errors were calibrated and removed by N-step averaging method to get a absolute surface topography.
In this paper, the absolute surface topography and the deformation of a stressed mirror with a diameter of 320 mm, spherical radius of 5200 mm were measured. The measuring results were consistent with the corresponding result of CMM and finite element simulation, indicating that this proposed method is on the level of micron in terms of accuracy and more suitable for the test of stressed mirror compared with interferometer and CMM.
Schematic diagram of the measurement system
Schematic diagram of stereoscopic PMD
Simulation of the systematic error distribution
Measuring device setup
Stressed mirror under test.
Schematic diagram of system pose parameter in calibration results
Fringe image in the vertical direction.
Heights measuring results of stressed mirrors at 6 rotation angles.
Systematic error distribution
Mirror shape after removing systematic errors
Results of stressed mirror measured by CMM
Theoretical influence function of each actuating motor.
Deformation measurement results of each actuating motor.
Comparison of theoretical deformation and measuring deformation of each actuating motor.
Theoretical target correction functions of 4 aberrations.
Deformation measurement results of 4 aberrations.