研究目的
To investigate the influence of form aberrations, particularly local deviations, on the volume value of spheres measured using a spherical interferometer, and to understand how these aberrations affect the wavefront and measurement uncertainty.
研究成果
The optical simulation provides deep insights into wavefront aberrations due to form deviations. Significant influences on volume value occur only for spheres with high form aberrations (e.g., above 350 nm pv for most real spheres). For lower aberrations, mean radius differences are negligible. The pv-value of difference topography increases quadratically with magnification, and the number and complexity of deviations affect measurement uncertainty, with real spheres showing larger effects than synthetic ones. This helps in setting limits for acceptable deviations in mass standard transfers.
研究不足
The simulation assumes optimal alignment and does not fully account for all real-world imperfections. The evaluation algorithm may not perfectly separate sphere surface information from reference surfaces, leading to residues in stitching. The study is limited to specific synthetic and real spheres, and results may not generalize to all types of topographies. The quadratic increase in pv-value with magnification indicates potential underestimation for complex structures.
1：Experimental Design and Method Selection:
The study uses optical simulations to model a spherical Fizeau interferometer setup. The simulation involves ray tracing and interferogram calculation to estimate wavefront aberrations caused by form deviations in spheres.
2：Sample Selection and Data Sources:
Synthetic data sets of spheres with local deviations (e.g., one or multiple peaks of 20 nm to 2000 nm) and real measured data from spheres like Si-PTB-12-03 and AVO28-S5c are used.
3：List of Experimental Equipment and Materials:
The setup includes a spherical interferometer with Fizeau lenses, a stabilized laser (wavelength 633 nm), fiber optics, collimator, quarter-wave plate, and charge-coupled device (CCD) for detection.
4：Experimental Procedures and Operational Workflow:
The simulation traces rays from the fiber through the interferometer to the CCD, calculates interferograms, and evaluates diameter values using phase-stepping algorithms. Spheres are rotated into multiple positions for comprehensive measurement.
5：Data Analysis Methods:
Data is analyzed using Zernike fits for wavefront determination, spherical harmonic functions for topography reconstruction, and difference topographies to compare simulated and input data. Statistical analysis includes calculating mean radius differences and peak-to-valley values.
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