A combined Twyman–Green and Mach–Zehnder interferometer especially designed for the characterization of refractive microlenses is presented. This instrument allows for the quantitative characterization of the microlens form, the transmitted wavefront errors, the radius of curvature and the front focal length without removing the sample under test. All of these microlens properties are important when benchmarking different microlens fabrication technologies (Ottevaere et al 2006 J. Opt. A: Pure Appl. Opt. 8 S407–29). The interferometer was calibrated by the random ball test method. This paper describes the optical design and demonstrates the performance with the characterization of the instrument bias and measurements of a typical microlens. The performance is also compared with that of a semi-commercial instrument.
We describe the application of a vector-based radius approach to optical bench radius measurements in the presence of imperfect stage motions. In this approach, the radius is defined using a vector equation and homogeneous transformation matrix formulism. This is in contrast to the typical technique, where the displacement between the confocal and cat's eye null positions alone is used to determine the test optic radius. An important aspect of the vector-based radius definition is the intrinsic correction for measurement biases, such as straightness errors in the stage motion and cosine misalignment between the stage and displacement gauge axis, which lead to an artificially small radius value if the traditional approach is employed. Measurement techniques and results are provided for the stage error motions, which are then combined with the setup geometry through the analysis to determine the radius of curvature for a spherical artifact. Comparisons are shown between the new vector-based radius calculation, traditional radius computation, and a low uncertainty mechanical measurement. Additionally, the measurement uncertainty for the vector-based approach is determined using Monte Carlo simulation and compared to experimental results.
A micro-refractive lens figure error measurement is performed at the confocal position with the interferometer in reflection mode. The wavefront in the interferometer reflecting from the test surface inherently has aberrations at some level, and reflection from an imperfect test surface further deviates the wavefront and adds to the interferometer aberrations. The interferometer aberration causes each ray of light to reflect off the test lens and back into the interferometer at a different angle. Consequently, the ray takes a different path back through the interferometer and therefore accumulates a different aberration. The result is a re-trace error which increases with the test lens surface curvature and becomes significant in the micro-optic range. The dependence of test part radius on micro-lens figureerror-measuring interferometer wavefront bias data was confirmed both experimentally and by software simulation. Results clearly indicate that the re-trace error increases with test lens surface curvature. The fact that re-trace errors depend on the radius of the test part implies that when calibrating the instrument even with a perfect artifact, the calibration is nominally valid only when measuring parts with the same approximate radius as the calibration artifact. A compact micro-interferometer useful for measuring several properties of micro-lenses including figure error, was developed to verify this phenomenon. The instrument has the capability of measuring micro-lenses with radii of curvature between 150 µm and 3 mm.
The self-calibration test known as the random ball test ͑RBT͒ is adapted and applied to instrument calibration for measurements of microrefractive lens figure error. The RBT exploits the symmetry properties of a microsphere, resulting in a low-uncertainty estimate of the instrument biases. One hundred surface patches on a 1-mm-diam steel sphere are imaged by commercial instruments then averaged together in software to determine the instrument bias for a 500-m radius of curvature test piece. The results show biases on the order of a few hundred nanometers peak-to-valley for a scanning white light interferometer and a Twyman-Green interferometer.
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