Improving optical bench radius measurements using stage error motion data

Abstract

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.

Laser differential confocal radius measurement system

“…The system repeatability can be further improved by enhancing the environment stability through strict environmental control. At the same time, the offset between the measurement results and the nominal value can be reduced by compensating for the environmental parameters, misalignment, and motion errors to further improve the accuracy of the system [7,12,13].…”

“…The air-bearing slider is made of granite, with traveling range of 1 m and straightness of 0.5 μm, which can reduce the motion error and radius measurement error effectively [11][12][13]. The system also uses a coaxial design; the optical paths of the differential confocal system and the DMI have been set on the same line, which reduces Abbe error.…”

Aerial wetting contact angle measurement using confocal microscopy

“…The basic principle behind the advanced confocal technique uses the difference in the relative locations of the cats-eye condition (when the focal point is coincident with the apex of surface) and the confocal condition (when the focal point is coincident with the centre of curvature) as a measure of the radius of curvature [15][16][17][18].…”

Laser differential confocal radius measurement

“…The main errors having effects on ROC measurement are the distance measurement error of laser interferometer, position errors at cat's-eye position A and confocal position B, wavefront aberrations of sphere measured and axial alignment errors, and so on [3,14,15].…”

“…It can be seen from Eqs. (2) and (15) that the offset ∆z A and ∆z B of points O A and O B are equal, the radius measurement error caused by the VPH axial offset δ is…”