Neil Gardner

Improving optical bench radius measurements using stage error motion data

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 cats 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.

Retrace error evaluation on a figure-measuring interferometer

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 figure-error-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.

Improving metrology for micro-optics manufacturing

Metrology is one of the critical enabling technologies for realizing the full market potential for micro-optical systems. Measurement capabilities are currently far behind present and future needs. Much of today’s test equipment was developed for the micro-electronics industry and is not optimized for micro-optic materials and geometries. Metrology capabilities currently limit the components that can be realized, in many cases. Improved testing will be come increasingly important as the technology moves to integration where it will become important to “test early and test often” to achieve high yields. In this paper, we focus on micro-refractive components in particular, and describe measurement challenges for this class of components and current and future needs. We also describe a new micro-optics metrology research program at UNC Charlotte under the Center for Precision Metrology and the new Center for Optoelectronics and Optical Communications to address these needs.

Ray-trace simulation of the random ball test to improve microlens metrology

Interferometer wavefront bias is a complicated function of the optics imperfections in the instrument. An interferometric measurement of the figure error on a micro-refractive lens requires careful calibration to separate instrument bias from errors on the part. A self-calibration method such as the random ball test is effective in accomplishing this task without the need for a high-quality calibration artifact. The test, an averaging technique applied to a series of sphere surface patches, allows for calibration of the interferometric wavefront bias. Recent studies of the random ball test have shown that the calibration is affected by ray-trace errors that depend on the curvature of the ball used for the test and becomes significant in the micro-optic range (radius less than 1 millimeter). A comprehensive ray-trace simulation of the random ball test with modifiable variables was created using MATLAB® and ZEMAX® to allow for further investigation into the relationship between test lens misalignment, curvature, numerical aperture, ball figure error, and interferometer bias. The basis for the model hinges on defining a sphere in terms of a set of spherical harmonic functions, and varying the amplitudes and the number of functions to adjust the figure error on the sphere. The flexible simulation can be fine-tuned and used to model a variety of interferometers with different specifications. Our ultimate goal is to confirm the validity of the RBT, determine an efficient method of implementation, and understand the aspects impacting calibration uncertainty.

Radius case study: optical bench measurement and uncertainty including stage error motions

This paper provides a case study for identifying radius measurement uncertainty on a commercially-available optical bench using a homogeneous transformation matrix (or HTM)-based formalism. In this approach, radius is defined using a vector equation, rather than relying solely on the recorded displacement between the confocal and cats eye null positions (i.e., the projection of the true displacement between these positions on the transducer axis). The vector-based approach enables the stage error motions, as well as other well-known error sources, to be considered through the use of HTMs. An important aspect of this mathematical radius definition is the intrinsic correction for measurement biases, such as cosine error (i.e., misalignment between the stage motion and displacement transducer axis) which would lead to an artificially small radius value if the traditional projection-based radius measurand were employed. Experimental results and measurement techniques are provided for the stage error motions, which are then combined with the setup geometry to determine the radius of curvature for a spherical artifact. Comparisons are shown between the vector-based radius calculation, traditional radius computation, and independent measurements using a coordinate measuring machine. The measurement uncertainty for the vector-based approach is determined using Monte Carlo simulation and is compared to experimental results.

Compact interferometer for micro-optic performance and shape characterization

We have focused on measurement needs for micro-refractive lenses and have developed a flexible and compact micro-interferometer that can be used to measure lens radius of curvature and form errors. Transmitted wavefront and back focal length measurements can be easily added to the instrument. This instrument addresses measurement needs for micro refractive lenses. The interferometer is based on a Mitutoyo metallurgical microscope and operates with a 633 nm helium neon source. The radius of curvature measurement is directly traceable, meaning an external artifact is not required for calibration. This requires a careful mechanical design, a detailed alignment procedure with estimates of alignment uncertainties, and stage error motion characterization with estimates of uncertainties. The instrument can also be used to measure some diffractive components and mold form errors. We describe the instrument in this paper and discuss design goals and measurement specifications.

Improving Radius Measurements on a Commercial Interferometer

We have applied a mathematical error motion compensation technique to improve radius measurements on a commercial instrument and removed a 0.14% bias from the measured radius value. The method uses a homogeneous transformation matrix formalism.

Traceable radius of curvature measurements on a micro-interferometer

Radius of curvature is a critical parameter to measure in the manufacturing of micro-refractive elements. It defines the power of the surface and provides important information about the stability and uniformity of the manufacturing process. The radius of curvature of an optical surface can be measured using an interferometer and radius slide where the distance is measured as the surface is moved between the confocal and cat’s eye positions. However, the radius of curvature for micro-refractive elements can be on the order of a few hundred microns and the uncertainty in the measurement due to stage error motions can become a significant portion of the tolerance. Typically the radius slide is calibrated using an artifact, but the radius of the artifact must be traceable to the base unit of length and the calibration is subject to misalignment errors. Alternatively, the stage error motions can be measured with standard machine tool metrology techniques and used to correct the errors in the radius of curvature measurement. This paper details the implementation of a directly traceable radius of curvature measurement on a micro-interferometer, including alignment procedures, measurement of stage error motions, displacement gauge calibration, and data analysis strategies.

Self-calibration for microrefractive lens measurements

Micro-optics are essential components for building compact optoelectronic and micro-electro-optical mechanical systems and micro-refractive lenses are an important example. Refractive lenses are continuous relief structures and details of their dimensional shape, refractive index and homogeneity strongly influence performance. Some dimensional and transmitted light properties of the refractive components can be measured with scanning white light interferometers (SWLI), profilometers, and phase-shifting micro-interferometers, however limitations exist with each method. Micro-interferometry is the most promising and can be used to measure radius of curvature, focal length, dimensional surface errors, and transmitted wavefront. However, methods have not been optimized to achieve low uncertainties. Systematic biases can be comparable to figure errors on the part, therefore a rigorous calibration method is needed. Current practice involves measuring a very high quality part and measured errors are equated to instrument biases. It is often difficult, however, to obtain such a part. The alternative is to use a self-calibration test. As an alternative, the random ball test can be applied to micro-interferometers and SWLIs for self-calibration. This paper details the implementation of this test for both types of instruments and describes the method of estimating the calibration uncertainty.

Measurement advances for micro-refractive fabrication

Micro-refractive lenses are critical components in many devices, yet characterization remains challenging. We have developed calibration methods for micro-interferometry to improve form error, transmitted wavefront, and radius of curvature measurements.