Angela Davies

Displacement Uncertainty in Interferometric Radius Measurements

Abstract Interferometric radius measurements may be completed using a radius bench, where radius is defined as the displacement between the confocal and cats eye nulls (identified using a figure measuring interferometer). Measurements of a Zerodur sphere have been completed on the X-ray Optics Calibration interferometer (XCALIBIR) and a coordinate measuring machine. Larger recorded disagreements than indicated by the current uncertainty analysis call for an exploration of the analysis model. This paper details uncertainties associated with the use of multiple displacement measuring interferometers (DMIs) to record motion in a single axis by treating the specific case of displacement measurement on XCALIBIR using three DMIs equally spaced around the optical axis.

Uncertainties in interferometric measurements of radius of curvature

The radius of curvature of spherical surfaces may be determined using the well-known radius, or optical, bench. In this method, a figure measuring interferometer is employed to identify the null positions at the center of curvature (confocal) and surface (cats eye) of the test optic. A linear slide provides motion between these positions and one or more displacement transducers is used to record the displacement between the cats eye and confocal positions and, hence, the radius of curvature. Measurements of a polished Zerodur sphere have been completed on the X-ray Optics Calibration Interferometer (XCALIBIR) using both Twyman-Green and Fizeau configurations. Mechanical measurements of the spherical artifact have also been completed using a coordinate measuring machine (CMM). Recorded disagreement between the individual transmission sphere measurements and CMM measurements under well-controlled environmental conditions is larger than the limits predicted from a traditional uncertainty analysis based on a geometric measurement model. Additional uncertainty sources for the geometric model, as well as a physical optics model of the propagation of light, are therefore suggested. The expanded uncertainty analysis is described.

Silicon wafer thickness variation measurements using the National Institute of Standards and Technology infrared interferometer

Decreasing depths of focus, coupled with increasing silicon wafer diameters, place greater restrictions on chucked wafer flatness in photolithography processes. A measurement device is described that measures thickness variation of double-sided polished wafers using an IR source and vidicon detector. Various possible instrument configura- tions are described with the focus on a setup that uses a collimated wavefront to produce interference fringes between the front and back surfaces of the plane parallel wafer. Experimental results are presented. These tests include (1) a drift test; (2) comparisons between measure- ments performed using different collimators and, subsequently, wave- fronts; (3) an exploration of the impact of phase change on reflection due to the wafer clamping method; and (4) an intercomparison with thickness measurements recorded by a capacitance gage-based instrument and surface measurements obtained using a separate visible wavelength interferometer.

Two-quadrant area structure function analysis for optical surface characterization

This paper describes the use of the area structure function (SF) for the specification and characterization of optical surfaces. A two-quadrant area SF is introduced because the one-quadrant area SF does not completely describe surfaces with certain asymmetries. Area SF calculations of simulation data and of a diamond turned surface are shown and compared to area power spectral density (PSD) and area autocorrelation function (ACF) representations. The direct relationship between SF, PSD, and ACF for a stationary surface does not apply to non-stationary surfaces typical of optics with figure errors.

Reflectometry-based wavelength scanning interferometry for thickness measurements of very thin wafers

With the development of microelectronics, the demand for silicon wafers is greatly increased for various purposes, especially the use of thin wafers for smart cards, cellular phones and stacked packages. In this paper, we describe an innovative scheme of combining wavelength scanning interferometry (4 nm tuning range centered at 1550 nm) with spectroscopic reflectometry that enables us to measure the thickness profile of thin wafers below 100 microm with high thickness resolution. The performance of this method is compared with that of an existing technique and verified by measuring several thin wafers.

3D surface mapping of freeform optics using wavelength scanning lateral shearing interferometry

Freeform optics have emerged as promising components in diverse applications due to the potential for superior optical performance. There are many research fields in the area ranging from fabrication to measurement, with metrology being one of the most challenging tasks. In this paper, we describe a new variant of lateral shearing interferometer with a tunable laser source that enables 3D surface profile measurements of freeform optics with high speed, high vertical resolution, large departure, and large field-of-view. We have verified the proposed technique by comparing our measurement result with that of an existing technique and measuring a representative freeform optic.

Micro-optic reflection and transmission interferometer for complete microlens characterization

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.

Self-calibration for transmitted wavefront measurements

Micro-optic components and subsystems are becoming increasingly important in optical sensors, communications, data storage, and many other diverse applications. To adequately predict the performance of the final system, it is important to understand the elements effect on the wavefront as it propagates through the system. The wavefront can be measured using interferometric means, however, random and systematic errors contribute to the measurement. Self-calibration techniques exploit symmetries of the measurement or averaging techniques to separate the systematic errors of the instrument from the errors in the test lens. If the transmitted wavefront of a ball lens is measured in a number of random orientations and the measurements are averaged, the only remaining deviations from a perfect wavefront will be spherical aberration from the ball lens and the systematic errors of the interferometer. If the radius, aperture, and focal length of the ball lens are known, the spherical aberration can be calculated and subtracted, leaving only the systematic errors of the interferometer. We develop the theory behind the technique and illustrate the approach with a description of the calibration of a microinterferometer used to measure the transmitted wavefront error of micro-optics.

Observations of alloying in the growth of Cr on Fe(001)

Abstract Using scanning tunneling microscopy, we observe the alloying of Cr with an Fe(001) substrate for various coverages at two temperatures. At low Cr coverage, the alloy consists of individual Cr impurities surrounded by Fe. Elemental identification is possible using surface states observed via tunneling spectroscopy. The alloy may be the cause of several magnetic anomalies observed in Cr/Fe structures.

Complete fringe order determination in scanning white-light interferometry using a Fourier-based technique

White-light interferometry uses a white-light source with a short coherent length that provides a narrowly localized interferogram that is used to measure three-dimensional surface profiles with possible large step heights without 2π-ambiguity. Combining coherence and phase information improves the vertical resolution. But, inconsistencies between phase and coherence occur at highly curved surfaces such as spherical and tilted surfaces, and these inconsistencies often cause what are termed ghost steps in the measurement result. In this paper, we describe a modified version of white-light interferometry for eliminating these ghost steps and improving the accuracy of white-light interferometry. Our proposed technique is verified by measuring several test samples.