Jonathan D. Ellis

High resolution heterodyne interferometer without detectable periodic nonlinearity

A high resolution heterodyne laser interferometer without periodic nonlinearity for linear displacement measurements is described. It uses two spatially separated beams with an offset frequency and an interferometer configuration which has no mixed states to prevent polarization mixing. In this research, a simple interferometer configuration for both retroreflector and plane mirror targets which are both applicable to industrial applications was developed. Experimental results show there is no detectable periodic nonlinearity for both of the retro-reflector interferometer and plane mirror interferometer to the noise level of 20 pm. Additionally, the optical configuration has the benefit of doubling the measurement resolution when compared to its respective traditional counterparts. Because of non-symmetry in the plane mirror interferometer, a differential plane mirror interferometer to reduce the thermal error is also discussed.

Simple heterodyne laser interferometer with subnanometer periodic errors

We describe a simple heterodyne laser interferometer that has subnanometer periodic errors and is applicable to industrial fields. Two spatially separated beams can reduce the periodic errors, and the use of a right-angle prism makes the optical configuration much simpler than previous interferometers. Moreover, the optical resolution can be enhanced by a factor of 2, because the phase change direction is opposite between reference and measurement signals. Experiments have demonstrated the periodic errors are less than 0.15 nm owing to the frequency mixing of the optical source. The improvements for reducing the frequency mixing of the optical system are also discussed.

Fiber-coupled displacement interferometry without periodic nonlinearity

Displacement interferometry is widely used for accurately characterizing nanometer and subnanometer displacements in many applications. In many modern systems, fiber delivery is desired to limit optical alignment and remove heat sources from the system, but fiber delivery can exacerbate common interferometric measurement problems, such as periodic nonlinearity, and account for fiber-induced drift. In this Letter, we describe a novel, general Joo-type interferometer that inherently has an optical reference after any fiber delivery that eliminates fiber-induced drift. This interferometer demonstrated no detectable periodic nonlinearity in both free-space and fiber-delivered variants.

First Demonstration of Ocular Refractive Change Using Blue-IRIS in Live Cats

PURPOSE To determine the efficacy of intratissue refractive index shaping (IRIS) using 400-nm femtosecond laser pulses (blue light) for writing refractive structures directly into live cat corneas in vivo, and to assess the longevity of these structures in the eyes of living cats. METHODS Four eyes from two adult cats underwent Blue-IRIS. Light at 400 nm with 100-femtosecond (fs) pulses were tightly focused into the corneal stroma of each eye at an 80-MHz repetition rate. These pulses locally increased the refractive index of the corneal stroma via an endogenous, two-photon absorption process and were used to inscribe three-layered, gradient index patterns into the cat corneas. The optical effects of the patterns were then tracked using optical coherence tomography (OCT) and Shack-Hartmann wavefront sensing. RESULTS Blue-IRIS patterns locally changed ocular cylinder by -1.4 ± 0.3 diopters (D), defocus by -2.0 ± 0.5 D, and higher-order root mean square (HORMS) by 0.31 ± 0.04 μm at 1 month post-IRIS, without significant changes in corneal thickness or curvature. Refractive changes were maintained for the duration they were tracked, 12 months post-IRIS in one eye, and just more than 3 months in the remaining three eyes. CONCLUSIONS Blue-IRIS can be used to inscribe refractive structures into live cat cornea in vivo that are stable for at least 12 months, and are not associated with significant alterations in corneal thicknesses or radii of curvature. This result is a critical step toward establishing Blue-IRIS as a promising technique for noninvasive vision correction.

Compact fiber-coupled three degree-of-freedom displacement interferometry for nanopositioning stage calibration

Heterodyne displacement interferometry is a widely accepted methodology capable of measuring displacements with sub-nanometer resolution in many applications. We present a compact heterodyne system capable of simultaneously measuring Z-displacement along with changes in pitch and yaw using a single measurement beam incident on a plane mirror target. The interferometers measurement detector utilizes differential wavefront sensing to decouple and measure these three degrees of freedom. Reliable rotational measurements typically require calibration; however, two analytical models are discussed which predict the readout of rotational scaling factors.

Development of a compact, fiber-coupled, six degree-of-freedom measurement system for precision linear stage metrology

A compact, fiber-coupled, six degree-of-freedom measurement system which enables fast, accurate calibration, and error mapping of precision linear stages is presented. The novel design has the advantages of simplicity, compactness, and relatively low cost. This proposed sensor can simultaneously measure displacement, two straightness errors, and changes in pitch, yaw, and roll using a single optical beam traveling between the measurement system and a small target. The optical configuration of the system and the working principle for all degrees-of-freedom are presented along with the influence and compensation of crosstalk motions in roll and straightness measurements. Several comparison experiments are conducted to investigate the feasibility and performance of the proposed system in each degree-of-freedom independently. Comparison experiments to a commercial interferometer demonstrate error standard deviations of 0.33 μm in straightness, 0.14 μrad in pitch, 0.44 μradin yaw, and 45.8 μrad in roll.

Femtosecond laser writing of freeform gradient index microlenses in hydrogel-based contact lenses

Femtosecond lasers can be used to write a variety of gradient index refractive devices. Writing devices with an arbitrary optical profile (i.e., freeform) requires knowing the functional dependence of the phase change that the wavefront will experience when passing through a region written under different exposure parameters. We measured this dependence as a function of writing speed and power in hydrogel-based contact lenses. Regions of constant refractive index change were written under different conditions and then the phase change was measured with a Mach-Zehnder interferometer and a phase retrieval algorithm. This functional dependence was tested by writing arbitrary Zernike polynomials with varying magnitudes.

Dynamic Doppler Frequency Shift Errors: Measurement, Characterization, and Compensation

Positioning calibration under dynamic conditions is becoming increasingly of interest for high precision fields, such as additive manufacturing and semiconductor lithography. Heterodyne interferometry is often used to calibrate a stages position because interferometry has a high dynamic range and direct traceability to the meter. When using heterodyne interferometry, filtering is routinely performed to process and determine the measured phase change, which is proportional to the displacement from one target location to another. The filtering in the signal processing introduces a phase delay dependent on the detection frequency, which leads to displacement errors when target velocity is non-constant as is the case in dynamic calibrations. This paper presents a phase delay compensation method by measuring instantaneous detection frequency and solving for the corresponding phase delay in a field-programmable gate array (FPGA) in real time. The FPGA hardware-in-the-loop simulation shows that this method can significantly decrease the displacement error from ±100s nm to ±3 nm in dynamic cases and it will still keep subnanometer resolution for quasi-static calibrations.

Toward interferometry for dimensional drift measurements with nanometer uncertainty

High-end industrial equipment evolves toward ever higher accuracies, and dimensional drift phenomena appear as a limitation for the required uncertainty level of precision metrology instrumentation. Detailed knowledge of the drift stability on timescales from minutes to weeks is needed for materials and constructional elements such as glued or bolted connections. We investigate a balanced, double-sided heterodyne interferometer for dimensional stability measurements. The complete interferometer includes an integrated refractometer and aims for a measurement uncertainty better than 100 pm. Measurements with a preliminary test setup of the instrument performance show an intrinsic stability of ±0.6 nm peak-to-peak over 23 h and 30 pm noise level at a timescale of a minute and shorter, limited by thermal and air refractive index fluctuations. Considerable improvement is expected for more stable ambient conditions and with dedicated, custom-made components.

Design of a folded, multi-pass Fabry–Perot cavity for displacement metrology

We present a folded, multi-pass cavity design for displacement measuring Fabry–Perot interferometry. The cavity length is designed to be one-quarter of the physical length needed for a typical Fabry–Perot interferometer by using a quarter-wave plate and a retroreflector. This enhances the displacement sensitivity by a factor of four, allowing for higher resolution in viewing the effects caused by mechanical motions, refractive index changes and frequency fluctuations from the laser source. Furthermore, the geometrical error motions are minimized by using a retroreflector due to its tip–tilt insensitivity. In this note, a theoretical analysis of the folded, multi-pass Fabry–Perot cavity is described and analyzed with Jones matrices in ideal and non-ideal designs.