Betty Lise Anderson

Total corneal power estimation: ray tracing method versus gaussian optics formula.

PURPOSE To evaluate with the use of corneal topographic data the differences between total corneal power calculated using ray tracing (TCP) and the Gaussian formula (GEP) in normal eyes, eyes that previously underwent laser in situ keratomileusis/photorefractive keratectomy (LASIK/PRK), and theoretical models. METHODS TCP and GEP using mean instantaneous curvature were calculated over the central 4-mm zone in 94 normal eyes, 61 myopic-LASIK/PRK eyes, and 9 hyperopic-LASIK/PRK eyes. A corneal model was constructed to assess the incident angles at the posterior corneal surface for both refracted rays and parallel rays. Corneal models with varying parameters were also constructed to investigate the differences between mean TCP and GEP (4-mm zone), and an optical design software validation was performed. RESULTS The TCP values tended to be less than GEP in normal and myopic-LASIK/PRK eyes, with the opposite relationship in some hyperopic-LASIK/PRK eyes having the highest anterior surface curvature. The difference between TCP and GEP was a function of anterior surface instantaneous radii of curvature and posterior/anterior ratio in postrefractive surgery eyes but not in normal eyes. In model corneas, posterior incident angles with parallel rays were greater than those with refracted rays, producing an overestimation of negative effective posterior corneal power; differences in magnitude between TCP and GEP increased with decreasing ratio of posterior/anterior radii of curvature, consistent with clinical results. CONCLUSIONS In eyes after refractive surgery, calculating posterior corneal power using the Gaussian formula and its paraxial assumptions introduces errors in the calculation of total corneal power. This may generate errors in intraocular lens power calculation when using the Gaussian formula after refractive surgery.

Optically produced true-time delays for phased antenna arrays

A device is described for generating true-time delays optically for microwave signals used in beam steering and beam shaping in phased-array antennas. The device can be adapted to provide delays from picoseconds to nanoseconds. A single, compact unit should provide parallel delays for more than 64 independent antenna elements with a greater than 6-bit resolution. The time delays are produced by multiple reflections in a mirror configuration with continuous refocusing. A single spatial light modulator selects independent optical path lengths for each of the parallel antenna elements. Amplitude control for beam shaping can be integrated into the device. The unit can be made rugged for harsh environments by use of solid-block construction. The operation of the true-time delay device is described, along with the overall system configuration. Preliminary experimental data are given.

Polynomial-based optical true-time delay devices with microelectromechanical mirror arrays

We previously reported optical true-time delay devices, based on the White cell, to support phased-array radars. In particular, we demonstrated a quadratic device, in which the number of delays obtainable was proportional to the square of the number of times the light beam bounced in the cell. Here we consider the possibilities when a microelectromechanical (MEM) tip/tilt mirror array with multiple stable states is used. We present and compare designs for quadratic, quartic, and octic cells using MEM mirror arrays with two, three, and five micro-mirror tilt angles. An octic cell with a three-state MEM can produce 6,339 different delays in just 17 bounces.

Optical true time delay for phased-array antennas: demonstration of a quadratic White cell

We have demonstrated a proof-of-concept optical device that can produce true time delays for a phased-array radar. This device combines White cells of differing lengths with a spatial light modulator to select between the paths on multiple bounces of a given beam. The approach can handle thousands of light beams and produce hundreds of different delays. The number of delays is proportional to the square of the number of bounces.

Demonstration of a linear optical true-time delay device by use of a microelectromechanical mirror array

We present the design and proof-of-concept demonstration of an optical device capable of producing true-time delay(s) (TTD)(s) for phased array antennas. This TTD device uses a free-space approach consisting of a single microelectromechanical systems (MEMS) mirror array in a multiple reflection spherical mirror configuration based on the White cell. Divergence is avoided by periodic refocusing by the mirrors. By using the MEMS mirror to switch between paths of different lengths, time delays are generated. Six different delays in 1-ns increments were demonstrated by using the Texas Instruments Digital Micromirror Device as the switching element. Losses of 1.6 to 5.2 dB per bounce and crosstalk of -27 dB were also measured, both resulting primarily from diffraction from holes in each pixel and the inter-pixel gaps of the MEMS.

Reconfigurable photonic switch based on a binary system using the White cell and micromirror arrays

We describe an N/spl times/N optical switch for use in cross-connects. It is a free-space device, based on multiple bounces in a pair of White cells sharing a spatial light modulator at one end. In a companion paper, we described various polynomial cells, in which the number of outputs was proportional to the number of bounces raised to some power. In the binary device described here, the number of possible outputs is proportional to the number two raised to the power of the number of bounces. It allows a 1024 /spl times/ 1024 switch using a single digital two-state tip/tilt micromirror array, four spherical mirrors, and a spot displacement device. It is highly scalable and insensitive to micromirror pointing accuracy.

Design and demonstration of a switching engine for a binary true-time-delay device that uses a White cell

Optical true-time-delay devices based on the White cell can be divided into two general types: polynomial cells, in which the number of delays that can be obtained is related to the number of times m that a beam bounces in the cell raised to some power, and exponential cells, in which the number of delays is proportional to some number raised to the power of m. In exponential cells, the topic to be addressed, the spatial light modulator switches between a delay element and a null path on each bounce. We describe an improved design of this switching engine, which contains a liquid-crystal switch and a White cell. We examine astigmatism and corrections for it and present a specific design.

Binary-counting true time delay generator using a white cell design and deformable mirror devices

We have shown a modified version of the binary white cell-based true time delay (TTD) generator architecture to allow the use of a deformable mirror device (DMD). If 10 bits of delay are required, then each beam will make 20 bounces and use 20 pixels on the DMD. A commercial DMD with 500,000 elements can thus in principle provide 10 bits of delay for 50,000 antenna elements.

Practical use of the spatial coherence function for determining laser transverse mode structure

The spatial coherence function of a beam exiting from a wave-guiding device can be used to determine the transverse modal composition of the fields which are supported within the structure. The strength of the spatial coherence technique is that it directly yields the relative modal weights which exist within the cavity. While this technique has received little attention in the past due to the experimental difficulties in measuring spatial coherence, a recently developed technique overcomes several of these problems. We demonstrate how the relative modal amplitudes may be extracted from the spatial coherence function for the case where the field distribution is described by Hermite-Gaussian polynomials. We point out some limitations of this method and discuss how these may be circumvented.

Demonstration of a quartic cell, a free-space true-time-delay device based on the white cell

The authors report on a design and demonstration of a quartic-style optical true-time-delay device based on a White cell. This device is designed for 81 sequential time delays with an incremental delay of 243 ps and a maximum delay of 19.683 ns. The time delays are implemented by free-space translations, with lens trains as needed for beam containment. A digital microelectromechanical tilting micromirror array is used to send the light into different delay paths