Appearance of bound states in random potentials with applications to soliton theory

We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg–de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.

Continuous measurement of accommodation in human factor applications

It has long been sought to measure ocular accommodation continuously in human factor applications such as driving or flying. Open-field autorefractors such as the Canon R-1 could be converted to allow continuous, objective recording, but steady eye fixation and head immobilisation were essential for the measurements to be valid. Image analysis techniques utilised by newer open-view autorefractors such as the Shin-Nippon SRW-5000 are more tolerant to head and eye movements, but perhaps the technique with the greatest potential for the measurement of accommodation in human factor applications is photoretinoscopy. This paper examines the development of techniques for high temporal measurements of accommodation and reports on the tolerance of one such recent commercial instrument, the PowerRefractor (PlusOptiX). The instrument was found to be tolerant to eye movements from the optical axis of the instrument (∼0.50 DS change in apparent accommodation with gaze 25° eccentric to the optical axis), longitudinal head movement (<0.25 DS from 8 cm towards and 20 cm away from the correct photorefractor to eye distance) and changes in background illuminance (<0.25 DS from 0.5 to 20 cd m-2 target luminance). The PowerRefractor also quantifies the direction of gaze and pupil size, but is unable to take measurements with small pupils <3.7 ±1.0 mm. © 2002 The College of Optometrists.