Volume 11, Issue 1-2

Encoders of angle based on rotating polarizers suffer from 180° ambiguity due to their inherent twofold rotational symmetry. This restricts their applications in motor and machine controls. We show that the ambiguity can be resolved through a geometrical mapping from a plane to a conical surface. Seen from the local surface normal, one full rotation of the cone gives one half rotation of the polarizer axis. With appropriate transmission or reflective optics and multiphase detection, we build high resolution, moderate accuracy, absolute-angle encoders without 180° ambiguity. Polymer birefringent retarders can be used similarly.

Optical encoders based on measurement of the axis-angle of linear polarizers offer high resolution and moderate accuracy, but are usually restricted to rotary measurement. We show that annular polymer sheet polarizer materials can be sheared into rectangular tapes, with a polarizing axis that varies linearly along the tape. This makes possible the construction of polarimetric linear absolute position encoders. We demonstrate also sheared polymer birefringent retarders, which function similarly, potentially with cost and size-flexibility advantages.

The crystalline lens makes an important contribution to the peripheral refraction of the human eye, which may affect the development and progression of myopia. However, little has been known about the peripheral optical features of the crystalline lens and its impacts on the peripheral ocular refraction. This study aims to investigate the relationship between the structural parameters of the crystalline lens and its peripheral power profile over a wide visual field. The peripheral power profile is defined with respect to the entrance and exit pupil centers along the chief rays. Analysis is performed by three-dimensional ray tracing through the gradient refractive index (GRIN) lens models built from measurement data. It has been found that the vergence of the wavefronts at the entrance and the exit pupil centers of the lens show an approximate linear correlation to each other for each field angle. The exponent parameters of the axial refractive index profile and the axial curvature profile, and the asphericity of the posterior lens surface are found to be the most influential parameters in the peripheral power profiles. The study also shows that there can be significantly different, sometimes unrealistic, power profiles in the homogeneous lens model compared with its corresponding GRIN model with the same external geometry. The theoretical findings on the peripheral lens properties provide a new perspective for both wide-field eye modelling and the design of intraocular lenses to achieve normal peripheral vision.

The article describes the way to calculate the distances, defined by the U.S. Federal Aviation Administration in the AC 70-1B document, essential for the flight safety in the case of illumination of aircraft pilots by laser radiation. FAA’s calculations and presented examples are simplified for the most common cases of a single circular beam, or circular beams sharing the same power, divergence and aperture. Proposed in this article calculation method was extended to multi-beam radiation sources characterized by different wavelengths, different divergences in two perpendicular planes and different powers. The impact of ellipticity of the beams on the calculated distances was shown. The presented analysis may be a supplement to the AC 70-1B document and may serve as a sample approach for those who need to deal with such laser sources. Laser pointers characterized by powers of up to 50 W as well as these with typical powers of several mW were considered. It was shown that even typical 1 mW laser pointers may still distract the aircraft pilots during landing or take-off which may have adverse consequences.