10 Mathematical retroreflectors

2011

Many optical systems need to be evaluated but they cannot be disassembled to test the imaging lens separately. Then, they have to be tested in a retroreflecting configuration, frequently called double-pass. A typical example of this procedure is in the optical eye. In this manuscript we will describe the different possibilities that might exist when these tests are performed. The main differences are due to the different optical properties of the surfaces on which the image is formed. We will describe the different system conditions and how they can be evaluated and implemented.

Precision Engineering, 2005

A brief survey of retroreflector designs and applications is presented. A novel multidirectional (as opposed to omnidirectional) retroreflector concept, which uses a four-mirror retroreflector subassembly with a common virtual reflection point (thus eliminating the Abbe error), is described. Applications include multilateration with interferometers, laser trackers, and electronic distance measurement surveying instruments-as well as other radiation sources, e.g., microwaves and acoustics. Example configurations are given.

RSC Adv.

A corner cube retroreflector (CCR) consists of three perpendicular flat surfaces and reflects the incident light back to its source.

Measurement, 2009

Determination of photometric properties of retroreflectors used especially on cars, motorways and clothes for safety of traffic is very important. To characterize the retroreflection properties of such materials, a retroreflection measurement system was constructed at TÜB _ ITAK-UME. The measurement system is composed of a lighting projector, a two-dimensional goniometer, reference and observation photometer heads with transimpedance amplifiers and an analog digital converter card with a developed software. The system is capable of measuring both luminous intensity and retroreflection coefficients of retroreflective materials at observation angles varying from 0.1°to 5°.

Nuclear Physics A, 1968

An explicit derivation of a general property of symmetry of the non-local optical potential is given by using the projection operators. Such a property, which in a particular case reduces to the symmetry in the position coordinates, insures the relation of reciprocity and follows from the reversibility of the original multi-channel system. * The sense of the term reciprocity used in this paper is defined in sect. 2 and is the same as in ref. ~).

Physics Letters A, 2006

We suggest a geometrical framework to discuss the action of slabs of negatively refracting materials. We show that these slabs generate the same orbits as normal materials, but traced out in opposite directions. This property allows us to confirm that the action of any lossless multilayer can be optically cancelled by putting it together with the multilayer constructed as the inverted mirror image, with ǫ and µ reversed in sign.

Applied Optics, 2014

By isolating a finite effective volume from a conventional triangular pyramid corner cube, we obtained truncated corner cube structures with greatly enhanced retroreflection efficiency. We explore an optimal truncated corner cube with near 100% retroreflection efficiency based on the expectation that the traveling paths of the optical rays can be localized in the finite effective volume of the structure, and, as a result, truncated corner cubes with perfect efficiency can be produced. As a case study, the retroreflection efficiency of a commercialized 3M truncated corner cube sample is evaluated. Furthermore, it is shown with numerical verification that a truncated corner cube array sheet with near-perfect retroreflection efficiency can be produced.

Inverse Problems, 2009

The concept of time reversal (TR) of scalar wave is reexamined from basic principles. Five different time reversal mirrors (TRM) are introduced and their relations are analyzed. For the boundary behavior, it is shown that for paraxial wave only the monopole TR scheme satisfies the exact boundary condition while for the spherical wave only the MD-mode TR scheme satisfies the exact boundary condition. The asymptotic analysis of the near-field focusing property is presented for two dimensions and three dimensions. It is shown that to have a subwavelength focal spot the TRM should consist of dipole transducers. The transverse resolution of the dipole TRM is linearly proportional to the distance between the point source and TRM. The mixed mode TRM has the similar (linear) behavior in three dimensions but in two dimensions the transverse resolution behaves as the square-root of the distance between the point source and TRM. The monopole TRM is ineffective to focus below wavelength. Contrary to the matched field processing and the phase processor, both of which resemble TR, TR in a weak-or non-scattering medium is usually biased in the longitudinal direction, especially when TR is carried out on a single plane with a finite aperture. This is true for all five TR schemes. On the other hand, the TR focal spot has been shown repeatedly in the literature, both theoretically and experimentally, to be centered at the source point when the medium is multiply scattering. A reconciliation of the two seemingly conflicting results is found in the random fluctuations in the intensity of the Green function for a multiply scattering medium and the notion of scattering-enlarged effective aperture.

Sensors

This paper is concerned with backscattered luminous signals, coming from a particular class of dielectric spheres illuminated by a coherent source. The purpose is to measure the lateral position of the sphere serving as an optical target, to achieve an overall contactless sensor of lateral position in space. Traditional approaches and theories such as ray-tracing and Mie scattering—as implemented in dedicated software—are applied to investigate their fitness for purpose in this application. No previous literature was found dealing with this specific case. Unfortunately, our observations did not match the theories’ predictions to an acceptable degree, and these approaches proved to be unsatisfactory. The rest of the paper focusses then on the development and comparison of suitable algorithms to compute the image coordinates of a representative point, which was in fact the true motivation of this work. Two original algorithms are proposed and discussed. Their robustness and repeatabil...