How to beat the Rayleigh limit?

The problem of achieving super-resolution, i.e. resolution beyond the classical Rayleigh distance of half a wavelength, is a real challenge in several imaging problems. The development of computer-assisted instruments and the possibility of inverting the recorded data has clearly modified the traditional concept of resolving power of an instrument. We show that, in the framework of inverse problem theory, the achievable resolution limit arises no longer from a universal rule but instead from a practical limitation due to noise amplification in the data inversion process. We analyze under what circumstances super-resolution can be achieved and we show how to assess the actual resolution limits in a given experiment, as a function of the noise level and of the available a priori knowledge about the object function. We emphasize the importance of the a priori knowledge of its effective support and we show that significant super-resolution can be achieved for "subwavelength sources", i.e. objects which are smaller than the probing wavelength.

Object Restoration Beyond the Rayleigh Limit in the Presence of Noise

info:eu-repo/semantics/published

Stability and Resolution in Electromagnetic Inverse Scattering - Part I

info:eu-repo/semantics/published

Positive regularised solutions in electromagnetic inverse scattering

Fredholm integral equations of the first kind are the mathematical model common to several electromagnetic, optical and acoustical inverse scattering problems. In most of these problems the solution must be positive in order to satisfy physical plausibility. We consider ill-posed deconvolution problems and investigate several linear regularization algorithms which provide positive approximate solutions at least in the absence of errors on the data.

Inversion of light scattering data by singular system analysis

We consider the problem of inverting experimental data obtained in light scattering experiments described by linear theories. We discuss applications to particle sizing and we describe fast and easy-to-implement algorithms which permit the extraction, from noisy measurements, of reliable information about the particle size distribution. © 1987, SPIE.

Supercontinuum Generation by Stimulated Raman Scattering and Parametric Four-Wave Mixing in Photonic Crystal Fibers

Supercontinuum generation is investigated experimentally and numerically in a highly nonlinear indexguiding photonic crystal optical fiber in a regime in which self-phase modulation of the pump wave makes a negligible contribution to spectral broadening. An ultrabroadband octave-spanning white-light continuum is generated with 60-ps pump pulses of subkilowatt peak power. The primary mechanism of spectral broadening is identified as the combined action of stimulated Raman scattering and parametric four-wave mixing. The observation of a strong anti-Stokes Raman component reveals the importance of the coupling between stimulated Raman scattering and parametric four-wave mixing in highly nonlinear photonic crystal fibers and also indicates that non-phase-matched processes contribute to the continuum. Additionally, the pump input polarization affects the generated continuum through the influence of polarization modulational instability. The experimental results are in good agreement with detailed numerical simulations. These findings demonstrate the importance of index-guiding photonic crystal fibers for the design of picosecond and nanosecond supercontinuum light sources. © 2002 Optical Society of America.