Boris Spektor

WAVE FIELDS IN THREE DIMENSIONS : ANALYSIS AND SYNTHESIS

Distributions of wave fields in three-dimensional domains are analyzed, synthesized, and generated experimentally. Fundamental limits are discussed and sampling conditions are derived for their generation, with use of a single diffractive element. A general design procedure, based on optimization algorithms, is developed and implemented. Experimental results show that special three-dimensional light distributions can be achieved with low-information-content elements in on-axis configurations.

Singular beam microscopy

Optical singularities are localized regions in a light field where one or more of the field parameters, such as phase or polarization, become singular with associated zero intensity. Singular beam microscopy exploits the fact that the strong variations of the optical field around the singularities are highly sensitive to changes in their neighborhood. As a consequence, analysis of the light field scattered from the object during a scanning process can yield useful information about the object features. We present a theoretical background, numerical simulations, and experimental results. Preliminary experiments have demonstrated a sensitivity of 20 nm in the position and size of simple objects, with theoretically estimated 1 nm capability under the assumption of a reasonable and conservative 30 dB signal to noise ratio.

Dark beams with a constant notch

Dark beams are wave fields carrying information in dark regions. We experimentally demonstrate dark beams that maintain a constant notch shape and size along a predetermined domain in free space. The energy is concentrated around the dark region with negligible sidelobes. These beams are generated with low-information-content phase-only diffractive elements in an on-axis configuration.

Unconventional light distributions in three-dimensional domains

Abstract Three-dimensional distributions of wave fields are synthesized using a new concept in the design of diffractive optical elements. The approach is demonstrated by the generation of light distributions such as ‘dashed nondiffracting beams’, ‘helicoidal beams’ and ‘dark beams’. Design procedures are described and physical characteristics investigated.

In-line optical surface roughness determination by laser scanning

Reliable in-line and in-situ measurement of structure of highly polished surfaces remains a major challenge for the modern industry. Evaluation of the wavefront of a scanning laser beam reflected from a surface allows one to establish a direct correlation between the statistics of the optical signal and the surface roughness. Phase structuring of the laser beam greatly increases the height sensitivity down to the nanometer level. High sampling rate allows one to collect a very large number of sampled data and provide a complete analysis of the surface structure rather than a single parameter such as the rms roughness.

Singular beam scanning microscopy: preliminary experimental results

High-sensitivity and a high-speed nanoscale measurement is an important subject in modern industry, especially when analysis of high-speed moving nanoscale objects on a surface is required. Several objectives in this direction can be achieved by using singular beam microscopy, which we investigate experimentally for the examination of small phase steps. We discuss the challenges of rigorous modeling of experiments employing high-numerical-aperture illumination and describe experimental results performed with a medium numerical aperture of 0.55. The investigated equivalent phase step heights reached as low as 10 nm (about 1/15 rad).

Tight focusing of wavefronts with piecewise quasi-constant phase

The Richards-Wolf approach to analyze tight focusing by high numerical aperture aplanatic optical systems can only be applied to incident waves having a planar (or negligibly curved) wavefront at the entrance pupil. In some cases, however, such as certain singular beams, the incident wave can be represented by a wavefront with, approximately, piecewise constant phase. For wavefronts of this kind we extend the validity of the Richards-Wolf approach to approximate evaluation of the field distribution in the vicinity of the geometrical focus. The proposed method is applied to the derivation of the focal distribution obtained by placing a mask with a π phase shift at the entrance pupil.

High-resolution surface feature evaluation using multiwavelength optical transforms

Surface feature evaluation with resolution beyond the classical diffraction limit can be achieved by a combined space--frequency representation of the scattered field. This was demonstrated in a measuring procedure where the surface was consecutively illuminated by a collection of focused beams and the diffracted data was measured in the far field. Mathematically, if the focused beam has a Gaussian profile, the optical system implements a Gabor transform. Other transformations, such as wavelet transforms can be obtained by properly structuring the illuminating beam. This work presents an approach where structured beams at several wavelengths are used. This additional information gathered by this procedure allows an increased resolution and the reduction of ambiguities that may occur in the analysis of single wavelength measurements.

On-axis binary-amplitude computer generated holograms

Abstract On-axis holograms are synthesized on positive binary-amplitude recording media. These holograms present unique characteristics: The signal is reconstructed around the optical axis without overlapping orders and it is the brightest order in the reconstruction plane, the coding procedure is fast, and the holograms can be implemented on low information content recording devices. Various examples and applications are discussed and the method is illustrated with an experimentally implemented array illuminator.

WAVE-FRONT SENSING BY PSEUDO-PHASE-CONJUGATE INTERFEROMETRY

A wave-front sensor based on pseudo-phase-conjugate interferometry is presented. We show that a pseudo-phase-conjugate interferometer is suitable for the measurement of phase distribution on a propagating wave. This new method may be employed for optical workshop applications and wave-front sensing for adaptive optics. The theoretical sensitivity of the interferometer is twice that of the Hartmann-Shack wave-front sensor. Preliminary laboratory experiments demonstrate excellent performance and consistency with computer simulations.