Andrei Brunfeld

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.

Diffraction of apertured Gaussian beams: solution by expansion in Chebyshev polynomials.

A differential equation satisfied by the diffraction integral as a function of the off-axis coordinate in the observation plane is derived and its solution is obtained by expansion in Chebyshev polynomials. The resulting series provides an analytic expression for the diffraction integral and is convenient for fast numerical computation. The efficiency of this approach allows us to use it in optimization of optical systems in which diffraction effects must be taken into consideration.

Focused-beam interaction with a phase step.

The interaction of a tightly focused laser beam with a step function is encountered in optical storage media, scanning microscopy, positioning and aligning systems, and various other applications. A theoretical and experimental investigation provides an improved description of the physical process and indicates the possibility of achieving extreme superresolution suitable for certain applications.

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.

Ellipsometry with a stabilized Zeeman laser.

A novel ellipsometric method was introduced in an earlier publication, based on a rotating plane polarized beam. We show that the method is substantially improved by using a stabilized Zeeman laser as the light source.

Vector simulations of dark beam interaction with nanoscale surface features

In earlier publications, it was shown that scanning of surfaces by dark beams can be exploited for sub-wavelength feature analysis. In this work, we present vector simulations based in Rigorous Coupled-Wave Analysis with the purpose to estimate the expected resolution of the method, both lateral (feature size) and axial (height). The dark beam used in this study has a line singularity generated by a π-phase step positioned in a Gaussian beam. Various combinations of the illumination and detection nuFmerical apertures (from NA=0.2 to NA=0.8) and different surface features were studied. Polarization effects which become significant at high numerical apetures, were considered as an additional source of information for the analysis. In the case of a sub-wavelength feature on an ideal surface, the resolution of the method is limited only by the electronics noise. In particular, under a reasonable assumption of a 105 signal to noise ratio, it is possible to detect a 0.2 nm step.

High Resolution Optical Profilometer

The objective of this work was the development of a noncontact method for the measurement of the wavyness of polished surfaces. To obtain simplified measuring procedures interferometric methods were abandoned in favor of a focus seeking system that was developed earlier for machined surface inspection. The system is based on differential detection of the reflected light through two properly prepared and adjusted filters. The filter structure and alignment were investigated to obtain linear response and maximum sensitivity that amounted to 20nm in preliminary experiments.

Micro Fabry-Perot sensor for surface measurement

A high accuracy surface inspection system for testing polished surfaces is based on a Fabry-Perot resonator. The inspected surface serves as a relay mirror in a cat-eye retroreflector incorporated into the resonating cavity, which makes the optical configuration insensitive to surface tilts. The laser wavelength is swept periodically over a given range, and the local surface height is obtained by timing the resonance occurrence during each sweep. An additional highly stable reference Fabry-Perot interferometer using the same laser is employed for obtaining differential measurements, yielding absolute height values, distinguishing between up and down defects. Due to the finesse of the multi-beam Fabry Perot interferometer relative to the two-beam Michelson interferometer response function, the height sensitivity is greatly enhanced. In order to detect small contamination particles, the interferometer was supplemented by a scattering detection channel integrated into the same compact optical head. The combination of the bright-field interferometric signal, yielding both the phase (surface height) and amplitude (surface reflectivity), and the dark-field scattering channel, allows one to build a sensitive and reliable defect detection and classification procedure. The interferometer was incorporated into high-speed high-accuracy in-line machines for inspection of the surfaces in data storage applications. With a 0.2 Angstroms resolution, the height rms repeatability at a surface scanning speed of 40 m/s is 1.5 Angstroms.

Polarization properties of speckle patterns scattered from rough conductors

The scattered field amplitude and its polarization and statistics are represented as functions of illuminating field, and surface statistics. The random contribution to the field is separated from its deterministic part and expanded into several terms of decreasing orders of magnitude for detailed study. Various terms can be emphasized by proper system design to extract specific information about surface parameters. Preliminary experiments confirm novel predictions related to the correlations of polarized speckle patterns.

Defect analysis with black beam interferometry

The method of Black BeamR Interferometry, which was developed for inspection of glass substrates in LCD manufacturing, is extended in order to achieve a detailed description and classification of defects and other features on the surface under inspection. With a properly arranged detection system, not only a high defect detectability is provided, but also the ability to discriminate between the up or down defects (bumps or pits) in addition to the possibility of measuring the defect geometry (for large defects or structures) and the equivalent defect volume. The method is described and the results of simulations and experiments are presented.