Theoretical and experimental study of optical diffractometry based on Fresnel diffraction from a transmission phase step.

We present experiments to study the optical diffractometry of Fresnel diffraction from transmission phase steps under illuminating sources with distinct spatial profiles. The experimental results are extended analytically with the Fresnel Gaussian shape invariant introduced in previous publications to calculate the propagation of a coherent illuminating source through optical setups. We use a narrow coherent illuminating source to permit extending the applicability of the method for clinical purposes and perform calculations with illuminating sources with different spatial profiles, including a non-diffracting Airy beam, to allow for the establishment of general sensitivity formulae within the paraxial region.

Gaussian beam with high spherical aberration focused by a singlet lens-shaped container for glucose measurements.

We describe a highly sensitive optical technique for glucose concentration measurements in liquid samples based on measuring the heights of the primary sidelobes of the normalized intensity profiles of a focused Gaussian beam with high spherical aberration. A singlet lens-shaped container, filled with the sample under test, is used to focus the beam at an observation plane placed close to the focusing region. The normalized intensity profile of the aberrated beam allows for accurate measurement of the sample glucose concentration.

Gaussian probe beam with high spherical aberration for glucose concentration measurement.

We demonstrate that an optical probe beam with high spherical aberration used for glucose concentration measurements gives better sensitivity compared to a probe beam free of aberrations, under similar conditions. We place a singlet focusing lens at a large distance from a laser source with a Gaussian intensity profile to obtain a spherically aberrated probe beam with negligible truncation. The aberrated probe beam propagates through a transparent liquid sample. Intensity profiles of the transmitted beam are recorded by means of a homodyne profiler to perform the glucose concentration measurements accurately.

Refractive index and geometrical thickness measurement of thin optical samples by a transmitted Gaussian beam.

We describe a technique for simultaneously measuring the local geometrical thickness and the refractive index of semi-transparent thin plates by means of the diffractive properties of a transmitted Gaussian beam. The technique is based on measuring the semi-width of the transmitted beam and the shift of the Gaussian centroid caused by introducing a tilt on the sample under test. A homodyne technique is devised to accurately characterize the Gaussian beam. Our proposal does not require any prior information of the sample under study. We present analytical support of our technique and we give experimental results.

Refractive index and geometrical thickness measurement of a transparent pellicle in air by Gaussian beam defocusing.

We demonstrate that it is possible to measure the local geometrical thickness and the refractive index of a transparent pellicle in air by combining the diffractive properties of a Gaussian beam with the analytical equations of the light that propagates through a thin layer. We show that our measurement technique is immune to inherent piston-like vibrations present in the pellicle. As our measurements are based on characterizing properly the Gaussian beam in a plane of detection, a homodyne technique for this purpose is devised and described. The feasibility of our proposal is confirmed by measuring local geometrical thicknesses and the refractive index of a commercially available stretch film.

X-ray optics simulation using Gaussian superposition technique.

We present an efficient method to perform x-ray optics simulation with high or partially coherent x-ray sources using Gaussian superposition technique. In a previous paper, we have demonstrated that full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, x-rays, acoustic waves, etc. We describe the technique and include some computer simulations as illustrative examples for x-ray optical component. We show also that this method can be used to study partial or total coherence illumination problem.

Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant.

Full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This method is similar to conventional ray tracing additionally preserving the undulatory behavior of the field distribution. That is, we are propagating a linear combination of Gaussian shaped wavelets; keeping always track of both, the ray trajectory, and the wave phase of the whole complex optical field. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, X-rays, acoustic waves, etc. We describe the technique and we include one-dimensional illustrative examples.

A technique for calculating the amplitude distribution of propagated fields by Gaussian sampling.

We present a technique to solve numerically the Fresnel diffraction integral by representing a given complex function as a finite superposition of complex Gaussians. Once an accurate representation of these functions is attained, it is possible to find analytically its diffraction pattern. There are two useful consequences of this representation: first, the analytical results may be used for further theoretical studies and second, it may be used as a versatile and accurate numerical diffraction technique. The use of the technique is illustrated by calculating the intensity distribution in a vicinity of the focal region of an aberrated converging spherical wave emerging from a circular aperture.

Overall characterization of assembled optical storage devices with a heterodyne microscope: a qualitative comparison with a confocal microscope.

We present local profile measurements of inner mirrorlike and external front-end polycarbonate surfaces at the same spot of assembled optical storage devices, a CD and a DVD, performed with a heterodyne scanning interferometer that uses Gaussian beams. We show that the heterodyne interferometer can reproduce the profiles of both surfaces with accurate precision. We describe a procedure for calibrating the instrument based on the measurement of reflecting calibrated gratings. To show the advantages that the heterodyne interferometer represents as a valuable tool for the characterization of optical disks, we include a comparison of experimental results obtained with a confocal microscope under similar working conditions.

Fresnel-Gaussian shape invariant for optical ray tracing.

We propose a technique for ray tracing, based in the propagation of a Gaussian shape invariant under the Fresnel diffraction integral. The technique uses two driving independent terms to direct the ray and is based on the fact that at any arbitrary distance, the center of the propagated Gaussian beam corresponds to the geometrical projection of the center of the incident beam. We present computer simulations as examples of the use of the technique consisting in the calculation of rays through lenses and optical media where the index of refraction varies as a function of position.

Inspection of commercial optical devices for data storage using a three Gaussian beam microscope interferometer.

Recently, an interferometric profilometer based on the heterodyning of three Gaussian beams has been reported. This microscope interferometer, called a three Gaussian beam interferometer, has been used to profile high quality optical surfaces that exhibit constant reflectivity with high vertical resolution and lateral resolution near lambda. We report the use of this interferometer to measure the profiles of two commercially available optical surfaces for data storage, namely, the compact disk (CD-R) and the digital versatile disk (DVD-R). We include experimental results from a one-dimensional radial scan of these devices without data marks. The measurements are taken by placing the devices with the polycarbonate surface facing the probe beam of the interferometer. This microscope interferometer is unique when compared with other optical measuring instruments because it uses narrowband detection, filters out undesirable noisy signals, and because the amplitude of the output voltage signal is basically proportional to the local vertical height of the surface under test, thus detecting with high sensitivity. We show that the resulting profiles, measured with this interferometer across the polycarbonate layer, provide valuable information about the track profiles, making this interferometer a suitable tool for quality control of surface storage devices.

Three Gaussian beam interferometric profilometer applied to the characterization of an optical flat.

A three-beam scanning optical interferometric microscopic technique applied to roughness characterization of optical flats is described. The technique is based on the heterodinization of three coherent optical beams. One of the beams, the probe beam, is focused on the surface under test. A second beam is obtained after being reflected by a reference surface. Finally, the last beam consists of one of the first orders of diffraction that emerges of a Bragg-cell. The three beams are coherently added at the sensitive surface of a photodetector that integrates the overall intensity of the beams. We show analytically that, the electrical signal at the output of the photodetector, is a time-varying signal whose amplitude is proportional to the surface local vertical height. We characterize experimentally the frequency response of the system by measuring the profile of three different gratings. We show measurements of the roughness of an optical flat processed by means of the frequency response of the system.

Heterodyne two beam Gaussian microscope interferometer.

We present a novel microscope interferometric technique based on the heterodinization of two Gaussian beams for measuring roughness of optical surfaces in microscopic areas. One of the beams is used as a probe beam, focussed and reflected by the surface under test. The second beam interferes with the first beam and introduces a time varying modulating signal. The modulating light beam is obtained from the first diffraction order of a Bragg cell. The two beams are superimposed and added coherently at the sensitive plane of a photodetector that integrates the overall intensity of the beams. We show analytically that it is possible to find appropriate working conditions in which the system has a linear response. Under these conditions, the size of the probe beam at the plane of detection as well as the amplitude of the time varying signal at the output of the photodetector, are both proportional to the local vertical height of the surface under test. As a narrow bandwidth amplifier is used to detect the time varying signal the system exhibits a high signal to noise ratio. We also include experimental results of the measurement of the topography of a sample consisting in a blazed-reflecting grating.