Tomaž Požar

Quadrature phase-shift error analysis using a homodyne laser interferometer

The influence of quadrature phase shift on the measured displacement error was experimentally investigated using a two-detector polarizing homodyne laser interferometer with a quadrature detection system. Common nonlinearities, including the phase-shift error, were determined and effectively corrected by a robust data-processing algorithm. The measured phase-shift error perfectly agrees with the theoretically determined phase-shift error region. This error is systematic, periodic and severely asymmetrical around the nominal displacement value. The main results presented in this paper can also be used to assess and correct the detector errors of other interferometric and non-interferometric displacement-measuring devices based on phase-quadrature detection.

Enhanced ellipse fitting in a two-detector homodyne quadrature laser interferometer

The choice of fitting methods for elliptically scattered data obtained with displacement-measuring homodyne quadrature laser interferometers significantly influences the accuracy of the interferometer. This is especially important when the data contain a lot of noise or provide only a segment of the ellipse. The ellipse parameters extracted by the fitting are used either to correct the data or the basic arctangent phase-unwrapping function in order to enhance the accuracy of the measured displacement by reducing the common nonlinearities. We propose the use of linear, ellipse-specific, least-squares fitting that is further bias-corrected using a linear algorithm. This stable fitting method provides a good balance between the accuracy of the fit and the computational efficiency, and never returns corrupt, non-ellipse parameters. It is therefore applicable for an online, uniform fringe subdivision when there is a demand for sub-nanometric resolution. An experimental confirmation of the improvement over traditional fitting methods was carried out with a single-pass, two-detector homodyne quadrature laser interferometer. We were able to operate the interferometer with nanometric accuracy, provided the data draw out at least a quarter-arc of an ellipse.

Optical measurements of the laser-induced ultrasonic waves on moving objects

We performed a single-shot, contactless measurement of ultrasonic waves on a laser-propelled rod with a homodyne quadrature laser interferometer (HQLI) during the entire duration of its motion. This is the first such experimental demonstration of the laser-induced motion of an elastic body where the most important mechanisms that reveal the nature of its motion are presented and explained. Furthermore, these measurements quantitatively demonstrate that the HQLI is an appropriate tool for monitoring high-amplitude (1.3 microm) and high-frequency (200 MHz) ultrasonic waves on moving objects. The applicability of the HQLI can also be extended to measure other optodynamic and high-frequency transient phenomena with a constant sensitivity and a resolution below 1 nm.

Optimization of displacement-measuring quadrature interferometers considering the real properties of optical components

We present the influence of alignment and the real properties of optical components on the performance of a two-detector homodyne displacement-measuring quadrature laser interferometer. An experimental method, based on the optimization of visibility and sensitivity, was established and theoretically described to assess the performance and stability of the interferometer. We show that the optimal performance of such interferometers is achieved with the iterative alignment procedure described.

From laser ultrasonics to optical manipulation.

During the interaction of a laser pulse with the surface of a solid object, the object always gains momentum. The delivered force impulse is manifested as propulsion. Initially, the motion of the object is composed of elastic waves that carry and redistribute the acquired momentum as they propagate and reflect within the solid. Even though only ablation- and light-pressure-induced mechanical waves are involved in propulsion, they are always accompanied by the ubiquitous thermoelastic waves. This paper describes 1D elastodynamics of pulsed optical manipulation and presents two diametrical experimental observations of elastic waves generated in the confined ablation and in the radiation pressure regime.

Dispersion of an optodynamic wave during its multiple transitions in a rod

A rod acquires linear momentum during a short-laser-pulse ablation of its front face. Initially, this momentum is localized within the propagating laser-induced mechanical pulse—the optodynamic wave—while later it is gradually transferred to the uniform motion of the entire rod. Among other effects, the dispersion of the optodynamic wave due to lateral inertia plays an important role in the linear-momentum transformation mechanism. We observed the dispersion using interferometric measurements of the rod’s rear-end staircaselike displacement. The displacements calculated using an analytical solution of Love’s equation for a laser-ablated free-free homogeneous rod agree well with our measured data.

Oblique reflection of a laser pulse from a perfect elastic mirror

An oblique reflection of a laser pulse from a fully reflective mirror is treated using the fundamental nonrelativistic conservation principles of energy and momentum. Since the mirror is considered as an elastic object, the reflection of light gives rise to an elastic wave with measurable amplitude that propagates within the mirror. Our results predict a larger Doppler shift in the reflected pulse for the most common setting, when the mirror is initially at rest, compared to the results obtained when the mirror is treated as rigid.

A homodyne quadrature laser interferometer for micro-asperity deformation analysis.

We report on the successful realization of a contactless, non-perturbing, displacement-measuring system for characterizing the surface roughness of polymer materials used in tribological applications. A single, time-dependent, scalar value, dubbed the collective micro-asperity deformation, is extracted from the normal-displacement measurements of normally loaded polymer samples. The displacement measurements with a sub-nanometer resolution are obtained with a homodyne quadrature laser interferometer. The measured collective micro-asperity deformation is critical for a determination of the real contact area and thus for the realistic contact conditions in tribological applications. The designed measuring system senses both the bulk creep as well as the micro-asperity creep occurring at the roughness peaks. The final results of our experimental measurements are three time-dependent values of the collective micro-asperity deformation for the three selected surface roughnesses. These values can be directly compared to theoretical deformation curves, which can be derived using existing real-contact-area models.

Mechanical wave motion due to the radiation pressure on gain or absorptive rods

The interaction of a light pulse with reflective and either a passive, lossy medium or an active medium with population inversion gives rise to elastic waves, already as a result of the change in the momentum carried by the incident light. We derived a 1D analytic displacement field that quantitatively predicts the shape and amplitude of such waves in semi-infinite and finite elastic rods in a half-space and infinite layer. The results are compatible with the conservation of momentum and energy of the light-matter system. They can be used as a signature for direct measurements of the radiation-pressure-induced elastic waves and to clarify the Abraham-Minkowski momentum dilemma.

1D problems of radiation pressure on elastic solids

We treat the light-matter interaction due to radiation pressure in one dimension using the fundamental, nonrelativistic conservation principles of energy and momentum. Additionally, we assume that the center of mass-energy maintains the same uniform motion if the interaction takes place or not. Since we handle solids as elastic objects, the results are consistent with the principle of causality and agree with recent experimental observations. We analyze the problem of reflection of a light pulse from a fully-reflective mirror and show that its reflection gives rise to an elastic wave with a measurable amplitude and a correct Doppler shift of the reflected pulse. We also analyze the problem of light pulse transmission into an anti-reflection coated, non-dispersive and lossless dielectric, where an elastic wave may as well be accompanied by a mechanical wave escorting the light pulse. We show that the Balazs rigid box thought experiment can be also realized in elastic dielectrics where some of the energy of the incident light is transferred to the wave motion. It follows from our approach that the electromagnetic momentum of the light pulse in the dielectric acquires Abraham’s form only when a single type of the mechanical waves accompanies the interaction.