ABSTRACT
An interferometric optical setup for diffraction-less spectroscopy is tested as an optical design for control of interference frequency. Its design is based on a Mach-Zehnder interferometer in which a pair of compound prisms is introduced in the interferometer path to obtain interference patterns, which avoids the diffraction phenomena and nonlinear dispersion found on spectrometers that use gratings. Computer simulations of the interference patterns generated by the proposed optical setup are presented, and confirmed by the experimental results of the optical implementation. The theory that describes an ideal optical setup and the experimental results show that in order to reduce the combined uncertainties of wavelength measurement, a precise control in angle deviation and magnification are required for the reduction of measurement uncertainties.
ABSTRACT
A quantized version of a continuous spiral phase filter with unitary topological charge, here denominated multi-step spiral phase filter (MSSPF), is proposed to extract phase from rotated spiral interferograms. Spiral interferograms are usually obtained from phase objects by registering the interference of its vortex filtered complex amplitude with a reference complex amplitude. The structure found in this kind of interferograms, depend on the number of steps used in the MSSPF that usually are assumed with an infinite number of steps for the continuous spiral phase filter. Reducing the number of steps of the MSSPF affects the residual phase error obtained after the phase extraction method. This error is therefore analysed here using a numerical simulation of a Mach-Zender interferometer with a MSSPF and a reduced number of steps. It is shown that, for our proposed method of rotated spiral interferograms, a residual error persists as the number of steps is increased approaching the residual error reported for the phase extraction method of single-shot spiral interferograms. Furthermore, it is shown that this novel technique can be applied without further modifications for phase contrast measurement. Experimental results show similar performance of this phase extraction technique, when compared to the results obtained with a commercial interferometer and with the numerical simulations.
ABSTRACT
The recently developed technique of high-speed phase-shifting speckle interferometry combined with temporal phase unwrapping allows dynamic displacement fields to be measured, even for objects containing global discontinuities such as cracks or boundaries. However, when local speckle averaging is included, small phase errors introduced at each time step are accumulated along the time axis, yielding total phase values that depend strongly on the speckle rereference rate. We present an analysis of the errors introduced in the phase evaluation by three sources: intensity errors, velocity errors, and speckle decorrelation. These errors are analyzed when they act both independently and together, for the most commonly used phase-shifting algorithms, with computer-generated speckle patterns. It is shown that, in a controlled out-of-plane geometry, errors in the unwrapped phase map that are due to speckle decorrelation rise as the time between rereferencing events is increased, whereas those due to intensity and velocity errors are reduced. It is also shown that speckle decorrelation errors are typically more important than the intensity and velocity errors. These results provide guidance as to the optimal speckle rereferencing rate in practical applications of the technique.
ABSTRACT
We investigate experimentally the optimal rate at which the reference speckle pattern should be updated when dynamic speckle interferometry is used to measure transient in-plane displacement fields. Images are captured with a high-speed camera and phase shifting and phase unwrapping are done temporally. For a wide range of in-plane velocities, up to a maximum of 40% of the Nyquist limit, the random errors in the calculated displacement field are minimized by updating the reference speckle pattern after a speckle displacement of 1/10 of the pixel spacing. The technique is applied to measurements of microscale deformation fields within an adhesive joint in a carbon-fiber epoxy composite.
ABSTRACT
In recent years the availability of high-speed digital video cameras has motivated the study of electronic speckle pattern interferometry (ESPI) in the time domain. To this end a properly sampled temporal sequence of N-fringe patterns is used to analyze the temporal experiment. Samples of temporal speckle images must fulfill the Nyquist criteria over the time axis. When the transient phenomena under study are too fast, the required sampling frequency over time may not be fulfilled. In that case one needs to extend the measuring range of the algorithm used to extract the modulating phase. We analyze how to use short laser pulses or short video acquisition times with fairly long temporal separation among them to estimate the modulating phase of a dynamic ESPI experiment. The only requirement is that the modulating phase being estimated be properly sampled in the spatial domain.
