We describe a system for measuring sub-surface displacement fields within a scattering medium using a phase contrast version of spectral Optical Coherence Tomography. The system provides displacement maps within a 2-D slice extending into the sample with a sensitivity of order 10 nm. The data for a given deformation state is recorded in a single image, potentially allowing sub-surface displacement and strain mapping of moving targets. The system is based on low cost components and has no moving parts. The theoretical basis for the system is presented along with experimental results from a simple well-controlled geometry consisting of independently-tilting glass sheets. Results are validated using standard two-beam interferometry. A modified system was used to measure through-the-thickness phase changes within a porcine cornea due to displacements produced by an increase in the intraocular pressure.
A rigid endoscope and three different object illumination source positions are used in pulsed digital holography to measure the three orthogonal displacement components from hidden areas of a harmonically vibrating metallic cylinder. In order to obtain simultaneous 3D information from the optical set up, it is necessary to match the optical paths of each of the reference object beam pairs, but to incoherently mismatch the three reference object beam pairs, such that three pulsed digital holograms are incoherently recorded within a single frame of the CCD sensor. The phase difference is obtained using the Fourier method and by subtracting two digital holograms captured for two different object positions.
It is reported for the first time the use of a very high speed camera in digital holographic interferometry with an out of plane sensitivity setup. The image plane holograms of a spherical latex balloon illuminated by a cw laser were acquired at a rate of 4000 frames per second, representing a time spacing between holograms of 250 microseconds, for 512 x 512 pixels at 8 bits resolution. Two types of tests were accomplished for a proof of principle of the technique, one with no constrains on the object which meant random movements due to non controlled environmental air currents, and the other with specific controlled conditions on the object. Results presented correspond to a random sample of sequential digital holograms, chosen from a 1 second exposure, individually Fourier processed in order to perform the usual comparison by subtraction between consecutive pairs thus obtaining the phase map of the object out of plane displacement, shown as a movie.
The combination of a high-speed TV holography system and a 3D Fourier-transform data processing is proposed for the analysis of multimode vibrations in plates. The out-of-plane displacement of the object under generic vibrational excitation is resolved in time by the fast acquisition rate of a high-speed camera, and recorded in a sequence of interferograms with spatial carrier. A full-field temporal history of the multimode vibration is thus obtained. The optical phase of the interferograms is extracted and subtracted from the phase of a reference state to yield a sequence of optical phase-change maps. Each map represents the change undergone by the object between any given state and the reference state. The sequence of maps is a 3D array of data (two spatial dimensions plus time) that is processed with a 3D Fourier-transform algorithm. The individual vibration modes are separated in the 3D frequency space due to their different vibration frequencies and, to a lesser extent, to the different spatial frequencies of the mode shapes. The contribution of each individual mode (or indeed the superposition of several modes) to the dynamic behaviour of the object can then be separated by means of a bandpass filter (or filters). The final output is a sequence of complex-valued maps that contain the full-field temporal history of the selected mode (or modes) in terms of its mechanical amplitude and phase. The proof-of-principle of the technique is demonstrated with a rectangular, fully clamped, thin metal plate vibrating simultaneously in several of its natural resonant frequencies under white-noise excitation.
An endoscope is used in pulsed digital holography to simultaneously evaluate in-plane and out- of-plane transient and harmonic displacements on a flat metallic plate. The plate is illuminated from two different directions. The optical path for each illumination direction is matched to its corresponding reference beam, but also in such a way that each object-reference beam pair optical path is mismatched such that they are incoherent and can be stored in a single CCD frame. As is typical in these types of interferometric arrangement, two digital holograms are needed to compare two different states of the plate. Each hologram is Fourier transformed and due to the incoherence introduced, two separate spectra are readily identified, each belonging to an object-reference beam pair. On comparing by subtraction the phase obtained from the two pulsed digital holograms, it is possible to gather quantitative in-plane and out-of- plane results from transient and harmonic displacements.
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