Panoramic reconstruction of quasi-cylindrical objects with digital holography and a conical mirror.

In this work, we present a panoramic digital holographic system for the first time capable of obtaining 3D information of a quasi-cylindrical object by using a conical mirror. The proposed panoramic digital holographic system is able to scan the entire surface of the object to determine the amplitude and phase simultaneously. This paper demonstrates the feasibility of analyzing quasi-cylindrical objects in a short time (0.5 s) with a single camera and a minimum number of optical components. In addition, it can be applied to determine not only topographic measurement of the cylindrical surface but also measurements of radial deformations. Experimental results are presented at different magnifications, thus illustrating its capabilities and versatility.

3D shape and strain measurement of a thin-walled elastic cylinder using fringe projection profilometry.

This paper describes an optical measurement system that is capable of simultaneously measuring a three-dimensional shape and circumferential train in a thin-walled cylinder. We used the fringe projection technique to obtain a three-dimensional shape and out-of-plane displacements, which were then associated with out-of-plane strain. Although 360 deg profilometry is not new, we propose an experimental setup that requires only one camera and one projector, since two mirrors are located at 120 deg with respect to the y-z plane of the reference system to obtain three distinct, complementary views of the sample studied. A sequence of images of the fringe pattern was captured and processed using the phase-shifting method, while the out-of-plane data were determined by comparing the specimen before and after deformation. A latex tube filled with liquid was used to perform mechanical testing. The cylinder was subjected to internal hydrostatic pressure that caused deformation. Experimental results were compared with analytical solutions, and the results show that out-of-plane strains can be accurately measured using the proposed method.

Dynamic parallel phase-shifting electronic speckle pattern interferometer.

Methods for measuring variations in diffuse surfaces using electronic speckle pattern interferometry (ESPI) are widely used and well known. In this research, we present an out-of-plane ESPI system coupled to a Michelson configuration to generate simultaneous parallel interferograms with different phase shifts. The system uses circular polarization states to generate parallel phase shifted interferograms. Due to the polarization states, the fringes do not experience a contrast reduction, thus avoiding measurement errors that affect spatial or temporal phase-shifting in interferometry. The basic operating principle of polarization modulation is described, and results that represent the temporal evolution of an aluminum plate are presented. The generation of two simultaneous patterns allows one to track the dynamic performance of the plate.

Phase stepping through polarizing modulation in electronic speckle pattern interferometry.

We have demonstrated a speckle out-of-plane interferometer that employs phase-stepping procedures by means of polarization modulation. The system generates circular polarization states with opposite signs at each arm of the system, which overlap at the output of the interferometer, to generate phase shifts operating a conventional linear polarizer; the emerging polarization states have been analyzed to obtain the shifts needed to process the optical phase. The phase-stepping technique is demonstrated with a two-step algorithm to measure out-of-plane displacement on a flat metal plate.

Application of speckle interferometry to the mechanical characterization of a biopolymer sample.

In this work, we present an optical and mechanical characterization of the behavior of an inhomogeneous biopolymer sample through the use of an in-plane electronic speckle pattern interferometer with a pulling system along the $y$y direction. The characterization of the sample subjected to stress comprised the acquisition of speckle patterns for 1360 states. Displacement maps and their corresponding strain maps were computed for every state. Since the information of the maps changes with size due to the sample being pulled at the upper end while it is clamped at the lower end, a scaling method to relate the maps to each other, point-to-point, is presented. The method allows the correct evaluation of sequential strain maps, which depicts the mechanical evolution of the material. Upon managing to relate the strain maps, it is possible to extract strain values for zones of interest from every map in order to build the respective stress-strain curves. Three stress-strain curves associated with three zones in the sample (upper, middle, and bottom) are constructed. When sequential displacement and deformation maps are optically obtained by the interferometer, we present a full-field characterization, along with the obtention stress-strain curves associated with the three zones of strain maps. The curves represent the inhomogeneous performance of the sample. Three different elastic moduli (${E_u} = 2.59\;{\rm MPa}$Eu=2.59MPa, ${E_m} = 1.97\;{\rm MPa}$Em=1.97MPa, and ${E_{b}} = 1.67\;{\rm MPa}$Eb=1.67MPa), associated with three respective zones, were obtained. The experimental results for a biopolymer sample here presented show that the technique, in conjunction with the scaling method, is a novel proposal to characterize inhomogeneous materials.

Optics theory and practice in Iberoamerica: introduction to the feature issue.

This feature issue of Applied Optics (AO) on Optics Theory and Practice in Iberoamerica (OTPI) collects significantly expanded refereed papers presented at the multiconference RIAO-OPTILAS-MOPM, held in Cancún, Mexico, Sept. 23-27, 2019. All authors who participated at the conference were contacted and invited to contribute to this special issue. Furthermore, the AO dedicated issue on OTPI was open to contributions from other practitioners in all related areas, through a call for papers published in AO.

Relative error in out-of-plane measurement due to the object illumination.

In this work the sensitivity vector is analyzed for collimated and divergent oblique illumination for an out-of-plane arrangement. In the case of collimated illumination, the variation of the sensitivity vector components was considered and a geometric model was proposed for its evaluation. The geometry of the optical setup used allowed us to find sensitivity mostly along the pulling direction; the other two components of the sensitivity vector were relatively small. We measured the displacement induced only along the pulling direction. Errors in the displacement measurement associated with divergent and collimated illumination can be predicted when the sensitivity vector is considered constant. Experimental and theoretical results are presented for the out-of-plane electronic speckle pattern interferometer. The analyzed object was an aluminum plate.

Multiwavelength wavefront detection based on a lateral shear interferometer and polarization phase-shifting techniques.

We present a multiwavelength analysis of a wavefront detected by a color camera and a lateral shear interferometer. The system employs polarization phase-shifting techniques by rotating a linear polarizer at the output and detecting the phase information through a frequency demodulation algorithm. By considering the phase modulation obtained by rotating the analyzer, a frequency filter centered on the desired peak carries the phase and amplitude information of the detected wavefront. Theoretical approach, the consideration of Jones matrices of each element, and experimental results show the feasibility of the implementation.

Dual-plane slightly off-axis digital holography based on a single cube beam splitter.

In order to recover the holographic object information, a method based on the recording of two digital holograms, not only at different planes but also in a slightly off-axis scheme, is presented. By introducing a π-phase shift in the reference wave, the zero-order diffracted term and the twin image are removed in the frequency domain during the processing of the recorded holograms. We show that the zero-order elimination by the phase-shifted holograms is better than working with weak-order beam and average intensity removal methods. For recording experimentally two π-shifted holograms at different planes slightly off-axis, a single cube beam splitter is used. Computer simulations and experimental results, carried out to validate our proposal, show a high accuracy of π/14 that can be comparable with phase-shifting digital holography. For high fringe spacing, our proposal could be applied in electron holography, avoiding high voltage in a biprism.

Determination of the mechanical properties of lumbar porcine vertebrae with 2D digital image correlation.

PURPOSE: To evaluate the strain fields and to calculate the modulus of elasticity and Poisson's ratio of trabecular bone of the 6 lumbar vertebrae of the porcine spine by a 2-dimensional digital image correlation (2D DIC). METHODS: This study was performed through a 2D DIC technique and the specimens were tested under compression. The resulting images were analyzed numerically by 2D DIC. Then, representative regions of interest were examined. The strain fields were determined and stress-strain curves were obtained. RESULTS: The full field measurement of the strain in the lumbar bone spine was evaluated and with this data, the Young's modulus and Poisson's ratio were determined. CONCLUSIONS: This research highlights the potential applications of noninvasive acquisition techniques in biomechanical analysis. This is useful in the mechanical characterization of bony structures and in the design of prostheses.

Parallel two-step phase shifting interferometry using a double cyclic shear interferometer.

A parallel two-step polarizing phase shifting interferometer based on a Double Cyclic Shear Interferometer (DCSI) is proposed in this paper for quantitative phase imaging. The system has the advantage of retrieving the derivative phase data map directly. Due to its configuration, it presents better stability against external configurations than other types of interferometers. The DCSI generates two π-shifted interferograms, which are recorded by the CCD camera in a single-shot. The separation between parallel interferograms can be varied in the two axes for convenience. To obtain the optical phase data map, a parallel phase shift between interferograms is obtained by rotating a half wave plate retarder. We analyzed the cases of four patterns with shifts of π/2 captured in two shots; the optical phase was processed by a four-step algorithm. Related experimental results obtained for microscopic transparent samples are presented.

Slope measurement of a phase object using a polarizing phase-shifting high-frequency Ronchi grating interferometer.

An interferometric method to measure the slope of phase objects is presented. The analysis was performed by implementing a polarizing phase-shifting cyclic shear interferometer coupled to a 4-f Fourier imaging system with crossed high-frequency Ronchi gratings. This system can obtain nine interference patterns with adjustable phase shifts and variable lateral shear. In order to extract the slope of a phase object, it is only analyzed using four patterns obtained in a single shot, and applying the classical method of phase extraction.