Erwin Hack

3D micro-scale deformations of wood in bending: Synchrotron radiation μCT data analyzed with digital volume correlation

A micro-scale three-point-bending experiment with a wood specimen was carried out and monitored by synchrotron radiation micro-computed tomography. The full three-dimensional wood structure of the 1.57x3.42x0.75mm(3) specimen was reconstructed at cellular level in different loading states. Furthermore, the full three-dimensional deformation field of the loaded wood specimen was determined by digital volume correlation, applied to the reconstructed data at successive loading states. Results from two selected regions within the wood specimen are presented as continuous displacement and strain fields in both 2D and 3D. The applied combination of synchrotron radiation micro-computed tomography and digital volume correlation for the deformation analysis of wood under bending stress is a novel application in wood material science. The method offers the potential for the simultaneous observation of structural changes and quantified deformations during in situ micro-mechanical experiments. Moreover, the high spatial resolution allows studying the influence of anatomical features on the fracture behaviour of wood. Possible applications of this method range from bio-mechanical observations in fresh plant tissue to fracture mechanics aspects in structural timber.

Invited Review Article: Measurement uncertainty of linear phase-stepping algorithms

Phase retrieval techniques are widely used in optics, imaging and electronics. Originating in signal theory, they were introduced to interferometry around 1970. Over the years, many robust phase-stepping techniques have been developed that minimize specific experimental influence quantities such as phase step errors or higher harmonic components of the signal. However, optimizing a technique for a specific influence quantity can compromise its performance with regard to others. We present a consistent quantitative analysis of phase measurement uncertainty for the generalized linear phase stepping algorithm with nominally equal phase stepping angles thereby reviewing and generalizing several results that have been reported in literature. All influence quantities are treated on equal footing, and correlations between them are described in a consistent way. For the special case of classical N-bucket algorithms, we present analytical formulae that describe the combined variance as a function of the phase angle values. For the general Arctan algorithms, we derive expressions for the measurement uncertainty averaged over the full 2π-range of phase angles. We also give an upper bound for the measurement uncertainty which can be expressed as being proportional to an algorithm specific factor. Tabular compilations help the reader to quickly assess the uncertainties that are involved with his or her technique.

High efficient superresolution combination filter with twin LCD spatial light modulators

A comparative study of pupil filters for transverse superresolution is presented in this article. We propose to combine the advantages of amplitude and phase filters in one complex filter that performs better than either phase or amplitude filters designed so far. The performance here refers to having a smaller spot size along with higher peak to side lobe intensity ratio. Using numerical simulation the limitations of phase and amplitude filters are assessed. The experimental verification of the designed combination filter is performed with two LCD spatial light modulators used for displaying separately the phase and amplitude part of the filter. Results obtained from this setup confirm the simulation.

Multiwavelength shearography for quantitative measurements of two-dimensional strain distributions

We report on the development of a multiwavelength speckle pattern shearing interferometer for the determination of two-dimensional strain distributions. This system is based on simultaneous illumination of the object with three diode lasers that emit at different wavelengths between 800 and 850 nm. Wavelength separation and image acquisition were performed with a special optical arrangement, including narrow-bandpass filters and three black-and-white cameras. The shearographic camera with a variable shearing element, in combination with the appropriate illumination geometry, permitted us to isolate all six displacement derivatives from phase-stepped fringe patterns. The optical system and the measurement procedure were validated with two different experiments. First, the shearographic sensor head was used for the determination of in-plane displacements, and, second, in-plane strain distributions of an aluminum block caused by temperature expansion were measured.

Terahertz holography for imaging amplitude and phase objects

A non-monochromatic THz Quantum Cascade Laser and an uncooled micro-bolometer array detector with VGA resolution are used in a beam-splitter free holographic set-up to measure amplitude and phase objects in transmission. Phase maps of the diffraction pattern are retrieved using the Fourier transform carrier fringe method; while a Fresnel-Kirchhoff back propagation algorithm is used to reconstruct the complex object image. A lateral resolution of 280 µm and a relative phase sensitivity of about 0.5 rad are estimated from reconstructed images of a metallic Siemens star and a polypropylene test structure, respectively. Simulations corroborate the experimental results.

An approach to the validation of computational solid mechanics models for strain analysis

The need to provide strong evidence of the validity of predictions from computational solid mechanics models used in engineering design decisions is discussed. A new procedure is proposed, based on image decomposition, for reducing the dimensionality of strain field data from models and experiments and then comparing the resultant feature vectors via a simple linear correlation in which validation is deemed to be achieved when the coordinate pairs from the two feature vectors lie within a scatter band defined by the minimum measurement uncertainty. The procedure is illustrated by some simple examples that allow the advantages and drawbacks of the approach to be highlighted. It is anticipated that the procedure could become part of a corporate plan or regulatory process for verification and validation of computational solid mechanics models.

Additive–subtractive two-wavelength ESPI contouring by using a synthetic wavelength phase shift

The addition correlation of two speckle fields by simultaneousillumination at different wavelengths is used for object contouring ina Twyman-Green-type interferometer. Fringe visibility is enhancedwhen the stochastic speckle background intensity obtained from areference plane modulation is subtracted. We calculate the contourphase map by using a phase-shift algorithm in the syntheticwavelength. A comparison with a sequential illumination, phasedifference method based on a laser wavelength phase shift isgiven. The test setup does not need to be stable on aninterferometric scale, and therefore a method is provided that lendsitself to applications in noisy environments.

Benign Joining of Ultrafine Grained Aerospace Aluminum Alloys Using Nanotechnology

Ultrafine grained aluminum alloys have restricted applicability due to their limited thermal stability. Metalized 7475 alloys can be soldered and brazed at room temperature using nanotechnology. Reactive foils are used to release heat for milliseconds directly at the interface between two components leading to a metallurgical joint without significantly heating the bulk alloy, thus preserving its mechanical properties.

A reference material for establishing uncertainties in full-field displacement measurements

A simple reference material for establishing the minimum measurement uncertainty of optical systems for measuring 3D surface displacement fields in deforming objects is described and its use demonstrated by employing 3D digital image correlation as an exemplar technique. The reference material consists of a stepped bar, whose dimensions can be scaled to suit the application, and that can be clamped rigidly at its thick end to create an idealized cantilever. The cantilever was excited at resonance to generate out-of-plane displacements and, in a separate experiment, loaded statically in-plane to provide in-plane displacement fields. The displacements were measured using 3D digital image correlation and compared to the predicted displacement fields derived from tip deflections obtained using a calibrated transducer that provided traceability to the national standard for length. The minimum measurement uncertainties were evaluated by comparing the measured and predicted displacement fields, taking account of the uncertainties in the input parameters for the predictions. It was found that the minimum measurement uncertainties were less than 3% for the Cartesian components of displacement present during static in-plane bending and less than 3 µm for out-of-plane displacements during dynamic loading. It was concluded that this reference material was more straightforward to use, more versatile and yielded comparable results relative to an earlier design.

THz holography in reflection using a high resolution microbolometer array.

We demonstrate a digital holographic setup for Terahertz imaging of surfaces in reflection. The set-up is based on a high-power continuous wave (CW) THz laser and a high-resolution (640 × 480 pixel) bolometer detector array. Wave propagation to non-parallel planes is used to reconstruct the object surface that is rotated relative to the detector plane. In addition we implement synthetic aperture methods for resolution enhancement and compare Fourier transform phase retrieval to phase stepping methods. A lateral resolution of 200 μm and a relative phase sensitivity of about 0.4 rad corresponding to a depth resolution of 6 μm are estimated from reconstructed images of two specially prepared test targets, respectively. We highlight the use of digital THz holography for surface profilometry as well as its potential for video-rate imaging.