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Phase step measurement and variable step algorithms in phase-shifting interferometry

A novel method, utilizing Lissajous figures and ellipse fitting, of calculating the phase difference between interferograms obtained from a phase shifting interferometer is described. Intensity bias and intensity modulation of interferograms are also calculated using this technique. Two new phase extraction algorithms are presented which use intensity and phase step information to calculate a surface from interferograms acquired with uneven phase steps. One algorithm allows surface phase to be calculated from two interferograms. Preliminary results from the Lissajous figure technique and the presented algorithms are discussed.

Phase-step insensitive algorithms for phase-shifting interferometry

Two novel phase extraction algorithms, in which step sizes need not be known or equal, are described. One algorithm requires a minimum of five interferograms from which intensity offset and intensity modulation are calculated at each pixel and the relative phase is calculated for all pixels with respect to a reference pixel. The other algorithm requires two phase stepping mechanisms and a minimum of ten interferograms. The intensity characteristics and reference phase step are calculated at each pixel and a previously published algorithm is used for the final phase calculation.

Importance of rotational beam alignment in the generation of second harmonic errors in laser heterodyne interferometry

We show, using a Jones matrix analysis, that rotating the two orthogonal linearly polarized inputs of a heterodyne interferometer relative to the polarizing beam splitter axes, produces second harmonic errors in an otherwise ideal interferometer. The error undergoes two cycles as the optical pathlength difference changes from 0 to 2pi. This behaviour is distinct from previously reported periodic errors resulting from polarization leakage and frequency mixing. It is found that as the angular misalignment increases, the amplitude of the periodic errors also increases, and may reach substantial values.

A comparison of different methods for x-ray diffraction line broadening analysis of Ti and Ag UHV deposited thin films: nanostructural dependence on substrate temperature and film thickness

The influence of substrate temperature and film thickness on the nanostructure of titanium (HCP) and silver (FCC) thin films deposited on glass substrates under UHV conditions by electron beam evaporation is investigated. The preferred orientation, nanostrain and stacking and twin fault probabilities in Ag and Ti films are determined as a function of film thickness and substrate temperature. A (111) preferred orientation is observed for silver films, which is dependent on both the film thickness and substrate temperature, with the highest value at a substrate temperature of 500 K. Ti/glass films showed a (002) preferred orientation. Nanostructural parameters such as the crystallite size (size of coherently diffracting domains) and nanostrain are evaluated using the Scherrer and Stocks–Wilson relations, the Williamson–Hall plot, and the single-Voigt (SV), double-Voigt (DV) and Warren–Averbach (WA) methods. Analysis of the results obtained using these methods showed that the most suitable approaches to x-ray diffraction line broadening analysis, applicable to both FCC and HCP polycrystalline thin film structures, are SV, DV and WA. The results show that the crystallite sizes increase with substrate temperature and film thickness, while the nanostrain and lattice constants decrease with thickness. The crystallite size distribution function was obtained from the size broadened part of the DV function, and the results show a shift in the maximum to larger sizes with increasing temperature and thickness.

In Situ Underwater Electronic Holographic Camera for Studies of Plankton

In this paper, we describe an underwater electronic holographic camera (eHoloCam) that has been developed for in situ studies of the distribution and dynamics of plankton and other marine organisms and particles. The eHoloCam uses an Nd-YAG pulsed laser to freeze-frame fast moving particles and a complementary metal-oxide-semiconductor (CMOS) sensor for high-resolution image capture. Digital holograms and holographic videos are recorded at rates from 5 to 25 Hz over a period of several hours. Data is stored locally on an embedded computer. The eHoloCam is capable of recording all organisms and particles located in a water volume of 36.8 cm3 in a single hologram frame. The recorded holographic videos may subsequently be reconstructed numerically at a desired image plane. The main optical and mechanical specifications for eHoloCam are also described. To record electronic holographic videos of marine organisms, the eHoloCam was deployed from a towed sampling frame [autorecording instrumented environmental sampler (ARIES)] on the research vessel RV Scotia at speeds up to 4 kn (about 2 mldrs-1) in the North Sea off the Shetland Isles. Various images of marine organisms obtained from this deployment are shown, together with preliminary measurements on the distribution of Calanus copepods.

Underwater digital holography for studies of marine plankton

Conventional and digital holographies are proving to be increasingly important for studies of marine zooplankton and other underwater biological applications. This paper reports on the use of a subsea digital holographic camera (eHoloCam) for the analysis and identification of marine organisms and other subsea particles. Unlike recording on a photographic film, a digital hologram (e-hologram) is recorded on an electronic sensor and reconstructed numerically in a computer by simulating the propagation of the optical field in space. By comparison with other imaging techniques, an e-hologram has several advantages such as three-dimensional spatial reconstruction, non-intrusive and non-destructive interrogation of the recording sampling volume and the ability to record holographic videos. The basis of much work in optics lies in Maxwells electromagnetic theory and holography is no exception: we report here on two of the numerical reconstruction algorithms we have used to reconstruct holograms obtained using eHoloCam and how their starting point lies in Maxwells equations. Derivation of the angular spectrum algorithm for plane waves is provided as an exact method for the in-line numerical reconstruction of digital holograms. The Fresnel numerical reconstruction algorithm is derived from the angular spectrum method. In-line holograms are numerically processed before and after reconstruction to remove periodic noise from captured images and to increase image contrast. The ability of the Fresnel integration reconstruction algorithm to extend the reconstructed volume beyond the recording sensor dimensions is also shown with a 50% extension of the reconstruction area. Finally, we present some images obtained from recent deployments of eHoloCam in the North Sea and Faeroes Channel.

Influence of deposition conditions and of substrate on the structure of uhv deposited erbium films

Abstract Erbium films of 250–700 nm thickness were deposited on Mo substrates of different roughness, at different substrate temperatures, for deposition rates of 0.5 nms −1 and 7.65 nms −1 under three different uhv conditions, namely standard, semi-rigorous and rigorous . Microstructures of these films were obtained by SEM, while the grain sizes were measured using an image analyser. The composition of the residual gas atmosphere, before and after evaporation of erbium at different T s , was investigated and its influence on the structure of films of varying thickness was established. It was found that the grain size increases with substrate temperature and deposition rate and its dependence on substrate temperature is consistent with the activation energy model proposed by Grovenor et al (1984, Acta Metall , 32 , 773) 1 ; while at temperatures lower than 675 K, where the number of mobile boundaries, according to Grovenor et al (1984, Acta Metall , 32 , 773) 1 , is limited to regime (b) (Zone T), the deposition rate also has a direct effect on the number of mobile boundaries and increases the effective activation energy directly. Results show that the vacuum condition of the uhv system has a direct effect on the microstructure (growth steps and layering) of erbium films. The poorer the vacuum condition, the more pronounced growth steps and layering will form. Growth steps are apparently associated with larger grains, although it may not be the true sizes of the grains which are measured. Clear Zone II structure is obtained for films of varying thickness deposited under rigorous uhv conditions, using different deposition rates. SEM and nuclear reaction analysis give evidence of diffusion of carbon atoms into the hot film and that this effect may be responsible for the increased prominence of re-nucleation.

Influence of substrate temperature, deposition rate, surface texture and material on the structure of uhv deposited erbium films

Abstract Structure of erbium films of 600 nm thickness deposited onto molybdenum substrates of different surface roughness (Rq=151, 500 and 850 nm), glass substrates, and amourphous carbon substrates, for substrate temperatures between 300 and 860 K, at 0.55 and 2.5 nm s−1 deposition rates, are investigated by electron microscopy and X-ray diffraction. The microstructures of the films broadly follow the trends of the Movchan and Demchishin and Thornton zone models, but show some departures in all zones, particularly prominent growth steps and layering. The grain size at a 2.5 nm s−1 deposition rate is found to be between two and five times larger, depending on substrate temperature, than at 0.55 nm s−1 under corresponding conditions, and the variation of grain size with temperature is found to be consistent with the activation energy model of Grovenor et al. X-ray diffraction analysis shows a (002) preferred orientation which reaches a maximum at a 575–775 K substrate temperature, and is stronger for the higher deposition rate. The microstructures and preferred orientations of erbium films are found to be influenced by the surface roughness and material of the substrate.

Polarization Effects in Heterodyne Interferometry

Abstract A detailed analysis of the polarization effects which lead to nonlinearity in the non-ideal optical heterodyne interferometer is presented. Extensive use is made of the coherency matrix representation by setting up a ‘cross-coherency matrix’ representation. A generalized treatment of periodic phase errors (nonlinearity) is then presented. Individual contributions to the nonlinearity have been characterized as either ‘independent’ or ‘dependent’ phase errors. In the single-pass plane-mirror heterodyne system, to which the approach is applied, phase errors for rotational misalignment of the nominally orthogonal linearly polarized input states, beam splitter leakage, non-orthogonality, ellipticity and the effect of misaligned polarizer-mixer are explicitly considered. The latter effect is found to produce nonlinearity only when in combination with any one of the first three and is therefore a dependent phase error. The nonlinearity arising from ellipticity is identical with that from rotational misa...

Visualization of fast-moving cells in vivo using digital holographic video microscopy

Digital in-line holography offers some significant advantages over conventional optical holography and microscopy to image biological specimens. By combining holography with digital video microscopy, an in-line holographic video microscope is developed and is capable of recording spatial 3D holographic images of biological specimens, while preserving the time dimension. The system enables high-speed video recording of fast cell movement, such as the rapid movement of blood cells in the blood stream in vivo. This capability is demonstrated with observations of fast 3-D movement of live cells in suspension cultures in response to a gentle shake to the Petri dish. The experimental and numerical procedures are incorporated with a fast reconstruction algorithm for reconstruction of holographic video frames at various planes (z axis) from the hologram and along the time axis. The current system enables both lateral and longitudinal resolutions down to a few micrometers. Postreconstruction processing of background subtraction is utilized to eliminate noise caused by scattered light, thereby enabling visualization of, for example, blood streams of live Xenopos tadpoles. The combination of digital holography and microscopy offers unique advantages for imaging of fast moving cells and other biological particles in three dimensions in vivo with high spatial and temporal resolution.