Geometric view of adaptive optics control

The objective of an astronomical adaptive optics control system is to minimize the residual wave-front error remaining on the science-object wave fronts after being compensated for atmospheric turbulence and telescope aberrations. Minimizing the mean square wave-front residual maximizes the Strehl ratio and the encircled energy in pointlike images and maximizes the contrast and resolution of extended images. We prove the separation principle of optimal control for application to adaptive optics so as to minimize the mean square wave-front residual. This shows that the residual wave-front error attributable to the control system can be decomposed into three independent terms that can be treated separately in design. The first term depends on the geometry of the wave-front sensor(s), the second term depends on the geometry of the deformable mirror(s), and the third term is a stochastic term that depends on the signal-to-noise ratio. The geometric view comes from understanding that the underlying quantity of interest, the wave-front phase surface, is really an infinite-dimensional vector within a Hilbert space and that this vector space is projected into subspaces we can control and measure by the deformable mirrors and wave-front sensors, respectively. When the control and estimation algorithms are optimal, the residual wave front is in a subspace that is the union of subspaces orthogonal to both of these projections. The method is general in that it applies both to conventional (on-axis, ground-layer conjugate) adaptive optics architectures and to more complicated multi-guide-star- and multiconjugate-layer architectures envisaged for future giant telescopes. We illustrate the approach by using a simple example that has been worked out previously [J. Opt. Soc. Am. A 73, 1171 (1983)] for a single-conjugate, static atmosphere case and follow up with a discussion of how it is extendable to general adaptive optics architectures.     

Three-dimensional shape measurement of non-full-field reflective surfaces

We describe a technique for the measurement of non-full-field reflective surfaces by using phase-stepping profilometry. We explain the principles of phase demodulation and discuss three-dimensional (3-D) height reconstruction in the case of measuring surfaces with reflective properties such as plain glass and mirrored glass. A number of required calibration algorithms are described to obtain surface slopes and reconstructed 3-D heights of the whole surface. Masking for non-full-field objects and the surface reconstruction procedure are demonstrated mathematically and algorithmically. Several experimental results are given for glass with different shapes and defects. Measurement of a spherical mirror with a known radius has also allowed us to show the performance of the proposed technique. This allows for the possibility to compare 3-D data from the known object with data taken from the measurement system.     

An apparatus for checking a reflective fiber optics pressure transducer

A new design is proposed for a system for examining the characteristics of a reflective fiber-optics pressure sensor. It is simple, reliable, and does not require complicated engineering, adjustment, or measurement operations in the manufacturing of the optical part. __________ Translated from Izmeritel’naya Tekhnika, No. 5, pp. 66–68, May, 2008.     

Geometric phase in optics and angular momentum of light

Abstract

The Physical mechanism of the geometric phase in terms of angular momentum exchange is elucidated. It is argued that the geometric phase arising out of the cyclic changes in the transverse mode space of Gaussian light beams is a manifestation of the cycles in the momentum space of the light. The apparent non-conservation of orbital angular momentum in the spontaneous parametric down conversion for the classical light beams is proposed to be related to the geometric phase.     

Emissivity measurements of reflective surfaces at near-millimeter wavelengths

We have developed an instrument for directly measuring the emissivity of reflective surfaces at near-millimeter wavelengths. The thermal emission of a test sample is compared with that of a reference surface, allowing the emissivity of the sample to be determined without heating. The emissivity of the reference surface is determined by one's heating the reference surface and measuring the increase in emission. The instrument has an absolute accuracy of Δε = 5 × 10(-4) and can reproducibly measure a difference in emissivity as small as Δε = 10(-4) between flat reflective samples. We have used the instrument to measure the emissivity of metal films evaporated on glass and carbon fiber-reinforced plastic composite surfaces. We measure an emissivity of (2.15 ± 0.4) × 10(-3) for gold evaporated on glass and (2.65 ± 0.5) × 10(-3) for aluminum evaporated on carbon fiber-reinforced plastic composite.     

Modeling and simulation of the optical response rod-functionalized reflective surfaces

In a variety of emerging energy applications such as photovoltaic conversion, thermo-electric conversion, electrochromic actuation, artificial photosynthesis, etc., the capture and trapping of light on a surface is a critical first step in a multistage process. The functionalization of a surface by adding small-scale features, such as fine-scale rods, to trap incoming light, is one possible approach. In this paper, a model that is amenable to large-scale computation is developed. The approach provides a computational tool that allows analysts to quickly study a wide variety of rod-like microstructures. Both analytical and large-scale computational results are presented.     

Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 lidar

Laser speckle can influence lidar measurements from a diffuse hard target. Atmospheric optical turbulence will also affect the lidar return signal. We present a numerical simulation that models the propagation of a lidar beam and accounts for both reflective speckle and atmospheric turbulence effects. Our simulation is based on implementing a Huygens-Fresnel approximation to laser propagation. A series of phase screens, with the appropriate atmospheric statistical characteristics, are used to simulate the effect of atmospheric turbulence. A single random phase screen is used to simulate scattering of the entire beam from a rough surface. We compare the output of our numerical model with separate CO(2) lidar measurements of atmospheric turbulence and reflective speckle. We also compare the output of our model with separate analytical predictions for atmospheric turbulence and reflective speckle. Good agreement was found between the model and the experimental data. Good agreement was also found with analytical predictions. Finally, we present results of a simulation of the combined effects on a finite-aperture lidar system that are qualitatively consistent with previous experimental observations of increasing rms noise with increasing turbulence level.     

The controlled fabrication and geometry tunable optics of gold nanotube arrays

Arrays of vertically aligned gold nanotubes are fabricated over several square centimetres which display a geometry tunable plasmonic extinction peak at visible wavelengths and at normal incidence. The fabrication method gives control over nanotube dimensions with inner core diameters of 15-30 nm, wall thicknesses of 5-15 nm and nanotube lengths of up to 300 nm. It is possible to tune the position of the extinction peak through the wavelength range 600-900 nm by varying the inner core diameter and wall thickness. The experimental data are in agreement with numerical modelling of the optical properties which further reveal highly localized and enhanced electric fields around the nanotubes. The tunable nature of the optical response exhibited by such structures could be important for various label-free sensing applications based on both refractive index sensing and surface-enhanced Raman scattering.     

Capacitive sensor arrays in dimensional analysis of surfaces

The theoretical aspects of dimensional analysis and shape reconstruction of surfaces by means of displacement sensor arrays are investigated. Although this analysis is focused on surface profiles and linear arrays of capacitive sensors, its results could be easily extended to surfaces and bidimensional arrays of displacement sensors. Capacitance variations related to sensor-to-surface displacements during array scanning are used in the reconstruction equations obtained from the analysis. The reconstruction accuracy depends mainly on the dimensional stability of the array, and it is independent from the array trajectory. The problems raised by nonideal array and sensor behavior, such as fringe effects and geometry deviations are discussed. Capacitance variations due to such effects are calculated and taken into account by means of an energy method. A reconstruction system based on the theoretical results is proposed, and its performance in the reconstruction process is evaluated by a computer simulation which accounts for measurement uncertainties. Simulation results confirm both the effectiveness of the method and the feasibility of the system. Its features are compared with those of other noncontact surface-measuring instruments, and possible applications are outlined     

Physical optics theory for the diffraction of waves by impedance surfaces

The solution of the scattering problem of waves by a half-screen with equal face impedances, which was introduced by Malyughinetz, is transformed into a physical optics integral by using the inverse edge point method. The obtained integral is applied to the diffraction problem of plane waves by an impedance truncated circular cylinder and the scattered waves are derived asymptotically. The results are examined numerically.     

Simulation of synthetic gecko arrays shearing on rough surfaces

To better understand the role of surface roughness and tip geometry in the adhesion of gecko synthetic adhesives, a model is developed that attempts to uncover the relationship between surface feature size and the adhesive terminal feature shape. This model is the first to predict the adhesive behaviour of a plurality of hairs acting in shear on simulated rough surfaces using analytically derived contact models. The models showed that the nanoscale geometry of the tip shape alters the macroscale adhesion of the array of fibres by nearly an order of magnitude, and that on sinusoidal surfaces with amplitudes much larger than the nanoscale features, spatula-shaped features can increase adhesive forces by 2.5 times on smooth surfaces and 10 times on rough surfaces. Interestingly, the summation of the fibres acting in concert shows behaviour much more complex that what could be predicted with the pull-off model of a single fibre. Both the Johnson–Kendall–Roberts and Kendall peel models can explain the experimentally observed frictional adhesion effect previously described in the literature. Similar to experimental results recently reported on the macroscale features of the gecko adhesive system, adhesion drops dramatically when surface roughness exceeds the size and spacing of the adhesive fibrillar features.     

Ordered arrays of ZnO nanorods grown on periodically polarity-inverted surfaces

Periodically polarity inverted (PPI) ZnO templates were fabricated using molecular beam epitaxy by employing MgO buffer layers. The polarity of ZnO film was controlled by the transformation of crystal structure from hexagonal to rocksalt due to the thickness of the MgO buffer layers. The polarity of ZnO in the PPI template was confirmed by AFM and PRM measurement. Higher growth rate and lower current value under positive supplied voltage in the region of Zn-polar were measured with comparing to that of O-polar. Holographic lithographic technique was employed for the realization of submicron pattern of periodical inverted polar ZnO over large area. After reaction using a carbothermal reduction, spatially well-separated ZnO nanorods with pitch of submicron were only observed in the Zn-polar regions. The possible reason for the difference of surface characteristics was considered as being due to the configuration of dangling bonds according to polarity.     

Dual-wavelength heterodyne differential interferometer for high-precision measurements of reflective aspherical surfaces and step heights

A dual-wavelength heterodyne differential interferometer was developed and tested together with scanning mechanics. To extend the range of unambiguity, two wavelengths were applied. This is important for measuring structures with surface discontinuities (reliefs, steps). The automatic adjustment of the interferometer with respect to the rotational symmetrical measuring surfaces (aspheres) is important. An adjustment is needed to scan the asphere through its vertex. Typical measurements on a sphere, an asphere, and steps are shown.     

Ordered arrays of polymeric nanopores by using inverse nanostructured PTFE surfaces

We present a simple, efficient, and high-throughput methodology for the fabrication of ordered nanoporous polymeric surfaces with areas in the range of cm(2). The procedure is based on a two-stage replication of a master nanostructured pattern. The process starts with the preparation of an ordered array of poly(tetrafluoroethylene) (PTFE) free-standing nanopillars by wetting self-ordered porous anodic aluminum oxide templates with molten PTFE. The nanopillars are 120?nm in diameter and approximately 350?nm long, while the array extends over cm(2). The PTFE nanostructuring process induces surface hydrocarbonation of the nanopillars, as revealed by confocal Raman microscopy/spectroscopy, which enhances the wettability of the originally hydrophobic material and facilitates its subsequent use as an inverse pattern. Thus, the PTFE nanostructure is then used as a negative master for the fabrication of macroscopic hexagonal arrays of nanopores composed of biocompatible poly(vinylalcohol). In this particular case, the nanopores are 130-140?nm in diameter and the interpore distance is around 430?nm. Features of such characteristic dimensions are known to be easily recognized by living cells. Moreover, the inverse mold is not destroyed in the pore array demolding process and can be reused for further pore array fabrication. Therefore, the developed method allows the high-throughput production of cm(2)-scale biocompatible nanoporous surfaces that could be interesting as two-dimensional scaffolds for tissue repair or wound healing. Moreover, our approach can be extrapolated to the fabrication of almost any polymer and biopolymer ordered pore array.     

Wettable arrays onto superhydrophobic surfaces for bioactivity testing of inorganic nanoparticles

Poly(l-lactic acid) superhydrophobic surfaces prepared by a phase-separation methodology were treated with 30 min exposition of UV/O₃ irradiation using hollowed masks in order to obtain patterned superhydrophilic squared-shaped areas. These wettable areas successfully confined bioactive glass nanoparticles (BG-NPs), by dispensing and drying individual droplets of BG-NPs suspensions. The obtained biomimetic chips were used to test the in vitro bioactivity of binary (SiO₂-CaO) and ternary (SiO₂-CaO-P₂O₅) nanoparticles produced using sol-gel chemistry by immersing such substrate in simulated body fluid (SBF). From SEM and EDX it was possible to conclude that the ternary system promoted an enhanced apatite deposition. This work shows the potential of using such flat disposable matrices in combinatory essays to easily evaluate the osteoconductive potential of biomaterials using small amounts of different samples.     

Highly corrected close-packed microlens arrays and moth-eye structuring on curved surfaces

The fabrication of near-micrometer-sized close-packed coherent microlens arrays on spheric or aspheric surfaces has been accomplished by use of a compact holographic projector system that was developed for producing multimicrometer down to submicrometer grid patterning on curved surfaces. The microlens arrays, which can be utilized as moth-eye relief structures, are formed in a photoimageable bisbenzocyclobutene polymeric resin by a photolytic process involving standing-wave interference patterns from the holographic projector system. Because of absorption, each integral microlenslet of the finished arrays possesses a near-paraboloid contour. The trajectories of the meridional rays from each microlenslet can be optimized to intersect at either a single point or a locus of points.     

Metal positioning on silicon surfaces using the etching of buried dislocation arrays

Large-area Si(001) nanopatterned surfaces obtained by etching dislocation line arrays have been used to drive the positioning of metallic islands. A method combining wafer bonding of (001) silicon on insulator layers and preferential chemical etching allows controlling the periodicity of square trench arrays in the 20-50 nm lateral periodicity range with an accuracy of less than 1 nm and a depth of about 4-5 nm. The interfacial area containing the dislocation line plane can be removed and a single crystal maintaining the morphological patterning can be obtained. It is shown that oxidized or deoxidized silicon nanopatterned surfaces can drive the positioning of Ni, Au and Ag islands for a 20 nm lateral periodicity and that a lateral long range order, directly transferred from the dislocation network, can be obtained in the Ni and Au cases.     

Odako growth of dense arrays of single-walled carbon nanotubes attached to carbon surfaces

A novel process is demonstrated whereby dense arrays of single-walled carbon nanotubes (SWNT) are grown directly at the interface of a carbon material or carbon fiber. This growth process combines the concepts of SWNT tip growth and alumina-supported SWNT base growth to yield what we refer to as “odako” growth. In odako growth, an alumina flake detaches from the carbon surface and supports catalytic growth of dense SWNT arrays at the tip, leaving a direct interface between the carbon surface and the dense SWNT arrays. In addition to being a new and novel form of SWNT array growth, this technique provides a route toward future development of many important applications for dense aligned SWNT arrays. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. This article is published with open access at Springerlink.com     

Superhydrophobic CuO@Cu2S nanoplate vertical arrays on copper surfaces

The present work reports a simple method to produce hierarchical CuO architectures on copper substrate through self-generation. Subsequently, CuO@Cu₂S composites have been successfully synthesized from the hierarchical CuO precursors via a facile solution-immersion process. These products were characterized by field-emission scanning electron microscopy, x-ray powder diffraction and x-ray photoelectron spectrum. The wettability of the products was also investigated. It was found that the wettability of the CuO@Cu₂S composite film could be easily changed from hydrophilic to superhydrophobic with simple fluorination modification. Compared with other methods, the method herein is mild, economical and easy to create large area superhydrophobic materials on copper substrate.     

Geometric confinement of directly deposited features on hydrophilic rough surfaces using a sacrificial layer

It is challenging to achieve high definition for inkjet-printed features on hydrophilic rough surfaces. In this study, a spreading diameter of ~5 mm was observed for a 10 pL inkjet droplet when it impacted onto a hydrophilic rough surface. A new geometric confinement method was employed to facilitate a much higher inkjet printing definition in the range of ~50 μm. A layer of water-soluble polyacrylic acid (PAA) was spin-coated onto a hydrophilic rough surface and then inkjet patterned. Subsequently, the PAA was made water-insoluble by subjecting the sample to a heat treatment with temperatures above 170 °C. The change in solubility of PAA during the heat treatment is found to be a crucial factor, which enables the physical confinement of the subsequently inkjet printed aqueous-based droplets. The thickness of the spin-coated sample also plays a critical role in the effectiveness of the physical confinement. The effectiveness of the proposed approach was demonstrated with an inkjet patterning process, in which a dielectric layer of 200 nm SiN _x on a textured silicon wafer was selectively etched using 10 pL inkjet-printed droplets resulting in a line width of ~75 μm. When using a 1 pL printhead, the etched line width was as fine as ~30 μm.