Strehl ratio of a Gaussian beam

We discuss the Strehl ratio of systems with a Gaussian pupil and determine the range of validity of its approximate expression based on the aberration variance. The results given are equally applicable to propagation of Gaussian beams. The uniform and weakly truncated pupils are considered as limiting cases of a Gaussian pupil. We show that the approximate expression for Strehl ratio in terms of the aberration variance yields a good estimate of the true value for a strongly truncated pupil but a much smaller value for a weakly truncated pupil.     

Solid state reactions of cordierite precursor oxides and effect of CaO doping on the thermal expansion behaviour of cordierite honeycomb structures

The extruded cordierite honeycomb structure from a stoichiometric formulation of talc, kaolinite, and alumina was subjected to TGA-DSC, dilatometric and XRD investigations. The experimental observations were made to identify the phase transformation sequence in order to understand the solid state reactions involved in the cordierite formation. A maximum cordierite content of 90% was achieved for the samples sintered at 1693 K with a soaking time of 4 h, corresponding to a lowest coefficient of thermal expansion (CTE) of 0.74 × 10^–6/K (along the direction of extrusion) was observed. Attempts were made to establish correlations with cordierite content, processing temperature and CTE of the samples. A few mechanisms are proposed to explain our observations. Attempts are also made to rationalize the low CTE observed along the direction of extrusion on the basis of orientation of anisotropic cordierite crystals as revealed by the transverse I-ratio calculated from the XRD patterns. Effect of CaO doping on CTE of cordierite has been studied in the present work. It was observed that though there is an increase in bulk thermal expansion of cordierite honeycombs on CaO doping due to the absence of micro-cracks as reveled by thermal cycling hysteresis, axial anisotropy was found to be reduced significantly.     

Creep fracture in Al-SiC metal-matrix composites

Creep fracture behaviour of pure aluminium-matrix composites with 10–30 vol% SiC particulates at 623 K is reported. A comparison of tensile and compression creep data shows the existence of a transition stress. Above this transition stress no steady state creep is observed in tension. This transition stress is related to a transition from intergranular to transgranular fracture. The origin of transition stress is perhaps associated with the diffusional relaxation of stress concentration at the matrix/particle interface by lattice diffusion. The intergranular creep fracture of composites appears to be similar to that of unreinforced aluminium and it is power-law creep controlled. The transgranular creep fracture occurs by void nucleation and growth. The nucleation strain for voids is quite small and hence the tertiary stage starts before the end of the primary stage. The ductile fracture models overestimate the strain to fracture and do not predict the observed stress dependence of strain to fracture.     

Low cycle fatigue behavior of Ti-6AI-2Sn-4Zr-6Mo: Part II. Cyclic deformation behavior and low cycle fatigue

A series of strain-controlled low cycle fatigue tests have been carried out on Ti-6-2-4-6 at room temperature primarily for solution-treated and aged material. Tension-compression testing at R = 1 produced softening, irrespective of the morphology of the primary α. The amount of softening increased with increasing strain. Tension-tension testing for R = 0 produced strengthening. Unaged specimens showed behavior similar to aged material for both R = ?1 and R = 0 testing. Annealing at 621 °C produced hardening for R = ?1 and softening for R = 0 testing. Aging at 210 °C of R = ?1 specimens produced strengthening. Fatigue life data revealed longer fatigue life for equiaxed (E) structures than for Widmanstätten plus grain boundary (W +GB)α structures. ForEα, increasing α particle size tends to reduce fatigue life. For W +GBα alloys the situation is more complex, and both a decrease and increase in fatigue life may be seen for increasing particle sizes. There is also a prior β grain size dependency. As a result of softening, the slope of the log Δε _p/2 vs logN _f curve continuously decreases with increasingN. Explanations of the softening and hardening behavior in terms of dislocation rearrangement are offered. An explanation of the role of microstructure on fatigue life has been offered in the companion paper.     

Surface enhanced coherent anti-stokes Raman scattering on nanostructured gold surfaces

Coherent anti-Stokes Raman spectroscopy (CARS) is a well-known tool in multiphoton imaging and nonlinear spectroscopy. In this work we combine CARS with plasmonic surface enhancement on reproducible nanostructured surfaces. We demonstrate strong correlation between plasmon resonances and surface-enhanced CARS (SECARS) intensities on our nanostructured surfaces and show that an enhancement of ～10(5) can be obtained over standard CARS. Furthermore, we find SECARS to be >10(3) times more sensitive than surface-enhanced Raman Spectroscopy (SERS). We also demonstrate SECARS imaging of molecular monolayers. Our work paves the way for reliable single molecule Raman spectroscopy and fast molecular imaging on plasmonic surfaces.     

Zernike circle polynomials and optical aberrations of systems with circular pupils

Zernike circle polynomials, their numbering scheme, and relationship to balanced optical aberrations of systems with circular pupils are discussed.     

Metallurgical Studies of Austenitic Stainless Steel 304 under Warm Deep Drawing

Austenitic stainless steel 304 was deep drawn with different blank diameters under warm conditions using 20 t hydraulic press. A number of deep drawing experiments both at room temperature and at 150 ℃ were conducted to study the metallography. Also, tensile test experiments were conducted on a universal testing machine up to 700 ℃ and the broken specimens were used to study the fractography of the material using scanning electron microscopy in various regions. The microstructure changes were observed at limiting draw ratio （LDR） when the cup is drawn at different temperatures. In austenitic stainless steel, martensite formation takes place that is not only affected by temperature, hut also influenced by the rate at which the material is deformed. In austenitic stainless steel 304, dynamic strain regime appears above 300 ℃ and it decreases the formability of material due to brittle fracture as studied in its fractography. From the metallographic studies, the maximum LDR of the material is observed at 150 ℃ before dynamic strain regime. It is also observed that at 150 ℃, grains are coarse in the drawn cups at LDR.     

Rapidly solidified microstructure of AI-8Fe-4 lanthanide alloys

AI-817e and AI-8Fe-4RE (cerium, erbium, neodymium and gadolinium) alloys were rapidly solidified by the melt-spinning technique. The microstructure and phases of alloy ribbons were studied using optical metallography, SEM, TEM and X-ray diffraction techniques. The study has indicated that Re additions to AI-8Fe: (1) result in formation of an increased amount of fine microstructure region, (2) increase the hardness and stability, and (3) generally suppress the formation of needle-type Al₃Fe compounds by substituting them with globular Al₃Fe₂RE compounds. The addition of gadolinium appears to produce the best results.