Steep Convex Research Articles

Phase measuring deflectometry for convex aspheric surface measurement.

This paper introduces what we believe to be a novel approach to accurately measure the shape of convex aspherical surfaces with large slope gradients. This approach employs a pre-distortion system to enhance the visibility of the structured light pattern that is captured by camera. The data processing involves iterative methods to obtain surface shape data. The initial step in the experimental calibration involves establishing a reference plane, which serves as the starting point for the iterative process. The calculation for slope is subsequently utilized to determine the initial slope of the surface under test, and the height of the tested element is derived by integrating these slopes. Through multiple iterations and continuous updating of the surface height, the precise and authentic true surface height is ultimately achieved. The method's accuracy is assessed through the measurement of a highly steep convex aspherical area with a diameter of 5.2mm and a radius of curvature of approximately 7.7mm. The proposed method demonstrates root mean square accuracy that can reach half a wavelength when compared to the measurement results obtained from high-precision profilers.

Interferometric grazing incidence test of rough steep convex aspherics: full 3D reconstruction of the object

A grazing incidence interferometric measurement procedure is applied to test rough convex steep rotationally symmetric aspherics. The measurement of rough surfaces is possible; i.e., without the need to polish the surfaces, due to the large effective wavelength (λeff=10µm) of the test. One measurement step using diffractive beam splitters and phase-shifting techniques delivers the surface information along one meridian. The full surface description can be stitched together from several phase results combined with appropriate object rotations. This publication includes, besides the short recapitulation of the measurement principle and experimental setup, a presentation of the simulated and measured data of an aspherical object under test. The data analysis of each meridian is focused on the elimination of the misalignment aberrations caused by specimen displacements. Finally, the stitching of multiple meridian regions to a 3D surface map of the specimen is shown.

Interferometric grazing incidence test of rough steep convex spherics: experimental data analysis.

Grazing incidence interferometry has been applied to plane, cylindrical, acylindrical, and general rod-like surfaces using diffractive beam splitters. Here, in a first step towards measuring aspherics, we demonstrate that also rough convex steep rotationally symmetric spherics can be measured along one meridian in a single step using diffractive beam splitters and phase shifting techniques. The measurement of rough surfaces is possible, i.e., without the need to polish the surfaces, due to the large effective wavelength (λeff≈10µm) of the test. We include, besides the short recapitulation of the measurement principle and experimental setup, a presentation of the measured data of one small meridian region for the special case of spherical objects under test. The subsequent data analysis combined with suitable simulations focuses on elimination of the misalignment aberrations from the results caused by specimen displacements in the setup.

Interferometric grazing incidence test of rough steep convex spherical and aspherical surfaces: first simulations and experimental proof of principle.

In the past, grazing incidence interferometry has been applied for rough plane, cylindrical, acylindrical, and general rod-like surfaces using diffractive beam splitters. Here, we demonstrate that also rough convex steep rotational symmetric spherical or aspherical surfaces can be measured along one meridian in a single step using diffractive beam splitters and phase-shifting techniques. The extension to the whole surface can be attained by successive meridional measurements of the surface under test by azimuthal adjustments. The principle of the method is given and for a spherical ball lens as an extremely curved surface simulated, and experimental data are presented. The features of the interferogram are discussed, and the experimental evaluation of a single meridian including the unwrapped phase data is shown.

Climate-induced mortality of Siberian pine and fir in the Lake Baikal Watershed, Siberia

Siberian pine (Pinus sibirica) and fir (Abies sibirica) (so called “dark needle conifers”, DNC) showed decreased radial growth increment within the Lake Baikal watershed since the 1980s with increasing mortality recorded since the year 2000. Tree ring width was strongly correlated with vapor pressure deficit, aridity and root zone moisture. Water stress from droughts made trees more susceptible to insect attacks causing mortality in about 10% of DNC stands within the Lake Baikal watershed.Within Siberia DNC mortality increased in the southern part of the DNC range. Biogeographically, tree mortality was located within the DNC – forest-steppes transition. Tree mortality was significantly correlated with drought and soil moisture anomalies. Within the interior of the DNC range mortality occurred within relief features with high water stress risk (i.e., steep convex south facing slopes with shallow well-drained soils). In general, DNC mortality in Siberia was induced by increased aridity and severe drought (inciting factors) in synergy with biotic attacks (contributing factor). In future climate scenarios with predicted increase in aridity DNC could be eliminated from the southern part of its current range and will be replaced by drought-resistant conifers and broadleaf species (e.g., Larix sibirica, Pinus silvestris, and Betula pubescence).

Subaperture stitching test of large steep convex spheres.

Limited by the aperture and f/number of the transmission sphere (TS), large convex spheres with very small R/number (ratio of the radius of curvature to the aperture) cannot be tested in a single measurement with a standard interferometer. We present the algorithm and troubleshooting for subaperture stitching test of a half meter-class convex sphere with R/0.61. Totally 90 off-axis subapertures are arranged on 5 rings around the central one. Since the subaperture is so small, its surface error is comparable with that of the TS reference error. Hence a self-calibrated stitching algorithm is proposed to separate the reference error from the measurements. Another serious problem is the nonlinear mapping between the subaperture's local coordinates and the full aperture's global coordinates. The nonlinearity increases remarkably with the off-axis angle. As a result, we cannot directly remove power from the full aperture error map as we usually do. Otherwise incorrect spherical aberration will be generated. We therefore propose the sphericity assessment algorithm to match the stitched surface error with a best-fit sphere. The residual is true surface error which can be used for corrective figuring or for tolerance assessment. The self-calibrated stitching and troubleshooting are demonstrated experimentally.

双胶合透镜法检测大相对孔径凸非球面透镜

It is difficult to fabricate and test convex aspherical surfaces,especially for steep convex aspheical surfaces.Based on the analysis of the conventional null test,a simple test system with cemented doublet for two steep convex ellipsoids was discussed.The wavefront of the both test system was less than 1/30λ RMS(Root Meat Square,λ=632.8nm).The convex aspheric lens had their successful application in practical optical system.The result showed that the null test for convex aspheric lens discussed in this paper is valid.Compared with the traditional test method,the cemented doublet offsets the spherical aberration generated by the sphere surface of the lens.So the proposed test method decreases the amount of the spherical aberration generated by the aspherical lens,with fewer elements, and reduces the system′s alignment difficulty.It was demonstrated to be an effective,high-precision testing method.

A novel comparative study of crystalline perfection and optical homogeneity in Nd:GGG crystals grown by the Czochralski technique with different crystal/melt interface shapes

Nd:GGG crystals (GGG is gadolinium gallium garnet) grown with different crystal/melt interface shapes (convex/flat/concave) by varying the seed rotation rate while using the Czochralski technique were studied for their optical homogeneity and crystalline perfection by optical polarization microscopy (OPM) and high-resolution X-ray diffractometry (HRXRD), respectively. It was found that there is a remarkable effect of seed rotation rate, which decides the shape of the crystal/melt interface, on the optical homogeneity and crystalline perfection. It was found experimentally that, as the rotation rate increases, the crystal/melt interface changes from convex to flat. If the rate further increases the interface becomes concave. With a steep convex interface (for low rotation rates), certain facets are concentrated in the small central portion of the crystal, and as the rate increases, these facets slowly move outward, leading to improved optical homogeneity and crystalline perfection as observed from the OPM and HRXRD results. The strain developed in the crystalline matrix as a result of segregation of oxygen in the crystals at low seed rotation rates as observed from HRXRD seems to be the reason for the observed optical inhomogeneity. The correlation between optical inhomogeneity and crystalline perfection for a variety of specimens with different shapes of the crystal/liquid interface obtained at different seed rotation rates is reported.

Strain-rate estimates for crevasse formation at an alpine ice divide: Mount Hunter, Alaska

AbstractCrevasse initiation is linked to strain rates that range over three orders of magnitude (0.001 and 0.163 a-1) as a result of the temperature-dependent nonlinear rheological properties of ice and from water and debris inclusions. Here we discuss a small cold glacier that contains buried crevasses at and near an ice divide. Surface-conformable stratigraphy, the glacier’s small size, and cold temperatures argue for limited rheological variability at this site. Surface ice-flow velocities of (1.2-15.5) ± 0.472 m a- 1 imply classic saddle flow surrounding the ice divide. Numerical models that incorporate field-observed boundary conditions suggest extensional strain rates of 0.003-0.015 a- 1 , which fall within the published estimates required for crevasse initiation. The occurrence of one crevasse beginning at 50 m depth that appears to penetrate close to the bed suggests that it formed at depth. Field data and numerical models indicate that a higher interior stress at this crevasse location may be associated with steep convex bed topography; however, the dynamics that caused its formation are not entirely clear.

Testing of steep convex aspheric surface with a Hartmann sensor by using a CGH

Most aspheric surfaces have been tested by interferometer with some null correctors. This approach, however, often fails when there are many aspherical terms or test surface is very steep because it is not easy to design the conventional null lens or CGH (Computer Generated Hologram). On the other hand, 3-D profilometer can measure aspheric surfaces without any null correctors; however, it takes some time to measure, which makes it unsuitable for the production line in the factory. In this paper, we apply the Hartmann test to the measurement of steep convex aspheric surfaces of which diameter is about 16 mm. In order to increase the measurement accuracy, we calibrated the test setup using a CGH that simulates the ideal test surface. We demonstrated that the significant amount of error in the test setup could be removed by this calibration process. The test results showed only 2 nm rms WFE (wave front error) difference even though the WFE of test setup was worsened by more than 0.13 mum rms. Since this method makes it possible to measure highly aspheric surface quickly and accurately, it can be used in the production line.

Unifying temperature effects on the growth rate of bacteria and the stability of globular proteins

The specific growth rate constant for bacterial growth does not obey the Arrhenius-type kinetics displayed by simple chemical reactions. Instead, for bacteria, steep convex curves are observed on an Arrhenius plot at the low- and high-temperature ends of the biokinetic range, with a region towards the middle of the growth range loosely approximating linearity. This central region has been considered by microbiologists to be the “normal physiological range” for bacterial growth, a concept whose meaningfulness we now question. We employ a kinetic model incorporating thermodynamic terms for temperature-induced enzyme denaturation, central to which is a term to account for the large positive heat capacity change during unfolding of the proteins within the bacteria. It is now widely believed by biophysicists that denaturation of complex proteins and/or other macromolecules is due to hydrophobic hydration of non-polar compounds. Denaturation is seen as the process by which enthalpic and entropic forces becomes imbalanced both at high and at low temperatures resulting in conformational changes in the enzyme structure that expose hydrophobic amino acid groups to the surrounding water molecules. The “thermodynamic” rate model, incorporating the heat capacity change and its effect on the enthalpy and entropy of the system, fitted 35 sets of data for psychrophilic, psychrotrophic, mesophilic and thermophilic bacteria well, resulting in biologically meaningful estimates for the important thermodynamic parameters. As these results mirror those obtained by biophysicists for globular proteins, it appears that the same or a similar mechanism applies to bacteria as applies to proteins.