Rapid and reliable reference sphere calibration for Fizeau interferometry

The calibration of reference surfaces becomes important in interferometry whenever the tolerances for the tested component are comparable to the imperfections of the reference surface itself. To achieve measurement accuracy better than the reference surface, its errors must be characterised and subtracted from the measurement result. We propose a rapid and simple technique utilising a flat mirror in the focus of the converging test wavefront and a partial occlusion of the test beam, to implement a double-pass self-calibration of the reference surface. Stitching together three or more measurements, with the beam stop appropriately rotated, yields the full-aperture calibration data. The method cannot detect point-antisymmetric errors, but common errors in reference spheres, such as spherical aberration and astigmatism, are point-symmetric and should still be adequately captured. For calibrating spherical surfaces in Fizeau interferometry, a ball of good sphericity can be measured against the reference surface in a number of random orientations. This averages out the errors of the ball and converges toward the stationary error in the reference sphere. Depending on the quality of the ball and the desired uncertainty, the number of orientations required can be large (50-100), which is laborious and time-consuming. We compare the performance of the new technique with the ball-averaging method and the so-called "cat's eye" method to assess the practical trade-offs involved.

We investigated the accuracy of a computer-assisted, respiratory inductive plethysmograph (Respicomp) on 50 awake human newborns who were lying supine. Breaths were selected with different rib cage (RC) to pneumotach (PNT) and abdomen (AB) to pneumotach (PNT) values. The equation RC/PNT + AB/PNT = 1 was solved using the least squares method (LSQ) of calculation of calibration factors. Validation of the calibration factors was performed with a range of consecutive breaths between 6 and 22. Of the 1,128 validation or revalidation breaths, 628 (56%) were within 10% of the simultaneously measured PNT volume, 1,024 (91%) were within 20%, and 1,128 (100%) were within 30%. The RC or AB compartment contributions to ventilation changed spontaneously in the awake newborns. This change eliminated the need to wait for varying sleep states to obtain calibration factors and reduced total time required for calibration. (Some loss of accuracy is a compromise with this method; the calibration factors obtained do not remain accurate while the infant is asleep.) This method provided a reliable and rapid calibration and validation technique of the respiratory inductive plethysmograph (Respicomp) on awake newborns.

Abstract: By using a CGH test plate fabricated with our equipment and techniques, we measured a perfect sphere surface. The measurement result is quantified into four parts: the figure error from the spherical surface under test; the figure error from the spherical reference surface; the error from hologram and the adjustment error from misalignment. The measurement result removed from the later three errors, shown excellent agreemen t with Zygo test of the same sphere surface. This verified that the measurement accuracy by using this kind of CGH coul d be very high. Key words : computer-generated hologram; convex aspheric surface; test 1. Introduction It is well known that the use of large and deep convex aspheric surfaces in reflective optical system allows improved performance with fewer elements. However, it is difficult and expensive to measure them accurately with traditional me thods [1-4]. Recently, a valid met hod by using computer-generated hologram (CGH) test plat has been studied [5-8]. In this method, the CGH was constructed using thermally selective oxidization to transfer a CGH pattern onto a metallic film on a curved substrate. However, the resolution and linear profile of the gr atings that compose the CGH was of inferior quality in comparison with that produced by use of lithography. This may decrease significantly surface measurement accuracy. Our lab has he ld the technology to transfer a large CGH pattern onto a concave lens surface with precise alignment [9-12]. The technology combined laser direct writing and lithography. And we have successfu lly test a convex aspheric surface wi th a CGH test plat fabricated with this method [13-14]. However, the measurement error was not analyzed, and the measurement result was not verified by compared with that of other methods. In this paper, we built an optical test system to measure a perfect sphere surface with 100mm of diameter and 279mm of radius of curvature. The system had two illumination lenses and a test plate with a CGH fabricated by using our new technology. We analyzed the errors existing in this test. The measurement result was quantified into four parts. One is the figure error from the spherical surface under test, and it can be gotten with absolute test method by using Zygo interferometer. One is the figure error from the spherical reference surface, and it can also be gotten with absolute test method by using Zygo interferometer. One is the error from hologram, and it can be verified by confirming the ring positions. One is the adjustment error from misalignment, but it can be removed by using the method of Zernike polynomials fitting and measuring twice[15]. The measurement result removed from the later three errors, shown excellent agreemen t with Zygo test of the same sphere surface. 1. The Optical system design

Fizeau interferometry is a flexible tool for optical surface metrology. Different transmission spheres (TSs) enable testing most spherical surfaces, and selecting a TS to measure form irregularity of a given surface is straightforward. New applications, however, have increased the variety of surfaces to test beyond spheres. Aspheres and freeforms are particularly challenging, as interferometers only resolve small deviations from a sphere without additional corrective optics. Furthermore, the surface irregularity specification may be accompanied by tolerances related to mid-spatial frequencies (MSFs), such as power-spectral density (PSD) or local slope. These MSF specifications may require spatial resolution beyond what a typical full aperture test provides. Subaperture stitching interferometry is particularly well-suited to measuring MSFs, and can also significantly increase non-null aspheric and freeform measurement capability. Selecting the most appropriate TS for a given surface, however, becomes more complicated. We explore how the surface specification interacts with the interferometer’s slope capture limit to determine an “optimal magnification” for that surface. We show how to select the most appropriate TS for the surface, given the optimal magnification and other interferometer constraints (e.g. cavity length, focusing range). We demonstrate this TS selection process for a toroid measurement (with 400 micrometers departure from best-fit sphere). We conclude with guidance for designing aspheres and freeforms that can be measured more easily with stitching interferometry.

To test the feasibility of using profilometers to extract information about IOL surfaces design. A standard monofocal IOL (Tecnis 1), a monofocal IOL that provided some depth of focus (Eyhance), an extended depth of focus IOL based on refractive optics (Mini Well) and a trifocal IOL based on diffractive optics were used in this study (Tecnis Synergy). The surface topography of the IOLs was measured by using a multimode optical profilometer. Posterior surface of Tecnis 1 IOL was spherical and the anterior surface aspherical. In the Eyhance IOL, posterior surface was spherical and anterior surface did not fit to any of our reference surfaces, indicating a higher order aspheric surface design. In the Mini Well Ready IOL, a best-fit sphere surface was obtained for the second surface and a high order aspherical surface design was deduced for the first surface. The anterior surface of the Synergy IOL was aspherical and the base curve of the diffractive structure fitted very well to a spherical surface. To consider an aspheric surface as possible best-fit surface provided more information than if only best-fit spherical surface was considered. The high order aspheric surface designs employed in the IOLs studied presented differences, regarding best-fit asphere surface, higher than 1 micron. These differences were correlated with the generation of spherical aberration complex profiles (with Zernike terms higher than 4th order) and with the production of distinct amounts of depth of focus. This method was also useful to deduce the base curve of diffractive surfaces.

A new technique for the measurement of surface form error of a test spherical surface with respect to a reference spherical surface, using wedge phase shifting Fizeau interferometer, is presented. A two stage measurement method is discussed. The individual surface form error of the test and reference spherical surfaces along with the residual wave front aberration introduced by the common optical elements in the Fizeau cavity are measured with respect to a plane reference surface using phase shifting interferometry. Finally, data subtraction is used to eliminate the effect of the residual wave front aberration introduced by common optical elements and thereby transforming the result as the surface form error of the test spherical surface with respect to the reference spherical surface. Results obtained for a test spherical surface is presented.

Ion beam figuring (IBF) is a novel technology for Ultra-precise optics. Material is removed from optic surface in atomic or molecular form by physical sputtering. Due to non-contact between the tool and the work piece, the problems involved in the conventional process are avoided, such as edge-effect and tool-wear. The ion beam figuring process is of high determinacy and high efficiency. All these properties make ion beam figuring one of the promising methods for producing mirrors of high precision with nm-rms accuracy. In this article, a new ion beam figuring system which contains doubled vacuum chambers is set up. Optics can be exchanged by a transport vehicle shuttling between the two vacuum chambers without opening the primary vacuum chamber and waiting for the ion source to cool completely, which means the efficiency can be increased greatly. A high performance processing robot contains three linear axes and two angular axes of motion, providing 5-axis ion source positioning capability with high accuracy. The angle can be up to 50° to figure very steep spherical and aspherical surfaces. Then, the beam removal function of Gaussian shape is obtained by an experimental method and it is extremely stable for a long time. Finally, two sample mirrors are figured by the ion beam figuring system: one is a fused silica flat mirror with a 100 mm diameter (90% effective aperture) and an ultra-precise flat mirror with a surface error of 0.89 nm rms, 14.7 nm PV is obtained; the other fused silica concave spherical mirror with a 100 mm aperture (90% effective aperture) and 420 mm radius of curvature is figured and a concave spherical mirror with 1 nm rms, 16.9 nm PV is obtained, which prove that the ion beam figuring system is favourable for the figuring process.

HighlightsStation aridity can cause overestimation of ETref at weather monitoring networks in irrigated areas.Station aridity was demonstrated in a mesoscale weather monitoring network.Station aridity is amplified in water-scarce irrigated areas during droughts.Station aridity should be accounted for to achieve water conservation through weather-informed irrigation.Abstract. Many weather monitoring networks such as the Oklahoma Mesonet provide estimates of reference evapotranspiration (ETref) to facilitate weather-informed irrigation decisions. However, weather stations that collect the required input data to estimate ETref using the widely applied ASCE standardized ETref equation are not typically installed over a reference surface, defined as a large expanse of dense, well-watered, stress-free grass or alfalfa having a specified height, surface resistance, and albedo. The deviation of actual surface conditions in the surrounding environment of the weather stations from the reference condition creates station aridity effects that can lead to overestimation of ETref. Daily hydroclimate datasets for a period of 20 years (2000-2019) were used to evaluate the prevalence and spatiotemporal characteristics of station aridity across the Oklahoma Mesonet. Station aridity was characterized based on mean dew point deviation (MDD = Tmin - Tdew), maximum relative humidity (RHmax), and normalized difference vegetation index (NDVI). Results demonstrate that station aridity is prevalent and highly variable in both space and time across the Oklahoma Mesonet, as it increases from southeast to northwest in the Oklahoma Panhandle. Larger average seasonal MDD (up to 13°C), lower RHmax (e.g., 57%), and lower NDVI (e.g., 0.22) were observed during extreme to exceptional drought of 2011 in western Oklahoma, where a majority of the state’s irrigated agriculture (88%) is located. Spatiotemporal patterns of station aridity demonstrate the profound effect of wet and dry periods that influence the utility of ETref estimates to improve agricultural water conservation during high irrigation requirement times in water-scarce irrigated areas. Keywords: Evapotranspiration, Irrigation requirement, Reference condition, Station aridity, Weather station.

It has long been recognized that aberrations of the optical system comprised of the interferometer cavity and the viewing system can result in distortion of fringes1-5. However, what is less understood is that the aberrations of the optical system, especially the viewing system, can influence the optical path difference (OPD) of interference fringes between the reference wavefront and the test wavefront due to the fact that rays from the test surface may not trace the exact same optical path as those from the reference surface. The propagation error that is produced by the optical system and the aberrated surface or optical system under test is basically pupil shear of the viewing system and is referred to here as the shearing error.

SUMMARY Synthetic pulse forms of core phases have been computed in models of an undulating core-mantle boundary or an undulating boundary layer at the base of the mantle. A simple detector has been applied to the pulse forms of PcP, PKP (BC and AB) and PKKP (BC). The detections are influenced by amplitude and waveform changes due to focusing, defocusing and interference. Numerical results are given for the increased bias and the change of variance of the traveltime residuals. The results for traveltime bias follow the observed trend in real data of core phases, although the computed bias is less than observations suggest. Special attention is paid to the underlying assumptions of seismic tomography. It is shown that these assumptions are not tenable for several of the phases and models considered here. In those cases, seismic tomography will produce models that are in poor agreement with the true model. The synthetics were computed by introducing the concepts of 3-D dynamic ray tracing with a Kirchhoff type of integral over a spherical reference surface. Simple expressions are given for propagating the ray propagators of 3-D dynamic ray tracing through spherically symmetric parts of the model.

A theory is developed for analyzing the structure of a focused random field in systems of large Fresnel numbers. The analysis provides a general expression for the cross-spectral density of the focused field in terms of the cross-spectral density of the random field on a spherical reference surface in the region of the diffracting aperture. The results are illustrated by considering the structure of the focal region in a field produced by focusing a partially coherent wave whose correlation function is frequently encountered in practice.

The surface is scanned along its symmetry axis in a Fizeau cavity with spherical reference surface. The coordinates x,y,z at the (moving) zone of normal incidence are derived from simultaneous phase-measurements at the apex and zone.

Operational meteorological satellites generally lack reliable onboard calibration systems for solar-imaging channels. Current methods for calibrating these channels and for normalizing similar channels on contemporaneous satellite imagers typically rely on a poorly calibrated reference source. To establish a more reliable reference instrument for calibration normalization, this paper examines the use of research satellite imagers that maintain their solar-channel calibrations by using onboard diffuser systems that rely on the sun as an absolute reference. The Visible Infrared Scanner (VIRS) on the Tropical Rainfall Measuring Mission(TRMM) satellite and the second Along-Track Scanning Radiometer (ATSR-2) on the second European Remote Sensing Satellite (ERS-2) are correlated with matched data from the eighth Geostationary Operational Environmental Satellite (GOES-8), the fifth Geostationary Meteorological satellite(GMS-5), and with each other to examine trends in the solar channels. VIRS data are also correlated with the Terra satellite’s Moderate Resolution Imaging Spectroradiometer (MODIS) provisional data as a preliminary assessment of their relative calibrations. As an additional check on their long-term stability, the VIRS data are compared to the relevant corresponding broadband shortwave radiances of the Clouds and the Earth’s Radiant Energy System (CERES) scanners on TRMM. No statistically significant trend in the calibration of the VIRS 0.65- and 1.64-mm channels could be detected from the comparisons with CERES data taken during 1998 and 2000. The VIRS-to-GOES-8 correlations revealed an annual degradation rate for the GOES-8 visible (0.67 mm) channel of ;7.5% and an initial drop of 16% in the gain from the prelaunch value. The slopes in the GOES-8 visible-channel gain trend lines derived from VIRS data taken after January 1998 and ATSR-2 data taken between October 1995 and December 1999 differed by only 1%‐2% indicating that both reference instruments are highly stable. The mean difference of 3%‐4.8% between the VIRS‐GOES-8 and ATSR-2‐GOES-8 gains is attributed to spectral differences between ATSR-2 and VIRS and to possible biases in the ATSR-2 channel-2 calibration. A degradation rate of 1.3% per year found for the GMS-5 visible channel was confirmed by comparisons with earlier calibrations. The MODIS and VIRS calibrations agreed to within 21% to 3%. Some of the differences between VIRS and the provisional MODIS radiances can be explained by spectral differences between the two instruments. The MODIS measures greater reflectance than VIRS for bright scenes. Although both VIRS and ATSR-2 provide temporally stable calibrations, it is recommended that, at least until MODIS calibrations are finalized, VIRS should be used as a reference source for normalizing operational meteorological satellite imagers because of its broader visible filter.

This study presents a new method for estimation and imaging of the area at risk (AaR) in myocardial infarction (MI). The values of the ST-segment deviations of 12-lead ECG signal were used as input parameters. Based on DECARTO model, the spherical surface was chosen as a reference surface to approximate the ventricular wall. On this surface, the spatial ST vector was projected. The center of AaR was defined as an intersection of the spatial ST vector with spherical surface; the size of the AaR was set to be proportional to the number of electrical leads with ST-segment deviations. The method was tested using data of 10 patients with acute MI. The visual comparison showed good agreement with the AaRECG estimates based originally on the Selvester QRS scoring as well as with a non-electrocardiographic imaging method (SPECT).

We present a lightweight mirror made of a magnesium alloy for applications to space-borne telescopes and optics in instruments. A non-flammable magnesium alloy was recently developed. We consider this alloy to be a promising material for a lightweight mirror due to its high stiffness, high fracture toughness, low density, and suitability for machining. First, small flat mirrors were fabricated to obtain and improve the fabrication conditions. Then, a 175-mm magnesium-alloy mirror, with a spherical mirror surface and a backside hexagonal cutout structure to reduce the mass of the mirror, was designed and fabricated. The spherical mirror surface was fabricated using a diamond-turning process. The evaluated residual of the surface figure of the 175-mm mirror from the design is 0.90 μm rms. The deformation caused by the jig used for the fabrication was one of the major factors that increased the residual of the surface figure. The surface roughness of the 175-mm mirror was evaluated, and values of Sa = 9.6 nm and Sq = 12.6 nm were obtained by averaging the data of four measurements with a 167 μm × 167 μm field of view. Methods to improve the mirror surface are discussed. We also discuss space-borne telescopes and instruments for which this magnesium alloy is one of promising materials.