Concave Spherical Surface Research Articles

A new focusing ultrasonic transducer and two foci acoustic lens for acoustic microscopy

The textured piezoelectric film of a new organic-based material produced by vapor deposition was used as an active element of a focusing ultrasonic transducer. The transducer exhibits near theoretical lateral and axial resolution, unipolar pulse response to a step voltage, and 30 dB insertion losses in an octave frequency band. The transducer is acoustically transparent over a wide frequency range and can be fabricated on a concave spherical surface of the standard acoustic lens. The resulting double transducer and two foci acoustic lens are capable of improving the quality of the surface structure imaging or of being used in continuous wave reflection acoustic microscopy.

Surface microroughness of optical glasses under deterministic microgrinding

Deterministic microgrinding of precision optical components with rigid, computer-controlled machining centers and high-speed tool spindles is now possible on a commercial scale. Platforms such as the Opticam systems at the Center for Optics Manufacturing produce convex and concave spherical surfaces with radii from 5 mm to ∞, i.e., planar, and work diameters from 10 to 150 mm. Aspherical surfaces are also being manufactured. The resulting specular surfaces have a typical rms microroughness of 20 nm, 1 μm of subsurface damage, and a figure error of less than 1 wave peak to valley. Surface roughness under deterministic microgrinding conditions (fixed infeed rate) with bound abrasive diamond ring tools with various degrees of bond hardness is correlated to a material length scale, identified as a ductility index, involving the hardness and fracture toughness of glasses. This result is in contrast to loose abrasive grinding (fixed nominal pressure), in which surface microroughness is determined by the elastic stiffness and the hardness of the glass. We summarize measurements of fracture toughness and microhardness by microindentation for crown and flint optical glasses, and fused silica. The microindentation fracture toughness in nondensifying optical glasses is in good agreement with bulk fracture toughness measurement methods.

Cratering Experiments into Curved Surfaces and Their Implication for Craters on Small Satellites

Impact craters were produced on mortar targets of cylindrical, spherical, and plane surfaces in order to evaluate the effect of curvature on the shape of large craters on nonplanar surfaces of smaller bodies. As the curvature of the target surface increases, the cross-sectional shape of the crater becomes flatter, and the crater diameter and ejecta mass increase. Diameter and ejecta mass of craters on a convex spherical surface are larger than those on cylindrical surfaces of the same curvature. The crater on the concave spherical surface has a smaller diameter, less ejecta mass, and a deeper bottom. Crater shape rapidly changes as the crater radius grows comparable to the curvature radius of the target surface. Some of these results agree on a cross-sectional shape of a large crater on Phobos. The cross-sectional shape of a large crater observed on Hyperion is also compared to the experiments.

Lens coating in thermal evaporation physical vapour deposition chambers: optimization of the geometrical configuration

Following established procedures to enhance layer thickness uniformity in the multiple substrate coating inside a thermal evaporation physical vapour deposition unit, the present study completes the analysis and extends the optimization to include all the relevant geometrical factors influencing the coating of concave or convex spherical surfaces held by a spherical (dome-shaped) calotte. The computer-aided method proposed is very useful for the improvement of layer thickness uniformity (i) all across a single lens surface, (ii) between both lens faces, and (iii) between coatings deposited on lenses placed at different positions on the calotte.

Isolation System for Equipment using Friction Pendulum Bearings. 1st Report. Shaking Table Tests and Response Analysis on Isolated Equipment.

During the last few years, as we enter a new era of a high-level information-oriented society, the number of buildings having multiple functions has been increasing. Seismic isolation technology can protect not only the structural elements of a building but also its primary function from destructive earthquake motion. It is with such background that many types of earthquake isolation floors or systems have already been developed and have spread throughout in Japan. Almost all isolation floors/systems developed with especially for critical equipment such as computer systems so far consist of coil springs to provide equipment a designed natural frequency and energy-absorbing devices such as friction dampers and oil dampers. However, these types of earthquake isolation floors or systems may become expensive although they perform satisfactorily. The friction pendulum bearings developed in this program can solve this problem. This device consists of an articulated friction slider which moves on a spherical concave surface and provides the supported equipment with a designed frequency obtained by a radius of curvature and gravity. The articulated friction slider dissipates energy as a friction damper. In this paper we conducted shaking table tests and theoretical analysis in order to investigate the performance of isolation and the restoring force characteristics of the earthquake isolation system using the friction pendulum bearings.

Direct determination of focal length by using Talbot interferometry

A new and simple technique for the determination of the focal length of positive lenses and concave spherical surfaces by Talbot interferometry is described. Results of measurements are presented. We show that high measurement accuracy can be achieved with this technique.

Ultrasound flow measurement apparatus

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Interaction between dislocations and cellular front of crystallization: (0001)SiO 2 face

The interaction between dislocations and a groove on the cellular growth front has been analyzed. It is shown that under certain conditions the dislocation outcrop at the groove bottom may be energetically advantageous. As a result, dislocations in the grown crystal should be located in the boundaries between neighboring cells. The criteria for dislocation capture by the groove are formulated. These criteria essentially depend on the crystallographic anisotropy in the dislocation energy and growth rate. The general theory is applied to the analysis of the dislocation structure formed by the pinacoidal quartz face growing from hydrothermal solutions. With this aim the anisotropy in growth rate in measured on concave spherical surfaces. The dislocation energy and its anisotropy for the [21̄1̄0], [21̄1̄1], [21̄1̄1̄], and [0001] Burgers vectors was calculated with the use of elastic constants at 350°C. The effects caused by dislocation piling along the boundaries and the corresponding experimental data are analyzed.

The cutting method of ceramic plates make use of spherical surface.

A cutting method for ceramic plate is proposed. This method is an application of the fracture of brittle materials under bending moment. Bending moment arise from compressive lode applied to the ceramic plate put between a concave and convex spherical surface. Then the ceramic plate is cut along the notches of desired shapes on one surface. The characteristics of the cutting method are: (1) Cutting can be carried out without dust, and the cutting sections are smooth. (2) The ceramic plate can be divided into many equal parts and cut simultaneously in square and traiangylar shapes during one compression. (3) Ceramic plate can be easily cut along various shapes such a curve and a circle. (4) This method can be cut a number of plates, almost instantly.

Asymptotic approximation and experimental study of electromagnetic fields excited by an electric dipole located over a conducting concave spherical surface

AbstractThe dome antenna has been proposed for scanning an antenna beam at a high speed in a wide angular range. For the design of a dome antenna, an electromagnetic analysis in the concave side of the conducting sphere is required. In connection with this problem, the electromagnetic field by an electric dipole placed on the concave surface of an open conducting sphere has been reported and analyzed in terms of the sum of the whispering gallery (WG) modes, continuous spectrum and ν = 0 (ν: wavenumber in the θ direction) by the authors. However, it has been pointed out that this expression has a problem for an arbitrary ka, although it provides a valid result for ka = nπ/2 (k: wavenumber, a: sphere radius, n: integer). It is also unattractive numerically since Legendre functions must be calculated by numerical integration. In this paper, an engineering application is attempted by using a high‐frequency approximation. By means of the approximate asymptotic solution and the previous expression, actual numerical calculations have been carried out. By way of comparison with experimental results, the validity of each expression is confirmed and its range of applicability is studied.

Scanning characteristics of spherical dome antenna composed of arcing dipole array antennas including the effects of mutual coupling between elements

AbstractFor a beam scanning at high speed over a wide angle, a dome antenna has been proposed. Past research on the dome antenna treated the dome parts as an ideal lens. However, the concrete arrangement of antenna elements outside and inside the dome and their mutual coupling have not been considered. Based on our past work on the electromagnetic field inside a concave spherical surface, this paper describes the results of analysis performed on the most fundamental dome antenna composed of arcing array antennas. For the array elements we considered dipole antennas. We obtained the radiation characteristics considering the mutual coupling among the elements of the radiators on the convex surface, the elements of the collector on the concave surface, and the coupling between the elements of the collector and the elements of the primary radiator. We determined the excitation currents in the elements of the primary radiator so that the currents in the elements of the radiator become co‐phase and uniform amplitude along the direction of the main beam. We obtained the radiation characteristics, and confirmed that over the range from 0 to 110°, beam scanning at almost a constant gain was possible. Next, we suppressed the levels of the sidelobes. We showed that up to a maximum of 18 dB, we suppressed the levels of the sidelobes compared to the co‐phase excitation. Finally, we discussed the influence of the mutual coupling between the elements of the radiator and the elements of the collector on the directivity.

Electromagnetic fields excited by an electric dipole located over a conducting concave spherical surface

AbstractThe dome antenna has been proposed for high‐speed scanning of the main beam of the antenna in a wide‐angle range. For the design of the dome antenna, an analysis for the electromagnetic field in the concave side of the conducting sphere is indispensable. In connection with this problem, several studies have been reported on the cylindrical concave surface. However, no report is available to date on the electromagnetic field for a practical concave conducting sphere for which both the source and the observation points are removed from the boundary. This paper describes the results of analysis for this type of electromagnetic problems. First, the integral expressions for the electric field are obtained in the form of a sum of Whispering Gallery (WG) modes and a continuous spectrum. In the derivation of the field expression, spurious diffracted waves are included due to a hypothetical conical absorber, and these waves are eliminated. A scheme is implemented in which the pole contribution of the wavenumbe in the zenith angle θ so that the numerical difficulty is removed. Actual numerical calculations have been performed and the validity and range of applicability have been studied for the expression. It is found that the expression derived in this paper provides a valid field solution for the case where kα (k is the wavenumber and α is the sphere radius) is sufficiently larger than unity and is an integral multiple of π/2.

Spherometry: description and error analysis of portable devices

This work discusses four portable instruments that measure the radius of a concave or convex spherical surface. Some methods used on spherical measuring machines are first described, followed by the ‘geometrical method” which is easily adaptable to portable instruments. A brief description of the design of each device is given with the radius computing formula (according to geometric principle). The instruments measure directly the arc-depth (sagittal height) of a spherical sector at a specific diameter and the radius is calculated from these two parameters. The work then describes the various factors that can influence the accuracy of the final result. The final accuracy depends on the inaccuracy level of each factor and its weight in the computing formula. The error analysis facilitates a better comparison of the instruments' precision levels, in order to choose the most appropriate instrument. The differential analysis also indicates the relationship between the change in measured height and changes in the surface's radius.

Mutual coupling between rectangular slot antennas on a conducting concave spherical surface

The surface fields excited by a horizontal magnetic source located on a conducting concave spherical surface have been formulated. The field expressions are obtained as a combination of ray-optical fields and simplified integrals under the condition that the radius of the spherical surface is much greater than the wavelength. Numerical calculations have been performed, and the calculated results for the surface fields have been corroborated with experiments. The results of these basic studies have been used in calculating the mutual coupling between rectangular slot antennas on the conducting concave spherical surface assuming the aperture field as the dominant mode in the wave guides connected with the slots. The numerical results have been compared with those for slots on a convex conducting surface. Experimental investigation of the mutual coupling has also been carried out.

Surface fields excited by a vertical electric point source located on a conducting concave spherical surface

AbstractWith the appearance of dome antenna in recent years, the necessity for analyzing the electromagnetic fields produced by a wave source placed on the concave side of a solid conducting surface has arisen. Some research on this problem for a conducting concave cylindrical surface has beem reported. However, no research which is of practical importance, has been conducted on the concave sphere. This paper describes the result of an analysis of the surface magnetic field produced by an electric point source placed on the concave side of an open conducting sphere. The analytical technique is based on the case of a concave cylindrical surface. First, a wave component traveling along the boundary is obtained from a representation of the field inside a closed conducting sphere and the field representation for an open sphere is derived. Next, the surface magnetic field for the case where the radius of the sphere is sufficiently large compared to the wavelength is represented in the form of the fields of geometrical optics and integrals. As in the cylindrical case, the result of concrete calculation shows that the resulting field agrees with the field near the wave source in the case of a vertical electric point source placed on an infinite ground plane and that a complicated interfering pattern is produced at a distance far from the wave source. Also, the appropriateness of this analytical result is confirmed through an experimental study.

Surface fields excited by a vertical electric point source located on a conducting concave spherical surface

Surface fields excited by a vertical electric point source located on a conducting concave spherical surface

The effect of optical unloading of a passive shutter on the energy parameters of a single-pulse ruby laser

The present paper presents the results of an experimental investigation of the effect of the shutter unloading coefficient on the energy parameters of a ruby laser. The unloading coefficient is understood to mean the ratio between the radiation densities on the shutter surfaces facing one another and the end surface of the active element. The measurements were carried out for two types of shutters: a shutter made of KS-19 glass and a shutter based on a solution of kryptocyanin in ethanol. The chosen shutters have substantially different spectroscopic parameters. The duration ~- of the excited state for KS-19 glass is 10 -? sec [3 ], while for kryptocyanin it is T ~ 10 -10 sec. The absorption cross section a s at the ruby lasing wavelength is estimated to be ~ 6 �9 10 -19 [3] and 4.10 -16 cm 2 respectively. The majority of other known media for passive shutters haveparameterswh ich fall in the interval between the indicated values. Since ~s is much greater than the absorption cross section of ions in ruby (ar = 2.5.10 -20 cm2), it follows that for Unloading of the shutter one-pulse lasing may be observed within certain limits [4]. The relative optical unloading of the shutter was accomplished by means of a telescopic system. The scattering component of the telescope was a concave spherical surface (R l = 127.6 mm) implemented using the end-face of the active element. A rod having a diameter of 10 mm and a length of the active portion equal to 120 mm was used; its surface was of the matte type. An iris 5 mm in diameter which isolated the uniformly pumped region of the ruby was mounted flush against the spherical surface. The second component of the telescopic system consisted of changeable plane-concave lenses made of K-8 glass which were mounted in optical contact with the shutter made of KS-19 glass or with the window of the vessel if a solution of kryptocyanin was used as the shutter. The lenses used had focal distances of 254, 354, 516, and 685 mm. The resonator was formed by a stack of two glass plates and a dielectric mirror having a reflection coefficient close to unity. The initial transmission of both types of shutter was chosen to be identical and equal to 0.25. The distance between the telescope components at which the lasing energy was maximal was selected for each removable lens, and the duration of the lasing was determined in this portion of the telescopic system. The values of the unloading coefficient of the shutter were 2.5, 5, 10, and 20 in the tests. The pumping was identical and equal to 600 J in all cases.

Caustic Surfaces and Irradiance for Reflection and Refraction from an Ellipsoid, Elliptic Paraboloid, and Elliptic Cone

General formulas are derived for the caustic surface and irradiance over an arbitrary receiver surface for point source radiation on collimated rays that are reflected or refracted by a curved surface. Specific formulas are obtained for light from a point source that is deflected by an ellipsoid, an elliptic paiaboloid, and an elliptic cone. As a numerical example caustic surfaces are calculated for a concave spherical surface and a concave paraboloid.

Heat Transfer and Forces on Concave Surfaces in a Free Molecular Flow

A Monte Carlo modeling technique is described for mathematically simulating free molecular flows over a concave spherical surface and a concave cylindrical surface of finite length. The half-angle of the surfaces may vary from 0 to 90 deg, and the incident flow may have an arbitrary speed ratio and an arbitrary angle of attack. Partial diffuse reflection and imperfect energy accommodation for molecules colliding with the surfaces are also considered. Results of heat transfer, drag, and lift coefficients are presented for a variety of flow conditions. The present Monte Carlo results are shown to be in very good agreement with certain available theoretical solutions.

Theory of Certain Diffraction Gratings Produced by the Holographic Method

It is now well known that a system of interference fringes photographed on a photographic plate has very interesting properties when used as a diffraction grating. This paper considers two cases. One is when the photographic plate is a plane surface; the aberration properties of this are worked out as a function of wavelength. There are three positions for which the spherical aberration is zero. Of these, one is of little interest as this is simply zero-order position. Another case considered was that of a photographic plate in the form of a concave spherical surface. In this case, there are three positions at which the spherical aberration is zero. The nature of variation of spherical aberration between these zero-aberration positions is presented in the form of curves computed from the theory of these gratings.