spherical mirror
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Abstract After introducing Leonardo da Vinci’s (LdV) predecessors in the field of light propagation research, his drawings on the topic of focussing light through a spherical mirror are analysed. The discovery of LdV is presented, according to which, at an infinitely distant source of rays, a small fragment of the canopy is enough to generate a focus, while the rest of the mirror forms caustics for which LdV did not indicate an application. An analytical description of the energy concentration in the focus and on the caustics is given, together with its reference to the geometric representation of the acoustic field in rooms. Using symmetry in the description of energy relations in acoustics and electromagnetism, the interference that occurs on the caustics produced by the acoustic and electromagnetic wave is discussed. It is explained why in the sound field in existing halls, instead of a whole caustic only its cusp is observed, which is perceived as a point-like sound focus. The size of the mirror aperture, shown graphically by LdV, is determined. How the development of receiving techniques increased the mirror aperture compared to the LdV estimate is also shown. The implementation of these improvements is presented via the example of the Arecibo and FAST radio telescopes.

Abstract In this work, we describe an interferometric method to generate ultra-short pulses below the Fourier limit. It is done by extending concepts first developed in the spatial domain to achieve sub-diffractive beams through the addition of a spatial chirp in one of the arms of a Michelson interferometer using a spherical mirror. To experimentally synthesize sub-Fourier pulses, we replace the spherical mirror with a water cell, since it produces chirp in the temporal domain. We also present an alternative procedure, based on asymmetrical interference between the widened pulse and the original pulse where the peaks of both pulses exhibit a temporal delay achieving the narrowing of ultra-short pulses with sub-Fourier scales. To characterize the performance of the system, we performed a preliminary assessment considering the percentage of FWHM shrinking obtained for each scheme. By means of a symmetrical configuration 7 and 12 \% pulse reductions were verified, both experimentally and analytically, while for the non-symmetrical configuration 10 and 24\% reductions were achieved corresponding to main lobe to side-lobes ratios of 10 and 30\% . The experimental setup scheme is simple, versatile and able to work with high-power laser sources and ultra-short pulses with a broad bandwidth at any central wavelength. The results presented in this work are promising and help to enlighten new routes and strategies in the design of coherent control systems. We envision that they will become broadly useful in different areas from strong field domain to quantum information.

An optical design for telescope with spherical primary mirror, planoidal surface and two-lens corrector is discussed. The spherical mirror hasn aperture ratio 1/2.69. After reflection from the spherical mirror, the wave front falls on a planoidal surface and “forms” the reflected wave front from a virtual mirror with e 2 = 1.576. After passing the two-lens corrector, the light is collected in the focal plane. A dot diagram in the focal plane shows that all three-order aberrations are successfully corrected. The effective field of view is 2 degrees. The aperture ratio is 1/2.28.

AbstractWe analytically, experimentally and computationally explore the solar radiation flux distribution in the interior region of a spherical mirror and compare it to that of a paraboloidal one with the same aperture area. Our investigation has been performed in the framework of geometrical optics. It is shown that despite one can assign a quasi focus, at half the radius, to a spherical mirror, the light concentration occurs as well on an extended line region which starts at half-radius on the optical axis. In contrast to a paraboloidal concentrator, a spherical mirror can concentrate the radiation parallel to its optical axis both in a point-focus and in a line-focus manner. The envelope of the reflected rays is also obtained. It is shown that the flux distribution has an axial symmetry. The radial dependence of the flux on a flat circular receiver is obtained. The flux longitudinal dependence is shown to exhibit three distinctive regions in the interval [0, R] (R is mirror radius). We obtain the radiational (optical) concentration ratio characteristics and find the optimal location of the flat receiver of a given size at which the concentration ratio is maximised. In contrast to a parabolic mirror, it is shown that this location depends on the receiver size. Our findings offers that in spherical mirrors one can alternatively use a line receiver and gains a considerable thermal energy harvest. Our results are supported by Monte Carlo ray tracing performed by Zemax optical software. Experimental validation has been performed in lab with a silver-coated lens as the spherical mirror.

The control of the shape of the optical part surface by the interference method has become an integral part of the process of their shaping. With a precisely focused interferometer interferometry allows obtaining an interference pattern similar to a topographic map of the error profile of the wave surface under investigation. The interferometer must form a map of the optical surface with high accuracy --- the permissible distortion of the interference fringe caused by an interferometer error should not exceed 0.1 of the distortion value caused by an error on the examined surface. The dependence of the interference pattern formation on the errors in the arrangement of the interferometer components, i.e., defocusing, was theoretically analyzed using Fourier transforms. The analysis was performed for an interferometer containing a laser illuminator, a concave spherical mirror with a central hole, coaxial to the illuminator, and a beamsplitting element in the form of a cube-prism with a semitransparent hypotenuse face. On the first flat face of the cube-prism, a microspherical concave mirror is made with the center located on the optical axis of the interferometer. A method for calculating the defocusing of a controlled spherical mirror and the corresponding wave aberration of the working wavefront is presented. An example of calculating the design parameters of the interferometer and the permissible defocusing of the controlled spherical mirror is given

Since there are not standard configurations of the Concentrating Photovoltaic (CPV) systems, several types of optics are designed and analyzed. In this paper, the optical performances of a spherical mirror and a commonly used Fresnel lens of the same diameter are compared, highlighting their impact on the CPV system energy performance. First, the absolute and percentual variation trends of optical concentration factor and optical efficiency as function of the distance between each optical system and receiver are analyzed. The concentration levels obtained by means of the spherical mirror are much higher than the Fresnel lens, with maximum values of optical efficiency equal to 72.8% and 24.1%, respectively. The analysis of the concentration reduction due to a solar-tracking failure has also allowed the estimation of the acceptance angle, thus observing that the spherical mirror requires a less accurate solar tracker with respect to the Fresnel lens, especially if a secondary optics is adopted. As for the energy comparison, the spherical mirror allows increase of the Triple-Junction (TJ) cell temperature up to about 65 °C higher than the environmental temperature and to reach an electrical power of about 15 W in correspondence of a concentrated solar radiation of 470 kW/m2. Finally, the deviation between the cumulative electric energy produced by the TJ cell in the cases of correct and incorrect solar tracking and for the configurations with and without secondary optics has been also evaluated for both the optics. The equations experimentally obtained in this paper represent a more accurate tool to describe the physical phenomenon in comparison with the equations theoretically obtained for similar CPV systems. The results can be used to design a real CPV system that adopts a Fresnel lens or a spherical mirror. The equations experimentally obtained in this paper represent a more accurate tool to describe the physical phenomenon in comparison with the equations theoretically obtained for similar CPV systems. The results can be used to design a real CPV system that adopts a Fresnel lens or a spherical mirror.

The article is devoted to the study of the category of the game and its embodiment in the form of specific game techniques in discourse. The research material was the work of M. Ende «Der Spiegel im Spiegel». The novelty of the research is seen in the fact that the combined connections of artistic stories form irrational worlds. The relevance of the study is due to the growing interest of researchers in the surrealist reflection of reality in a literary text. It is shown in the work that play is a process of personality formation and a kind of free human activity. Special attention is paid to the theoretical analysis of fairytale discourse. The principle of semantic and compositional connection of individual works of the cycle of stories is brought into consideration. The article deals with the issues of realization by characters of literary texts of the key parameters of play and non-play in mythological discourse. Attention is paid to the main variants of human behavior. The question is also raised about the physical properties of mirrors, which are implicit markers of various symbols. Special attention is paid to the spherical mirror. It is shown that M. Ende’s work is based on the principle of the panoramic reflection effect. 

A computational tool is developed to measure the local deformations in optical surfaces from the interference patterns obtained by the Chalmers test principle and from the analysis of a reflective optical surface using a commercial Fizeau interferometer of the ZYGO. The tests were made on a concave spherical mirror with a radius of curvature of 60 cm and a diameter of 13 cm. To obtain the measurements of local deformations, a computational tool proposed for the localization of dark fringes is used by evaluating the maximum and minimum of the image obtained in the interference patterns. The results obtained show that the computational tool allows locating fringes within an interference pattern, allowing faster inter-fringe measurements and assigning an error on the surface in terms of wavelength.

AbstractThe in situ and real-time measurement of curvature changes of optically reflecting surfaces is a key element to better control bottom-up fabrication processes in the semiconductor industry, but also to follow or adjust mirror deformations during fabrication and use for space or optics industries. Despite progresses made in the last two decades thanks to laser deflectometry-based techniques, the community lacks an instrument, easy to use, robust to tough environments and easily compatible with a large range of fabrication processes. We describe here a new method, called magnification inferred curvature (MIC), based on the determination of the magnification factor of the virtual image size of a known object created by a reflecting curved surface (the substrate) acting as a spherical mirror. The optical formalism, design, and proof of concept are presented. The precision, accuracy, and advantages of the MIC method are illustrated from selected examples taken from real-time growth monitoring and compared with state-of-the-art laser deflectometry-based instruments.

In Vietnam, the technology of fabricating spherical surfaces of glass lenses by the loose abrasive grinding method has been researched and widely applied. However, this technology does not really match the needs of grinding and polishing optically the sphere on the basis of alloy steel. This paper introduces some initial results in researching the technology of optical mirror polishing of alloy steel materials. The issues studied include the selection of processing methods and equipment, design and manufacture of auxiliary tools and machining tools, testing and setting up machining processes, and the methodology for characterisation product quality. A spherical mirror of 50 mm in diameter, 70 mm in spherical radius, based on alloy steel material has been optically polished. Test results show that the sample meets the requirements for optical products (N=1; ΔN=1, surface roughness Rz=0.05 μm).