Variable Curvature Mirror Research Articles

Optimization of the Reflective Surface Shape of a Variable Curvature Mirror

Optimization of the Reflective Surface Shape of a Variable Curvature Mirror

Active Optics—Progress in Modeling of Tulip-like Variable Curvature Mirrors

We present new results obtained from the modeling of a tulip-like variable curvature mirror (VCM) in the case of a central force that reacts to its contour. From Nastran finite element analysis, we shows that 3-D optimizations, using non-linear static flexural option, with an appropriate solution sequence, provide an accurate tulip-like VCM thickness distribution. This allows us to take into account boundary conditions, including the thin outer collarette and its link to a rigid ring. Modeling with a quenched stainless steel chromium substrate provides diffraction-limited optical surfaces. Rayleigh’s quarter-wave criterion is performed over a zoom range from flat up to f/3.5 convexity over a 13 mm clear aperture and 10 daN central force. The optical testing results of a prototype tulip-like VCM elaborated from the previous analytic theory, show quasi-diffraction-limited figures for a zoom range up to f/5. The present modeling results should significantly help in the future construction of such VCMs with a zoom range extended up to f/3.5.

Active Optics—Advances of Cycloid-like Variable Curvature Mirrors for the VLTI Array

Elasticity theory and active optics led us to the discovery of three geometrical configurations of variable curvature mirrors (VCMs) that are either cycloid-like or tulip-like thickness distributions. Cycloid-like VCMs are generated by a uniform load—air pressure—applied over the mirror rear surface, and reacts without any bending moment along its circular contour. This particular VCM configuration is of practical interest because it smoothly generates accurate optical curvatures, varying from plane at rest to spherical curvatures up to f/2.9 over 16-mm aperture under 6.5-bar air pressure. Starting from the thin plate theory of elasticity and modeling with NASTRAN finite element analysis, one shows that 3-D optimizations—using a non-linear static flexural option—provide an accurate cycloid-like thickness distribution. VCM elasticity modeling in quenched stainless steel–chromium substrates allows the obtaining of diffraction-limited optical surfaces: Rayleigh’s criterion is achieved over a zoom range from flat to f/3.6 over 13-mm clear aperture up to 6-bar loading. These VCMs were originally developed and built at the Marseille Observatory in 1975 and implemented as a cat’s-eye mirror of IR Fourier-transform interferometers for laboratory recording of fast events in gas molecular spectroscopy. Later, for high-angular resolution astronomy with the ESO VLTI array—an interferometer made of 8 m Unit Telescopes (UTs) and 1.8 m Auxiliary Telescopes (ATs)—such VCMs were inevitable components to provide in a 3″ co-phased field-of-view since 1998. They were implemented (1) as cat’s eye mirrors of the height delay-lines beam recombination lab and (2) as ATs mirror-pair for output pupil conjugation of the movable x–y baseline. From the ESO-AMU approved convention of making 10 VCM spares up to 2024, the present modeling should provide a diffraction-limited extended field-of-view. It is pure coincidence that present results from modeling with an outer collarette are identical to results from analytic theory without collarette.

Variable Curvature Mirror with Variable Thickness and Its Application in Space-Borne Optical Camera

Variable Curvature Mirror with Variable Thickness and Its Application in Space-Borne Optical Camera

Solving, analyzing, manufacturing, and experimental testing of thickness distribution for a cycloid-like variable curvature mirror.

A cycloid-like variable curvature mirror (VCM) for zoom-imaging systems was investigated. An analytical-deformation solution to a thin-elastic plate with a cycloid-like thickness distribution and simply supported boundary condition under uniform pressure was found using a small parameter method. The finite-element analysis of the thin-elastic plate and designed VCM showed a good correlation with the analytical solution. The VCM was manufactured and polished to the initial shape with a root mean square (RMS) of 1/80λ. Finally, with air-pressure-based actuation testing under 0.07 MPa, the VCM deforms approximately 36.89µm and maintains the RMS surface performance of 1/10λ, 1/40λ with and without spherical aberrations, respectively.

Elastic bending of variable curvature mirrors: validation of a simplified analytical method.

This work explores the variable curvature mirror's (VCM) elastic bending rules through modeling it as a thinelasticplate with an exponential thickness distribution actuated with a uniform pressure under simply supported boundary conditions. By using the small-parameter method, the general analytical expression of a plate's deflection is worked out. The results calculated by the analytical solution are compared to the finite element analysis of a VCM model with the same specific parameters. We demonstrate that the two have a good correlation with the each other. This analytical solution is an effective way to predict a VCM's deflection.

环形线负载驱动变曲率反射镜技术

环形线负载驱动变曲率反射镜技术

Carbon-fiber-reinforced polymer variable-curvature mirror used for optical zoom imaging: prototype design and experimental demonstration

In recent years, optical zoom imaging without moving elements has received much attention. The key to realizing this technique lies in the design of the variable-curvature mirror (VCM). To obtain enough optical magnification, the VCM should be able to change its radius of curvature over a wide range. In other words, the VCM must be able to provide a large sagittal variation, which requires the mirror material to be robust during curvature variation, require little force to deform, and have high ultimate strength. Carbon-fiber-reinforced polymer (CFRP) satisfies all these requirements and is suitable for fabricating such a VCM. Therefore, in this research, a CFRP prototype VCM has been designed, fabricated, and tested. With a diameter of 100 mm, a thickness of 2 mm, and an initial radius of curvature of 1740 mm, this VCM can provide a maximum 23-μm sagittal variation and a minimum and maximum radius of curvature of 1705 and 1760 mm.

Active optics for high-dynamic variable curvature mirrors

Variable curvature mirrors of large amplitude are designed by using finite element analysis. The specific case studied reaches at least a 800 mum sag with an optical quality better than lambda/5 over a 120 mm clear aperture. We highlight the geometrical nonlinearity and the plasticity effect.

Development of a variable curvature mirror for the delay lines of the VLT interferometer

This paper presents the variable curvature mirror (vcm) serving for beam management purposes in the interferometric mode of the Very Large Telescope (VLT). This special device located in the delay line system provides for a precise positioning of the pupil image of an individual telescope in the recombination laboratory. The particularity of this active mirror is its continuous variable curvature from (2800 mm)-1 to (84 mm)-1 which has to be achieved with a reasonable optical quality. This large curvature variation needed in the system, lead us to extend the classical theory of elasticity to the range of large deformations (i.e. the achieved flexions are larger than the mirror's thickness). This new approach, in the domain of active optics, gave us a theoretical support to determine the physical parameters of the mirror (thickness distribution, loading configuration). Today the vcm system has been thoroughly tested and its performances evaluated. The experimental results have shown good agreements with the theory.

The Method for Pulsed Light Generation of CO<SUB>2</SUB> Laser Output by Variable Curvature Mirror

This paper describes a new method to change from quasi-CW CO2 Laser to repeated pulse type by variable curvature mirror. The variable curvature mirror is made of piezoelectric material Pb (Zr-Ti) O2 with polished thin brass plate as a mirror and forced to periodic vibration with applied A. C. voltage (frequency 3-9 kHz effective value 0-10 V). As a result the output of quasi- CW CO2 Laser changed to repeated pulse type, single or double pulses appear during one period of mirror vibration. The peak output of the pulse train is 10-35 times compared with quasi-CW output, and the duration of a pulse is 10 μs.

CO<SUB>2</SUB>Laser Power Control using Variable Curvature Mirror

This paper describes the new power control method for the CO2laser which utilizes variable curvature mirror. The variable curvature mirror is made from Pb (Zr-Ti) O2-attached brass disk. If radius of curvature is changed from 10m to 0.8m, powers are increased continuously about 3 times at the wavelength of 10.6±0.01μm. The radius of laser beam were 5mm and oscillation modes are Gauss type.

Tunable resonator with a mirror of variable curvature

A variable-curvature mirror, deformed by the application of a concentrated load at its center, was developed. It was established that the deflected surface was nearly spherical. This mirror was used in a search for the optimal variant of the resonator of an electric-discharge CO2 laser. The mode composition was studied using either a germanium exit mirror or metallized mirrors with central apertures of different diameters.