Paraboloidal Mirror Research Articles

Adjustment of two-mirror collimators with off-axis aspheric mirrors

This paper discusses a method of adjusting a two-mirror collimator whose output mirror is a concave off-axis paraboloidal mirror, while its input mirror is either a flat mirror or a convex off-axis aspheric mirror. Two laser beams, a system of stops, and also two beamsplitters and a flat mirror are initially used during the adjustment to specify the direction of the axes of the aspheric base surfaces of the off-axis mirrors and the direction of the axis of the pencil of rays formed by the collimator, along with the position of the focal plane of the collimator. The optical system of a Twyman-Green interferometer is then formed whose signal branch includes the mirror elements of the adjustable collimator, as well as a flat mirror for implementing an autocollimation ray path in it. The adjustment is done with enhanced sensitivity, accuracy, and reliability because of the double pass of the signal beam through the adjustable collimator and by monitoring the state of the adjustment from the interference pattern.

Fine ELID Grinding on the Symmetric Paraboloidal Mirror of Quartz

Quartz has excellent optical properties and thus it is often used as the material of mirror and lens. However, it is almost impossible to be machined by cutting due to its brittle and high hardness. Grinding is a common method for machining quartz. One of the authors designed a new type of a paraboloidal mirror of quartz for the neutron optical devices. The fabrication process of this mirror was investigated in this experiment. A jig with two grooves of 90 degrees was made and two workpieces were stuck on the jig using the wax melt at about 60 degrees centigrade. The two workpieces were first ground applying ELID (electrolytic in-process dressing) grinding method with #325 and #1200 cast iron bonding diamond abrasive wheels. Then the ground surface was polished with CeO2 slurry. The finished surface roughness was Ra2.0nm and rms2.4nm and its form error about 2μm. After coating process, its properties of focusing neutron beam were measured. The results were that the reflecting rate was 42%, gain 1.9 and 2.3mm×10.1mm beam focused to 1.6mm×2.1mm.

Generation of hard X-rays using an ultrafast fiber laser system

We report the first hard X-ray source driven by a femtosecond fiber laser. The high energy fiber CPA system incorporated a 65mum LMA fiber amplifying stage which provided 300-fs recompressed pulses and diffraction limited beam quality with M(2) < 1.07. A deformable mirror was used to optimize the wavefront and the spot size was focused down to 2.3 mum with an f/1.2 paraboloidal mirror. 50muJ was deposited on the nickel target with 2x10(15)-W/cm(2) focal intensity and a distinctive Ni K(alpha)-line (7.48 keV) emission was measured with 5x10(-8) energy conversion efficiency.

Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2)

Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2)

Characterization of focal field formed by a large numerical aperture paraboloidal mirror and generation of ultra-high intensity (1022 W/cm2)

We describe a method to measure the aberrations of a high numerical aperture off-axis paraboloid and correct for the aberrations using adaptive optics. It is then shown that the characterized aberrations can be used to accurately calculate the electromagnetic field at the focus using the Stratton–Chu vector diffraction theory. Using this methodology, an intensity of 7×1021 W/cm2 was demonstrated by focusing a 45-TW laser beam with an f/0.6, 90∘ off-axis paraboloid after correcting the aberrations of the paraboloid and the low-energy reference beam. The intensity can be further increased to 1×1022 W/cm2 by including in the correction algorithm the wavefront difference between the reference beam and the high-energy beam.

Geometrical considerations on the directivity of reflected light from a paraboloidal mirror

A divergence angle of the light emanated from an optical source composed of a source of light with finite size and a paraboloidal reflector is analyzed on the basis of geometrical considerations. The divergence angle distributions of the reflected light rays from each reflection point on the paraboloidal mirror are numerically calculated as parameters of the shapes of a lamp arc body and a paraboloidal reflector. It has been found from the analyses that the divergence angle can be reduced by prolongation of the optical path length PO to the reflection point P on the paraboloidal mirror from the focal point O of it, at which the center of the extent of the arc is located. A new approach different from conventional one to reduce the divergence angle of the light rays emanated from the optical source is proposed. The new configurations of the optical source composed of a source of light with finite size and a paraboloidal reflector or a spheroidal converging reflector are shown and discussed.

Grazing Incidence Pumping X-Ray Laser Scheme with Applicationof Paraboloid Mirrors

A grazing incidence pumping x-ray laser scheme using JIGUANG II isproposed. We investigate the characteristics of the focusing ofparabolas, and obtain the optimal intensity distributions in the targetsurfaces with paraboloid mirrors of different parameters by thevectorial ray-tracing. Kinetic simulations are carried out. The resultsshow that due to the enhancement of absorption by the selectable plasmaregion (gain region), saturated amplification of the x-ray laser can beachieved with 100 mJ energy in pre and pumping pulses, respectively, on3 mm Ti targets.

Orthogonal aberration functions for high-aperture optical systems: erratum

In a recent paper [J. Opt. Soc. Am. A21, 832 (2004)], aberration functions that are a complete, orthogonal, and normalized set over a weighted spherical pupil were developed. The results apply to electromagnetic, aplanatic, or paraboloidal mirror systems. An equation in this paper is corrected. Further work has led to a general aberration function that is also presented.

Design of a Super-Paraboloidal Solid Immersion Mirror for Near-Field Recording

We design a superparaboloidal solid immersion mirror (SP-SIM) using a tilt paraboloidal mirror and total internal reflection for application to the optical flying head for near-field recording. The design parameters are optimized in terms of the symmetric beam intensity on the high-numerical-aperture focusing system. Since the SP-SIM has two functions, namely, as an objective lens and a folding mirror, the height and weight of the optical flying head can be reduced.

Development of Ni/Ti supermirrors with large- m and a curved surface

Nickel/titanium supermirrors with critical reflection angles θ c of m=3–5 times the critical angle of total reflection of natural Ni θ c Ni were fabricated on silicon substrates 3 in . in diameter and 3 mm in thickness by a DC magnetron sputtering system using the facing targets technique, and the neutron reflectivity of the supermirrors was evaluated for cold neutrons of 8.8 A ̊ in wavelength. The supermirrors with 532 layers and with 468 layers achieved a reflectivity of 84% and 53% at their θ c of m=2.9 and 3.7, respectively, while supermirrors with more than 630 layers had reduced reflectivity at angles smaller than θ c. This reduction resulted from the formation of a non-multilayered pillar structure due to the growth of interface roughness between layers. Using supermirrors with m not more than 3, we designed a paraboloidal focusing mirror and proposed a prototype to obtain approximately 5 times the utilizable neutrons at the focal point for cold neutrons of 8 A ̊ .

Orthogonal aberration functions for high-aperture optical systems.

Aberration functions that are a complete, orthogonal, and normalized set over a weighted spherical pupil are developed. A general weighting is considered, for which special cases are applicable to systems satisfying the Abbe sine condition and the Herschel condition. Paraboloidal mirrors are also considered. This weighting can also be used to account empirically for Fresnel reflection losses in the optical system. The functions can be expressed in an analytic form. Expressions are given for 24 low-order aberrations.

Development of Ni/Ti supermirrors with large-m and a curved surface

Nickel/titanium supermirrors with critical reflection angles θc of m=3–5 times the critical angle of total reflection of natural Ni θcNi were fabricated on silicon substrates 3in. in diameter and 3mm in thickness by a DC magnetron sputtering system using the facing targets technique, and the neutron reflectivity of the supermirrors was evaluated for cold neutrons of 8.8Å in wavelength. The supermirrors with 532 layers and with 468 layers achieved a reflectivity of 84% and 53% at their θc of m=2.9 and 3.7, respectively, while supermirrors with more than 630 layers had reduced reflectivity at angles smaller than θc. This reduction resulted from the formation of a non-multilayered pillar structure due to the growth of interface roughness between layers. Using supermirrors with m not more than 3, we designed a paraboloidal focusing mirror and proposed a prototype to obtain approximately 5 times the utilizable neutrons at the focal point for cold neutrons of 8Å.

A simple ray tracing method for measuring the vertex radius of curvature of an aspheric mirror

We introduce a simple ray tracing method for measuring the vertex radius of curvature in situ, based on projecting spot array rays onto the surface of an aspheric mirror, and receiving the incident and the reflected rays. The method was used to measure the vertex radiuses of curvature of a spherical mirror and a paraboloidal mirror, the relative accuracy of better than 0.5% has been obtained.

Null test for a highly paraboloidal mirror.

A circular null computer-generated hologram (CGH) was used to test a highly paraboloidal mirror (diameter, 90 mm; f number, 0.76). To verify the null CGH test a classic autocollimation test with a flat mirror was performed. Comparing the results, we show that the results of the null CGH test show good agreement with results of the autocollimation test.

Omnidirectional video

Omnidirectional video enables direct surround immersive viewing of a scene by warping the original image into the correct perspective given a viewing direction. However, novel views from viewpoints off the camera path can only be obtained if we solve the three-dimensional motion and calibration problem. In this paper we address the case of a parabolic catadioptric camera --- a paraboloidal mirror in front of an orthographic lens --- and we introduce a new representation, called the circle space, for points and lines in such images. In this circle space, we formulate an epipolar constraint involving a 4×4 fundamental matrix. We prove that the intrinsic parameters can be inferred in closed form from the two-dimensional subspace of the new fundamental matrix from two views if they are constant or from three views if they vary. Three-dimensional motion and structure can then be estimated from the decomposition of the fundamental matrix.

Design considerations for a highly segmented mirror.

Design issues for a 30-m highly segmented mirror are explored, with emphasis on parametric models of simple, inexpensive segments. A mirror with many small segments offers cost savings through quantity production and permits high-order active and adaptive wave-front corrections. For a 30-m f/1.5 paraboloidal mirror made of spherical, hexagonal glass segments, with simple warping harnesses and three-point supports, the maximum segment diameter is approximately 100 mm, and the minimum segment thickness is approximately 5 mm. Large-amplitude, low-order gravitational deformations in the mirror cell can be compensated if the segments are mounted on a plate floating on astatic supports. Because gravitational deformations in the plate are small, the segment actuators require a stroke of only a few tens of micrometers, and the segment positions can be measured by a wave-front sensor.

Exact ray-trace beam for an off-axis paraboloid surface.

When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameter that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.

202 Ultraprecision Fabrication of Glass Ceramic Aspherical Mirror by ELID grinding Method

Glass-ceramic aspherical mirrors used as optical elements in space astronomical observatory must be machined with very high profile accuracy and surface smoothness. Precision grinding processes are very effective in fabrication of such profiles. In particular, ELID (Electrolytic In-Process Dressing) grinding method is possible to achieve ultraprecision smooth surface of hard and brittle materials. To obtain ultra smooth surface required by astronomical observatory, final polish process which required long time after conventional grinding process was necessary. ELID grinding method using an ultraprecision grinding machine tool with nano-level hydrostatic guide will be very effective in reducing the time required for finial polishing process. In this paper, a new ELID grinding system is introduced and experimental results of fabricating glass-ceramic paraboloidal mirror are discussed.

Design and performance considerations of cat's-eye retroreflectors for use in open-path Fourier-transform-infrared spectrometry.

A ray-tracing analysis of cat's-eye retroreflectors for use in active open-path Fourier-transform-infrared (OP/FT-IR) spectrometry and the results of testing f/0.5 and f/1.75 cat's-eye retroreflectors built in our laboratory with a commercial active OP/FT-IR spectrometer are presented. The ray-tracing model is based on the optical characteristics of a commercial single-telescope monostatic OP/FT-IR spectrometer and explores trends in cat's-eye behavior in practical but rigorous field conditions encountered during transportable outdoor use. All mirrors modeled are paraboloids for which the focal ratios of the primary mirror are f/0.5, f/1.75, and f/3. The effect of the focal ratio of the primary mirror, the focal length of the secondary mirror, and the off-axis alignment of the primary and the secondary mirror have been evaluated as a function of path length, including variable input-beam divergence, between the spectrometer and the cat's-eye. The paraboloidal mirrors comprising the primary and secondary of the cat's-eye retroreflectors tested were made in our laboratory by spin casting liquid epoxy-graphite composite mixtures followed by in situ polymerization with no postpolishing.

All-optoelectronic continuous wave THz imaging for biomedical applications

We present an all-optoelectronic THz imaging system for ex vivo biomedical applications based on photomixing of two continuous-wave laser beams using photoconductive antennas. The application of hyperboloidal lenses is discussed. They allow for f-numbers less than 1/2 permitting better focusing and higher spatial resolution compared to off-axis paraboloidal mirrors whose f-numbers for practical reasons must be larger than 1/2. For a specific histological sample, an analysis of image noise is discussed.