Paraboloidal mirrors

Paraboloidal mirrors are used in two ways in FT-IR spectrometers. Any beam emanating from a focus may be collimated by a paraboloidal mirror. For example, radiation from the infrared source is collimated by a paraboloidal mirror before being passed through the interferometer. Alternatively, a collimated beam may be focused by a paraboloidal mirror (e.g., the collimated light emerging from the interferometer is focused at the center of the sample compartment by such a mirror). It is rare that the central ray of the collimated beam coincides with the axis of the paraboloid thus, the segments of the paraboloidal mirrors used in FT-IR spectrometers are usually referred to as ojf-axis paraboloids. 

The diameter of the image at the focus of mirror A, is given to a first approximation by 

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A paraboloidal mirror will similarly collect over two axes... 

Figure 12. Optical arrangement by Fuller and Griffiths (25) for diffuse reflectance spectroscopy P, paraboloidal mirror E, ellipsoidal mirror S, sample D, detector...

As Raman scattering is a weak process, photons are precious and high collection efficiency is desired for a higher signal-to-noise ratio. Specialized optics such as Cassegrain microscope objectives and nonimaging paraboloidal mirrors have been employed to increase both the collection spot size and the effective numerical aperture of the optical system.10... 

The experimental setup is illustrated in Fig. 16.1. The 30 fs laser pulses can be split into successive pulses separated by a variable time period that act as prepulses and interacting pulses, respectively. Circularly and linearly (s- and p-) polarized incident laser pulses can be obtained using wave plates. Using an off-axis //3 paraboloid mirror, up to 75% of the 650 mJ laser energy can be collected into a focal spot with a diameter of less than 10 pm,... 

Other conic sections exist paraboloidal mirrors, ellipsoidal mirrors, and hyperboloidal mirrors. In paraboloidal mirrors, all rays (from infinity or not) converge at the same focus. In ellipsoidal mirrors, all rays emanating at focus... 

In the case of paraboloid mirrors, all rays passing through the focus are reflected parallel to the optical axis (or vice versa). 

Fig. 46. Optical diagram of the Polytec MIR 160 Fourier spectrometer (No. 5b in Tables 2, 3, 4). M 1, M 2, M 5, M 6, M 7 plane mirrors M 3, M 4 paraboloid mirrors MS spherical mirror MT toroid mirrors G Globar source S high pressure Hg-lamp L He-Ne-laser IS Interferometer scanner BS beampslitter PC photo-cell D pyroelectric detector WL white light source...

Fig. 4.2. Schematic of a commercial FTS (BOMEM DA8, discontinued). The two ellipsoid mirrors and the two paraboloid mirrors are identical so that the mounting is symmetric (the image of the entrance iris is at the sample location). The scan mirror tube is vertical. The two symmetrical sample locations allow the permanent mounting of two different detectors and the redirecting mirror to transfer the modulated beam to external experimental set-ups...

The design of the IBS facility is based on an off-axis paraboloidal mirror with a focal length of 25 mm mounted above the heater, which captures the infrared radiation and directs the radiation into the spectrometer. The assembly of the heating block and platinum hot-plate is located such that the surface of the platinum is slightly above the focal point of the off-axis paraboloidal mirror. By... 

The Bragg concentrator configuration we considered for performance evaluation has been a set of confocal paraboloidal mirrors. The paraboloids do not offer the best imaging performance, even though they allow to achieve angular resolutions of a few arcmin, that represent a remarkable improve-... 

Littrow Simple arrangement 1 mirror 3 reflections Slit positions allow compact system and minimize astigmatism Susceptible to coma aberration Needs paraboloid mirror Slits are close together The cunrature of the slit image is wavelength dependent... 

A typical setup for a reflection-absorption experiment is shown in Figure 4. IR radiation is passed from the spectrometer through a polarizer onto an off-axis paraboloidal mirroi which focuses the beam at an incident angle 9 onto the sample surface. A focal length >15 cm is advisable in order to keep the cone angle of the focused radiation at the sample surface small. From there the beam is reflected in the specular direction, is recollimated by a second off-axis paraboloidal mirror, and is focused onto the detector. Since a monolayer of an adsorbate on a smooth substrate is equal to only mol cm ... 

The optical apertures used in near-field microscopy are usually prepared by pulling a heated optical fibre until it breaks [25]. The sides of the tips are coated with aluminum. The typical diameters of the apertures produced by this technique are 60 10 nm, which is about one tenth of the optical wavelength. The transmission of such a tip ranges from 10 to 10 . The near-field tip is mounted on a xyz-piezo-electric (PZT) tube scanner to control the fine approach (2) to the surface and the lateral dithering (x,y) of the tip. The coarse z positioning was achieved by a coupled spring and steel plate comparable to the setup described in [30]. The sample was connected to a small glass hemisphere to minimize losses due to internal reflections and mounted in the focus of a paraboloid mirror with a numerical aperture of NA = 0.98. The whole setup, paraboloid mirror, sample, and PZT tube with the fibre tip, was then mounted inside a cryostat and immersed in superfluid Helium at 1.8 K. 

In this section, we describe both photovoltaic applications, where the primary is a lens, and thermal electric applications, where the primary is a paraboloidal mirror. In each case, we discuss only the point focus configura-... 

The measurement geometry of a dual-paraboloidal mirror reflectometer is shown in Fig. 2 in cross section. The orientation of the top (sample) paraboloid is similar to that of the hemispheroidal mirror with its open side lying in the X-Y plane. Because of circular symmetry about the Z axis, only the F-Z cross section is shown. The axes of the two paraboloids are collinear, with the sample centered on the axes. The sample and detector (or source) are located at Z = 0 and Z = — Lp, respectively. The radius of the sample paraboloidal mirror is given by 2f, where is its focal length. For comparison purposes, a quantity s" = rJ2f, analogous to the eccentricity, is defined for the sample paraboloid, where is the sample radius. The lower paraboloid has a focal length and radius 2fo- The separation between the focal points of the two paraboloids is denoted by Lp. 

Fig. 2. Dual-paraboloidal mirror reflectometer geometric parameters. The upper paraboloid has a focal length /, and radius 2L The lower paraboloid has a focal length /p and radius 2/ .

The image size on the detector (0/2jr), and hence the magnification of the mirror, depends on the BRDF of the sample. For Lambertian samples, the magnification will be a maximum. Knowledge of the maximum linear magnification of a hemispheroidal or dual-paraboloidal mirror is required to... 

The maximum magnification of a dual-paraboloid system has been evaluated by Hanssen (46) for the case of equal focal-length parabolas and coincident foci. If we define a quantity s" = rJ2f, then the maximum linear magnification of a dual-paraboloidal mirror withy = /d and Lp = 0 is given exactly by... 

Fig. 3. Maximum linear magnification from Ref. (46) for a hemispherical, hemiellipsoidal, and dual-paraboloidal mirror for the geometries discussed in the text. For the hemisphere, the ratio of the sample to hemisphere radius was set at 0.05.

Figure 3.19 Schematic (not to scale) of the new IRENI beamline at the SRC (Madison). For clarity, only 4 out of the 12 M4 mirrors are shown in this diagram of the beamline. The first optical components are 12 identical toroidal mirrors (Ml) located 2m from the source, working in unity t o collect the available horizontal fan of radiation. A set of 12 identical paraboloidal mirrors (M3), with 250 mm focal lengths, collimate the beams and deflect them at 90° in the horizontal plane. The collimated beams are then combined and rearranged to form a 4x3 matrix by a set of 12 plane mirrors (M4) and directed by a single flat mirror to the interferometer and to the microscope. (Reprinted from ref. 105.)...

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