Schwarzschild objective

A gravitationally massive object (allegedly) from which fight cannot escape. The Schwarzschild radius is the radius of the black hole that defines the event horizon the distance at which fight cannot escape... 

The schematic in Fig. 3.8 shows a simplified layout for an IR microspectrometer based on a staring-type FPA detection system. The system also uses Schwarzschild objectives, but the apertures for constraining the microscope s sensitive location... 

Figure 3.1 X Calculated intensity profiles for a simple, full aperture objective (Airy pattern, left) and a Schwarzschild objective with central obscuration (right). The same NA and wavelength were used for both calculations. Note the large first-order diffraction ring for die Schwarzschild objective.

Figure 3.12 Calculated sensitivity as a function of radial distance from the center of an objective s diffraction pattern, comparing the nonconfocal case for a Schwarzschild and a conventional objective (no obscuration). The plateau near 5 p,m distance for Schwarzschild corresponds to the first diffraction minima. Thus, only j of the sensitivity is located in the diffraction pattern s central peak. Contrast this to the Airy pattern where more than 80% is contained in the central maximum.

Figure 3.14 Calculated sensitivity as a function of radial distance from the center of an objective diffraction pattern, comparing Schwarzschild objective used in a nonconfocal (solid line) and confocal (dash-dot line) configuration. The plateau still occurs near 5 [im distance for both cases, but the enclosed sensitivity has been increased to more than 80%. Also note how the confocal case approaches 100% more quickly as a function of radial distance.

Figure 3.16 Example of an imaging artifact. Left object consisting of an opaque specimen except for a 12 p,m diameter circular aperture. Right calculated transmission image for a single (nonconfocal) Schwarzschild objective with NA = 0.65 and for k = 6 p,m. Note the dark patch in the center, suggesting the presence of absorbing material inside the hole.

Figure 3.17 Imaging artifact for a specimen consisting of a thin uniform layer except for a 12 pm diameter hole (aperture), using a nonconfocal 32 x Schwarzschild objective (NA = 0.65) and X = 6 pm. Solid line calculated absorption profile through the diameter of the hole. Solid circles measured absorption profile for an actual specimen. Note the poor absorption contrast (—50%) and bump at the holes center (15 pm location).

Figure 3.18 Calculated images for a 14 pm diameter ring-shaped object at X = 6 pm. Left actual object center image for a nonconfocal 32x Schwarzschild objective with NA = 0.65 right image for a confocal 32x Schwarzschild objective with NA = 0.65.

If these ideas are correct, then the azimuthal frequency associated with each QPO pair must obey Mua > 3 x 0.931M kHz (recall that k and v lie below the corresponding va). Then Fig. 2 discloses that the QPO source must lie at r < 5GMc 2 QPO pairs are associated with compact objects, and they are inner disk phenomena. In fact, 5GMc 2 falls below risco for Schwarzschild, so that some QPO pairs are Kerr BH phenomenon. Abramowicz et al. [9] have estimated a 0.9 for GRO J1655-40 rapidly rotating BHs exist in nature (more in Sec. 4). 

The condenser goes by two names some call it a Cassegrain, while others call it a Schwarzschild objective. The present author has always been rather confused about the difference between a Cassegrain and a Schwarzschild objective but, aiming to resolve such confusion, contacted one of the designers of the first FT-IR microscopes. Bob Messerschmidt (now with Rare Light, Inc.), as to their difference. His reply to this question was as follows ... 

The only solution of the field equations without ruinous approximations was obtained by Schwarzschild. It serves as a model for isolated objects and is too localized for cosmology. A concise critical summary of the cosmological models was recently published by Mamone Capria (2005) and our more superficial treatise that follows will concentrate only on those aspects of immediate relevance. 

Virtually all of the galactic mass is in the form of a singularity at the galactic center. The bulge, disk, and halo of stars represent an infinitesimal fine mist of stellar-scale objects within the galaxy s Schwarzschild radius". 

In contrast to VIS microscopes with a system of glass lenses, IR microscopes are built around reflecting components. The heart of most infrared microscopes is a Cassegrainian or Schwarzschild objective, see Fig. 5.14. 

Schwarzschild radius A critical radius of a body of given mass that must be exceeded if light is to escape from that body. It equals 2GM/( , where G is the gravitational constant, c is the speed of iight, and Mis the mass of the body. If the body collapses to such an extent that its radius is less than the Schwarzschild radius the escape velocity becomes equal to the speed of light and the object becomes a biack hoie. The Schwarz-schiid radius is then the radius of the hole s event horizon, it is named after Karl Schwarzschild (1873-1916). 

Because of the very small effective source size, the spatial resolution of SR-FTIR for micro-spectroscopy is usually only limited by the wavelength, X, of the IR light [9]. Schwarzschild microscope objectives are used to focus the broad spectrum of IR light onto the sample, and these objectives typically have relatively large numerical apertures in the range 0.5-0.6. While diffraction will naturally limit the spot size on the sample [10], one can also use a single aperture before the sample to exactly define the illuminated sample region. In such a situation, the diffraction-limited spatial resolution is approximately 2X/3 [11], which corresponds to 1.7 pm (at 4000 cm ) and 13 pm (at 500 cm ) the two extremes of typical mid-IR measurements. 

Another elegant approach was suggested by Meunier et. al. who presented a custom made objective based on a modified Schwarzschild objective. Its optic axis is perpendicular to the studied layer and consequently the complete area is in focus. The design is ideally suited for dynamic investigations and the alignment is easier than for the previously discussed solution. 

The Schwarzschild objectives are a catoptric design based on two spherical (or approximately spherical) mirrors centered on a common optic axis. Typical magnifications range from 6x up to 74x, with 15x and 32x (or 36x) used most frequently. Numerical apertures (NA) vary from about 0.3 up to nearly 0.7,... 

Schematic of a Schwarzschild-type objective having finite conjugates. The central obscuration results in a reduction ( 20%) of the throughput and redistribution of energy within the beam waist at the focus.

The schematic in Figure 7.3 shows a simplified layout for an FTIR microspectrometer based on a staring-type FPA detection system. The FTIR spectrometer is similar (if not identical) to that used in the scanning instrument, except that it may require step-scan to allow time for reading out all pixels of the FPA at each optical retardation (scanning mirror position) of the interferometer. The system also uses Schwarzschild objectives, but the apertures for constraining the microscope s sensitive location are left open, i.e. they do not provide any spatial discrimination. Thus, the microscope s first objective... 

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