Cardinal point

Abstract: An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is riot restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture a on the image side, in the whole range 0 ≤ α ≤ 90°. The limiting case α → 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in lowaperture systems.

Abstract: We describe the design, construction, and performance of the Sloan Digital Sky Survey Telescope located at Apache Point Observatory. The telescope is a modified two-corrector Ritchey-Chretien design which has a 2.5-m, f/2.25 primary, a 1.08-m secondary, a Gascoigne astigmatism corrector, and one of a pair of interchangeable highly aspheric correctors near the focal focal plane, one for imaging and the other for spectroscopy. The final focal ratio is f/5. The telescope is instrumented by a wide-area, multiband CCD camera and a pair of fiber-fed double spectrographs. Novel features of the telescope include: (1) A 3 degree diameter (0.65 m) focal plane that has excellent image quality and small geometrical distortions over a wide wavelength range (3000 to 10,600 Angstroms) in the imaging mode, and good image quality combined with very small lateral and longitudinal color errors in the spectroscopic mode. The unusual requirement of very low distortion is set by the demands of time-delay-and-integrate (TDI) imaging; (2) Very high precision motion to support open loop TDI observations; and (3) A unique wind baffle/enclosure construction to maximize image quality and minimize construction costs. The telescope had first light in May 1998 and began regular survey operations in 2000.

Abstract: Several conceivable methods for the formation of optical images by x-rays are considered, and a method employing concave mirrors is adopted as the most promising. A concave spherical mirror receiving radiation at grazing incidence (a necessary arrangement with x-rays) images a point into a line in accordance with a focal length f=Ri/2 where R is the radius of curvature and i the grazing angle. The image is subject to an aberration such that a ray reflected at the periphery of the mirror misses the focal point of central rays by a distance given approximately by S=1.5Mr2/R, where M is the magnification of the image and r is the radius of the mirror face. The theoretically possible resolving power is such as to resolve point objects separated by about 70A, a limit which is independent of the wave-length used. Point images of points and therefore extended images of extended objects may be produced by causing the radiation to reflect from two concave mirrors in series. Sample results are presented.

Abstract: Optical microscopy and manipulation methods rely on the ability to focus light to a small volume. However, in inhomogeneous media such as biological tissue, light is scattered out of the focusing beam. Disordered scattering is thought to fundamentally limit the resolution and penetration depth of optical methods1,2,3. Here we demonstrate, in an optical experiment, that scattering can be used to improve, rather than deteriorate, the sharpness of the focus. The resulting focus is even sharper than that in a transparent medium. By using scattering in the medium behind a lens, light was focused to a spot ten times smaller than the diffraction limit of that lens. Our method is the optical equivalent of highly successful methods for improving the resolution and communication bandwidth of ultrasound, radio waves and microwaves4,5,6. Our results, obtained using spatial wavefront shaping, apply to all coherent methods for focusing through scattering matter, including phase conjugation7 and time-reversal4. Light is scattered out of a focusing beam when an inhomogeneous medium is placed between the lens and the focal plane. Now, scientists experimentally demonstrate that scattering can be exploited to improve, rather than deteriorate, the focusing resolution of a lens by using wavefront shaping to compensate for scattering.