Big League Cryogenics and Vacuum The LHC at CERN A typical astronomical instrument must maintain about one cubic meter at a pressure of <0.1 millitorr. The Large Hadron Collider at CERN is 27 kilometers in circumference and contains two beam pipes that must be held <10^{-9} millitorr for months at a time. The accelerator uses hundreds of superconducting magnets which must be cooled to <4K. 700,000 liters of superfluid liquid helium (superfluid to minimize distribution losses and improve energy transfer). 200 kilometers of cryogenic piping, 40,000 junctions, 1700 cryogenic valves...
Optics, Ray Tracing, and Optical Design
Geometrical vs. Physical Optics Geometrical Optics traces rays through the system Reflection and refraction occur based on purely geometrical relationships (e.g. Snell's Law) Images are constructed from the intersection points of a bundle of individually traced rays with a focal plane. Rays do not interact with one another. Physical Optics accounts for the wave nature of light. An incident ray is represented by a plane wavefront. Wave propagation and interference determine the illumination within the system. Naturally accounts for interference and diffraction.
Geometrical vs. Physical Optics A raytrace of a parabolic mirror will produce an infinitesimally small point image for an object on the axis of a parabola at infinite distance. In reality, the image size is limited by diffraction to an Airy pattern. http://library.thinkquest.org/22915/reflection.html
Geometrical Optics and Surfaces The basic unit of optical design is the surface (not the lens...). Surfaces can redirect rays either through reflection / refraction obscuration/scattering diffraction (but this is physical optics) A surface can also serve as a stop without redirecting any rays. A stop is simply an obscuration/hole.
Reflection Reflection simply requires equal angles of incidence and emergence for a ray independent of material. The only wavelength dependent quantity is reflection efficiency (which will not affect image shape).
Reflection and Virtual Images
Refraction and Snell's Law Note that the refractive index, n, is a wavelength dependent quantity http://www.haverford.edu/physics-astro/songs/snell.htm
Raytracing 101: The Paraxial Approximation A raytrace follows the propagation of a ray through an optical system one surface at a time, calculating the deviation from reflection or refraction at each surface. The paraxial approximation provides a starting point for the overall system layout image positions, focal lengths, etc. - by calculating ray propagation infinitesimally close to the optical axis. This is the regime where sin = and thus where images are perfect and their positions are readily calculated. Due to aberration the paraxial focus can be significantly different from the best focal position.
Focal Length, f/number, and the Lensmakers Equation The focal length of a lens is the distance from the lens (actually from its principal plane) to the lens' focus when imaging a point source at infinite distance (parallel incident rays). In practice, the paraxial focal length of the lens is quoted.
Aside One of my Favorite Books...
Focal Length and the Lensmaker's Equation The focal length of a lens is the distance from the lens (actually its principal plane) to the lens' focus when imaging a point source on the optical axis. For a ''thin'' lens the focal length is given by This equation applies for a thin lens in vacuum (or air). n is the refractive index of the lens material r is the radius of curvature (convex to the left is positive curvature)
Focal Ratio The focal ratio (f/#) characterizes the rate of convergence of a bundle of rays as they form an image. A lens (or system of lenses) will have a fixed focal length, but its focal ratio will depend on the aperture of its stop. Focal ratio is simply the inverse of the beam's divergence per unit length. a beam that broadens 1 cm for every 10 cm of propagation is an f/10 beam.
Focal Ratio and Depth of Field f/8 f/2 High focal ratios (e.g. f/20) imply a narrow pencil of converging rays a slow (from photographic exposure time) optical system. Low focal ratios (e.g. f/2) indicate convergence over a wide angle and thus a fast system.
Focal Ratio and Depth of Field Fast systems are prone to optical aberration (due to the large range of ray angles incident on the optics. f/8 f/2 difficult to focus. A small shift in focal plane position produces significant blurring of the image Essential for wide-field imaging or broadband spectroscopy (where a wide range of angles much to be focused onto a surface)
Raytracing 101: Ray Height In analyzing a lens system, particularly one that is axially symmetric, characteristics of ray propagation can be paramaterized in terms of ray height from the optical axis. Rays of infinitesimal height are the paraxial rays. For most real optics, image position (as defined by ray intersection is a function of ray height). That is, an optic will focus light from different radial zones on the optic at different distances producing an aberrated image.
Raytracing 101: Ray Height
Tracking of rays can be accomplished computationally or, even, physically.
Images and Objects A lens will form an image of an object at a position dictated by the focal length. Images and objects can be virtual, meaning that divergent rays imply the existence of an object at their apparent convergent point. Images, either real or virtual, serve as objects for subsequent elements.
Conjugate Images and Objects An object and its corresponding image are ''conjugate'' points. The conjugate of an object at infinite distance is an image one focal length from the lens. An object placed at a focal point has its conjugate image at infinite distance. Emergent rays from the lens are parallel -- the basis of ''collimation''
Locating Conjugate Points By identifying a ray through a focus or parallel to the optical axis a ray through lens center one can graphically construct an image corresponding to a given object.
Compound Optics Virtually all optical systems contain two or more elements. Most systems can be reduced to an equivalent single thin lens. The final focus (and focal ratios) can be propagated through the system one object/image pair at a time.
Compound Optics Virtually all optical systems contain two or more elements. Most systems can be reduced to an equivalent single thin lens. The final focus (and focal ratios) can be propagated through the system one object/image pair at a time.
Cassegrain Telescopes as Compound Optics A cassegrain telescope is a two-optic system. The primary forms a real image. The secondary, which has a negative focal length, relays this real image to another real image in the focal plane. In a cassegrain configuration the secondary interrupts the converging beam from the primary before the real image forms, but the image is there for calculation's sake nonetheless.
Cassegrain Telescopes as Compound Optics A cassegrain telescope is a two-optic system. The primary forms a real image. The secondary, which has a negative focal length, relays this real image to another real image in the focal plane. In a cassegrain configuration the secondary interrupts the converging beam from the primary before the real image forms, but the image is there for calculation's sake nonetheless.
Gregorian Telescopes In the Gregorian configuration the secondary mirror lies beyond the prime focus of the primary. A real image is formed in space ahead of the secondary.
Infrared Design Reimaging Optics Most CCD detectors are placed directly at the primary focal plane of the telescope. Such a configuration would sacrifice considerable sensitivity to thermal background for infrared work. An infrared system should view a little warm solid angle as possible, preferably only seeing low-emissivity mirror surfaces on the way to the cold sky. Place focal plane here??
Blackbody Radiation Ambient thermal blackbody emission becomes significant at room temperature (300K) at wavelengths longward of 2 micrometers. 1.2 1.6 2.2 B(300K, 1.0um) = 1.7e-06 B(300K, 2.0um) = 1.4e+03 B(300K, 3.0um) = 5.7e+05 B(200K, 2.0um) = 8.9e-03
Blackbody Emission/Detection Geometry
Blackbody Geometry The Planck equation quantifies the amount of light emitted by a unit area of a perfect blackbody into a given solid angle per unit bandpass. Imperfect emitters are characterized by their emissivity as a function of wavelength,. Astronomically, the solid angle of interest is the aperture of the telescope as seen from the surface of the target. Similarly the blackbody area of interest is the surface area of the blackbody viewed by a pixel. If the blackbody is unresolved then the area of interest is the projected area of the entire blackbody.
Infrared Design Reimaging Optics In order to limit the rays seen by the detector, collimate and re-image the primary focal plane. Re-imaging provides two advantages Control over final platescale as the f/# of the final focus is now under the designer's control. The collimating lens forms an image of the primary mirror (which is as good as having the original right there) within the cold volume of the instrument. All warm surfaces can be masked. Place re-imaging optics here!
Infrared Design Issues Reimaging Optics An image of the telescope primary (pupil) is formed about one focal length behind the collimating lens. In addition to being the location to mask off high emissivity surfaces, this location is also ideal for placing filters, polarizers, grisms light from a star is spread uniformly over the full aperture the pupil marks a minimum diameter waist in the optical system permitting the smallest components Pupil Image Cassegrain focal plane Reimaged Focal Plane
Infrared Design Issues Reimaging Optics Reimaging in practice The TripleSpec slit viewing optics.
Lens aberrations The paraxial approximation holds for cases where sin (the small angle approximation). More exactly, the series expansion of sin is: Classical aberrations of optical systems can be traced to the third order terms in the expansion. These 5 classical aberrations -- spherical, coma, astigmatism, distortion, and field curvature were enumerated by von Seidel and bear his name.
Spherical Aberration An ''on-axis'' aberration which arises from different radial zones on an optic having different focal lengths. A parabola is the only single optical element free of spherical aberration.