Aberration Any deviation from a spherically converging wavefront after the optical system has finished processing light is called an aberration. Aberration is commonly defined in one of two ways. The most convenient ray-optics usage expresses it as a deviation from the point of geometric focus. The wave optics convention defines it as deviation from a perfect converging sphere. These two seemingly different definitions are closely related. The slope of the wavefront determines the direction of ray propagation in a homogeneous medium.

Accommodation A biological adjustment to changing light or focusing conditions.

Achromat Literally meaning "without color," the term is used in astronomical optics to indicate a two-element refractor lens corrected for the dispersion of glass (chromatic aberration) over the color range of interest. The term achromat is a misnomer. For most doublets, only two colors are deliberately brought to a common focus, but the resulting folded spectrum offers much less dispersion than exists in simple lenses. (See refractor, apochromat, secondary spectrum, dispersion, and chromatic aberration.)

Airy disk (Named after early 19th century scientist Sir George Airy.) The appearance of the central peak in the focused diffraction pattern superficially resembles a disk. The illusion is made stronger since the peak is surrounded by a zero-intensity region. The disk has a soft edge, so the effective radius of the central diffraction spot varies with the brightness of the image. Brighter spots look bigger. (See resolution.)

Analytic geometry Originated by Pierre de Fermat and René Decartes in the early 17th century and further developed by later mathematicians, analytic geometry is a way of reducing geometrical relationships to algebra.

Angle A division of a circle. Four measures are common in this book: radians ("natural" or unitless), degrees, arcminutes, and arcseconds. The measure denoted in the upper left hand corner of the star-test plots is a reduced angle valid for all instruments, the angle in radians times the ratio DA. (See resolution.)

Annealed If materials are melted and allowed to cool below their solidification temperature too quickly, they will exhibit permanent strains. Improperly annealed glass deforms under the influence of grinding and over time to make the surface shape uncontrollable. Almost never appearing in glasses made specifically for optical use, it often occurs in glass disks adapted for optics, but cast with another use in mind.

Aperture The opening through which parallel light enters the telescope. Aperture is typically measured as the diameter of the most restrictive opening of the telescope before the light is focused. Some confusion may exist with the abbreviated photographic terminology that uses the term "aperture" interchangeably with "focal ratio." Aperture is not used that way here.

Aperture stop A physical obstruction (usually a circular hole) placed somewhere in front of the telescope. The function of the aperture stop is to limit the aperture in a specific plane. (See field stop.)

Apochromat If three chosen colors are simultaneously focused, the lens is said to be apochromatic. The classical definition also includes corrections for spherical aberration and coma. Because three colors within the spectral range of interest are held to a common focus, secondary spectrum is markedly reduced. (See also achromat, refractor, secondary spectrum, and chromatic aberration.)

Apodization Shading the aperture to diminish diffraction rings. This term has come to refer to modifying the transmission and phase of the aperture to achieve any sort of diffraction pattern change.

Arcminute 1/60 of a degree or '721,600 of a full circle. (See also arcsecond, degree, radian, and angle.)

Arcsecond '/60 of an arcminute, '/3600 of a degree, or '/1,296,000 of a full circle. 1 arcsecond = 4.848 x 10-6 radians. (See arcminute, degree, radian, and angle.)

Aspheric surface In optics, a concave or convex surface that superficially resembles a sphere but has another shape. Most commonly applied to conic sections spun on their axes.

Astigmatism An aberration that results from two radii of curvature oriented at right angles to one another on an optical surface. (See aberration.)

Attenuation A diminishing of wave intensity that includes diffraction, scattering, spreading of the beam, and absorption.

Bandwidth/bandpass The frequency range passed by a given filter.

Barlow lens A diverging lens placed near focus to increase the effective focal length of an instrument without appreciably increasing the telescope's physical size.

Bench test An indoor, laboratory-style test generally used during the fabrication of optics. Because of the necessarily compact nature of the testing geometry, most bench tests of astronomical instruments use secondary references or complicated data reduction procedures.

Catadioptric A mixed lens-mirror system that makes up the objective or main optical group.

Caustic A region where rays of light cross each other and pile up. Focus is a caustic, but this word also refers to the one-dimensional focusing that occurs with astigmatism or even the quasi-focusing that occurs in systems suffering from aberrations. In geometric optics, caustics are regions where the ray-tracing formalism breaks down.

Chromatic aberration Color errors caused by the dispersion of light in glass. Bringing the colors to different focus points has two forms of damaging effect on the image: all colors except those in focus are imaged as expanded disks, and magnifications vary with color. (See refractor, achromat, dispersion, and apochromat.)

Collimation Here, collimation is used to indicate achieving accurate alignment. More properly, it refers to the generation of a flat wavefront, but good alignment and a good wavefront are usually inseparable.

Coma An aberration that occurs when some optical systems are tilted. Rare in quality refractors, it is very common in reflectors and catadioptric systems. Coma results in a fan-like distortion. (See aberration)

Corrector (See Schmidt corrector and meniscus.)

Correlation An expression of the similarity of two functions as they are offset from one another. If the functions are precisely the same, the maximum correlation is one.

Criterion (resolution) In astronomical optics, this term refers to a certain separation in resolved objects (as in "the stars were separated just at the Rayleigh criterion"). Colloquially, it has been also used for stating optical quality, as in "the 74-wavelength Rayleigh criterion," although this terminology is properly replaced by "the '/4-wavelength limit." (See Rayleigh tolerance or Rayleigh criterion.)

Curtate cycloid A cycloid is the path followed by a point on the rim of a wheel. A curtate cycloid is the path of a point nearer the axle.

Dawes criterion A separation angle of about 1.02X/D. It occurs between the loose Rayleigh criterion and the tight Sparrow criterion.

Decibel A change in intensity of sound (or any signal) by a factor of 10 was originally termed "a bel." Since this change was too coarse, bels were never used. People much preferred the finer "decibel" measure. The dB level of I1 referenced to I2 is 10 logio( IJI2).

Defocus The amount of defocus as used here is more precisely the defocusing aberration measured in wavelengths of light. This number is not to be confused with defocus distance, or how far one must move the eyepiece to obtain defocusing aberration. (See Table 5-1.)

Degree 1/360 of a full circle. The reason early mathematicians probably used such a peculiar number is because it can be divided into so many whole number portions: 180, 120, 90, 72, 60, 45, 36, 30, 20, 18, 16, 15, 12, 10, 8, 6, 5, 4, 3, and 2. This measure was very helpful before the decimal number system was invented (with its compact algorithm for long division). Also equal to n/180 or about 757.3 radian. (See arcminute, arcsecond, radian, and angle.)

Dielectric A non-conducting material that becomes polarized in an electric field (i.e., that develops "electric poles" similar to "magnetic poles"'). Many such materials are transparent to visible light. Glass, polyester, air, and quartz are all examples of dielectrics.

Diffraction-limited Used conventionally as an equivalent for the l/14-wavelength RMS wavefront deviation limit of Marechal. Colloquially, it is used to mean the same thing as the 1/4-wavelength Rayleigh limit, but that usage is only true for broadly-varying wavefront deformations such as correction error.

Diopter A measure of lens focusing strength. A lens having a strength of 2 diopters has a focal length of '/2 meter, 3 diopters has a focal length of l/3 meter, etc. Thus, the human eye, which is focused at a distance of about an inch, has a native strength of roughly 40 diopters. Focusing corrections typical in eyeglasses—1 to 4 diopters— are minor adjustments.

Dispersion Frequency or color dependence of optical effects. Dispersion in refractive materials leads to desirable effects in spectroscopes and undesirable effects when white-light images are the goal. The phenomenon of chromatic aberration in lenses is a difference of focal lengths for light at various portions of the spectrum. It results in the breaking of white light into rainbow colors.

Doublet Two lenses placed in close proximity that act as if they were a single unit. Used to correct various single-lens defects, especially chromatic aberration. (See achromat and chromatic aberration.)

Dynamic range The intensity range over which a sensor or emitter is approximately linear. Dynamic range is typically written in decibels.

Effective Effective is applied to another quantity such as focal length or focal ratio. Complicated multi-element systems like Cassegrain telescopes or the use of a Barlow lens on a telescope demand some sort of leveling terminology to make their description comparable. "Effective focal length," for example, is the same as the focal length if the complicated optics were replaced by a single thin lens. "Effective focal ratio" is determined by examining how precipitously the light cone converges to focus. Cassegrain telescopes are much shorter than their effective focal lengths and ratios indicate.

Evanescent waves Waves that can only occur at the interface between media of different optical characteristics. They cannot propagate away from the interface and are bound to that surface.

Field stop A mask defining the field near focus. It is usually visible in the eyepiece as a sharply defined circle. This circle is not the edge of the main lens or mirror, but is contained in the eyepiece itself. It can be seen in most eyepieces by removing the eyepiece and turning it upside down. It is the sharp-edge opening through which the lenses can be seen. (See aperture stop.)

Figure (Noun) The surface shape of an optical surface. (Verb) To perform polishing operations to achieve the proper shape.

Focal length If an infinitely distant target is imaged by a lens or mirror, the focal length of the optical element is the distance from the lens or mirror such that the sharpest image of the target is found. Here, if no other indication is given, the focal length refers to the effective focal length of the objective system, rather than the eyepiece.

Focal ratio The ratio between the effective focal length and the aperture is the focal ratio. It is written as F = f/D, where F is the focal ratio, D the diameter of the aperture, and / the focal length. By convention, a 6-inch telescope with a focal length of 48 inches is referred to as an "f/8" system because 48/6 equals 8.

Fourier transform A mathematical procedure used to derive the frequency content of a function.

Foucault test A test using an obscuring edge placed near a point or slit focus.

Fraunhofer lines Dark lines in the solar spectrum labeled by the alphabet.

Fresnel zone A conceptual device to keep track of the phase sign. At locations where the wave is above its average value, it is in a positive Fresnel zone, and where the wave is below its average value, it is in a negative Fresnel zone. Thus, a given Fresnel zone applies only at an instant of time and is only an approximation of what is really happening.

Gaussian function A function of form Ae ~x/w' , with amplitude A and 1/e half-width w. Random deviations often follow a Gaussian distribution, as does the well-known "bell curve."

Geometric shadow In the light-as-particles ray tracing approximation, the geometric shadow consists of the regions beyond the cone extending from the aperture and passing through focus.

Grit Loose particles of abrasive used in grinding optical surfaces. Grit sizes range from coarse sandlike grains to powdered finishing abrasives.

Hyperboloid A three-dimensional surface having a blunted cone shape.

Incoherent When two waves are added, they are said to be incoherent if they have no phase relationship with one another. At one instant, they may add constructively, and at the next, subtract destructively. Coherent light is usually derived from the same atomic transition or the same cavity resonance (in lasers), incoherent light from unrelated transitions. Severely restricting the geometry (as in focusing light on one or more slits) will often achieve approximate spatial coherence of even temporally incoherent light. In the star test, light is emitted from an insensibly small point, a star or a pinhole, so the Huygens-Fresnel principle treats it as coherent (See interference.)

Index of refraction (See refractive index.)

Intensity As used here, intensity is proportional to the wave value squared. Actually, this number is not intensity as defined radiometrically, but the misuse has become customary.

Interference When intensity is calculated from the sum of two coherent waves, it is figured something like this equation: I= ( W1+W2)2 = (Wl)2+(W2)2+2W1 W2. The term on the end of the equation is called the interference term. If W2 = - W1, this term completely cancels the first two. If W2 = W1, the intensity is doubled. For incoherent light, this term can be anything at a given instant, but it averages over longer times to zero.

Iris An aperture stop that is adjustable in diameter. The eye has an iris and most cameras have a leaf-type iris used to adjust the aperture ratio. An iris is typically placed in or near a pupil in an afocal beam of light. (See aperture stop.)

Knife-edge test Colloquial expression for the Foucault test.

Lap A contraction of "lapping tool," it is a disk coated with pitch and powdered polishing agent in a slurry of water. Laps are used to polish optics. Typically, they are crossed by trenches ("channels") that have been cut into the lap to ease conformance to the optical element being worked.

Longitudinal As used here, an orientation along the axis of the instrument. The opposite of transverse. The conventional image as viewed in an eyepiece is a transverse slice. A longitudinal slice is usually in a plane passing through the centers of the objective and eyepiece.

Magnification Literally, the object size divided by the image size. The usefulness of this term breaks down when we talk about very distant, very large objects. In astronomical telescopes, it is much more common to speak of angular magnification. Angular magnification refers to the angle subtended by the object in the eyepiece divided by the angle subtended without optical aid. Thus, if we look at the half-degree Moon in binoculars with a magnification of 7, we should see an image that extends an apparent 3.5 degrees.

Magnitude The magnitude difference between two stars is — 2.51og10( I1/ I2). Thus, if one star is 10 times brighter than another, it is only 2.5 magnitudes brighter. Magnitude is similar to the decibel scale used in electronics or sound and the Richter scale of earthquakes. For historical reasons, it increases with dimmer stars.

Meniscus Optically, a meniscus is a strongly bent lens with a great deal of curvature but little focusing power. In other words, its curvature on the rear side is very near that of its front. The corrector lens of a Maksutov telescope is a meniscus.

Micrometer A unit of measure equal to 10-6 meters. Twenty years ago, this unit was in common use as the "micron." Actually, by international convention, all metric units of length are denoted "-metre," but this convention is not followed here.

Microripple A surface roughness originating from a correlated area on the order of 1 mm across. Microripple is usually of very small amplitude.

Model, modeling Fitting a phenomenon to a mathematical system that may or may not be physically derived. The fit can be empirical, with no scientific basis, but the best and most extensible models are usually derived from fundamental theory.

Modulation transfer function MTF predicts the ability of an optical system to preserve light-dark contrast in periodic targets with finer and finer bar spacing.

Newtonian telescope The parabolic reflector was first announced by Sir Isaac Newton in 1672. It was not useful for astronomical purposes until John Hadley made the first approximately paraboloidal surface in 1721.

Normalized An integral that is normalized has been reduced to a value of one in an ideal case. Thus, an integral of, say, energy over the aperture is multipled by a constant to yield a value of 1.00. Such a procedure is useful in comparisons of imperfect apertures to perfect ones.

Objective The main image-forming element or group of elements in a telescope. Often, it is useful to equate "objective" with "non-removable" optics in the system.

Oblate spheroid A conic surface of revolution that is flatter in the middle. An oblate spheroidal mirror focused at infinity has more spherical aberration than a sphere.

Optical transfer function Full complex form of the spatial-frequency transfer function. Its absolute value is the modulation transfer function. Gives the contrast and shift in position of a sinusoidal bar pattern.

Overcorrected A form of low-order spherical aberration in which marginal rays cross beyond the focus of central rays. In Newtonian telescopes, an over-corrected mirror is hyperboloidal. (See undercorrected.)

Paraboloid A theoretical curve between prolate spheroids and hyperboloids. Represents the ideal in making Newtonian telescope mirrors.

Paraxial focus The focus of rays incident at or near the center of the mirror and parallel to the axis of the instrument. Seldom the same as "best" focus.

Photodetector A sensor capable of detecting one or a few individual photons.

Pit An unpolished crater left over from the grinding process remaining in a polished surface.

Polychromatic Having many colors. White light is polychromatic.

Primary aberrations Pure low-order forms of aberrations. Examples include coma, spherical aberration, and astigmatism, etc. (Also called Seidel aberrations.)

Primary ripple Coarse, quasi-periodic roughness having a spacing about the same as the channels in the lapping tool. (See lap.)

Prolate spheroid A conic surface of revolution intermediate between a sphere and a paraboloid.

Quantum mechanics A name applied to the wave theory of matter. When wavelike particles are caught in a potential well (such as an electron in the Coulomb field of an atom), the requirement that the waves precisely fit in these wells demands that only certain energy states be occupied. Thus, energy can only be added or subtracted to such systems in discrete steps (called quanta).

Radian The measure of angle equal to moving one unit along the perimeter of a circle with unit radius. A radian is the "natural" measure of angle in that it is unitless. The word "radians" is actually a placeholder. A frequency of 2n radians/second is the same thing as 2n/second. An angle of 2n means that one full cycle of a circle has been traversed. (See angle, arcminute, arcsecond, and degree.)

Radiator An elemental source of secondary waves used in the Huygens-Fresnel theory of diffraction.

Rayleigh criterion When a double star is separated by an amount equal to the radius of either star's Airy disk, the separation is said to be just at the Rayleigh criterion. Most observers are able to resolve stars separated by less than this amount, but they do so more by shape of the pair rather than darkening between them.

Rayleigh tolerance or limit Optics that satisfy Rayleigh's limit produce wavefronts that can be enclosed by concentric shells with radii differing by '/4 wavelength of yellow-green light. (See RMS.)

Refractive index The ratio of the speed of light in empty space to the speed of light in a material. Examples: water has a refractive index of 1.3 and most glasses are somewhere over 1.5. Refractive index varying with wavelength is a conventional way of describing dispersion.

Resolution A measure of optical quality that depends solely on whether two equally bright incoherent points or bands of light are distinguishable. (See modulation transfer function and optical transfer function.)

RMS Stands for "root mean square," or the square root of the averaged deviations squared. In telescopes, RMS is used as a measure of surface quality of optical elements, with lower values for more perfect optics.

Rouge (or Jeweler's rouge) A powdered oxide of iron used in polishing compounds.

Scattering Diffraction from randomly distributed optical defects or obstructions.

Schiefspiegler A German word meaning "oblique reflector." A schiefspiegler is a telescope that avoids the additional diffraction of central obstruction by using tilted, round mirrors.

Schmidt corrector A plate placed in the incoming parallel beam to introduce an equal and opposite amount of spherical aberration to that produced by the rest of the optical system. The typical curve defining a Schmidt corrector is a 4th-order radial polynomial.

Secondary spectrum The residual chromatic aberration that exists in the bright portions of the spectrum (among the deliberately corrected wavelengths) even after a good attempt has been made at fixing color error. (See chromatic aberration, achromatic, apochromatic, and dispersion.)

Seidel aberrations The earliest formal description of spherical aberration, coma, astigmatism, field curvature, and distortion using polynomials and trigonometric functions. Also called the "primary" aberrations, or the first non-trivial components of a generalized aberration expansion.

Shading (See apodization.)

Signal-to-noise ratio (SNR) A comparison between the amount of interesting information to the amount of non-interesting information as it is transferred through a system. Because the noise power is usually so much less than the signal power, the SNR is usually given in decibels. Higher SNRs are desirable. (See decibels.)

Sparrow criterion If the separation of two points of light is set to where the diffraction structure creates a flat isthmus bridging them, then they are said to be separated by the Sparrow criterion.

Speckles Little points of light surrounding the image produced from rough surfaces or turbulent media. Speckles are caused by interference.

Spherical aberration When the converging wavefront is subtracted from a sphere centered on best focus, any remainder described by radial polynomials of low order is called "spherical aberration."

Strehl ratio The ratio of the maximum central brightness of an aberrated aperture's image to what it would be if the aberration were removed. A Strehl ratio of 0.8 is associated with the 1/4 - wavelength Rayleigh tolerance.

Substrate A telescope mirror is a layer of metal about 100 nanometers thick. The glass holding it is properly termed the "substrate."

Superposition If the combined effects of two waves are no more complicated than the simple sum of the waves, the system is called linear, and the net effect is called a linear superposition of the two waves. In other words, no effect arises from one wave's influence on the other. Intense light beams do not obey superposition in nonlinear media. All optical phenomena in this book are assumed to be linear. (See interference).

Telephoto A rear lens element that lengthens the effective focal length. Differs from a Barlow lens primarily in that it cannot be removed and was specifically designed to work with the optical system.

Undercorrected As used here, a type of low-order spherical aberration in which marginal rays cross nearer to the objective than the central rays.

Wave function The three-dimensional function describing a wave, generally including its amplitude, phase, and direction of propagation.

Wavelet Here, this term refers to the tiny subsequent waves emitted by the Huygens-Fresnel radiators. It also refers to a mathematical method used in signal processing, but that usage does not apply in this book.

Wedge A prismatic aberration of refractor lenses. Although wedge can result from a lens that is actually thicker on one side, it can also result from a decentered symmetric lens.

Zones A contraction of "zonal defects," they are a special case of spherical aberration. "Zones" can be thought of as localized circular corrugations on the surface.

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