## Glossary

Abbe's number of a glass see reciprocal dispersive power.

Abbe sine condition or sine condition optical design condition which cancels spherical aberration and linear coma. In third-order theory of aberrations, a system which satisfies the sine condition is said to be aplanatic.

Abbe sphere locus of the intersection of input and output conjugate rays in a centered system satisfying the sine condition.

Acomatic grating diffraction grating which provides an aberration correction for coma.

Active compensator deformable mirror able to generate one or several flexure modes for correcting aberration modes. Such compensators are useful for the photosensitive recording of aberration corrected holographic gratings.

Active optics controlled process which is either non time-dependant or with low frequency bandpass. Used in optics for aspherization methods, replication methods, in-situ variable shape mirrors and telescope mirror alignments.

Active optics co-addition law law which determines an optical surface as resulting from co-addition of elastical flexure and spherical figuring.

Active submaster deformable substrate which is used as intermediate stage optics in the double replication process of obtaining aberration corrected gratings or, more generally, aspherized surfaces.

Adaptive optics high frequency bandpass control essentially concerned with the wavefront corrections caused by the atmospheric degradation.

Aerial extremely long focal length refracting telescopes built in the period 16401690 and made of a single lens objective.

Afocal system or afocal telescope null powered optical system which is mainly used as beam expander, beam compressor, or retro-reflective system.

Anamorphotic systems optical systems whose optical power - and imaging scale - differs in the two principal directions. Such systems generally include cylindrical components.

Anastigmatism property of an optical system which is free from third-order spherical aberration, coma, and astigmatism.

Anticlastic surface surface whose product of the two principal curvatures, generated by flexure, is negative. A product of opposite sign corresponds to a synclastic surface.

Aperture ratio or focal ratio or f-ratio For a surface alone: ratio f /D of its focal length over its clear aperture diameter. For a telescope: ratio of the efl over the light-gathered beam diameter. This ratio is usually denoted f/{f /D}, e.g. f/ 1orf/5.

Aplanatism property of an optical system which is free from third-order spherical aberration and coma.

Aspherized reflective grating diffraction grating on a rigid substrate which has been aspherized via a double replication process by use of an active submaster.

Astatic levers counterweight and lever arrangements used as support systems for telescope mirrors.

Astigmatism length distance between the sagittal and tangential focii of an astigmatic beam of rays.

Bending or cambrure of a lens mean curvature of a lens.

Biconicoid surface optical surface whose conic sections differ in the x- and y-directions.

Biplate form or closed biplate form mirror substrate designed with two similar vase forms built-in together at their contour to form a closed cavity.

Blaze angle of a diffraction grating angle of the facets of the relief lines with respect to the local plane of the grating surface. In a given diffraction order (usually -1) blazed gratings - ruled or holographic - are much more efficient than sinusoidal line gratings.

Boundary conditions in elasticity free edge, (movable) simply supported edge, (movable) built-in edge, unmovable simply supported edge and unmovable built-in edge are the five basic boundaries at the edge of a solid plate.

Buckling elastic instability of a beam, plate, shell, or truss when overpassing a critical load.

Cambrure or bending of a lens mean curvature of a lens.

Camera obscura hole in a high-ceilinged room allowing to observe the sunspots without use of any lens. First mentioned by Al-Haytham (Alhazen), the imaging effect is provided by the Fraunhofer diffraction of the hole.

Cantilever beam or girder which is built-in at one end.

Characteristic function function derived by R.W. Hamilton to establish the analytic form of optics third-order aberrations.

Cassegrain focus focal surface of a reflecting telescope formed behind the primary mirror via a central hole in it.

Catadioptrics branch of optics involving optical systems made of both refractive and reflective surfaces.

Catoptrics branch of optics involving optical systems made of reflective surfaces or mirrors only.

Cat's eye system an afocal system where the light returns from were it comes. A moving cat's eye system translating on delay line carriage of a two-arm interferometer is generally a retro-reflective system equipped with a variable curvature at its focus for optical path compensation of the field of view.

Centered system optical system only formed of axisymmetric surfaces which are distributed on a common axis.

### Chief ray of a beam see principal ray.

Clairaut doublet lens stigmatic and achromatic objective made of two cemented lenses of different glass. The French refer to this lens simply as a "Clairaut."

Clairaut-Mossotti doublet lens aplanatic and achromatic objective made of two cemented lenses of different glass.

Clear aperture (optical) aperture which physically determines the cross-section of an optical beam used by an optical surface. Usually specified by its diameter for a circular aperture.

Clebsch's polynomials infinite set of four-term series where each series is a radial component of the general non-axisymmetric solutions of Poisson's equation of thin plate theory when the holed or non-holed plate is axisymmetric.

Clebsch-Seidel modes superposable elastic modes which belong to a subclass of the optics triangular matrix.

Closed biplate form or biplate form mirror substrate designed with two similar vase forms built-in together at their contour to form a closed cavity.

Closed shell closed form made of two linked vase shells which can be bent by inner pressure or inner partial vacuum. When the two vase shells are identical, and linked to their flat outer bases, the arrangement is said to be a flat closed shell, otherwise it is said to be a curved closed shell.

Coma neutral point of a two-mirror telescope intersection point of the axes of the mirrors when the on-axis coma is nulled at the resulting focus.

Conicoid axisymmetric optical surface whose meridian section is a conic.

Conic constant or Schwarzschild constant constant which determines the as-phericity of a conicoid surface.

Constringence of a glass see reciprocal dispersive power.

Coude focus optical arrangement using mainly a set of folding plane mirrors -the coude train - which allows the beams of a telescope to converge in an underground room - the coude room.

Couder's law or flexure scaling law for mirrors under gravity law which scales the flexure of mirrors supported by horizontal point-pads as d4/t2, where d and t are the diameter and thickness of the mirror.

Ctd constant thickness distribution (opposite to variable thickness distribution -vtd).

Cycloid form axisymmetric geometry formed by a front plane surface and a variable thickness distribution which remains finite at the center and tends vertically towards zero at the edge - like a cycloid.

Deformed conicoid optical surface whose shape departs from a conicoid by a fifth or a higher-order term. Belongs to the spheroid class.

Descartes' ovoid or ovoid surface optical surface providing the stigmatism, i.e. correcting the spherical aberration at all orders. Introduced by Descartes for singlet lenses. The conicoids belong to a subclass of ovoids.

Dialytic system or dialytic telescope a system where the axial chromatism of a single objective lens is corrected by a smaller negative lens - or doublet lens -located near the middle of the system.

Dioptrics branch of optics involving optical systems made of refractive surfaces or lenses only.

Dispersive power of a glass relative variation of the refractive index of a glass with respect to the value of mean index minus unity over a given spectral range [5n/(n0 - 1)]. The reciprocal of this number is the Abbe number v, sometimes called V-number.

Double vase form or double vase shell single substrate for two distinct mirrors whose concentric surfaces form a continuous figure. The substrate is made of two built-in and concentric vase forms or vase shells.

Eccentricity dimensionless quantity which is related to the conic constant of conicoid.

Efl or effective focal length resulting focal length of an optical system for a given wavelength.

Effective focal length - often denoted efl resulting focal length of an optical system.

Eikonal function aberration function derived from Hamiltonian and reintroduced to optics by Bruns as related to the aberration wavefront function.

Elastic deformability ratio or flexibility ratio intrinsic ability of a material to provide an elongation or a flexure. This dimensionless ratio can be defined as the quotient of the usable limit tensile stress to the Young modulus (OTnm/E).

Elastic relaxation figuring or stress figuring active optics aspherization method which uses the elastic relaxation of the stresses applied during spherical figuring. Compared to the zonal figuring method which uses small tools, this method uses full-size aperture tools and thus produces extremely continuous surfaces, i.e. free from ripples.

Elastica or elasticae curves of the flexure of a thin circular rod or wire first introduced by Euler.

Enlarging monocular or spyglass early such systems were a chance arrangement of eyeglass lenses available on the 1600s market with positive objective lens and negative eye lens. This provided an amusing but poorly magnifying system from which Galilei invented the telescope.

Entrance pupil or input pupil pupil or aperture stop in which all axial and field beams enter through an optical system. The conjugate is the exit pupil, and also called output pupil. The entrance pupil of a two-mirror telescope can be either the primary or the secondary mirror.

Erect image image in which all directions are similar to the object. A classical different case is an inverted image.

Etendue invariant see optical etendue.

Ewing-Muir process stressing process of a material which allows one to extend the linearity range of the stress-strain relation.

Fermat's principle principle of least time which governs the light propagation and determines the geodesics of optical paths. It states that the light path - or ray trajectory - between two points is the path which corresponds to a minimal or a stationary path.

Field binodal astigmatism at the focal surface of a two-mirror telescope field distribution of the astigmatism showing two least confusion images when the on-axis coma is nulled. Caused by an angular error between the axes of the mirrors.

Finite element analysis computational modeling which, in elasticity, allows accurate determination of the deformations of a solid by basic use of the element stress-strain relations.

Fizeau test interferometric determination of an optical surface shape by use of a fringe pattern formed with respect to a reference surface.

Flexibility ratio or elastic deformability ratio intrinsic ability of a material to provide an elongation or a flexure. This dimensionless ratio can be defined as the quotient of the usable limit tensile stress to the Young modulus (orum/E).

Flexural hysteresis stres-strain hysteresis loop which is shown by metallic alloys when the stressing reaches or slightly overpasses the elastic limit. Brittle materials, such as glass and vitrocerams, do not exhibit flexural hysteresis.

Flexural rigidity or rigidity of a plate quantity which involves the Young modulus, Poisson's ratio and third power of the thickness.

Flexure scaling law for mirrors under gravity or Couder's law law which scales the flexure of mirrors supported by horizontal point-pads as d4/t2, where d and t are the diameter and thickness of the mirror.

### Focal ratio see aperture ratio.

Foucault test or knife-edge test wavefront analysis of the light distribution reflected by the mirror under test by use of a knife-edge partly occulting the convergent region of a beam.

Gaussian theory or paraxial theory of optics basic theory where any ray forms a small angle with respect to the system axis such that the sine and tangent functions are approximated by that angle itself.

Hamilton characteristic function first general form of the wavefront function.

Holosteric mirror mirror whose particular geometry is machined in a single piece.

Homocentric system optical system where the principal rays in the image space are converging towards a common center; so, the image focal surface is curved and normal to this center direction.

Homothetic transformation congruence of rays usual optical transformation where the conjugate of a paraxial ray remains a paraxial ray with the same ho-mothetic height as that of the whole beam.

Huygens-Fresnel principle basic method for the explanation of diffraction effects of light. The principle states that any point of a wavefront give rise to secondary disturbances which are spherical wavelets and, at any later instant, the spacial light distribution may be regarded as the sum of these wavelets.

Hysteresis see flexural hysteresis.

Imager-spectrograph telescope post-focal instrument which exhibits both an imaging mode and a spectrographic mode.

In situ stressing deformable optical surface which is stressed during an astronomical observation.

Inverse square law (optics) law which governs the light energy propagation as the inverse square of the distance.

Inversion transformation congruence of rays optical transformation where a paraxial ray becomes a marginal ray. Systems realizing this transformation were first described by Mersenne for two confocal paraboloid mirrors used in the retrore-flective form.

Inverted image image in which up and down and left and right are interchanged. A different case is an erect image. The human eye forms an inverted image on the retina.

Isoplanatic system optical system which is free from coma only.

Kerber's condition (1886) condition for minimizing the chromatic variation of spherical aberration - or spherochromatism. This expresses that the least confusion focus must be determined by a pupil ray height equal to a/3/2 = 0.866. For the central color, this corresponds to the algebraic slope balance of the wavefront.

Kirchhoff's condition boundary condition at the free edge of a plate when the flexure is non-axisymmetric. This condition is set by nulling the net shearing force at the edge of the plate.

Large deformation theory elasticity theory of plates which takes into account the in-plane displacements of the neutral surface.

Large torsion theory elasticity theory elaborated by Saint-Venant which treats torsion cases where the cross-section of a non-circular beam does not remain plane.

Lagrange invariant invariant of the action of an optical system which is equivalent to a one-dimensional representation of the optical etendue, i.e. of the total energy transported by the optical system for a given spectral bandpass 8X.

Linear coma third-order field aberration which includes the odd sum of all image height terms.

Linear product law of a weakly conical shell law which relates the product of the thickness by the flexure of the shell as a linear function of the axial coordinate.

Littrow mounting of a diffraction grating geometrical arrangement where the diffraction angle for the central wavelength is equal and of opposite sign to the incidence angle.

Love-Kirchhoff hypotheses small deformation hypotheses which state that any point located on normal lines to the middle surface of a solid remains on normal lines to the deformed middle surface and that the thickness does not vary in flexure.

Marginal ray ray which passes at or near the edge of a pupil.

Mean curvature focal surface focal surface of least confusion imaging of an optical system. Merges into the Petzval surface once the spherical aberration, coma and astigmatism are nulled.

Meniscus form axisymmetric geometry resulting from the volume delimited by two axially separated surfaces of similar or quasi-similar curvature, or by two concentric surfaces.

Mersenne two-mirror telescopes afocal telescopes made of two confocal paraboloid mirrors.

Multimode deformable mirror meniscus form or vase-form mirror equipped with a set of radial arms on which are applied distributions of axial forces on each end. These configurations allow the superposition of the Clebsch-Seidel modes, a subclass of the triangle matrix optical modes.

Nasmyth focus focal surface of a reflective telescope formed on the platform of an altazimuth mount by a plane - Nasmyth - mirror operating 90° beam deviations about the telescope axis.

Navier's relations or stress-strain relations fundamental linear relations of elasticity which links the six stress components to the six strain components of the facets of a volume element of a solid.

Nebular f-ratio of a spectrograph camera f-ratio in the direction perpendicular to the dispersion.

Net shearing forces transversal forces in length unit which act in loaded plates. These forces, denoted Vx,Vy or Vr, allow determination of the equilibrium reactions.

Neutral surface surface where the stress distribution through the thickness of the solid remains null during elastic bending. For small deformations the neutral surface is also the middle surface.

Non-centered system optical system including one or several non-axisymmetric surfaces where a general axis of symmetry does not exist.

Normal congruence a pencil of light can be seen as formed by a continuous set of propagation lines called a congruence. If a wavefront surface is orthogonal to all these lines, then the pencil is a normal congruence. If not so, the pencil is a skew congruence (e.g. electron optics).

Normal rectilinear congruence in photon optics and light propagation in isotropic media each curve of the normal congruence pencil is a straight line; the normal congruence is then said to be rectilinear.

Null-power zone ratio of a pseudo-plane-aspheric surface ratio of the null slope radius over its clear aperture radius.

Null test optical test requiring the use of a corrector made of one or more lenses or mirrors, or of a hologramatic correction - either used on or off axis - which provides the complete aberration compensation of the output wavefront so the resulting fringe deviation is zero.

### Oblate ellipsoid flattened ellipsoid.

Optical etendue invariant (Jacquinot's) an invariant quantity when the light propagation occurs through a perfect optical system. For a given bandpass 8X, the etendue represents the total energy transported by an optical system.

Optical despaces the five basic displacements for the alignment of an axisym-metric optical piece which consist of piston (z translation), lateral centering (x and y translations), and tip-tilt (x and y rotations).

Optics triangular matrix in any centered system formed of axisymmetric optical surfaces belonging to the surface class with continuous tangent plane, any wavefront surface can be defined by a polynomial sum X anmrn cos mQ where m < n. Hence, the anm coefficients form a triangular matrix.

Ovoid surface or Descartes' ovoid optical surface providing the stigmatism, i.e. correcting the spherical aberration at all orders. Introduced by Descartes for singlet lenses. The conicoids belong to a subclass of ovoids.

Paraxial theory of optics see Gaussian optics.

Petzval condition optical design condition for obtaining a flat image field whilst the spherical aberration, coma and astigmatism are nulled.

Petzval theorem theorem which allows deriving the Petzval curvature of an optical system as a function of the curvatures of its surfaces and of the refractive indices separating them.

Plastic deformation permanent residual deformation of a material after a stress loading cycle whose level overpassed its limit elastic stress.

Point spread function or psf function representing the intensity distribution of the light in the image region of the Gaussian focal plane.

Poisson's equation of elasticity fourth derivative biharmonic equation of the thin plate theory.

Principal ray or chief ray of a beam a ray which starts from a given source point in the field, then passes through the vertex of an entrance pupil, and propagates through an optical system up to reaching an image focal plane.

Prime focus focal surface formed by the primary mirror of a telescope.

Prolate ellipsoid elongated ellipsoid.

Punctum proximum distance minimum distance at which the eye can accommodate. This distance is typically 15-18 cm for a young adult.

Pupil or stop aperture which delimits the common cross-section area of all the beams. Any optical system is defined by an input pupil or an output pupil.

Quarter-wave criterion (Rayleigh's) criterion which confers a centered system the ability to form diffraction limited images on its axis. The output wavefront must be included between two concentric surfaces separated of A/4.

Retro-reflective system an afocal system where the light returns from were it comes. A moving cat's eye system translating on delay line of a two-arm interferometer is generally a retro-reflective system.

Reciprocal dispersive power of a glass this number defined by the Abbe number v = (n0 - 1)/5n expresses the intrinsic variation of the refractive index of a glass. This is the reciprocal number of the dispersive power. The Abbe number of a glass is sometimes called the constringence or V-number.

Ripple errors of a surface slope discontinuities which provide high spatial frequency errors of the wavefront and thus degrades the diffracted image quality. Usually caused by local retouches during the figuring of optical surfaces.

Rumsey telescope flat-field anastigmat three-reflection telescope.

Rupture stress or ultimate strength stress level at which a material ruptures.

Rupture tensile stress or ultimate tensile strength stress level at which a brittle material is brought to rupture by tension.

Sagittal ray fans meridian ray fans of an optical system which provide the tangential focii locus of the tangential focal surface.

### Schwarzschild constant see conic constant

Saint-Venant's principle principle of equivalence of the elastic deformations of a solid in the application of equivalent boundary conditions applied over a small region. This principle is useful in active optics design for finding an optimal and practicable geometrical configuration and its associated load distribution.

Schwarzschild's eikonal function related to the aberration wavefront function and closely similar to Schwarzschild's perturbation function in the motion of planets, and that Schwarzschild called Seidel's eikonal.

Secondary spectrum residual chromatic error due to the inherent difficulty of perfectly achromatizing doublet lenses.

Seidel theory or third-order theory theory which allows determination of the amount of each primary aberration - or third-order aberration - of a complete optical system. The sine of any ray angle is approximated by the first two terms of its expansion.

Serrurier's truss mechanical truss of special concept which compensates for the decentering and tilt errors between the primary and secondary mirrors of large telescopes due to the tube flexure under gravity.

Shack-Hartmann test analytic determination of a wavefront shape from the two-dimensional lateral shifts of pencils autocollimated on subpupils of the surface to test. The wavefront is reconstructed from measurements of local slopes in the pupil.

Shear strain elastic relative displacement which occurs between two parallel plane facets of a solid when the facets remain parallel.

Shearing forces (radial) transversal forces in length unit, usually denoted Qr, which act in concentric circular sections of bent axisymmetric plates.

Sine condition (Abbe's) see Abbe sine condition.

Sine refraction law (Snell's) sine law which determines the refractive angle of a ray when emerging in a new refractive medium.

Skew invariant property of a skew ray in a centered system which is used to establish Abbe's sine condition.

Speculum mirror mirror made of bell metal or CuSn25 alloy, i.e. bronze, which may include arsenic for a better optical polish.

Spherochromatism chromatic variation of spherical aberration.

Spheroid axisymmetric optical surface whose meridian section is expressed by an even polynomial series of the radius.

Spyglass see enlarging monocular.

Stacked triangles or whiffletrees assembly of pivoting triangles or beams arranged on successive levels for use as telescope mirror support systems.

Stigmatism property of an optical system which is - at least - free from third-order spherical aberration.

Stop or pupil aperture which delimits the common cross-section area of all the beams. Any optical system is defined by an input pupil or an output pupil.

Strehl intensity ratio intensity ratio which characterizes the light concentration of an optical system. If the ratio is at least 0.8 or greater, then the system is well corrected and so-called "diffraction limited."

Stress figuring or elastic relaxation figuring active optics aspherization method which uses the elastic relaxation of the stresses applied during spherical figuring. Compared to the zonal figuring method which uses small tools, this method uses full-size aperture tools and thus produces extremely continuous surfaces, i.e. free from ripples.

Stress lap polishing optical figuring alternative by controlled flexible tools - of smaller size than the surface clear aperture - which match the aspherical surface to minimize ripple errors.

Stress polishing last stage of stress figuring or elastic relaxation figuring.

Stress-strain relations or Navier's relations fundamental linear relations of elasticity which links the six stress components to the six strain components of the facets of a volume element of a solid.

Synclastic surface surface whose product of the two principal curvatures, generated by flexure, is positive. A product of opposite sign corresponds to an anticlastic surface.

Tangential ray fans ray fans laying in a perpendicular direction to a meridian plane of a system which provide the sagittal focii locus of the sagittal focal surface.

Telecentric system optical system where the principal rays in the image space are parallel to the system axis; so, the image focal surface is a plane.

Telephoto effect of a two-mirror telescope ratio which characterizes the effective focal length with respect to the telescope length. Allows classification of various designs as a function of the compactness.

Theory of shallow spherical shells elasticity theory which takes into account the significant curvature of the middle surface and the "in-plane" radial and tangential tensions appearing on it during flexure.

Theory of weakly conical shell elasticity theory elaborated for the aspherization of grazing incidence telescope mirrors.

Thick plate theory elasticity theory which takes into account all the shear components of the deformation of a plate.

Thin plate theory elasticity theory elaborated by Poisson and based on Love-Kirchhoff hypotheses.

Third-order theory of optics or Seidel theory theory which allows the determination of the amount of each primary aberration - or third-order aberration - of a complete optical system. The sine of any ray angle is approximated by the first two terms of its expansion.

### Triangle matrix modes see optics triangular matrix.

Tulip form axisymmetric geometry formed by a front plane surface and a variable thickness distribution which tends towards infinity - like a stem - at the center and tends vertically towards zero at the edge.

Ultimate strength or rupture stress stress level at which a material is brought to rupture.

Ultimate tensile strength or rupture tensile stress stress level at which a brittle material is brought to rupture by tension.

Uni-constant theory early theory of elasticity where the Poisson's ratio of all materials were implicitly v = 1/4.

Vase form axisymmetric geometry formed by an inner plate or meniscus, of constant or quasi-constant thickness, built-in to a somewhat thicker outer cylinder.

Vase shell vase form whose inner meniscus is with significant curvature.

Variable thickness vase form vase-form mirror whose clear aperture is the surface of an inner built-in meniscus or plate of slightly variable thickness distribution.

V-number of a glass see reciprocal dispersive power.

Vtd variable thickness distribution (opposite to constant thickness distribution -ctd).

Whiffletrees or stacked triangles assembly of pivoting triangles or beams arranged on successive levels for use as telescope mirror support systems.

White pupil mounting spectrographic arrangement where the telescope pupil is transferred in a particular location. This mounting, originated by Baranne, is mainly used for high spectral resolution systems.

Wolter two-mirror systems grazing incidence systems for X-ray focusing. Type I of three is made of two convergent axisymmetric mirrors. Its compactness provides a basic design for all space telescopes.

Wolter-Schwarzschild (WS) telescope grazing incidence two-mirror system strictly satisfying Abbe's sine condition.

Yield strength stress level at which the deformation of a metal alloy exhibits a specified deviation from stress-strain linearity and thus reaches the plastic domain.

Zernike circle polynomials Zernike rms polynomials normalized representations of a wavefront or of an optical surface.

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