APQ Wiki – Optics and Telescope Technology
The APQ Wiki explains key terms in technical and astronomical optics and directly links related topics. This edition contains 175 terms. In addition to concise definitions, formulas, schematic diagrams, cross-references, and literature references are provided wherever technically useful. The expanded scope now also covers precision-optics manufacturing, optical testing, optomechanics, optical-system synthesis, and the interaction between optics and detectors.
Terminology: The number of optical elements in an objective is described by terms such as Doublet, Triplet, Quadruplet, and Multiplet. These structural terms are distinct from chromatic correction classes such as Dichromat, Trichromat, Apochromat, Polychromat, and Superachromat. Calcium fluoride is written as CaF₂.
Formulas and diagrams are intended to place a term in context; they do not replace a complete specification or system analysis. For Strehl, MTF, spot diagrams, chromatic correction, and tolerancing in particular, wavelengths, field points, focus conditions, spectral weighting, and test conditions must be stated.
A–Z: A | B | C | D | E | F | G | H | I | K | L | M | N | O | P | Q | R | S | T | U | V | W | Z | Literature and further reading
A
Abbe diagram
Graphical representation of optical glasses using their Abbe number and usually refractive index or a relative partial dispersion. Extended glass maps also reveal departures from the normal dispersion line and therefore support material selection for chromatic correction. See also: Partial dispersion
Graphical representation of optical glasses using their Abbe number and usually refractive index or a relative partial dispersion. Extended glass maps also reveal departures from the normal dispersion line and therefore support material selection for chromatic correction. See also: Partial dispersion
Schematic: positions of glasses in a dispersion representation; anomalous materials can deviate from the normal glass line.
Abbe number
The Abbe number (also Abbe constant or constringence) characterizes the dispersion of a transparent optical material. It is denoted by the Greek letter ν; νd is commonly used for the d-line definition and νe for the e-line definition. For comparable refractive index, a larger Abbe number generally means lower chromatic dispersion in the visible range. See also: Dispersion
The Abbe number (also Abbe constant or constringence) characterizes the dispersion of a transparent optical material. It is denoted by the Greek letter ν; νd is commonly used for the d-line definition and νe for the e-line definition. For comparable refractive index, a larger Abbe number generally means lower chromatic dispersion in the visible range. See also: Dispersion
Formulas:νd = (nd − 1) / (nF − nC)νe = (ne − 1) / (nF′ − nC′)
Abbe sine condition
Condition for coma-free imaging of an axial object point at finite aperture. It relates ray height, refractive index, and ray angle on the object and image sides and is a central criterion of aplanatism. See also: Aplanat / aplanatism
Condition for coma-free imaging of an axial object point at finite aperture. It relates ray height, refractive index, and ray angle on the object and image sides and is a central criterion of aplanatism. See also: Aplanat / aplanatism
Formula: n y sin u = n′ y′ sin u′
Aberration
General term for departures of a real image from the ideal geometrical or diffraction-limited image. Important forms include Spherical aberration, Coma, Astigmatism, Field curvature, Distortion, and chromatic aberrations.
General term for departures of a real image from the ideal geometrical or diffraction-limited image. Important forms include Spherical aberration, Coma, Astigmatism, Field curvature, Distortion, and chromatic aberrations.
Absorption
Conversion of part of the incident optical radiant power into other forms of energy within a material. Together with reflectance and transmission, it determines the spectral losses of an optical system. See also: Reflectance, Transmission
Conversion of part of the incident optical radiant power into other forms of energy within a material. Together with reflectance and transmission, it determines the spectral losses of an optical system. See also: Reflectance, Transmission
Formula: A(λ) = 1 − R(λ) − T(λ)
Achromat
Optical system in which two selected wavelengths have the same paraxial focus. An achromat reduces primary chromatic aberration but leaves a secondary spectrum. The term describes the correction class, not the number of lenses. See also: Chromatic error, Secondary spectrum
Optical system in which two selected wavelengths have the same paraxial focus. An achromat reduces primary chromatic aberration but leaves a secondary spectrum. The term describes the correction class, not the number of lenses. See also: Chromatic error, Secondary spectrum
Active optics
Relatively slow control of the shape or position of large optical components in order to compensate quasi-static errors caused by gravity, temperature, and mechanical loads. It must be distinguished from the faster adaptive optics.
Relatively slow control of the shape or position of large optical components in order to compensate quasi-static errors caused by gravity, temperature, and mechanical loads. It must be distinguished from the faster adaptive optics.
Adaptive optics
Method for rapid, usually closed-loop correction of time-varying wavefront errors by means of a wavefront sensor, controller, and deformable optical element. In astronomy it is used primarily to compensate atmospheric turbulence. See also: Wavefront error
Method for rapid, usually closed-loop correction of time-varying wavefront errors by means of a wavefront sensor, controller, and deformable optical element. In astronomy it is used primarily to compensate atmospheric turbulence. See also: Wavefront error
Air gap
Defined axial spacing between two optical surfaces filled with air or another gas. Air gaps are independent design parameters and influence aberrations, thermal behavior, reflection losses, and assembly tolerances.
Defined axial spacing between two optical surfaces filled with air or another gas. Air gaps are independent design parameters and influence aberrations, thermal behavior, reflection losses, and assembly tolerances.
Airy disk
The central bright region of the diffraction pattern produced by an ideal circular aperture. Its size is set by wavelength and Focal ratio and provides a fundamental scale for diffraction-limited imaging.
The central bright region of the diffraction pattern produced by an ideal circular aperture. Its size is set by wavelength and Focal ratio and provides a fundamental scale for diffraction-limited imaging.
Formula: r1 = 1.22 λ N (radius to the first minimum in the image plane)
Anastigmat
Optical system in which astigmatism is largely corrected over the intended image field. Photographic and scientific anastigmats normally also minimize other field aberrations such as coma and field curvature; the term is therefore meaningful only together with field size, spectral range, and image-quality criterion. See also: Astigmatism, Field curvature
Optical system in which astigmatism is largely corrected over the intended image field. Photographic and scientific anastigmats normally also minimize other field aberrations such as coma and field curvature; the term is therefore meaningful only together with field size, spectral range, and image-quality criterion. See also: Astigmatism, Field curvature
Anomalous partial dispersion
Departure of a material's relative partial dispersion from the normal relationship followed by conventional optical glasses. Such materials, including fluorophosphate glasses and crystalline CaF₂, provide additional degrees of freedom for correcting the secondary spectrum. See also: Partial dispersion, Fluorite (CaF₂)
Departure of a material's relative partial dispersion from the normal relationship followed by conventional optical glasses. Such materials, including fluorophosphate glasses and crystalline CaF₂, provide additional degrees of freedom for correcting the secondary spectrum. See also: Partial dispersion, Fluorite (CaF₂)
Anti-reflection coating
A thin-film system applied to optical surfaces to reduce Fresnel reflections and thereby increase Transmission and contrast. Broadband multilayer coatings are matched to the intended spectral range and substrate materials.
A thin-film system applied to optical surfaces to reduce Fresnel reflections and thereby increase Transmission and contrast. Broadband multilayer coatings are matched to the intended spectral range and substrate materials.
Aperture stop
Stop that determines the angular extent of the axial ray bundle and therefore the effective aperture of the system. Its image in object space is the entrance pupil; its image in image space is the exit pupil. See also: Entrance pupil, Exit pupil
Stop that determines the angular extent of the axial ray bundle and therefore the effective aperture of the system. Its image in object space is the entrance pupil; its image in image space is the exit pupil. See also: Entrance pupil, Exit pupil
Schematic: aperture stop and field stop limit different parts of the ray bundle; chief and marginal rays are used for description.
Aplanat / aplanatism
Aplanatism denotes simultaneous correction of spherical aberration and coma for a specified object and image point. Under suitable conditions, an aplanatic system satisfies the Abbe sine condition. See also: Spherical aberration, Coma
Aplanatism denotes simultaneous correction of spherical aberration and coma for a specified object and image point. Under suitable conditions, an aplanatic system satisfies the Abbe sine condition. See also: Spherical aberration, Coma
Apochromat
An optical system with substantially more advanced chromatic correction than an achromat. In the classical Abbe definition, three wavelengths are brought to a common axial focus and the Spherochromatism (Gauss error) is corrected for two widely separated wavelengths. In astronomy, “APO” is sometimes used more broadly; the actual polychromatic image quality remains decisive.
An optical system with substantially more advanced chromatic correction than an achromat. In the classical Abbe definition, three wavelengths are brought to a common axial focus and the Spherochromatism (Gauss error) is corrected for two widely separated wavelengths. In astronomy, “APO” is sometimes used more broadly; the actual polychromatic image quality remains decisive.
Artificial star
Artificial point source used to test, align, and evaluate telescope optics. A source at finite distance does not produce exactly parallel incident rays, so source diameter, distance, and, where applicable, collimator geometry must be chosen and documented appropriately.
Artificial point source used to test, align, and evaluate telescope optics. A source at finite distance does not produce exactly parallel incident rays, so source diameter, distance, and, where applicable, collimator geometry must be chosen and documented appropriately.
Formula: α ≈ d / L
APQ context: For reliable test results, source diameter d, distance L, and any preceding collimator must be documented.
Schematic: a small point source can be used directly at finite distance or through a collimator as an artificial star.
Asphere
An optical surface whose shape departs from a sphere or plane. Aspheres can correct selected aberrations with fewer elements or design degrees of freedom, but place higher demands on manufacturing and metrology.
An optical surface whose shape departs from a sphere or plane. Aspheres can correct selected aberrations with fewer elements or design degrees of freedom, but place higher demands on manufacturing and metrology.
Astigmatism
An off-axis aberration in which sagittal and tangential ray bundles have different focal positions. As a result, an object point is not imaged as a point in a single plane.
An off-axis aberration in which sagittal and tangential ray bundles have different focal positions. As a result, an object point is not imaged as a point in a single plane.
Athermalization
Optomechanical design intended to compensate temperature-induced changes in refractive indices, lengths, and spacings so that a critical system quantity—often the focus position—remains as constant as possible over the specified temperature range. dn/dT, thermal expansion, and the mount are considered together. See also: Coefficient of thermal expansion (CTE)
Optomechanical design intended to compensate temperature-induced changes in refractive indices, lengths, and spacings so that a critical system quantity—often the focus position—remains as constant as possible over the specified temperature range. dn/dT, thermal expansion, and the mount are considered together. See also: Coefficient of thermal expansion (CTE)
Formula: d(BFL) / dT ≈ 0
APQ context: At APQ, athermalization is closely linked to the mechanical compensation of large objectives and their mounts.
Schematic: the aim of athermalization is to greatly reduce focus shift with temperature.
Atmospheric refraction
Refraction of astronomical light in Earth's atmosphere. The effect shifts the apparent direction of an object and is wavelength dependent; at large zenith distances it can produce appreciable atmospheric dispersion.
Refraction of astronomical light in Earth's atmosphere. The effect shifts the apparent direction of an object and is wavelength dependent; at large zenith distances it can produce appreciable atmospheric dispersion.
Autocollimation
Test or alignment method in which a ray bundle emitted by an optical system is reflected by a mirror and returned through the system. This produces a double pass that makes certain angular and imaging errors especially sensitive.
Test or alignment method in which a ray bundle emitted by an optical system is reflected by a mirror and returned through the system. This produces a double pass that makes certain angular and imaging errors especially sensitive.
APQ context: Autocollimation is the basis of the autocollimation telescope and many double-pass test setups.
Schematic: an emitted beam is reflected by a plane mirror and returned through the same optical channel.
Autocollimator / autocollimation telescope (AKF)
Measuring telescope that combines collimator and observing telescope in a common optical path. An illuminated reticle is projected outward through the objective, reflected by a surface, and observed again, allowing very small angular deviations to be measured precisely.
Measuring telescope that combines collimator and observing telescope in a common optical path. An illuminated reticle is projected outward through the objective, reflected by a surface, and observed again, allowing very small angular deviations to be measured precisely.
Schematic: operating principle of an autocollimation telescope with a common transmit and receive path.
B
Back focus
The available mechanical distance from a defined mounting or reference plane to the intended image plane. In photographic systems, the combined optical/mechanical path of adapters, filters, camera, and any corrector must match the specified back focus.
The available mechanical distance from a defined mounting or reference plane to the intended image plane. In photographic systems, the combined optical/mechanical path of adapters, filters, camera, and any corrector must match the specified back focus.
Literature: [WS08]
Birefringence
Property of anisotropic media to have different refractive indices for different polarization directions. An incident ray can therefore split into ordinary and extraordinary components.
Property of anisotropic media to have different refractive indices for different polarization directions. An incident ray can therefore split into ordinary and extraordinary components.
Formula: Δn = ne − no
Blocking filter
An optical filter that selectively suppresses unwanted spectral regions while transmitting the desired band. In an optical system it must be determined whether the filter merely limits the detector band or is an integral part of the intended spectral system design.
An optical filter that selectively suppresses unwanted spectral regions while transmitting the desired band. In an optical system it must be determined whether the filter merely limits the detector band or is an integral part of the intended spectral system design.
C
Centering
Accurate alignment of optical surfaces and elements relative to a reference axis. Decenter and tilt can generate asymmetric aberrations and significantly degrade the calculated performance of a high-quality objective.
Accurate alignment of optical surfaces and elements relative to a reference axis. Decenter and tilt can generate asymmetric aberrations and significantly degrade the calculated performance of a high-quality objective.
Centering error
Departure of optical surfaces or elements from the intended common reference axis. Decenter and tilt can generate asymmetric aberrations, particularly coma and astigmatism. Centering errors are therefore manufacturing, assembly, and alignment quantities.
Departure of optical surfaces or elements from the intended common reference axis. Decenter and tilt can generate asymmetric aberrations, particularly coma and astigmatism. Centering errors are therefore manufacturing, assembly, and alignment quantities.
Central obstruction
Central blockage of the entrance aperture, typically by a secondary mirror and its support in reflecting telescopes. It changes the diffraction distribution and therefore the PSF and MTF even when the outer aperture diameter remains unchanged.
Central blockage of the entrance aperture, typically by a secondary mirror and its support in reflecting telescopes. It changes the diffraction distribution and therefore the PSF and MTF even when the outer aperture diameter remains unchanged.
Formula: ε = d/D; free-area fraction = 1 − ε2
APQ context: Refractive APQ objectives have no central secondary-mirror obstruction; comparisons with reflector systems should take this difference into account.
Schematic: annular free aperture with central obstruction d inside outer diameter D.
Chief ray
Ray from an off-axis object point that passes through the center of the aperture stop. It is a principal construction ray for field position, pupil imaging, telecentricity, and vignetting. See also: Aperture stop, Telecentricity
Ray from an off-axis object point that passes through the center of the aperture stop. It is a principal construction ray for field position, pupil imaging, telecentricity, and vignetting. See also: Aperture stop, Telecentricity
Schematic: the chief ray passes through the center of the aperture stop; marginal rays bound the bundle.
Chromatic aberration
Wavelength dependence of imaging caused by the Dispersion of optical materials. Principal forms are longitudinal chromatic aberration, lateral chromatic aberration, and wavelength-dependent variation of monochromatic aberrations.
Wavelength dependence of imaging caused by the Dispersion of optical materials. Principal forms are longitudinal chromatic aberration, lateral chromatic aberration, and wavelength-dependent variation of monochromatic aberrations.
Chromatic error
General term for chromatic imaging errors. These include longitudinal color, lateral color, and wavelength-dependent changes in monochromatic aberrations. See also Chromatic aberration and Spherochromatism (Gauss error).
General term for chromatic imaging errors. These include longitudinal color, lateral color, and wavelength-dependent changes in monochromatic aberrations. See also Chromatic aberration and Spherochromatism (Gauss error).
Chromatic focal shift
The wavelength-dependent position of the best or paraxial focus. A focal-shift curve s′(λ) directly shows how well an objective is longitudinally color-corrected across its intended spectral range.
The wavelength-dependent position of the best or paraxial focus. A focal-shift curve s′(λ) directly shows how well an objective is longitudinally color-corrected across its intended spectral range.
Formula: Δs'(λ) = s'(λ) − s'(λref)
Schematic: wavelength-dependent position of the paraxial focus.
APQ context: In broadband APQ systems, not only the coincidence of selected reference wavelengths but also the behavior across the entire working range is important.
Clear aperture
The actually usable, mechanically unobstructed diameter or cross-section of an optical element or system. It must be distinguished from the nominal size of a lens blank or cell.
The actually usable, mechanically unobstructed diameter or cross-section of an optical element or system. It must be distinguished from the nominal size of a lens blank or cell.
Coefficient of thermal expansion (CTE)
Material parameter for relative length change with temperature. Different expansion coefficients of glass, crystal, mount, and tube affect spacings, clamping forces, and focus position and are therefore key input quantities for athermalization. See also: Athermalization
Material parameter for relative length change with temperature. Different expansion coefficients of glass, crystal, mount, and tube affect spacings, clamping forces, and focus position and are therefore key input quantities for athermalization. See also: Athermalization
Formula: α = (1/L) · dL/dT
Coherence / coherence length
Measure of the ability of optical waves to maintain a stable phase relationship. Temporal coherence is related to spectral bandwidth and determines coherence length; spatial coherence characterizes correlations across the wavefront.
Measure of the ability of optical waves to maintain a stable phase relationship. Temporal coherence is related to spectral bandwidth and determines coherence length; spatial coherence characterizes correlations across the wavefront.
Formula: Lc ≈ λ² / Δλ (for narrowband radiation, approximately)
Collimation
Alignment of optical elements and axes so that a system reaches its intended geometrical configuration. In a refractor this includes, among other things, Centering, tilt, and the positions of objective, tube, and image plane.
Alignment of optical elements and axes so that a system reaches its intended geometrical configuration. In a refractor this includes, among other things, Centering, tilt, and the positions of objective, tube, and image plane.
Collimator
Optical system that converts light from a source near its focal plane into an approximately parallel beam, or performs the inverse function. Collimators are used in optical testing, angular measurement, and simulation of objects at infinity.
Optical system that converts light from a source near its focal plane into an approximately parallel beam, or performs the inverse function. Collimators are used in optical testing, angular measurement, and simulation of objects at infinity.
Coma
An off-axis aberration in which a point object produces an asymmetric, comet-like point-spread function. Coma is one of the primary monochromatic aberrations and typically increases with field angle.
An off-axis aberration in which a point object produces an asymmetric, comet-like point-spread function. Coma is one of the primary monochromatic aberrations and typically increases with field angle.
Compensating lens cell
A mechanical objective cell whose design influences temperature-induced length and diameter changes so that optically critical relative positions and stress states remain controlled over the intended temperature range.
A mechanical objective cell whose design influences temperature-induced length and diameter changes so that optically critical relative positions and stress states remain controlled over the intended temperature range.
APQ context: Thermal and mechanical compensation is an independent part of the overall system in large, broadband-corrected APQ objectives.
Literature: [H81]
Conic constant
Parameter describing the type and curvature departure of a conic surface from a sphere. Together with vertex curvature it defines rotationally symmetric conic surfaces such as ellipsoids, paraboloids, and hyperboloids.
Parameter describing the type and curvature departure of a conic surface from a sphere. Together with vertex curvature it defines rotationally symmetric conic surfaces such as ellipsoids, paraboloids, and hyperboloids.
Formula: z(r) = r² / [R · (1 + √(1 − (1+K) r²/R²))]
Coudé focus / Coudé optical path
Telescope optical path in which additional mirrors direct the light to a largely stationary focus. Heavy or sensitive instruments such as high-resolution spectrographs can therefore be operated in a fixed location.
Telescope optical path in which additional mirrors direct the light to a largely stationary focus. Heavy or sensitive instruments such as high-resolution spectrographs can therefore be operated in a fixed location.
Crystal
Solid with long-range ordered atomic structure. Optical crystals can be anisotropic and may exhibit birefringence; crystalline CaF₂ is therefore fundamentally different from amorphous optical glass. See also: Fluorite (CaF₂)
Solid with long-range ordered atomic structure. Optical crystals can be anisotropic and may exhibit birefringence; crystalline CaF₂ is therefore fundamentally different from amorphous optical glass. See also: Fluorite (CaF₂)
Cutoff spatial frequency
Highest spatial frequency transferred by an ideal diffraction-limited incoherent imaging system. Above this frequency the MTF is zero. The cutoff therefore depends on wavelength and f-number. See also: Spatial frequency
Highest spatial frequency transferred by an ideal diffraction-limited incoherent imaging system. Above this frequency the MTF is zero. The cutoff therefore depends on wavelength and f-number. See also: Spatial frequency
Formula: νc = 1 / (λ N)
D
Damped least squares (DLS)
Numerical optimization method in which parameter changes are obtained from a locally linearized least-squares problem with additional damping. The damping stabilizes the iteration and limits excessively large steps, making DLS a widely used method in optical design.
Numerical optimization method in which parameter changes are obtained from a locally linearized least-squares problem with additional damping. The damping stabilizes the iteration and limits excessively large steps, making DLS a widely used method in optical design.
Formula: Δp = −(Jᵀ W J + μI)−1 Jᵀ W r
Defocus
Axially symmetric wavefront error caused by displacement of the image plane from the optimum focus position. Defocus changes the point-spread function and is represented as a separate mode in Zernike descriptions.
Axially symmetric wavefront error caused by displacement of the image plane from the optimum focus position. Defocus changes the point-spread function and is represented as a separate mode in Zernike descriptions.
Depth of focus / diffraction depth of focus
Axial range around the nominal image plane within which defocus does not exceed a specified image-quality criterion. For a diffraction-limited system, the permissible depth of focus scales approximately with wavelength λ and the square of the f-number N.
Axial range around the nominal image plane within which defocus does not exceed a specified image-quality criterion. For a diffraction-limited system, the permissible depth of focus scales approximately with wavelength λ and the square of the f-number N.
Formula: Δz ≈ ±2 λ N² (approximation; criterion-dependent)
Dichromat
An optical system in which a chromatic correction condition is satisfied for two selected colors or wavelengths. The term describes a chromatic correction class, not the number of lens elements.
An optical system in which a chromatic correction condition is satisfied for two selected colors or wavelengths. The term describes a chromatic correction class, not the number of lens elements.
Diffraction
Wave-optical phenomenon in which light deviates from purely geometrical propagation at finite apertures and edges. Even with a perfect optical system, diffraction determines the finite size of the Airy disk and therefore the fundamental diffraction limit. See also: Diffraction limit
Wave-optical phenomenon in which light deviates from purely geometrical propagation at finite apertures and edges. Even with a perfect optical system, diffraction determines the finite size of the Airy disk and therefore the fundamental diffraction limit. See also: Diffraction limit
Formula: θR ≈ 1.22 λ / D
Diffraction limit
A condition in which imaging performance is governed primarily by the wave nature of light rather than by geometrical aberrations. “Diffraction limited” is not a complete quality statement unless wavelength, field point, spectral weighting, and criterion are specified.
A condition in which imaging performance is governed primarily by the wave nature of light rather than by geometrical aberrations. “Diffraction limited” is not a complete quality statement unless wavelength, field point, spectral weighting, and criterion are specified.
Dispersion
The wavelength dependence of the Refractive index of an optical material. Normal, anomalous, and partial dispersion are key degrees of freedom in correcting chromatic aberrations.
The wavelength dependence of the Refractive index of an optical material. Normal, anomalous, and partial dispersion are key degrees of freedom in correcting chromatic aberrations.
Distortion
A field-dependent change in image scale that makes straight lines or geometrical proportions appear distorted. Distortion affects geometrical position rather than primarily local point sharpness.
A field-dependent change in image scale that makes straight lines or geometrical proportions appear distorted. Distortion affects geometrical position rather than primarily local point sharpness.
dn/dT
Temperature coefficient of the refractive index of an optical material. It specifies how strongly n changes with temperature and, together with thermal length change, is a key parameter in athermalization. See also: Refractive index, Athermalization
Temperature coefficient of the refractive index of an optical material. It specifies how strongly n changes with temperature and, together with thermal length change, is a key parameter in athermalization. See also: Refractive index, Athermalization
Formula: dn/dT = ∂n / ∂T
Double-pass autocollimation (DPAC)
Test method in which light passes twice through the optical system under test and returns to the source after reflection from a high-quality flat mirror. The double pass increases the sensitivity to certain wavefront errors relative to a single pass; the setup, reference surface, and evaluation method must therefore be stated unambiguously.
Test method in which light passes twice through the optical system under test and returns to the source after reflection from a high-quality flat mirror. The double pass increases the sensitivity to certain wavefront errors relative to a single pass; the setup, reference surface, and evaluation method must therefore be stated unambiguously.
APQ context: DPAC is particularly suitable for qualitative and quantitative testing of complete objectives, but it does not replace a description of the actual test geometry.
Doublet
A term widely used in astronomy for an objective or lens group consisting of two optical elements. “Doublet” describes element count only; it does not imply a particular chromatic correction class.
A term widely used in astronomy for an objective or lens group consisting of two optical elements. “Doublet” describes element count only; it does not imply a particular chromatic correction class.
E
ED glass
A collective term for optical glasses with low or special dispersion (“Extra-low Dispersion”). The designation alone does not define the performance of an objective; the specific glass, mating glasses, and complete optical design are decisive. See also: Dispersion
A collective term for optical glasses with low or special dispersion (“Extra-low Dispersion”). The designation alone does not define the performance of an objective; the specific glass, mating glasses, and complete optical design are decisive. See also: Dispersion
Encircled Energy
The fraction of the total energy of a point-spread function contained within a circle of radius r around the image centroid. It combines diffraction and aberration effects and is particularly useful for detector and survey applications.
The fraction of the total energy of a point-spread function contained within a circle of radius r around the image centroid. It combines diffraction and aberration effects and is particularly useful for detector and survey applications.
Formula: EE(r) = [∫0r 2πρ I(ρ) dρ] / [∫0∞ 2πρ I(ρ) dρ]
Entrance pupil
The image of the aperture stop as seen from object space. In many telescopes it approximately coincides with the clear objective aperture; its position and size affect ray bundles, Vignetting, and Telecentricity.
The image of the aperture stop as seen from object space. In many telescopes it approximately coincides with the clear objective aperture; its position and size affect ray bundles, Vignetting, and Telecentricity.
Exit pupil
The image of the aperture stop formed by the image-side portion of an optical system. In an astronomical telescope, its diameter is approximately the objective diameter divided by the Magnification.
The image of the aperture stop formed by the image-side portion of an optical system. In an astronomical telescope, its diameter is approximately the objective diameter divided by the Magnification.
Formula: dA = D / V = fEP / N
F
Fermat's principle
Fundamental principle of geometrical optics stating that the actual light path between two points has stationary optical path length. The laws of reflection and refraction can be derived from it.
Fundamental principle of geometrical optics stating that the actual light path between two points has stationary optical path length. The laws of reflection and refraction can be derived from it.
Field angle
Angle of an object point, or of its chief ray, with respect to the optical axis. Field angle is a fundamental specification for evaluating wide-field systems and must be stated for spot diagrams, MTF, and other image-quality criteria. See also: Chief ray
Angle of an object point, or of its chief ray, with respect to the optical axis. Field angle is a fundamental specification for evaluating wide-field systems and must be stated for spot diagrams, MTF, and other image-quality criteria. See also: Chief ray
Formula: θ ≈ arctan(y′ / f)
Field corrector
An optical correction group designed to improve imaging away from the field center. A field corrector can reduce Field curvature, Astigmatism, and, depending on the design, additional off-axis aberrations; its function is therefore broader than simple field flattening.
An optical correction group designed to improve imaging away from the field center. A field corrector can reduce Field curvature, Astigmatism, and, depending on the design, additional off-axis aberrations; its function is therefore broader than simple field flattening.
Schematic: a field corrector reduces field curvature and can simultaneously correct additional field aberrations.
APQ context: APQ uses “field corrector” as the general term for corresponding correction optics.
Field curvature
An Aberration in which the best image surface is curved rather than flat. Without correction, a flat camera or detector cannot therefore be optimally focused at the center and edge at the same time.
An Aberration in which the best image surface is curved rather than flat. Without correction, a flat camera or detector cannot therefore be optimally focused at the center and edge at the same time.
Field of view
The angular range in object space covered by the optical system or detector. For small angles, field of view is approximately proportional to sensor size and inversely proportional to Focal length.
The angular range in object space covered by the optical system or detector. For small angles, field of view is approximately proportional to sensor size and inversely proportional to Focal length.
Formula: Ω ≈ 2 arctan [dsens / (2 f)]
Field stop
Stop that limits the extent of the usable object or image field. Unlike the aperture stop, it primarily determines the field rather than the aperture of an axial ray bundle. See also: Aperture stop
Stop that limits the extent of the usable object or image field. Unlike the aperture stop, it primarily determines the field rather than the aperture of an axial ray bundle. See also: Aperture stop
Schematic: field stop and aperture stop perform different functions in an optical system.
Fizeau interferometer
Interferometric test arrangement in which reference and test waves are generated at closely spaced optical surfaces or by means of a reference optic. Fizeau interferometers are widely used in precision optics because they measure surface and wavefront deviations with high accuracy.
Interferometric test arrangement in which reference and test waves are generated at closely spaced optical surfaces or by means of a reference optic. Fizeau interferometers are widely used in precision optics because they measure surface and wavefront deviations with high accuracy.
Formula: Δφ = 2π · OPD / λ
Fluorite (CaF₂)
Crystalline calcium fluoride with very low Dispersion, pronounced anomalous partial dispersion, and high Transmission over a broad spectral range. Optical CaF₂ is a crystal, not an optical glass.
Crystalline calcium fluoride with very low Dispersion, pronounced anomalous partial dispersion, and high Transmission over a broad spectral range. Optical CaF₂ is a crystal, not an optical glass.
APQ context: CaF₂ is a key material in selected APQ Fluorite Polychromats.
Fluorophosphate glasses
Special optical glasses containing fluoride and phosphate constituents that can exhibit very low Dispersion and anomalous partial dispersion. In suitable combinations they enable highly advanced chromatic correction.
Special optical glasses containing fluoride and phosphate constituents that can exhibit very low Dispersion and anomalous partial dispersion. In suitable combinations they enable highly advanced chromatic correction.
Focal distance / back focal distance
Axial distance from a focus or ray intersection to a specified reference surface. This distance is not identical to focal length because it depends on the locations of the principal planes and on the selected mechanical reference. See also: Focal length
Axial distance from a focus or ray intersection to a specified reference surface. This distance is not identical to focal length because it depends on the locations of the principal planes and on the selected mechanical reference. See also: Focal length
Focal length
A paraxial characteristic of an optical system that determines, among other things, image scale and Field of view. For objects at infinity, it is the distance from the image-side principal plane to the paraxial focus.
A paraxial characteristic of an optical system that determines, among other things, image scale and Field of view. For objects at infinity, it is the distance from the image-side principal plane to the paraxial focus.
Focal ratio
The ratio of Focal length f to effective clear aperture D. A smaller number denotes a “faster” system with a larger ray angle and greater demands on aberration correction.
The ratio of Focal length f to effective clear aperture D. A smaller number denotes a “faster” system with a larger ray angle and greater demands on aberration correction.
Formula: N = f / D
Focal reducer-corrector
An optical group that reduces the effective Focal length and therefore the Focal ratio while simultaneously correcting specified aberrations. Reduction alone does not make a high-quality corrector; field size, spectral range, and sensor position must be part of the design.
An optical group that reduces the effective Focal length and therefore the Focal ratio while simultaneously correcting specified aberrations. Reduction alone does not make a high-quality corrector; field size, spectral range, and sensor position must be part of the design.
Formula: k = fnew / fsys; Nnew = k Nsys
APQ context: APQ therefore deliberately uses the term “focal reducer-corrector” rather than the shortened “reducer.”
Focus shift
A shift of the optimum focus caused by wavelength, temperature, filters, mechanical tolerances, or other influences. Chromatic focus shift is a measure of longitudinal color; thermal focus shift describes temperature-induced focus change.
A shift of the optimum focus caused by wavelength, temperature, filters, mechanical tolerances, or other influences. Chromatic focus shift is a measure of longitudinal color; thermal focus shift describes temperature-induced focus change.
Foucault knife-edge test
Classical test in which a knife edge near focus blocks portions of the returning beam. Brightness distributions or zonal measurements permit conclusions about form errors of rotationally symmetric optical surfaces.
Classical test in which a knife edge near focus blocks portions of the returning beam. Brightness distributions or zonal measurements permit conclusions about form errors of rotationally symmetric optical surfaces.
Fourier transform
Mathematical transformation between the spatial and spatial-frequency domains. In linear imaging theory it connects, among other quantities, the PSF and the OTF. See also: Point Spread Function (PSF), Optical Transfer Function (OTF)
Mathematical transformation between the spatial and spatial-frequency domains. In linear imaging theory it connects, among other quantities, the PSF and the OTF. See also: Point Spread Function (PSF), Optical Transfer Function (OTF)
Formula: F(ν) = ∫ f(x) · e−i2πνx dx
Fraunhofer lines
Historical designation for prominent absorption lines in the solar spectrum. Lines such as C, d, F, F′, and C′ are traditionally used as reference wavelengths for Abbe numbers, refractive indices, and chromatic correction.
Historical designation for prominent absorption lines in the solar spectrum. Lines such as C, d, F, F′, and C′ are traditionally used as reference wavelengths for Abbe numbers, refractive indices, and chromatic correction.
Fresnel and Fraunhofer diffraction
Two approximation regimes of diffraction. Fresnel diffraction describes finite propagation distances with curved wavefronts; Fraunhofer diffraction describes the far-field case or its realization in a focal plane.
Two approximation regimes of diffraction. Fresnel diffraction describes finite propagation distances with curved wavefronts; Fraunhofer diffraction describes the far-field case or its realization in a focal plane.
Fresnel equations
Relations for the amplitude and power of reflected and transmitted light at an interface. The coefficients depend on refractive indices, angle of incidence, and polarization and form the basis for evaluating uncoated interfaces and optical coatings.
Relations for the amplitude and power of reflected and transmitted light at an interface. The coefficients depend on refractive indices, angle of incidence, and polarization and form the basis for evaluating uncoated interfaces and optical coatings.
Formula: R(0°) = |(n₁ − n₂)/(n₁ + n₂)|²
Fused silica
High-purity amorphous silicon dioxide with good UV transmission, high thermal stability, and relatively low thermal expansion. Unlike crystalline quartz, fused silica is isotropic and is classified as an optical glass.
High-purity amorphous silicon dioxide with good UV transmission, high thermal stability, and relatively low thermal expansion. Unlike crystalline quartz, fused silica is isotropic and is classified as an optical glass.
G
Geometrical optics
Description of light propagation using rays. It is appropriate when wavelength effects such as diffraction and interference are negligible for the problem under consideration and forms the basis of paraxial imaging, ray tracing, and classical aberration theory.
Description of light propagation using rays. It is appropriate when wavelength effects such as diffraction and interference are negligible for the problem under consideration and forms the basis of paraxial imaging, ray tracing, and classical aberration theory.
Grinding, lapping, and polishing
Fundamental processing stages in precision optics. Grinding establishes geometry and removes material; lapping or fine grinding reduces form error and subsurface damage; polishing produces the optically active surface with very low roughness. Modern processes such as MRF supplement this chain deterministically. See also: Magnetorheological Finishing (MRF)
Fundamental processing stages in precision optics. Grinding establishes geometry and removes material; lapping or fine grinding reduces form error and subsurface damage; polishing produces the optically active surface with very low roughness. Modern processes such as MRF supplement this chain deterministically. See also: Magnetorheological Finishing (MRF)
H
Hartmann test
Wavefront test in which a mask with multiple openings divides the aperture into sub-bundles. The measured positions of the resulting spots at one or more planes provide local ray slopes and thereby information about the wavefront. See also: Wavefront error, Shack-Hartmann wavefront sensor (Hartmann-Shack sensor)
Wavefront test in which a mask with multiple openings divides the aperture into sub-bundles. The measured positions of the resulting spots at one or more planes provide local ray slopes and thereby information about the wavefront. See also: Wavefront error, Shack-Hartmann wavefront sensor (Hartmann-Shack sensor)
Formula: ∂W/∂x ≈ Δx / L
Schematic: a Hartmann mask divides the aperture into sub-bundles; their spot positions contain local wavefront-slope information.
Herzberger dispersion formula
Empirical dispersion formula for representing the wavelength dependence of refractive index over a broad spectral range. It is particularly useful in broadband chromatic design and in analyses of superachromatic systems.
Empirical dispersion formula for representing the wavelength dependence of refractive index over a broad spectral range. It is particularly useful in broadband chromatic design and in analyses of superachromatic systems.
Huygens' principle
Wave-optical principle according to which every point on a wavefront can be regarded as the source of secondary wavelets and the new wavefront is the envelope of those wavelets. It provides an intuitive basis for propagation and diffraction.
Wave-optical principle according to which every point on a wavefront can be regarded as the source of secondary wavelets and the new wavefront is the envelope of those wavelets. It provides an intuitive basis for propagation and diffraction.
I
Illumination / relative illumination
Field-dependent illuminance or relative signal level in the image plane. It is affected by natural angular dependencies, pupil imaging, and vignetting and must be distinguished from image quality itself. See also: Vignetting
Field-dependent illuminance or relative signal level in the image plane. It is affected by natural angular dependencies, pupil imaging, and vignetting and must be distinguished from image quality itself. See also: Vignetting
Formula: Erel(θ) = E(θ) / E(0)
Image contrast / contrast transfer
Image contrast describes the brightness difference between bright and dark image structures. The frequency-dependent contrast transfer of a linear imaging system is described by the modulation transfer function (MTF). See also: Modulation Transfer Function (MTF)
Image contrast describes the brightness difference between bright and dark image structures. The frequency-dependent contrast transfer of a linear imaging system is described by the modulation transfer function (MTF). See also: Modulation Transfer Function (MTF)
Formula: C = (Imax − Imin) / (Imax + Imin)
Image field
The region of the image plane over which an optical system provides usable image quality. It may be stated as a linear image dimension, image circle, or angular range in object space.
The region of the image plane over which an optical system provides usable image quality. It may be stated as a linear image dimension, image circle, or angular range in object space.
Interference
Superposition of coherent optical waves, producing spatial or temporal intensity modulation that depends on their phase difference. Interference is the operating principle of many optical metrology methods and filters.
Superposition of coherent optical waves, producing spatial or temporal intensity modulation that depends on their phase difference. Interference is the operating principle of many optical metrology methods and filters.
Formula: I = I₁ + I₂ + 2√(I₁I₂) cos Δφ
Interference filter
Thin-film optical filter whose spectral transmission is produced by constructive and destructive interference in one or more dielectric layers. Center wavelength and passband generally depend on angle of incidence and refractive index.
Thin-film optical filter whose spectral transmission is produced by constructive and destructive interference in one or more dielectric layers. Center wavelength and passband generally depend on angle of incidence and refractive index.
APQ context: With fast beams and large image fields, the angular dependence of interference filters must be evaluated together with the optics.
Interferogram
Recorded interference pattern containing information about the optical path difference between test and reference wavefronts. Quantitative evaluation can yield surface form, wavefront error, or derived aberration coefficients. See also: Wavefront
Recorded interference pattern containing information about the optical path difference between test and reference wavefronts. Quantitative evaluation can yield surface form, wavefront error, or derived aberration coefficients. See also: Wavefront
Formula: Δφ = 2π · OPD / λ
Interferometry
A measurement method in which the Wavefront under test is superimposed on a reference wavefront. The resulting interference pattern permits highly accurate determination of form, surface, and wavefront deviations.
A measurement method in which the Wavefront under test is superimposed on a reference wavefront. The resulting interference pattern permits highly accurate determination of form, surface, and wavefront deviations.
Isoplanatism / isoplanatic field
Condition under which the point-spread function or wavefront distortion can be regarded as effectively invariant over a limited field. In atmospheric imaging the isoplanatic angle specifies the angular region over which approximately the same turbulence correction is valid.
Condition under which the point-spread function or wavefront distortion can be regarded as effectively invariant over a limited field. In atmospheric imaging the isoplanatic angle specifies the angular region over which approximately the same turbulence correction is valid.
K
Kinematic mounting
Mounting principle that constrains the six rigid-body degrees of freedom in a defined, minimally overconstrained manner. Proper kinematic mounting reduces stress and makes positioning reproducible under adjustment, assembly, and temperature changes.
Mounting principle that constrains the six rigid-body degrees of freedom in a defined, minimally overconstrained manner. Proper kinematic mounting reduces stress and makes positioning reproducible under adjustment, assembly, and temperature changes.
APQ context: Kinematic principles are particularly relevant for adjustable and temperature-sensitive APQ assemblies.
Literature: [Y08]
L
Lateral chromatic aberration
Transverse chromatic aberration in which magnification or the image height of an off-axis object point depends on wavelength. This produces wavelength-dependent lateral shifts across the image field.
Transverse chromatic aberration in which magnification or the image height of an off-axis object point depends on wavelength. This produces wavelength-dependent lateral shifts across the image field.
Lateral magnification
Ratio of image size to object size in paraxial imaging. Depending on the sign convention, the sign indicates the orientation of the image.
Ratio of image size to object size in paraxial imaging. Depending on the sign convention, the sign indicates the orientation of the image.
Formula: β = y′/y = −b/g
Longitudinal chromatic aberration
Chromatic aberration in which different wavelengths have different axial focal positions. Its behavior can, for example, be described by the chromatic focal shift. See also: Chromatic focal shift
Chromatic aberration in which different wavelengths have different axial focal positions. Its behavior can, for example, be described by the chromatic focal shift. See also: Chromatic focal shift
Low-stress optical mount
Mounting concept that holds optical components securely without introducing impermissible stresses, and resulting form or refractive-index changes, through assembly forces, temperature changes, or mismatched expansion coefficients. Contact geometry, clamping force, and material pairing are part of the optical system design.
Mounting concept that holds optical components securely without introducing impermissible stresses, and resulting form or refractive-index changes, through assembly forces, temperature changes, or mismatched expansion coefficients. Contact geometry, clamping force, and material pairing are part of the optical system design.
APQ context: For large high-precision APQ objectives, low-stress mounting together with thermal compensation is essential.
Literature: [Y08]
M
Magnetorheological Finishing (MRF)
A deterministic fine-polishing process in which a magnetically controlled polishing suspension forms a locally defined removal tool. MRF is suitable for targeted correction of residual figure errors on high-quality optical surfaces.
A deterministic fine-polishing process in which a magnetically controlled polishing suspension forms a locally defined removal tool. MRF is suitable for targeted correction of residual figure errors on high-quality optical surfaces.
APQ context: MRF is particularly useful for high-precision surface correction when conventional full-aperture polishing reaches its limits.
Literature: [M07]
Magnification
In visual astronomical observation, the ratio of telescope Focal length to eyepiece focal length. Useful magnification is also limited by aperture, Seeing, contrast, and the observed object.
In visual astronomical observation, the ratio of telescope Focal length to eyepiece focal length. Useful magnification is also limited by aperture, Seeing, contrast, and the observed object.
Formula: V = ftel / fEP
Literature: [S00]
Marginal ray
Ray from an object point that touches the edge of the effective aperture stop. Marginal rays bound a ray bundle and, together with the chief ray, are important construction rays for aperture, field, and vignetting. See also: Aperture stop, Chief ray
Ray from an object point that touches the edge of the effective aperture stop. Marginal rays bound a ray bundle and, together with the chief ray, are important construction rays for aperture, field, and vignetting. See also: Aperture stop, Chief ray
Schematic: marginal rays bound the bundle; the chief ray passes through the center of the aperture stop.
Material inhomogeneity
Spatial variation of optical material properties within a component, especially refractive index n. Refractive-index inhomogeneity can generate wavefront errors even when the geometrical surface form is correct. See also: Refractive index
Spatial variation of optical material properties within a component, especially refractive index n. Refractive-index inhomogeneity can generate wavefront errors even when the geometrical surface form is correct. See also: Refractive index
Formula: Δn = n(x,y,z) − nref
Measurement uncertainty
Parameter describing the range of values reasonably associated with a measurement result after relevant uncertainty contributions are taken into account. High-precision statements about wavefront, centering, or surface form are meaningful only with stated test conditions and uncertainty considerations.
Parameter describing the range of values reasonably associated with a measurement result after relevant uncertainty contributions are taken into account. High-precision statements about wavefront, centering, or surface form are meaningful only with stated test conditions and uncertainty considerations.
Formula: uc = √∑(ci ui)2
Melt data
Measured optical properties of a specific glass melt, especially refractive indices at defined wavelengths and derived dispersion data. They can differ slightly from nominal catalog values and form the basis for a melt fit in highly corrected designs. See also: Melt fit
Measured optical properties of a specific glass melt, especially refractive indices at defined wavelengths and derived dispersion data. They can differ slightly from nominal catalog values and form the basis for a melt fit in highly corrected designs. See also: Melt fit
Melt fit
Adjustment or re-optimization of an optical design to the actually measured melt data of the available glass batches. This allows small deviations of real refractive indices and dispersions from catalog values to be included in highly corrected systems. See also: Melt data
Adjustment or re-optimization of an optical design to the actually measured melt data of the available glass batches. This allows small deviations of real refractive indices and dispersions from catalog values to be included in highly corrected systems. See also: Melt data
APQ context: In broadband-corrected high-performance objectives, melt fitting can make an important contribution to preserving the calculated chromatic correction in actual production.
Merit function
Scalar function that combines selected image-quality targets, design constraints, and weights into a numerical quantity for optimization. The optimum is sought by varying selected system parameters while respecting applicable bounds and constraints.
Scalar function that combines selected image-quality targets, design constraints, and weights into a numerical quantity for optimization. The optimum is sought by varying selected system parameters while respecting applicable bounds and constraints.
Formula: MF = ∑ wi [qi − qi,target]2
Modulation Transfer Function (MTF)
The magnitude of the Optical Transfer Function. It describes how much contrast of a sinusoidal object pattern is retained in the image at a given spatial frequency. An MTF specification is unambiguous only together with wavelength or spectral weighting, field point, focus, and reference scale.
The magnitude of the Optical Transfer Function. It describes how much contrast of a sinusoidal object pattern is retained in the image at a given spatial frequency. An MTF specification is unambiguous only together with wavelength or spectral weighting, field point, focus, and reference scale.
Formula: MTF(ν) = |OTF(ν)|
Schematic: the MTF describes transferred contrast as a function of spatial frequency.
Monochromat
Optical system whose correction or evaluation is referenced to a single wavelength or a very narrow spectral band. The term denotes a spectral correction condition, not the number of lens elements.
Optical system whose correction or evaluation is referenced to a single wavelength or a very narrow spectral band. The term denotes a spectral correction condition, not the number of lens elements.
Literature: [HR84]
Multiplet
Multi-element optical system comprising several lens elements or groups. Like doublet, triplet, or quadruplet, the term describes structural complexity and is distinct from a chromatic correction class.
Multi-element optical system comprising several lens elements or groups. Like doublet, triplet, or quadruplet, the term describes structural complexity and is distinct from a chromatic correction class.
Literature: [HR84]
N
Numerical aperture
A dimensionless measure of the opening angle of a ray bundle. In air and for small angles, it is approximately related to the Focal ratio of an imaging system.
A dimensionless measure of the opening angle of a ray bundle. In air and for small angles, it is approximately related to the Focal ratio of an imaging system.
Formula: NA = n sin u; for small angles in air: NA ≈ 1/(2N)
Nyquist frequency
One half of the sampling frequency of a discrete sampling system. Spatial frequencies above the Nyquist frequency can appear as lower frequencies without suitable prefiltering (aliasing); Nyquist frequency therefore links optical MTF and detector pixel pitch.
One half of the sampling frequency of a discrete sampling system. Spatial frequencies above the Nyquist frequency can appear as lower frequencies without suitable prefiltering (aliasing); Nyquist frequency therefore links optical MTF and detector pixel pitch.
Formula: νN = 1 / (2p)
Schematic: pixel pitch p sets the Nyquist limit of spatial sampling.
O
Oil coupling
Coupling adjacent lens surfaces with a thin optical-fluid layer. This can strongly reduce reflections at internal interfaces and provide design freedom; material compatibility, long-term stability, and thermomechanical behavior are part of the design.
Coupling adjacent lens surfaces with a thin optical-fluid layer. This can strongly reduce reflections at internal interfaces and provide design freedom; material compatibility, long-term stability, and thermomechanical behavior are part of the design.
APQ context: Oil coupling is a characteristic construction feature of several high-grade APQ objective designs.
Optical glass
Amorphous homogeneous material with controlled optical and thermal properties for manufacturing optical components. Important properties include refractive index, dispersion, transmission, homogeneity, and thermal behavior. Crystalline CaF₂ is not an optical glass. See also: Refractive index, Dispersion
Amorphous homogeneous material with controlled optical and thermal properties for manufacturing optical components. Important properties include refractive index, dispersion, transmission, homogeneity, and thermal behavior. Crystalline CaF₂ is not an optical glass. See also: Refractive index, Dispersion
Optical tolerancing
Specification of permissible deviations of design parameters and analysis of their effect on system performance. Typical variables include radii, thicknesses, spacings, refractive indices, decenter, tilt, and assembly errors. Tolerancing connects the nominal design with a realistically manufacturable system.
Specification of permissible deviations of design parameters and analysis of their effect on system performance. Typical variables include radii, thicknesses, spacings, refractive indices, decenter, tilt, and assembly errors. Tolerancing connects the nominal design with a realistically manufacturable system.
Optical Transfer Function (OTF)
A complex function describing the amplitude and phase transfer of a linear, shift-invariant imaging system as a function of spatial frequency. Its magnitude is the Modulation Transfer Function (MTF); its phase is called the Phase Transfer Function (PTF).
A complex function describing the amplitude and phase transfer of a linear, shift-invariant imaging system as a function of spatial frequency. Its magnitude is the Modulation Transfer Function (MTF); its phase is called the Phase Transfer Function (PTF).
Formula: OTF(ν) = FT{PSF} / FT{PSF}|ν=0
P
Paraxial region / Gaussian optics
Approximation regime of geometrical optics for small ray heights and small angles to the optical axis. In this region sin u ≈ tan u ≈ u; focal lengths, principal positions, and paraxial focal distances are described to first order.
Approximation regime of geometrical optics for small ray heights and small angles to the optical axis. In this region sin u ≈ tan u ≈ u; focal lengths, principal positions, and paraxial focal distances are described to first order.
Formula: sin u ≈ tan u ≈ u
Partial dispersion
Measure of the refractive-index difference of a material between two selected spectral lines. Relative partial dispersions normalize this difference to a reference dispersion and permit comparison of glasses independent of their absolute dispersion.
Measure of the refractive-index difference of a material between two selected spectral lines. Relative partial dispersions normalize this difference to a reference dispersion and permit comparison of glasses independent of their absolute dispersion.
Formula: Px,y = (nx − ny) / (nF − nC)
Petzval sum
A paraxial quantity describing image-field curvature as determined by refractive powers and refractive indices in an optical system. A suitable distribution of positive and negative optical powers can reduce or compensate Petzval curvature.
A paraxial quantity describing image-field curvature as determined by refractive powers and refractive indices in an optical system. A suitable distribution of positive and negative optical powers can reduce or compensate Petzval curvature.
Phase transfer function (PTF)
Phase of the complex optical transfer function (OTF). Whereas the MTF describes the magnitude of contrast transfer, the PTF describes spatial-frequency-dependent phase shifts introduced by the imaging system. See also: Optical Transfer Function (OTF)
Phase of the complex optical transfer function (OTF). Whereas the MTF describes the magnitude of contrast transfer, the PTF describes spatial-frequency-dependent phase shifts introduced by the imaging system. See also: Optical Transfer Function (OTF)
Formula: OTF(ν) = MTF(ν) · ei·PTF(ν)
Pixel scale
Angular extent on the sky imaged onto one detector pixel. Pixel scale is determined by pixel size and effective focal length and is essential for matching seeing, optical resolution, and sampling. See also: Focal length, Sampling
Angular extent on the sky imaged onto one detector pixel. Pixel scale is determined by pixel size and effective focal length and is essential for matching seeing, optical resolution, and sampling. See also: Focal length, Sampling
Formula: s [arcsec/Pixel] ≈ 206265 · p / f
Plane-parallel plate
Optical element with two ideally parallel plane surfaces. At normal incidence, a plate of thickness t and refractive index n produces an axial focus shift; at oblique incidence, lateral beam displacement and additional aberration contributions occur.
Optical element with two ideally parallel plane surfaces. At normal incidence, a plate of thickness t and refractive index n produces an axial focus shift; at oblique incidence, lateral beam displacement and additional aberration contributions occur.
Formula: Δs ≈ t · (1 − 1/n) (paraxial, in air)
Point Spread Function (PSF)
The two-dimensional intensity distribution of the image of an ideal point source. The PSF contains the combined effects of diffraction, aberrations, and other system influences; its Fourier transform is linked to the Optical Transfer Function (OTF).
The two-dimensional intensity distribution of the image of an ideal point source. The PSF contains the combined effects of diffraction, aberrations, and other system influences; its Fourier transform is linked to the Optical Transfer Function (OTF).
Polarization
Description of the time-dependent orientation of the electric-field vector of a light wave. Linear, circular, and elliptical polarization are common states; reflection, birefringence, and stress in optical materials can alter the polarization state.
Description of the time-dependent orientation of the electric-field vector of a light wave. Linear, circular, and elliptical polarization are common states; reflection, birefringence, and stress in optical materials can alter the polarization state.
Polychromat
An optical system with advanced chromatic correction across several colors or a broad spectral range. In Haferkorn’s terminology, polychromatism denotes a design extending beyond simpler chromatic correction conditions. Its actual quality must always be evaluated over the specified spectral range and with relevant image-quality criteria.
An optical system with advanced chromatic correction across several colors or a broad spectral range. In Haferkorn’s terminology, polychromatism denotes a design extending beyond simpler chromatic correction conditions. Its actual quality must always be evaluated over the specified spectral range and with relevant image-quality criteria.
APQ context: APQ uses “Polychromat” for its broadband-corrected objective systems; the term must not be equated with the number of lens elements.
Principal planes and principal points
Reference planes and points of first-order optics for a centered optical system. They permit a compound system to be represented by equivalent first-order quantities and define, among other things, where effective focal lengths and conjugate distances are referenced.
Reference planes and points of first-order optics for a centered optical system. They permit a compound system to be represented by equivalent first-order quantities and define, among other things, where effective focal lengths and conjugate distances are referenced.
Q
Quadruplet
A term widely used in astronomy for an objective or lens group consisting of four optical elements. “Quadruplet” describes the element count and does not automatically define the chromatic correction class.
A term widely used in astronomy for an objective or lens group consisting of four optical elements. “Quadruplet” describes the element count and does not automatically define the chromatic correction class.
APQ context: APQ Fluorite Quadruplet Polychromats combine four elements with broadband chromatic and geometrical correction.
Literature: [KJ10]
Quantum efficiency
The wavelength-dependent fraction of photons incident on a detector that produce registered photoelectrons or charge carriers. System performance requires QE to be considered together with Transmission, pixel size, read noise, and dark current.
The wavelength-dependent fraction of photons incident on a detector that produce registered photoelectrons or charge carriers. System performance requires QE to be considered together with Transmission, pixel size, read noise, and dark current.
Formula: η(λ) = Ne− / Nph
Schematic: detector quantum efficiency depends on wavelength.
Literature: [S00]
R
Rayleigh quarter-wave criterion
Historical approximation according to which a maximum optical path difference of about λ/4 is often taken as a boundary for approximately diffraction-limited imaging. It must not be confused with the Rayleigh resolution criterion.
Historical approximation according to which a maximum optical path difference of about λ/4 is often taken as a boundary for approximately diffraction-limited imaging. It must not be confused with the Rayleigh resolution criterion.
Formula: PV(OPD) ≲ λ / 4
Reflectance
Ratio of reflected to incident optical radiant power at a surface or system. It depends on wavelength, angle of incidence, polarization, refractive indices, and coatings.
Ratio of reflected to incident optical radiant power at a surface or system. It depends on wavelength, angle of incidence, polarization, refractive indices, and coatings.
Formula: R(λ) = Pref(λ) / Pin(λ)
Refractive index
The ratio of the speed of light in vacuum to the phase velocity in a material. Refractive index depends on wavelength and temperature; its spectral variation is the basis of Dispersion.
The ratio of the speed of light in vacuum to the phase velocity in a material. Refractive index depends on wavelength and temperature; its spectral variation is the basis of Dispersion.
Formula: n(λ) = c / vph(λ)
Residual spectrum
Wavelength-dependent focal or imaging error remaining after chromatic correction. The shape and magnitude of the residual spectrum are decisive for how well an achromat, apochromat, superachromat, or polychromat is corrected over its intended spectral range.
Wavelength-dependent focal or imaging error remaining after chromatic correction. The shape and magnitude of the residual spectrum are decisive for how well an achromat, apochromat, superachromat, or polychromat is corrected over its intended spectral range.
Resolving power
The ability of an optical system to image closely spaced object structures separately. For an ideal circular aperture, the Rayleigh criterion describes the angular separation of two equally bright point sources. In astronomical practice, Seeing, contrast, detector sampling, and Signal-to-noise ratio can be more limiting than diffraction alone.
The ability of an optical system to image closely spaced object structures separately. For an ideal circular aperture, the Rayleigh criterion describes the angular separation of two equally bright point sources. In astronomical practice, Seeing, contrast, detector sampling, and Signal-to-noise ratio can be more limiting than diffraction alone.
Formula: θR = 1.22 λ / D
Schematic: separation of two diffraction patterns according to the Rayleigh criterion.
RMS wavefront error
The root-mean-square deviation of a real Wavefront from a selected reference wavefront after defined terms such as tilt and defocus have been removed. RMS and peak-to-valley (PV) values are not directly interchangeable.
The root-mean-square deviation of a real Wavefront from a selected reference wavefront after defined terms such as tilt and defocus have been removed. RMS and peak-to-valley (PV) values are not directly interchangeable.
Formula: σW = √[(1/A) ∫A (W − W̄)2 dA]
S
Sagittal and tangential planes
Two mutually perpendicular reference planes for off-axis ray bundles. The tangential or meridional plane contains the optical axis and chief ray; the sagittal plane is perpendicular to it. Different focal positions in the two planes characterize astigmatism. See also: Chief ray, Astigmatism
Two mutually perpendicular reference planes for off-axis ray bundles. The tangential or meridional plane contains the optical axis and chief ray; the sagittal plane is perpendicular to it. Different focal positions in the two planes characterize astigmatism. See also: Chief ray, Astigmatism
Schematic: sagittal and tangential/meridional planes of an off-axis ray bundle.
Sampling
Discrete acquisition of a continuous image distribution by pixels. For digital imaging, the sampling must match the highest relevant spatial frequency; sampling that is too coarse causes aliasing and can make fine structures appear distorted. See also: Spatial frequency
Discrete acquisition of a continuous image distribution by pixels. For digital imaging, the sampling must match the highest relevant spatial frequency; sampling that is too coarse causes aliasing and can make fine structures appear distorted. See also: Spatial frequency
Formula: νN = 1 / (2p)
Schematic: a spatial frequency is sampled at discrete pixel positions.
Secondary spectrum
The residual longitudinal chromatic aberration of an achromatically corrected system between or outside the reference wavelengths used for achromatization. Anomalous partial dispersion and additional design degrees of freedom can reduce it substantially.
The residual longitudinal chromatic aberration of an achromatically corrected system between or outside the reference wavelengths used for achromatization. Anomalous partial dispersion and additional design degrees of freedom can reduce it substantially.
Seeing
Time-varying image blur and image motion caused by atmospheric turbulence. In ground-based astronomy, seeing often limits the practically achievable Resolving power more strongly than the telescope’s diffraction limit.
Time-varying image blur and image motion caused by atmospheric turbulence. In ground-based astronomy, seeing often limits the practically achievable Resolving power more strongly than the telescope’s diffraction limit.
Literature: [S00]
Seidel aberrations
Classical third-order monochromatic aberrations: spherical aberration, coma, astigmatism, field curvature, and distortion. Seidel theory provides qualitative and quantitative insight into the origin of these aberrations and their dependence on field and aperture.
Classical third-order monochromatic aberrations: spherical aberration, coma, astigmatism, field curvature, and distortion. Seidel theory provides qualitative and quantitative insight into the origin of these aberrations and their dependence on field and aperture.
Shack-Hartmann wavefront sensor (Hartmann-Shack sensor)
Wavefront sensor using a microlens array to divide the entrance aperture into many subapertures. The displacement of each focused spot from a reference position gives the local wavefront slope, from which the wavefront is reconstructed. See also: Wavefront reconstruction
Wavefront sensor using a microlens array to divide the entrance aperture into many subapertures. The displacement of each focused spot from a reference position gives the local wavefront slope, from which the wavefront is reconstructed. See also: Wavefront reconstruction
Formula: ∂W/∂x ≈ Δx / fML, ∂W/∂y ≈ Δy / fML
APQ context: Both “Shack-Hartmann” and “Hartmann-Shack” are used; “Shack-Hartmann” is more common in the international technical literature.
Schematic: microlenses form spots; their displacements from reference positions give local wavefront slopes.
Signal-to-noise ratio
The ratio of useful signal to the statistical variation of all relevant noise components. In detector practice these include photon noise from signal and background, dark current, and read noise.
The ratio of useful signal to the statistical variation of all relevant noise components. In detector practice these include photon noise from signal and background, dark current, and read noise.
Formula: SNR ≈ S / √(S + B + D + R2)
Literature: [S00]
Snell's law / law of refraction
Relationship between the angles of incidence and refraction at an interface between two isotropic media.
Relationship between the angles of incidence and refraction at an interface between two isotropic media.
Formula: n₁ sin θ₁ = n₂ sin θ₂
Spatial frequency
Number of periodic brightness or structure variations per unit length in the image plane, or per angular or object-space interval. Spatial frequency is the independent variable of the MTF and links resolution, contrast, and detector sampling. See also: Modulation Transfer Function (MTF)
Number of periodic brightness or structure variations per unit length in the image plane, or per angular or object-space interval. Spatial frequency is the independent variable of the MTF and links resolution, contrast, and detector sampling. See also: Modulation Transfer Function (MTF)
Formula: ν = 1 / P
Spectral responsivity
Wavelength-dependent response of a detector or complete system to incident radiation. Depending on the definition, it can include detector quantum efficiency, gain, optical transmission, and filter response and must not be equated with quantum efficiency alone. See also: Quantum efficiency
Wavelength-dependent response of a detector or complete system to incident radiation. Depending on the definition, it can include detector quantum efficiency, gain, optical transmission, and filter response and must not be equated with quantum efficiency alone. See also: Quantum efficiency
Spectrograph / spectroscopy
A spectrograph disperses radiation spectrally and images the spectrum onto a detector. Spectroscopy is the analysis of spectral intensity distributions and lines; resolution, throughput, and spectral response are determined by the optics, slit or fiber, dispersive element, and detector.
A spectrograph disperses radiation spectrally and images the spectrum onto a detector. Spectroscopy is the analysis of spectral intensity distributions and lines; resolution, throughput, and spectral response are determined by the optics, slit or fiber, dispersive element, and detector.
Spherical aberration
Spherical aberration: marginal and paraxial rays have different axial intercepts even though they originate from the same axial object point. The error depends on aperture and on the shapes of the optical surfaces. See also: Aberration
Spherical aberration: marginal and paraxial rays have different axial intercepts even though they originate from the same axial object point. The error depends on aperture and on the shapes of the optical surfaces. See also: Aberration
Spherochromatism (Gauss error)
The chromatic dependence of Spherical aberration, internationally usually called spherochromatism. An objective can be very well corrected for spherical aberration at a reference wavelength yet show different spherical aberration at other wavelengths. In broader usage, “Gauss error” is occasionally extended to the chromatic variation of other aberrations. See also: Aberration
The chromatic dependence of Spherical aberration, internationally usually called spherochromatism. An objective can be very well corrected for spherical aberration at a reference wavelength yet show different spherical aberration at other wavelengths. In broader usage, “Gauss error” is occasionally extended to the chromatic variation of other aberrations. See also: Aberration
Spot diagram
A geometrical plot of selected ray intercepts in an image plane. Spot diagrams show the form and extent of geometrical aberrations for defined field points and wavelengths, but by themselves do not contain complete diffraction information.
A geometrical plot of selected ray intercepts in an image plane. Spot diagrams show the form and extent of geometrical aberrations for defined field points and wavelengths, but by themselves do not contain complete diffraction information.
Schematic: geometrical ray intercepts relative to a reference circle. No APQ measurement data.
APQ context: Spot-diagram comparisons are meaningful only when scale, wavelengths, field angles, weighting, and focus conditions are comparable.
Star test
Test of a telescope using intra-focal, extra-focal, and focused diffraction images of a star source. The star test is highly sensitive to aberrations and alignment errors but quantitative interpretation requires controlled conditions for seeing, wavelength, obstruction, and defocus.
Test of a telescope using intra-focal, extra-focal, and focused diffraction images of a star source. The star test is highly sensitive to aberrations and alignment errors but quantitative interpretation requires controlled conditions for seeing, wavelength, obstruction, and defocus.
APQ context: An artificial star can simplify testing provided its finite distance and source size are adequately taken into account.
Schematic: comparison of intra-focal and extra-focal diffraction patterns in the star test.
Stray light
Unwanted radiation in the image plane that does not follow the ideal geometrical path from the observed object. Sources include surface roughness, particles, ghost reflections, mounts, and inadequate baffling. Stray light especially reduces the contrast of faint structures. See also: Image contrast / contrast transfer
Unwanted radiation in the image plane that does not follow the ideal geometrical path from the observed object. Sources include surface roughness, particles, ghost reflections, mounts, and inadequate baffling. Stray light especially reduces the contrast of faint structures. See also: Image contrast / contrast transfer
Strehl ratio
The ratio of the peak intensity of the real Point Spread Function (PSF) to that of the ideal diffraction-limited PSF at equal total energy and aperture. Strehl depends on wavelength, field, and focus; polychromatic Strehl values additionally require a defined spectral weighting.
The ratio of the peak intensity of the real Point Spread Function (PSF) to that of the ideal diffraction-limited PSF at equal total energy and aperture. Strehl depends on wavelength, field, and focus; polychromatic Strehl values additionally require a defined spectral weighting.
Formula: S = Imax,real / Imax,ideal; for small errors: S ≈ exp[−(2πσW/λ)2]
Stress birefringence
Birefringence induced by mechanical stress in originally isotropic transparent materials. Differences in principal stresses produce a refractive-index difference through the photoelastic effect and can affect polarization and wavefront.
Birefringence induced by mechanical stress in originally isotropic transparent materials. Differences in principal stresses produce a refractive-index difference through the photoelastic effect and can affect polarization and wavefront.
Formula: Δn = C · (σ1 − σ2)
Superachromat
According to Herzberger and McClure, an advanced achromatic system corrected for four colors. The term denotes a chromatic correction class and by itself says nothing about field performance, Spherical aberration, or a very broad UV-to-NIR operating range.
According to Herzberger and McClure, an advanced achromatic system corrected for four colors. The term denotes a chromatic correction class and by itself says nothing about field performance, Spherical aberration, or a very broad UV-to-NIR operating range.
Surface form error
Deviation of a real optical surface from its specified nominal form after defined alignment and removal of permitted degrees of freedom. It must be distinguished from surface roughness and cosmetic surface defects. See also: Surface roughness
Deviation of a real optical surface from its specified nominal form after defined alignment and removal of permitted degrees of freedom. It must be distinguished from surface roughness and cosmetic surface defects. See also: Surface roughness
Surface quality / scratch-dig
General term for the quality of an optical surface with respect to localized defects such as scratches, pits, or edge chips. Scratch-dig is a widely used, primarily cosmetic classification and must not be confused with form error or surface roughness. See also: Surface roughness
General term for the quality of an optical surface with respect to localized defects such as scratches, pits, or edge chips. Scratch-dig is a widely used, primarily cosmetic classification and must not be confused with form error or surface roughness. See also: Surface roughness
Surface roughness
Short-spatial-wavelength component of surface deviation from ideal form. Roughness influences stray light and losses in particular and is specified using suitable statistical parameters over a defined spatial bandwidth.
Short-spatial-wavelength component of surface deviation from ideal form. Roughness influences stray light and losses in particular and is specified using suitable statistical parameters over a defined spatial bandwidth.
Formula: Rq = √[(1/L) ∫ z(x)2 dx]
Synthesis of optical systems
Systematic generation of an optical design from specified functions, constraints, and performance targets. It includes preliminary calculation or a starting system, selection of structure and materials, correction, numerical optimization, evaluation, and subsequent tolerancing.
Systematic generation of an optical design from specified functions, constraints, and performance targets. It includes preliminary calculation or a starting system, selection of structure and materials, correction, numerical optimization, evaluation, and subsequent tolerancing.
APQ context: The development of broadband polychromats is a synthesis problem in which chromatic, monochromatic, and field-dependent correction targets must be met simultaneously.
System throughput
Fraction of incident radiant power or photons that reaches the detector after all optical losses. Spectral system throughput combines transmissions, reflectances, filters, and, where applicable, geometrical losses.
Fraction of incident radiant power or photons that reaches the detector after all optical losses. Spectral system throughput combines transmissions, reflectances, filters, and, where applicable, geometrical losses.
Formula: τsys(λ) = ∏ Ti(λ) · ∏ Rj(λ)
T
Telecentricity
A property of an optical system in which chief rays in object space or image space run parallel to the optical axis. Image-side telecentricity stabilizes incidence angles on sensors and filters but is not required for every astronomical application.
A property of an optical system in which chief rays in object space or image space run parallel to the optical axis. Image-side telecentricity stabilizes incidence angles on sensors and filters but is not required for every astronomical application.
Thin-lens equation
Paraxial relationship among focal length f, object distance g, and image distance b for a thin lens or an equivalently represented system. The signs depend on the convention used.
Paraxial relationship among focal length f, object distance g, and image distance b for a thin lens or an equivalently represented system. The signs depend on the convention used.
Formula: 1/f = 1/g + 1/b
Through-Focus RMS
Evaluation of an RMS-based image-quality criterion over multiple focus positions. Depending on the analysis, this may be RMS spot radius or RMS wavefront error, for example; the exact quantity used must therefore be stated.
Evaluation of an RMS-based image-quality criterion over multiple focus positions. Depending on the analysis, this may be RMS spot radius or RMS wavefront error, for example; the exact quantity used must therefore be stated.
Total internal reflection
Complete reflection at an interface from an optically denser to an optically less dense medium when the angle of incidence exceeds the critical angle.
Complete reflection at an interface from an optically denser to an optically less dense medium when the angle of incidence exceeds the critical angle.
Formula: sin θc = n₂ / n₁ (n₁ > n₂)
Transmission
The ratio of radiant power transmitted by an optical element or system to incident radiant power. Spectral transmission T(λ) includes material absorption, reflection losses, and any filter action.
The ratio of radiant power transmitted by an optical element or system to incident radiant power. Spectral transmission T(λ) includes material absorption, reflection losses, and any filter action.
Formula: T(λ) = Pout(λ) / Pin(λ)
Transverse aberration
Lateral displacement of a real ray intersection from the ideal paraxial or geometrical image point in a specified image plane. Transverse aberrations are commonly evaluated in ray-fan or spot diagrams.
Lateral displacement of a real ray intersection from the ideal paraxial or geometrical image point in a specified image plane. Transverse aberrations are commonly evaluated in ray-fan or spot diagrams.
Trichromat
A chromatic correction class in which three selected colors or wavelengths satisfy a common paraxial focus condition. The term must be distinguished from the mechanical/optical construction as Doublet, Triplet, or Quadruplet.
A chromatic correction class in which three selected colors or wavelengths satisfy a common paraxial focus condition. The term must be distinguished from the mechanical/optical construction as Doublet, Triplet, or Quadruplet.
Triplet
A term used in astronomy and also by Haferkorn for an objective or lens group consisting of three optical elements. “Triplet” describes element count; a triplet is not automatically an Apochromat or Trichromat.
A term used in astronomy and also by Haferkorn for an objective or lens group consisting of three optical elements. “Triplet” describes element count; a triplet is not automatically an Apochromat or Trichromat.
U
UBVRI spectral range
A photometric filter system consisting of U (ultraviolet), B (blue), V (visual), R (red), and I (near infrared). Modern practice often combines Johnson U/B/V with Cousins R/I. Effective wavelengths are not universal constants; they depend on the actual passbands, detector, and source spectrum.
A photometric filter system consisting of U (ultraviolet), B (blue), V (visual), R (red), and I (near infrared). Modern practice often combines Johnson U/B/V with Cousins R/I. Effective wavelengths are not universal constants; they depend on the actual passbands, detector, and source spectrum.
Schematic: positions of the UBVRI bands; actual system curves and effective wavelengths depend on detector and source.
Unvignetted image circle
The circular region in the image plane within which there is no geometrical obstruction by cells, stops, or downstream components. An unvignetted image circle does not automatically guarantee uniform illumination or constant image quality.
The circular region in the image plane within which there is no geometrical obstruction by cells, stops, or downstream components. An unvignetted image circle does not automatically guarantee uniform illumination or constant image quality.
V
Vignetting
A field-dependent reduction in light caused by geometrical obstruction or by the natural angular dependence of an imaging system. Mechanical vignetting must be distinguished from natural illumination falloff.
A field-dependent reduction in light caused by geometrical obstruction or by the natural angular dependence of an imaging system. Mechanical vignetting must be distinguished from natural illumination falloff.
W
Wave optics
Description of optical phenomena using the wave nature of light. It includes interference, diffraction, coherence, and polarization and complements geometrical optics where a pure ray model is insufficient.
Description of optical phenomena using the wave nature of light. It includes interference, diffraction, coherence, and polarization and complements geometrical optics where a pure ray model is insufficient.
Wavefront
A surface of equal phase of an optical wave. For an ideal point focus, the converging wavefront is spherical; departures from the ideal reference wavefront describe system aberrations.
A surface of equal phase of an optical wave. For an ideal point focus, the converging wavefront is spherical; departures from the ideal reference wavefront describe system aberrations.
Wavefront error
The difference between a real and an ideal reference wavefront. It may be specified as a spatial function, an RMS value, or a peak-to-valley value. A meaningful specification states wavelength, aperture, measurement/calculation conditions, and any removed terms.
The difference between a real and an ideal reference wavefront. It may be specified as a spatial function, an RMS value, or a peak-to-valley value. A meaningful specification states wavelength, aperture, measurement/calculation conditions, and any removed terms.
Formula: PV = Wmax − Wmin
Wavefront reconstruction
Mathematical determination of a spatial wavefront from measured local slopes, phase data, or intensity data. In a Shack-Hartmann sensor, for example, gradients derived from spot displacements are integrated or fitted to a basis such as Zernike polynomials. See also: Wavefront, Shack-Hartmann wavefront sensor (Hartmann-Shack sensor)
Mathematical determination of a spatial wavefront from measured local slopes, phase data, or intensity data. In a Shack-Hartmann sensor, for example, gradients derived from spot displacements are integrated or fitted to a basis such as Zernike polynomials. See also: Wavefront, Shack-Hartmann wavefront sensor (Hartmann-Shack sensor)
Wavefront-shearing interferometry
Interferometric method in which a wavefront is superimposed with a spatially shifted or tilted copy of itself. The resulting fringes contain primarily information about local wavefront gradients.
Interferometric method in which a wavefront is superimposed with a spatially shifted or tilted copy of itself. The resulting fringes contain primarily information about local wavefront gradients.
Wide-field system
An optical system designed for high image quality over a comparatively large field angle or image circle. As the field increases, Coma, Astigmatism, Field curvature, Distortion, lateral color, and Vignetting become increasingly important.
An optical system designed for high image quality over a comparatively large field angle or image circle. As the field increases, Coma, Astigmatism, Field curvature, Distortion, lateral color, and Vignetting become increasingly important.
APQ context: In APQ Wide-Field Polychromats, a large field and a broad spectral range are treated as a combined system requirement.
Z
Zernike polynomials
Orthogonal polynomial functions on the unit disk used to describe wavefront errors over a circular pupil. Individual modes can be associated with familiar aberration forms such as defocus, astigmatism, or coma; the numbering and normalization convention must be stated. See also: Wavefront error
Orthogonal polynomial functions on the unit disk used to describe wavefront errors over a circular pupil. Individual modes can be associated with familiar aberration forms such as defocus, astigmatism, or coma; the numbering and normalization convention must be stated. See also: Wavefront error
Formula: W(ρ,φ) = ∑ aj Zj(ρ,φ)
Schematic: examples of typical Zernike error forms; the drawing is not a quantitative wavefront map.
Zonal error
Rotationally symmetric surface or wavefront error confined to particular radial zones of the aperture. Zonal errors can occur as local contributions to spherical aberration and can be detected by tests with radial resolution. See also: Spherical aberration
Rotationally symmetric surface or wavefront error confined to particular radial zones of the aperture. Zonal errors can occur as local contributions to spherical aberration and can be detected by tests with radial resolution. See also: Spherical aberration
Literature and further reading
- [H81] Haferkorn, Heinz: Optik. Physikalisch-technische Grundlagen und Anwendungen. Harri Deutsch, Thun/Frankfurt am Main, 1981, ISBN 3-87144-570-3.
- [H67] Haferkorn, Heinz: Untersuchungen zur Glasauswahl und zur Vorrechnung bei Triplets. Dissertation, Technische Hochschule Ilmenau, 1967.
- [H86] Haferkorn, Heinz: Bewertung optischer Systeme. VEB Deutscher Verlag der Wissenschaften, Berlin, 1986.
- [HM63] Herzberger, Max; McClure, Nancy R.: "The Design of Superachromatic Lenses". Applied Optics 2 (6), 553–560, 1963. DOI: 10.1364/AO.2.000553.
- [KJ10] Kingslake, Rudolf; Johnson, R. Barry: Lens Design Fundamentals. 2. Auflage, Academic Press/Elsevier, 2010.
- [S00] Schroeder, Daniel J.: Astronomical Optics. 2. Auflage, Academic Press, 2000, ISBN 0-12-629810-6.
- [M07] Malacara, Daniel (Hrsg.): Optical Shop Testing. 3. Auflage, Wiley, 2007, ISBN 978-0-471-48404-2.
- [BW99] Born, Max; Wolf, Emil: Principles of Optics. 7., erweiterte Auflage, Cambridge University Press, 1999.
- [WS08] Smith, Warren J.: Modern Optical Engineering. 4. Auflage, McGraw-Hill, 2008.
- [B90] Bessell, M. S.: "UBVRI passbands". Publications of the Astronomical Society of the Pacific 102, 1181–1199, 1990. DOI: 10.1086/132749.
- [Sch17] Schubert, Ingo: Wissensspeicher Feinoptik 17.4. Saale Betreuungswerk der Lebenshilfe Jena gGmbH, Jena, 2017. ISBN 978-3-00-046972-5.
- [Su08] Suiter, Harold Richard: Star Testing Astronomical Telescopes – A Manual for Optical Evaluation and Adjustment. 2. Auflage, Willmann-Bell, Richmond, 2008.
- [PS01] Platt, Ben C.; Shack, Roland: "History and Principles of Shack-Hartmann Wavefront Sensing". Journal of Refractive Surgery 17 (5), S573–S577, 2001. DOI: 10.3928/1081-597X-20010901-13.
- [Y08] Yoder, Paul R., Jr.: Mounting Optics in Optical Instruments. 2. Auflage, SPIE Press, Bellingham, 2008. ISBN 978-0-8194-7129-1.
- [RV88] Rutten, Harrie G. J.; van Venrooij, Martin A. M.: Telescope Optics: Evaluation and Design. Willmann-Bell, Richmond, 1988. ISBN 0-943396-18-2.
- [R90] Riekher, Rolf: Fernrohre und ihre Meister. 2., stark bearbeitete Auflage, Verlag Technik, Berlin, 1990. ISBN 3-341-00791-1.
- [L17] Laux, Uwe: Astrooptik – Optiksysteme für die Astronomie. 3. Auflage, 2017. ISBN 978-3-937981-65-9.
- [G85] Grimsehl, Ernst: Lehrbuch der Physik. Band 3: Optik. 18. Auflage, neu bearbeitet von Heinz Haferkorn, B. G. Teubner, Leipzig, 1985.
- [HR84] Haferkorn, Heinz; Richter, Wolfgang: Synthese optischer Systeme. VEB Deutscher Verlag der Wissenschaften, Berlin, 1984.