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Glossary

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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A

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ABCD matrix
Matrix describing the effect of the lens system on ray coordinates (h,u) in the paraxial approximation.
Aberration
Blurring or distortion of the image formed by a lens. See also Seidel aberration.
Abbe V-value
Also known as the Abbe number. A measure of invariability of refractive index with wavelength. The higher V, the less variation. The Abbe V-value is given by V = (nd - 1)/(nF - nC) where nd is the refractive index for d light (587.56nm, Helium yellow), nF is the refractive index for F light (486.13nm, Hydrogen blue), and nC is the refractive index for C light (656.27nm, Hydrogen red). Wavelengths are from the table of atomic lines.
achromat
An achromatic lens.
achromatic
No first order focal shift with wavelength. Parabolic residual dependence is called "secondary color". Can be thought of as having two wavelengths at which focal shift is zero. See also apochromatic.
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afocal
A lens system that does not focus a parallel bundle of rays. An example of such a system is a laser beam expander.
Airy disk
The diffraction pattern of a circular aperture, named after Sir George Biddel Airy. By convention the radius of the Airy disk is the radius of the first minimum of the ideal diffraction pattern. The value of the radius is approximately 1.22 times the wavelength times the focal ratio of the lens.
anamorphic
A system forming an image but with different magnification vertically than horizontally.
anastigmatic
Having zero astigmatism at some off-axis field point. Refers to the astigmatism of an axially symmetric imaging system. Synonym: stigmatic.
aperture stop
The limiting aperture of an imaging system. The aperture stop is used to specify where the rays from the object are aimed. Often some rays are vignetted elsewhere in the system.
aplanat
An aplanatic lens.
aplanatic
Free of both spherical aberration and coma.
apochromatic
Next level of wavelength independence beyond achromatic. Having focal shift zero at three wavelengths.
astigmatism
Difference in the focus between sagittal and tangential ray fans for off-axis field points. Systems that are not axisymmetric can have astigmatism even on axis; this is called linear astigmatism.
axial ray
Same as marginal ray.

B

back focal length
The distance from the last glass surface to the focus.

C

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Cardinal points
The paraxial properties of an axisymmetric lens can be described in terms of its cardinal points. The cardinal points of a lens are: first nodal point, first principal focus, first principal point, second nodal point, second principal focus, and second principal point.
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chief ray
The ray starting at the field point furthest from axis and passing through the center of the aperture stop. In typical lens design programs rays by default are aimed at the center of the entrance pupil, which is not quite the same thing, in general, but usually close enough. Iterative adjustment of the ray aiming to hit the center of the aperture stop is sometimes provided as a special option.
CODE V®
A lens design program for the Windows platform. CODE V® is a registered trade mark.
coma
A blurring and displacement of image points away from the optical axis.
conic section
The curve in the (r,z) plane satisfying the relation
c*r^2 - 2*z + c*p*z^2 = 0
is a conic section. Revolving this curve about the z axis produces the surface called a conicoid.
conicoid
Surface of revolution obtained by revolving a conic section about the z axis. Includes spherical surfaces as special cases.
cut-off frequency
The maximum spatial frequency that can be transmitted by the lens. This is the reciprocal of the product of the wavelength and the working focal ratio.

D

damped least squares
The traditional optimization algorithm of lens design. More widely known as the Levenberg-Marquardt algorithm.
diffraction
The spreading of light by an aperture, due to the wave nature of light.
dispersion
Variation of the refractive index with wavelength.
distortion
The deformation of an image without the introduction of blurring. Usually graphed as a percentage change of the image height from the image height extrapolated from the paraxial regime, as a function of image height. See also Seidel aberrations.
doublet
A lens consisting of two singlets in close proximity. The singlets often have mating shapes and are glued together. These singlets are usually differing dispersion in order to make the doublet achromatic.

E

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entrance pupil
The image of the aperture stop as viewed from the object side of the lens.
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exit pupil
The image of the aperture stop as viewed from the image side of the lens.

F

field curvature
Deviation of the image surface from a plane.
field point
A point on the object being imaged.
finite conjugate system
A system where the object and image are at finite distance from the lens.
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first focal length
Distance between first focal point and first principal point.
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first nodal point
Nodal point for reverse beam. A reverse ray aimed at this point will exit the lens travelling parallel to its initial direction.
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first principal focus
Focal point for reverse beam. Reverse rays parallel to the axis will converge on this point
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first principal point
Principal point for reverse beam. The point containing the principal plane, where a thin lens can replace the lens, for reverse rays.
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focal length
The ratio between the distance off-axis that an image point is formed and the input angle (to be precise, the input transverse momentum).
focal ratio (f-number, f/#)
The ratio of the focal length of the lens to the diameter of the exit pupil. A lens with focal ratio 2.8 is called an f/2.8 lens. The notation with capitalized F is deprecated.
Fraunhofer diffraction
Far-field diffraction. In an imaging system, for instance, when the focal ratio is large, so the exit pupil subtends a small angle, as viewed from the image point.
Fresnel diffraction
Near-field diffraction. In an imaging system, for instance, when the focal ratio is small, so the exit pupil subtends a small angle, as viewed from the image point.

G

glass
In lens design, any material used to refract light.
glass code
Usually a six digit code. The first three digits are one thousand times the fractional part of the refractive index at D light, the second three digits are ten times the Abbe V-value.
GRIN lens
GRIN means "gradient index". A GRIN lens is a lens whose glass has a nonuniform refractive index. A ray of light not only refracts upon entering the lens, it also moves along a curved path within the lens on account of the nonunform refractive index.

H

hexapolar pattern
Pattern formed by a point, surrounded by a ring of 6 points, surrounded by a ring of 12 points, surrounded by a ring of 18 points, etc. Hexapolar pattern of order N has 1+3N(N+1) points (i.e., a hex number) In lens design this concept is modified to put all the points on a ring at the same distance from the center.
hex number
Number of the form 1+3N(N+1) where N=0,1,2,... Interesting link: http://mathworld.wolfram.com/HexNumber.html
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Huygens-Fresnel principle
The approximation to diffraction theory in which each point on the optical wavefront is taken to be a source of spherical wavelets whose superposition generates the wavefront downstream. This principle can be used to calculate the effect of diffraction on the image of a point source formed by a lens system. Each point on the wavefront in the exit pupil generates a spherical wavelet and the coherent sum of these wavelets at the image plane gives the spot shape including the effect of diffraction.

I

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Image surface
The surface on which the image is measured.
infinite conjugate system
A system where the object is infinitely far from the lens. The image is at finite distance from the lens unless the system is also afocal.

J

K

L

Lens
A system for deflecting light rays, often with the purpose of forming an image of an object. A lens can consist of more than one simple lens or singlet.
Levenberg-Marquardt algorithm
A robust solver for nonlinear least-squares problems. Known in the lens design community as damped least squares.
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Line-spread function (LSF)
The intensity distribution formed by imaging a line. The LSF is a function of the distance perpendicular to the image of the line.

M

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marginal ray
A ray starting on axis and having maximum angle, that is, grazing the edge of the aperture stop. Also known as the axial ray.
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momentum
The momentum of a ray is the product of the refractive index and the unit vector indicating the direction of propagation. For negative refractive index the ray moves in the direction opposite its momentum. Usually refers to the transverse momentum used in conjunction with the transfer matrix.
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MTF
Modulation transfer function. Describes the contrast reduction introduced by a lens. It is the magnitude of the optical transfer function (OTF).

N

Nelder-Mead algorithm
Also known as the nonlinear simplex method. A robust solver for nonlinear minimization problems in multi-dimension. It is a direct search method that automatically updates its step size.
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Nodal points
See first nodal point and second nodal point.

O

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Object surface
The surface at which the field points (point sources of rays) lie.
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OPD
Optical path difference.
OPD
Optical path length.
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OSC
Offense against the sine condition.
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OTF
Optical transfer function. Complex-valued function describing the contrast and phase of the image of an object thata is a sinusoidal pattern. The modulation transfer function (MTF) is the magnitude of the OTF.
OSLO®
A lens design program for the Windows and Linux platforms. OSLO® is a registered trade mark.

P

paraxial
The regime where rays are close enough to the optical axis and sufficiently parallel to it that their propagation can be described using linear (a.k.a. Gaussian) optics.
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Petzval sum
Sum over all surfaces of the product of the curvature of the surface to the change in the reciprocal of the refractive index when crossing the surface. For an anastigmatic system, the Petzval sum is proportional to the field curvature.
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Point-spread function (PSF)
The intensity distribution formed by imaging a point. The PSF is a function of two coordinates (x,y) on the image surface.
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pupil
Any image of the aperture stop. A lens may have pupils in additon to the entrance and exit pupil.

Q

R

ray
In the geometrical approximation, a ray describes the trajectory of a electromagnetic wave packet (light pulse) through a physicial system. In a uniform material, rays travel in straight lines. Rays are refracted at the interface between materials of differing refractive index.
refraction
Change of ray direction at the interface of two materials of differing refractive index.
refractive index
Material property equal to the ratio of the speed of light in vacuum to the speed of light in the material.

S

sag
The distance between the surface profile and a plane tangent to the surface.
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sagittal
Perpendicular to the plane formed by the field point and the axis of the optical system. Also known as transverse. Usage: sagittal focus.
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second focal length
Distance between second focal point and second principal point.
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second nodal point
Nodal point for forward beam. A forward ray aimed at this point will exit the lens travelling parallel to its initial direction.
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second principal focus
Focal point for forward beam. Forward rays parallel to the axis will converge on this point.
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second principal point
Principal point for forward beam. The point containing the principal plane, where a thin lens can replace the lens, for forward rays.
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Seidel aberrations
Set of five third-order aberrations calculated from paraxial data. These aberrations are named spherical aberration, coma, astigmatism, field curvature, and distortion. Seidel aberrations are interpreted as coming from surfaces indpendently, allowing one to judge which surfaces are compensating each other's aberrations.
singlet
A simple lens comprising a monolithic piece of glass.
symplectic
The entangling of ray position and direction required to obey physical law. The mapping of rays from the input to the output of a physcial system like a lens is described by a symplectic transformation. In the paraxial approximation the map is linear and the lens is described by a transfer matrix that is a symplectic matrix.
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system surface
In LensForge, the first surface after the object surface, other than coordinate breaks.

T

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tangential
In the plane formed by the field point and the axis of the optical system. Also known as radial or meridional. Usage: tangential focus.
telecentric
Having chief rays parallel to the axis for all field points. A lens can be designed to be telecentric on the input side, the output side, or both. If both, it is called a "telecentric lens".
toric lens
A lens with a toroidal surface. Toric lenses are used in spectacles, for example, to correct (linear) astigmatism.
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transfer matrix
Matrix describing the effect of the lens system on ray coordinate (p,q) in the paraxial approximation.
triplet
A lens consisting of three singlets in close proximity. The singlets often have mating shapes and are glued together.

U

V

vignetting
The termination of rays by apertures other than the aperture stop. Vignetting is a powerful way to limit aberrations in an imaging system, although at the expense of intensity uniformity.

W

X

Y

Z

ZEMAX®
A lens design program for the Windows platform. ZEMAX® is a registered trade mark.

See also