Optics For Dummies
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Some non-rotationally symmetric lenses are, for example, cylindrical or toric lenses. These lenses have differing vertical and horizontal cross sections.
Currently, more and more compact video camera systems are using rotationally symmetric aspherical lens systems. Imaging errors can be reduced which occur mainly from slight conical form spherical aberrations of spherical lenses Fig. The lens is placed a certain distance from the object Object distance a.
The direction of propagation is defined from the object to lens for this system. The region before the lens is referred to as the object space. In the even of a real image, the image space lies behind the lens. The distance between the lens and the image is referred to as the image distance a'.
Fiber optics
Figure 10 has sufficient parameters to calculate the most important dimensional quantities of an imaging system, such as linear magnification, acceptance angle, and field of view FOV. These are called paraxial rays. One of the most important equations characterizing optical imaging is the conjugate distance equation. For a given lens of focal length f, the expression relates the object and image distance. This expression is based on the assumption that the lens thickness t is small relative to a and a', so that the lens is considered thin. This may deviate from expected magnification due to effects such as magnification distortion or deviations from paraxial assumptions.
For small angles of FOV, both quotients should be identical. The actual image of an object through single converging lens has a negative magnification m By combining Equations 8 , 9 and 10 , the following useful relationships apply to paraxial systems:. Paraxial systems with thin lenses are a simplified configuration for crudely analyzing optical systems. They present a special case. Thick lenses have two refracting surfaces to which the thin lens parameters can be applied. They are referred to as principle planes object side h, image side h'.
The corresponding intersection points with the optical axes are principle or nodal points H and H'. Equation 8 is used by replacing object and image distances with nodal points.
Compatible con los siguientes dispositivos:
Here, z and z' are the distance to the object and image from their respective focal points. In general, the object principle plane is nearer the object than the image principle plane, but this can be reversed with thick lenses and unique surface configurations. The intersection of the polished lens surface with the optical axes is called the object vertex, S, and the image vertex, S'. The corresponding distances between vertex and object or image are referred to as the back focus, s and s'. Optical systems usually contain converging and diverging lenses made of different materials.
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Such systems are known as compound lens systems. A compound lens system can also produce an object and image principle plane. The intersection of the outer most lens surface with the optical axes defines the vertex and associated back focus. Lenses in an optical system can have different shapes or bends with radii r 1 and r 2.
Note that for most compound systems rotationally symmetric , the center point of all refractive surfaces lies on the optical axes. If the radius is to the left of the lens toward the object , it is negative by convention and to the right of the lens it is positive.
By way of this lens bending, the location of the principle plane can be influenced. The lens collapses to a single principle plane. It is possible for the image side principle plane, H', to be closer to the object than the corresponding object side principle plane, H HH' r 1 - r 2. Figure In choosing a meniscus lens b , as opposed to a symmetrical lens a , the object related back focus can be shortened, thus maintaining the same focal length.
Examples: condensor, lenses, telescopic systems, etc. For understanding optical configurations and instruments, the choice of the principle plane location is an important characteristic. For example, large focal length lenses with short back foci can be conceptualized. The arrangement of several single lens systems into a compound lens system will combine the different bendings, glasses, thicknesses of individual lenses, and lens distances into a single system.
A single object side and image side principle plane describe such a system. This is especially true of systems whose object or image back focus is infinite. This is usually true of photographic lenses where the object is at infinity and the image side back focus is very short.
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The included angle between the outermost ray and the optical axis is related to the aperture of a lens. According to Equation 22 , systems with large aperture have small aperture numbers. The aperture numbers of most lenses are assigned a number according to the diaphragm range. This range is defined such that a step in aperture number reflects a factor of 2 change in the light flux. The diaphragm range is as follows:. Optical professionals sometimes refer to the numerical aperture of a lens system.
This is defined as:. From Equation 22 the relationship between numerical aperture and aperture number can be readily seen. See Equation Frequently, lens systems project an object onto an image sensor in the image space that is made of photosensitive material. Most magnification ranges between If one concretely wants to know the effective aperture number, Feff, of an imaging system magnification m , it can be derived from Equations 8 , 10 , and 22 :.
F eff.. For single lens systems, the lens diameter can act as the iris at the principle plane. Irises, also called aperture stops, are precise mechanical apertures, which restrict light rays transmitted through a lens. This restricting is obviously related to the aperture number.
Optics for Dummies by Galen C. Duree
The free diameter in Equation 22 can be replaced with the aperture diameter. The iris defines the amount of light flux transmitted by an optical system. Figure 16 schematically shows the rays transmitted through an optical system with an iris. Typically, the middle ray of a ray bundle principle ray intersects the optical axis at the iris plane. The corresponding peripheral ray is restricted by the iris. Depending on the lens system, the position of the iris may be in the middle of system or shifted in front of, or behind, the precise center. In general, by shifting the location of the iris, the oblique aberrations of a lens system such as coma, astigmatism, distortion, lateral color can be influenced and minimized.
A lens stack will, in most cases, create a virtual image of the iris in image planes in front of, and behind the iris. The iris image appears as a typical limiting ray diameter when viewing the lens.
Optics For Dummies
These iris images are also called pupils. The front and back images of the iris are called entrance pupil EP and exit pupil XP , respectively.
Galen Duree, Jr. Chemical Engineering: Solutions to the Problems in Volume 1. Computers were once connected over long distances by telephone lines or over shorter distances copper Ethernet cables, but fiber cables are increasingly the preferred method of networking computers because they're very affordable, secure, reliable, and have much higher capacity. An under filled numerical aperture is therefore desired for measurement applications. Humans have spent centuries studying light, yet it remains something of a mystery. Instead of linking its offices over the public Internet, it's perfectly possible for a company to set up its own fiber network if it can afford to do so or more likely buy space on a private fiber network. The author of a popular book about fiber-optic history describes how Charles Kao figured out the theory of modern fiber-optic communications a half century ago.
Figure 17 is a schematic diagram of the pupils. Ray bundles emitted from the object or in the reverse direction from the image are restricted by their respective pupils, and their propagation direction is defined. The magnitude is given by the following expression.
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