Rochon prisms are similar to Wollaston prisms in that both beams are transmitted, but in this polarizer one beam is transmitted undeviated while the other is transmitted at wavelength dependent angle. View Product

Let S (fig. 1) be any optical system, rays proceeding from an axis point O under an angle u1 will unite in the axis point O'1; and those under an angle u2 in the axis point O'2. If there is refraction at a collective spherical surface, or through a thin positive lens, O'2 will lie in front of O'1 so long as the angle u2 is greater than u1 (under correction); and conversely with a dispersive surface or lenses (over correction). The caustic, in the first case, resembles the sign > (greater than); in the second < (less than). If the angle u1 is very small, O'1 is the Gaussian image; and O'1 O'2 is termed the longitudinal aberration, and O'1R the lateral aberration of the pencils with aperture u2. If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O'1 there is a circular disk of confusion of radius O'1R, and in a parallel plane at O'2 another one of radius O'2R2; between these two is situated the disk of least confusion.[8]

Polarizer examples

By opening the stop wider, similar deviations arise for lateral points as have been already discussed for axial points; but in this case they are much more complicated. The course of the rays in the meridional section is no longer symmetrical to the principal ray of the pencil; and on an intercepting plane there appears, instead of a luminous point, a patch of light, not symmetrical about a point, and often exhibiting a resemblance to a comet having its tail directed towards or away from the axis. From this appearance it takes its name. The unsymmetrical form of the meridional pencil—formerly the only one considered—is coma in the narrower sense only; other errors of coma have been treated by Arthur König and Moritz von Rohr,[13] and later by Allvar Gullstrand.[12][8]

Sir Isaac Newton was probably the discoverer of astigmation; the position of the astigmatic image lines was determined by Thomas Young;[10] and the theory was developed by Allvar Gullstrand.[11][12][8] A bibliography by P. Culmann is given in Moritz von Rohr's Die Bilderzeugung in optischen Instrumenten.[13][8]

Circular wavefront profiles associated with aberrations may be mathematically modeled using Zernike polynomials. Developed by Frits Zernike in the 1930s, Zernike's polynomials are orthogonal over a circle of unit radius. A complex, aberrated wavefront profile may be curve-fitted with Zernike polynomials to yield a set of fitting coefficients that individually represent different types of aberrations. These Zernike coefficients are linearly independent, thus individual aberration contributions to an overall wavefront may be isolated and quantified separately.

As in Fourier synthesis using sines and cosines, a wavefront may be perfectly represented by a sufficiently large number of higher-order Zernike polynomials. However, wavefronts with very steep gradients or very high spatial frequency structure, such as produced by propagation through atmospheric turbulence or aerodynamic flowfields, are not well modeled by Zernike polynomials, which tend to low-pass filter fine spatial definition in the wavefront. In this case, other fitting methods such as fractals or singular value decomposition may yield improved fitting results.

Wire grid polarizers consist of many thin wires arranged parallel to each other. Light that is polarized along the direction of these wires is reflected, while light that is polarized perpendicular to these wires is transmitted. Because the principle of parallel wires is wavelength independent, wire grid polarizers cover a very large wavelength range well into the IR, limited by material or AR coating absorption. This design is very robust, with excellent environmental stability and a large acceptance angle. While most wire grid polarizers use glass substrates, thin film wire grid polarizers offer a more economical solution. View Product

The classical imaging problem is to reproduce perfectly a finite plane (the object) onto another plane (the image) through a finite aperture. It is impossible to do so perfectly for more than one such pair of planes (this was proven with increasing generality by Maxwell in 1858, by Bruns in 1895, and by Carathéodory in 1926, see summary in Walther, A., J. Opt. Soc. Am. A 6, 415–422 (1989)). For a single pair of planes (e.g. for a single focus setting of an objective), however, the problem can in principle be solved perfectly. Examples of such a theoretically perfect system include the Luneburg lens and the Maxwell fish-eye.

Linear Glass Polarizing Filters are ideal for OEM integration and prototyping. With a fair surface flatness, they balance exceptional polarization performance (95% polarization efficiency) with a less robust extinction ratio, and feature a single filter transmission of 30%. View Product

Extinction Ratio and Degree of Polarization: The polarizing properties of a linear polarizer are typically defined by the degree of polarization or polarization efficiency, P, and its extinction ratio, ρp. Following the formalism given in the Handbook of Optics, the principal transmittances of the polarizer are T1 and T2. T1 is the maximum transmission of the polarizer and occurs when the axis of the polarizer is parallel to the plane of polarization of the incident polarized beam. T2 is the minimum transmission of the polarizer and occurs when the axis of the polarizer is perpendicular to the plane of polarization of the incident polarized beam.

Similar to the High Contrast Plastic Linear Polarizers, High Contrast Linear Polarizing Film is another option for imaging applications requiring polarizers with flexibility in shape and rigidity. Polarizing Film is available in sheets with a variety of thicknesses, and can be cut to size or fashioned to a desired shape. View Product

Reflective polarizers transmit the desired polarization and reflect the rest. They either use a wire grid, Brewster’s angle, or interference effects. Brewster’s angle is the angle at which, based on the Fresnel equations, only s-polarized light is reflected. Because the p-polarized light is not reflected while the s-polarized light is partially reflected, the transmitted light is enriched in p-polarization.

ITOS GmbH is a division of Edmund Optics that has provided both custom and off-the shelf polarization solutions to the German and European markets since 1993. The ITOS division expands Edmund Optics' polarization manufacturing and metrology capabilities, providing customers with a wider range of standard and custom polarization optics.

The preceding review of the several errors of reproduction belongs to the Abbe theory of aberrations, in which definite aberrations are discussed separately; it is well suited to practical needs, for in the construction of an optical instrument certain errors are sought to be eliminated, the selection of which is justified by experience. In the mathematical sense, however, this selection is arbitrary; the reproduction of a finite object with a finite aperture entails, in all probability, an infinite number of aberrations. This number is only finite if the object and aperture are assumed to be infinitely small of a certain order; and with each order of infinite smallness, i.e. with each degree of approximation to reality (to finite objects and apertures), a certain number of aberrations is associated. This connection is only supplied by theories which treat aberrations generally and analytically by means of indefinite series.[8]

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Glass with weaker dispersive power (greater v {\displaystyle v} ) is named crown glass; that with greater dispersive power, flint glass. For the construction of an achromatic collective lens ( f {\displaystyle f} positive) it follows, by means of equation (4), that a collective lens I. of crown glass and a dispersive lens II. of flint glass must be chosen; the latter, although the weaker, corrects the other chromatically by its greater dispersive power. For an achromatic dispersive lens the converse must be adopted. This is, at the present day, the ordinary type, e.g., of telescope objective; the values of the four radii must satisfy the equations (2) and (4). Two other conditions may also be postulated: one is always the elimination of the aberration on the axis; the second either the Herschel or Fraunhofer Condition, the latter being the best vide supra, Monochromatic Aberration). In practice, however, it is often more useful to avoid the second condition by making the lenses have contact, i.e. equal radii. According to P. Rudolph (Eder's Jahrb. f. Photog., 1891, 5, p. 225; 1893, 7, p. 221), cemented objectives of thin lenses permit the elimination of spherical aberration on the axis, if, as above, the collective lens has a smaller refractive index; on the other hand, they permit the elimination of astigmatism and curvature of the field, if the collective lens has a greater refractive index (this follows from the Petzval equation; see L. Seidel, Astr. Nachr., 1856, p. 289). Should the cemented system be positive, then the more powerful lens must be positive; and, according to (4), to the greater power belongs the weaker dispersive power (greater v {\displaystyle v} ), that is to say, crown glass; consequently the crown glass must have the greater refractive index for astigmatic and plane images. In all earlier kinds of glass, however, the dispersive power increased with the refractive index; that is, v {\displaystyle v} decreased as n {\displaystyle n} increased; but some of the Jena glasses by E. Abbe and O. Schott were crown glasses of high refractive index, and achromatic systems from such crown glasses, with flint glasses of lower refractive index, are called the new achromats, and were employed by P. Rudolph in the first anastigmats (photographic objectives).[8]

Since the aberration increases with the distance of the ray from the center of the lens, the aberration increases as the lens diameter increases (or, correspondingly, with the diameter of the aperture), and hence can be minimized by reducing the aperture, at the cost of also reducing the amount of light reaching the image plane.

Aberration can be analyzed with the techniques of geometrical optics. The articles on reflection, refraction and caustics discuss the general features of reflected and refracted rays.

The Gaussian theory is only an approximation; monochromatic or spherical aberrations still occur, which will be different for different colors; and should they be compensated for one color, the image of another color would prove disturbing. The most important is the chromatic difference of aberration of the axis point, which is still present to disturb the image, after par-axial rays of different colors are united by an appropriate combination of glasses. If a collective system be corrected for the axis point for a definite wavelength, then, on account of the greater dispersion in the negative components — the flint glasses, — overcorrection will arise for the shorter wavelengths (this being the error of the negative components), and under-correction for the longer wavelengths (the error of crown glass lenses preponderating in the red). This error was treated by Jean le Rond d'Alembert, and, in special detail, by C. F. Gauss. It increases rapidly with the aperture, and is more important with medium apertures than the secondary spectrum of par-axial rays; consequently, spherical aberration must be eliminated for two colors, and if this be impossible, then it must be eliminated for those particular wavelengths which are most effectual for the instrument in question (a graphical representation of this error is given in M. von Rohr, Theorie und Geschichte des photographischen Objectivs).[8]

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If, in the first place, monochromatic aberrations be neglected — in other words, the Gaussian theory be accepted — then every reproduction is determined by the positions of the focal planes, and the magnitude of the focal lengths, or if the focal lengths, as ordinarily happens, be equal, by three constants of reproduction. These constants are determined by the data of the system (radii, thicknesses, distances, indices, etc., of the lenses); therefore their dependence on the refractive index, and consequently on the color,[8] are calculable.[25] The refractive indices for different wavelengths must be known for each kind of glass made use of. In this manner the conditions are maintained that any one constant of reproduction is equal for two different colors, i.e. this constant is achromatized. For example, it is possible, with one thick lens in air, to achromatize the position of a focal plane of the magnitude of the focal length. If all three constants of reproduction be achromatized, then the Gaussian image for all distances of objects is the same for the two colors, and the system is said to be in stable achromatism.[8]

Transmission: This value either refers to the transmission of light polarized linearly in the direction of the polarization axis, or to the transmission of unpolarized light through the polarizer. Parallel transmission is the transmission of unpolarized light through two polarizers with their polarization axes aligned in parallel, while crossed transmission is the transmission of unpolarized light through two polarizers with their polarization axes crossed. For ideal polarizers transmission of linearly polarized light parallel to the polarization axis is 100%, parallel transmission is 50% and crossed transmission is 0%. This can be calculated with Malus’ law as described in Introduction to Polarization.

Even if the image is sharp, it may be distorted compared to ideal pinhole projection. In pinhole projection, the magnification of an object is inversely proportional to its distance to the camera along the optical axis so that a camera pointing directly at a flat surface reproduces that flat surface. Distortion can be thought of as stretching the image non-uniformly, or, equivalently, as a variation in magnification across the field. While "distortion" can include arbitrary deformation of an image, the most pronounced modes of distortion produced by conventional imaging optics is "barrel distortion", in which the center of the image is magnified more than the perimeter (figure 3a). The reverse, in which the perimeter is magnified more than the center, is known as "pincushion distortion" (figure 3b). This effect is called lens distortion or image distortion, and there are algorithms to correct it.

With an ideal lens, light from any given point on an object would pass through the lens and come together at a single point in the image plane (or, more generally, the image surface). Real lenses do not focus light exactly to a single point, however, even when they are perfectly made. These deviations from the idealized lens performance are called aberrations of the lens.

If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture—there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e.g. in photography. In most cases the surface is concave towards the system.[8]

PolarizersPhysics

Should there be in two lenses in contact the same focal lengths for three colours a, b, and c, i.e. f a = f b = f c = f {\displaystyle f_{a}=f_{b}=f_{c}=f} , then the relative partial dispersion ( n c − n b ) ( n a − n b ) {\displaystyle (n_{c}-n_{b})(n_{a}-n_{b})} must be equal for the two kinds of glass employed. This follows by considering equation (4) for the two pairs of colors ac and bc. Until recently no glasses were known with a proportional degree of absorption; but R. Blair (Trans. Edin. Soc., 1791, 3, p. 3), P. Barlow, and F. S. Archer overcame the difficulty by constructing fluid lenses between glass walls. Fraunhofer prepared glasses which reduced the secondary spectrum; but permanent success was only assured on the introduction of the Jena glasses by E. Abbe and O. Schott. In using glasses not having proportional dispersion, the deviation of a third colour can be eliminated by two lenses, if an interval be allowed between them; or by three lenses in contact, which may not all consist of the old glasses. In uniting three colors an achromatism of a higher order is derived; there is yet a residual tertiary spectrum, but it can always be neglected.[8]

An image-forming optical system with aberration will produce an image which is not sharp. Makers of optical instruments need to correct optical systems to compensate for aberration. Aberrations are particularly impactful in telescopes, where they can significantly degrade the quality of observed celestial objects. Understanding and correcting these optical imperfections are crucial for astronomers to achieve clear and accurate observations.[4]

Glan-Laser polarizers are special versions of Glan-Taylor polarizers with a high laser damage threshold. These typically have higher quality crystals, better polished surfaces and the rejected beam is allowed to escape via escape windows, decreasing unwanted internal reflections and thermal damage due to the absorption of the rejected beam. View Product

In order to render spherical aberration and the deviation from the sine condition small throughout the whole aperture, there is given to a ray with a finite angle of aperture u* (width infinitely distant objects: with a finite height of incidence h*) the same distance of intersection, and the same sine ratio as to one neighboring the axis (u* or h* may not be much smaller than the largest aperture U or H to be used in the system). The rays with an angle of aperture smaller than u* would not have the same distance of intersection and the same sine ratio; these deviations are called zones, and the constructor endeavors to reduce these to a minimum. The same holds for the errors depending upon the angle of the field of view, w: astigmatism, curvature of field and distortion are eliminated for a definite value, w*, zones of astigmatism, curvature of field and distortion, attend smaller values of w. The practical optician names such systems: corrected for the angle of aperture u* (the height of incidence h*) or the angle of field of view w*. Spherical aberration and changes of the sine ratios are often represented graphically as functions of the aperture, in the same way as the deviations of two astigmatic image surfaces of the image plane of the axis point are represented as functions of the angles of the field of view.[8]

In fig. 6, taken from M. von Rohr's Theorie und Geschichte des photographischen Objectivs, the abscissae are focal lengths, and the ordinates wavelengths. The Fraunhofer lines used are shown in adjacent table.[8]

Wollaston prisms are birefringent polarizers that are designed to transmit but separate both polarizations. In contrast with the Glan-type polarizers, both beams are completely polarized and usable. The orthogonally polarized beams exit the polarizer symmetrically at a wavelength dependent angle from the incident beam. View Product

If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i.e. their distance from the axis. This distance replaces the angle u in the preceding considerations; and the aperture, i.e., the radius of the entrance pupil, is its maximum value.[8]

polarizer中文

Polarizers are defined by a few key parameters, some of which are specific to polarization optics. The most important characteristics are:

This aberration is quite distinct from that of the sharpness of reproduction; in unsharp, reproduction, the question of distortion arises if only parts of the object can be recognized in the figure. If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g., a focusing screen, intersects the ray passing through the middle of the stop. This assumption is justified if a poor image on the focusing screen remains stationary when the aperture is diminished; in practice, this generally occurs. This ray, named by Abbe a principal ray (not to be confused with the principal rays of the Gaussian theory), passes through the center of the entrance pupil before the first refraction, and the center of the exit pupil after the last refraction. From this it follows that correctness of drawing depends solely upon the principal rays; and is independent of the sharpness or curvature of the image field. Referring to fig. 4, we have O'Q'/OQ = a' tan w'/a tan w = 1/N, where N is the scale or magnification of the image. For N to be constant for all values of w, a' tan w'/a tan w must also be constant. If the ratio a'/a be sufficiently constant, as is often the case, the above relation reduces to the condition of Airy, i.e. tan w'/ tan w= a constant. This simple relation (see Camb. Phil. Trans., 1830, 3, p. 1) is fulfilled in all systems which are symmetrical with respect to their diaphragm (briefly named symmetrical or holosymmetrical objectives), or which consist of two like, but different-sized, components, placed from the diaphragm in the ratio of their size, and presenting the same curvature to it (hemisymmetrical objectives); in these systems tan w' / tan w = 1.[8]

where m and n are nonnegative integers with n ≥ m {\displaystyle n\geq m} , Φ is the azimuthal angle in radians, and ρ is the normalized radial distance. The radial polynomials R n m {\displaystyle R_{n}^{m}} have no azimuthal dependence, and are defined as

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Polarization

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Wire Grid Polarizing Cube Beamsplitters are polarizing cube beamsplitters that use a wire grid polarizer in between the hypotenuses of the two prisms. These polarizers combine the easy alignment of polarizing cube beamsplitters with the large angle acceptance and environmental stability of wire grid polarizers. View Product

The focal lengths are made equal for the lines C and F. In the neighborhood of 550 nm the tangent to the curve is parallel to the axis of wavelengths; and the focal length varies least over a fairly large range of color, therefore in this neighborhood the color union is at its best. Moreover, this region of the spectrum is that which appears brightest to the human eye, and consequently this curve of the secondary on spectrum, obtained by making f C = f F {\displaystyle f_{C}=f_{F}} , is, according to the experiments of Sir G. G. Stokes (Proc. Roy. Soc., 1878), the most suitable for visual instruments (optical achromatism,). In a similar manner, for systems used in photography, the vertex of the color curve must be placed in the position of the maximum sensibility of the plates; this is generally supposed to be at G'; and to accomplish this the F and violet mercury lines are united. This artifice is specially adopted in objectives for astronomical photography (pure actinic achromatism). For ordinary photography, however, there is this disadvantage: the image on the focusing-screen and the correct adjustment of the photographic sensitive plate are not in register; in astronomical photography this difference is constant, but in other kinds it depends on the distance of the objects. On this account the lines D and G' are united for ordinary photographic objectives; the optical as well as the actinic image is chromatically inferior, but both lie in the same place; and consequently the best correction lies in F (this is known as the actinic correction or freedom from chemical focus).[8]

Although defocus is technically the lowest-order of the optical aberrations, it is usually not considered as a lens aberration, since it can be corrected by moving the lens (or the image plane) to bring the image plane to the optical focus of the lens.

Brewster windows are uncoated windows that are placed at Brewster’s angle. A single Brewster window has a relatively poor extinction ratio. While this extinction ratio is sufficient for many laser cavity applications due to the many round trips in this cavity, for other applications it can be enhanced by placing multiple Brewster windows in succession (also called a pile of plates). Due to the dependence on the Fresnel equations the acceptance angle is very small for Brewster windows, limiting their use to tightly collimated beams. View Product

A point O (fig. 2) at a finite distance from the axis (or with an infinitely distant object, a point which subtends a finite angle at the system) is, in general, even then not sharply reproduced if the pencil of rays issuing from it and traversing the system is made infinitely narrow by reducing the aperture stop; such a pencil consists of the rays which can pass from the object point through the now infinitely small entrance pupil. It is seen (ignoring exceptional cases) that the pencil does not meet the refracting or reflecting surface at right angles; therefore it is astigmatic (Gr. a-, privative, stigmia, a point). Naming the central ray passing through the entrance pupil the axis of the pencil or principal ray, it can be said: the rays of the pencil intersect, not in one point, but in two focal lines, which can be assumed to be at right angles to the principal ray; of these, one lies in the plane containing the principal ray and the axis of the system, i.e. in the first principal section or meridional section, and the other at right angles to it, i.e. in the second principal section or sagittal section. We receive, therefore, in no single intercepting plane behind the system, as, for example, a focusing screen, an image of the object point; on the other hand, in each of two planes lines O' and O" are separately formed (in neighboring planes ellipses are formed), and in a plane between O' and O" a circle of least confusion. The interval O'O", termed the astigmatic difference, increases, in general, with the angle W made by the principal ray OP with the axis of the system, i.e. with the field of view. Two astigmatic image surfaces correspond to one object plane; and these are in contact at the axis point; on the one lie the focal lines of the first kind, on the other those of the second. Systems in which the two astigmatic surfaces coincide are termed anastigmatic or stigmatic.[8]

With Damage Thresholds up to 0.3 J/cm2 @ 200 fs @ 800nm, these Ultrafast Thin Film Polarizers are ideal for high powered Ti:Sapphire and Ytterbium doped lasers in the NIR range. These polarizers impart minimal dispersion when separating S and P polarizations and are available in transmissive and reflective versions. View Product

If a constant of reproduction, for instance the focal length, be made equal for two colors, then it is not the same for other colors, if two different glasses are employed. For example, the condition for achromatism (4) for two thin lenses in contact is fulfilled in only one part of the spectrum, since d n 2 / d n 1 {\displaystyle dn_{2}/dn_{1}} varies within the spectrum. This fact was first ascertained by J. Fraunhofer, who defined the colors by means of the dark lines in the solar spectrum; and showed that the ratio of the dispersion of two glasses varied about 20% from the red to the violet (the variation for glass and water is about 50%). If, therefore, for two colors, a and b, f a = f b = f {\displaystyle f_{a}=f_{b}=f} , then for a third color, c, the focal length is different; that is, if c lies between a and b, then f c < f {\displaystyle f_{c}

Mounted Linear Glass Polarizing Filters come in a variety of standard thread sizes and are able to be threaded into imaging systems to reduce glare and hot spots. Additionally, they can be stacked for variable optical density effects. View Product

Aberrations fall into two classes: monochromatic and chromatic. Monochromatic aberrations are caused by the geometry of the lens or mirror and occur both when light is reflected and when it is refracted. They appear even when using monochromatic light, hence the name.

Polarization is an important characteristic of light. Polarizers are key optical elements for controlling your polarization, transmitting a desired polarization state while reflecting, absorbing or deviating the rest. There is a wide variety of polarizer designs, each with its own advantages and disadvantages. To help you select the best polarizer for your application, we will discuss polarizer specifications as well as the different classes of polarizer designs.

The nature of the reproduction consists in the rays proceeding from a point O being united in another point O'; in general, this will not be the case, for ξ', η' vary if ξ, η be constant, but x, y variable. It may be assumed that the planes I' and II' are drawn where the images of the planes I and II are formed by rays near the axis by the ordinary Gaussian rules; and by an extension of these rules, not, however, corresponding to reality, the Gauss image point O'0, with coordinates ξ'0, η'0, of the point O at some distance from the axis could be constructed. Writing Dξ'=ξ'-ξ'0 and Dη'=η'-η'0, then Dξ' and Dη' are the aberrations belonging to ξ, η and x, y, and are functions of these magnitudes which, when expanded in series, contain only odd powers, for the same reasons as given above. On account of the aberrations of all rays which pass through O, a patch of light, depending in size on the lowest powers of ξ, η, x, y which the aberrations contain, will be formed in the plane I'. These degrees, named by J. Petzval[16] the numerical orders of the image, are consequently only odd powers; the condition for the formation of an image of the mth order is that in the series for Dξ' and Dη' the coefficients of the powers of the 3rd, 5th...(m-2)th degrees must vanish. The images of the Gauss theory being of the third order, the next problem is to obtain an image of 5th order, or to make the coefficients of the powers of 3rd degree zero. This necessitates the satisfying of five equations; in other words, there are five alterations of the 3rd order, the vanishing of which produces an image of the 5th order.[8]

Optical path length: The length light must travel through the polarizer. Important for dispersion, damage thresholds, and space constraints, optical path lengths can be significant in birefringent polarizers but are usually short in dichroic polarizers.

Circular polarizers are not a separate type of polarizer, as they are the combination of a linear polarizer with a correctly aligned quarter waveplate. The polarizer linearly polarizers the incident light, and the quarter waveplate at 45° turns this linearly polarized light into circularly polarized light. The advantage is that the polarizer and waveplate axes are always aligned correctly relative to each other so no alignment is necessary and there is no concern of generating elliptically polarized light. They are ideal for reducing flare in imaging applications and are available in left and right-handed versions. View Product

The meaning of PRISM is a polyhedron with two polygonal faces lying in parallel planes and with the other faces parallelograms.

TECHSPEC High Energy Laser Line Polarizers are used to transmit P-polarized light while reflecting S-polarized light. With high laser damage thresholds and extinction ratios for optimal performance, these polarizers are ideal for a wide range of laser applications. The UV grade fused silica substrate maximizes performance, while the hard anti-reflection coating makes these durable polarizers easy to clean and simple to align. View Product

Consisting of a polymer polarization film layered between two flat pieces of optical glass, NIR Linear Polarizers are ideal for NIR sources including low power lasers and LEDs. View Product

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Broadband polarizing plate beamsplitters are coated windows, placed at an angle, that transmit p-polarization and reflect s-polarization. The coating on the plate generally works in either interference or internal Brewster’s angle principles. In contrast to many birefringent polarizers, both the reflected and transmitted beams are usable. These beamsplitters are useful in weight or space constrained applications and where laser damage threshold and a short optical path length are important. A disadvantage is the appearance of ghost reflections from the second surface and beam deviation. These also exist in ultrafast versions which are ideal for femtosecond pulsed lasers. View Product

The expression for these coefficients in terms of the constants of the optical system, i.e. the radii, thicknesses, refractive indices and distances between the lenses, was solved by L. Seidel;[17] in 1840, J. Petzval constructed his portrait objective, from similar calculations which have never been published.[18] The theory was elaborated by S. Finterswalder,[19] who also published a posthumous paper of Seidel containing a short view of his work;[20] a simpler form was given by A. Kerber.[21] A. Konig and M. von Rohr[22]: 317–323  have represented Kerber's method, and have deduced the Seidel formulae from geometrical considerations based on the Abbe method, and have interpreted the analytical results geometrically.[22]: 212–316 [8]

The largest opening of the pencils, which take part in the reproduction of O, i.e., the angle u, is generally determined by the margin of one of the lenses or by a hole in a thin plate placed between, before, or behind the lenses of the system. This hole is termed the stop or diaphragm; Abbe used the term aperture stop for both the hole and the limiting margin of the lens. The component S1 of the system, situated between the aperture stop and the object O, projects an image of the diaphragm, termed by Abbe the entrance pupil; the exit pupil is the image formed by the component S2, which is placed behind the aperture stop. All rays which issue from O and pass through the aperture stop also pass through the entrance and exit pupils, since these are images of the aperture stop. Since the maximum aperture of the pencils issuing from O is the angle u subtended by the entrance pupil at this point, the magnitude of the aberration will be determined by the position and diameter of the entrance pupil. If the system be entirely behind the aperture stop, then this is itself the entrance pupil (front stop); if entirely in front, it is the exit pupil (back stop).[8]

Damage threshold: The laser damage threshold is determined by the material used as well as the polarizer design, with birefringent polarizers typically having the highest damage threshold. Cement is often the most susceptible element to laser damage, which is why optically contacted beamsplitters or air spaced birefringent polarizers have higher damage thresholds.

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If rays issuing from O (fig. 1) are concurrent, it does not follow that points in a portion of a plane perpendicular at O to the axis will be also concurrent, even if the part of the plane be very small. As the diameter of the lens increases (i.e., with increasing aperture), the neighboring point N will be reproduced, but attended by aberrations comparable in magnitude to ON. These aberrations are avoided if, according to Abbe, the sine condition, sin u'1/sin u1=sin u'2/sin u2, holds for all rays reproducing the point O. If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence; the sine condition then becomes sin u'1/h1=sin u'2/h2. A system fulfilling this condition and free from spherical aberration is called aplanatic (Greek a-, privative, plann, a wandering). This word was first used by Robert Blair to characterize a superior achromatism, and, subsequently, by many writers to denote freedom from spherical aberration as well.[8]

Glan-Thompson polarizers have the largest acceptance angle of the Glan-type polarizers. Cement is used to join the prisms together, which causes a low optical damage threshold. View Product

Dichroic polarizers transmit the desired polarization and absorb the rest. This is achieved via anisotropy in the polarizer; common examples are oriented polymer molecules and stretched nanoparticles. This is a broad class of polarizers, going from low cost laminated plastic polarizers to precision high cost glass nanoparticle polarizers. Most dichroic polarizers have good extinction ratios relative to their cost. Their damage thresholds and environmental stability are often limited, although glass dichroic polarizers outperform plastic dichroic polarizers in this aspect. Dichroic polarizers are well suited for microscopy, imaging and display applications, and are often the only choice when very large apertures are necessary.

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Newton failed to perceive the existence of media of different dispersive powers required by achromatism; consequently he constructed large reflectors instead of refractors. James Gregory and Leonhard Euler arrived at the correct view from a false conception of the achromatism of the eye; this was determined by Chester More Hall in 1728, Klingenstierna in 1754 and by Dollond in 1757, who constructed the celebrated achromatic telescopes. (See telescope.)[8]

The eyepiece, also called the ocular lens, is a low power lens. · The objective lenses of compound microscopes are parfocal. · The field of view is widest on the ...

Half wave plate

Glan-Taylor polarizers have a higher optical damage threshold than Glan-Thompson due to an air gap instead of cement in between the two constituent prisms. They have a shorter optical path length but also a smaller acceptance angle than Glan-Thompson polarizers. View Product

Insert main image shown at top of tool here Looking for a custom polarizer? Edmund Optics® offers custom polymer polarizers and retarders in a wide range of film types, sizes, and shapes. Products include linear and circular polymer polarizers, and retarders. To obtain pricing information for our most popular laser-cut polarizing films please enter your requirements below. If you cannot find what you are looking for please contact our product support team and we will be happy to assist you with your enquiry.

Broadband polarizing cube beamsplitters are similar to polarizing plate beamsplitters, but the coating is placed in between two right angle prisms. Mounting and aligning polarizing cube beamsplitters is easier than plate beamsplitters and there is less beam deviation, but they have a longer optical path length, take up more space and weigh more. They are ideal for collimated light sources and are more efficient than wire grid polarizing cube beamsplitters. (Non-polarizing cube beamsplitters exist as well; for more information on these, please read What are Beamsplitters?) View Product

In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point.[1] Aberrations cause the image formed by a lens to be blurred or distorted, with the nature of the distortion depending on the type of aberration. Aberration can be defined as a departure of the performance of an optical system from the predictions of paraxial optics.[2] In an imaging system, it occurs when light from one point of an object does not converge into (or does not diverge from) a single point after transmission through the system. Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.[3]

The aberrations of the third order are: (1) aberration of the axis point; (2) aberration of points whose distance from the axis is very small, less than of the third order — the deviation from the sine condition and coma here fall together in one class; (3) astigmatism; (4) curvature of the field; (5) distortion.[8]

For two thin lenses separated by a distance D {\displaystyle D} the condition for achromatism is D = v 1 f 1 + v 2 f 2 {\displaystyle D=v_{1}f_{1}+v_{2}f_{2}} ; if v 1 = v 2 {\displaystyle v_{1}=v_{2}} (e.g. if the lenses be made of the same glass), this reduces to D = ( f 1 + f 2 ) / 2 {\displaystyle D=(f_{1}+f_{2})/2} , known as the condition for oculars.[8]

Acceptance angle: The acceptance angle is the largest deviation from design incidence angle at which the polarizer will still perform within specifications. Most polarizers are designed to work at an incidence angle of 0° or 45°, or at Brewster’s angle. The acceptance angle is important for alignment but has particular importance when working with non-collimated beams. Wire grid and dichroic polarizers have the largest acceptance angles, up to a full acceptance angle of almost 90°.

In practice it is more advantageous (after Abbe) to determine the chromatic aberration (for instance, that of the distance of intersection) for a fixed position of the object, and express it by a sum in which each component conlins the amount due to each refracting surface.[26][27][8] In a plane containing the image point of one color, another colour produces a disk of confusion; this is similar to the confusion caused by two zones in spherical aberration. For infinitely distant objects the radius Of the chromatic disk of confusion is proportional to the linear aperture, and independent of the focal length (vide supra, Monochromatic Aberration of the Axis Point); and since this disk becomes the less harmful with an increasing image of a given object, or with increasing focal length, it follows that the deterioration of the image is proportional to the ratio of the aperture to the focal length, i.e. the relative aperture. (This explains the gigantic focal lengths in vogue before the discovery of achromatism.)[8]

where ρ {\displaystyle \rho } is the normalized pupil radius with 0 ≤ ρ ≤ 1 {\displaystyle 0\leq \rho \leq 1} , ϕ {\displaystyle \phi } is the azimuthal angle around the pupil with 0 ≤ ϕ ≤ 2 π {\displaystyle 0\leq \phi \leq 2\pi } , and the fitting coefficients a 0 , … , a 8 {\displaystyle a_{0},\ldots ,a_{8}} are the wavefront errors in wavelengths.

Instead of making d f {\displaystyle df} vanish, a certain value can be assigned to it which will produce, by the addition of the two lenses, any desired chromatic deviation, e.g. sufficient to eliminate one present in other parts of the system. If the lenses I. and II. be cemented and have the same refractive index for one color, then its effect for that one color is that of a lens of one piece; by such decomposition of a lens it can be made chromatic or achromatic at will, without altering its spherical effect. If its chromatic effect ( d f / f {\displaystyle df/f} ) be greater than that of the same lens, this being made of the more dispersive of the two glasses employed, it is termed hyper-chromatic.[8]

Chromatic aberration occurs when different wavelengths are not focussed to the same point. Types of chromatic aberration are:

The constancy of a'/a necessary for this relation to hold was pointed out by R. H. Bow (Brit. Journ. Photog., 1861), and Thomas Sutton (Photographic Notes, 1862); it has been treated by O. Lummer and by M. von Rohr (Zeit. f. Instrumentenk., 1897, 17, and 1898, 18, p. 4). It requires the middle of the aperture stop to be reproduced in the centers of the entrance and exit pupils without spherical aberration. M. von Rohr showed that for systems fulfilling neither the Airy nor the Bow-Sutton condition, the ratio a' cos w'/a tan w will be constant for one distance of the object. This combined condition is exactly fulfilled by holosymmetrical objectives reproducing with the scale 1, and by hemisymmetrical, if the scale of reproduction be equal to the ratio of the sizes of the two components.[8]

The final form of a practical system consequently rests on compromise; enlargement of the aperture results in a diminution of the available field of view, and vice versa. But the larger aperture will give the larger resolution. The following may be regarded as typical:[8]

Clear aperture: The clear aperture is typically most restrictive for birefringent polarizers as the availability of optically pure crystals limits the size of these polarizers. Dichroic polarizers have the largest available clear apertures as their fabrication lends itself to larger sizes.

The condition for the reproduction of a surface element in the place of a sharply reproduced point — the constant of the sine relationship must also be fulfilled with large apertures for several colors. E. Abbe succeeded in computing microscope objectives free from error of the axis point and satisfying the sine condition for several colors, which therefore, according to his definition, were aplanatic for several colors; such systems he termed apochromatic. While, however, the magnification of the individual zones is the same, it is not the same for red as for blue; and there is a chromatic difference of magnification. This is produced in the same amount, but in the opposite sense, by the oculars, which Abbe used with these objectives (compensating oculars), so that it is eliminated in the image of the whole microscope. The best telescope objectives, and photographic objectives intended for three-color work, are also apochromatic, even if they do not possess quite the same quality of correction as microscope objectives do. The chromatic differences of other errors of reproduction seldom have practical importance.[8]

In addition to these aberrations, piston and tilt are effects which shift the position of the focal point. Piston and tilt are not true optical aberrations, since when an otherwise perfect wavefront is altered by piston and tilt, it will still form a perfect, aberration-free image, only shifted to a different position.

Thin Film polarizers utilize a thin-film dielectric coating to separate a beam into s- and p-polarization, commonly at a 45 degree AOI. They are often specified for optimal transmission/reflection performance at laser line wavelengths.

The extinction performance of a linear polarizer is often expressed as 1 / ρp : 1. This parameter ranges from less than 100:1 for economical sheet polarizers to 106:1 for high quality birefringent crystalline polarizers. The extinction ratio typically varies with wavelength and incident angle and must be evaluated along with other factors like cost, size, and polarized transmission for a given application.

The circle polynomials were introduced by Frits Zernike to evaluate the point image of an aberrated optical system taking into account the effects of diffraction. The perfect point image in the presence of diffraction had already been described by Airy, as early as 1835. It took almost hundred years to arrive at a comprehensive theory and modeling of the point image of aberrated systems (Zernike and Nijboer). The analysis by Nijboer and Zernike describes the intensity distribution close to the optimum focal plane. An extended theory that allows the calculation of the point image amplitude and intensity over a much larger volume in the focal region was recently developed (Extended Nijboer-Zernike theory). This Extended Nijboer-Zernike theory of point image or 'point-spread function' formation has found applications in general research on image formation, especially for systems with a high numerical aperture, and in characterizing optical systems with respect to their aberrations.[15]

A ray proceeding from an object point O (fig. 5) can be defined by the coordinates (ξ, η). Of this point O in an object plane I, at right angles to the axis, and two other coordinates (x, y), the point in which the ray intersects the entrance pupil, i.e. the plane II. Similarly the corresponding image ray may be defined by the points (ξ', η'), and (x', y'), in the planes I' and II'. The origins of these four plane coordinate systems may be collinear with the axis of the optical system; and the corresponding axes may be parallel. Each of the four coordinates ξ', η', x', y' are functions of ξ, η, x, y; and if it be assumed that the field of view and the aperture be infinitely small, then ξ, η, x, y are of the same order of infinitesimals; consequently by expanding ξ', η', x', y' in ascending powers of ξ, η, x, y, series are obtained in which it is only necessary to consider the lowest powers. It is readily seen that if the optical system be symmetrical, the origins of the coordinate systems collinear with the optical axis and the corresponding axes parallel, then by changing the signs of ξ, η, x, y, the values ξ', η', x', y' must likewise change their sign, but retain their arithmetical values; this means that the series are restricted to odd powers of the unmarked variables.[8]

Construction: Polarizers come in many forms and designs. Thin film polarizers are thin films similar to optical filters. Polarizing plate beamsplitters are thin, flat plates placed at an angle to the beam. Polarizing cube beamsplitters consist of two right angle prisms mounted together at the hypotenuse. Birefringent polarizers consist of two crystalline prisms mounted together, where the angle of the prisms is determined by the specific polarizer design.

Polarizer Filter

In optical systems composed of lenses, the position, magnitude and errors of the image depend upon the refractive indices of the glass employed (see Lens (optics) and Monochromatic aberration, above). Since the index of refraction varies with the color or wavelength of the light (see dispersion), it follows that a system of lenses (uncorrected) projects images of different colors in somewhat different places and sizes and with different aberrations; i.e. there are chromatic differences of the distances of intersection, of magnifications, and of monochromatic aberrations. If mixed light be employed (e.g. white light) all these images are formed and they cause a confusion, named chromatic aberration; for instance, instead of a white margin on a dark background, there is perceived a colored margin, or narrow spectrum. The absence of this error is termed achromatism, and an optical system so corrected is termed achromatic. A system is said to be chromatically under-corrected when it shows the same kind of chromatic error as a thin positive lens, otherwise it is said to be overcorrected.[8]

Birefringent polarizers transmit the desired polarization and deviate the rest. They rely on birefringent crystals, where the refractive index of light depends on its polarization. Unpolarized light at non-normal incidence will split into two separate beams upon entering the crystal, as the refraction for s- and p-polarized light will be different. Most designs consist of two joined birefringent prisms, where the angle they are joined at and the relative orientation of their optical axes determine the functionality of the polarizer. Because these polarizers require optically pure crystals they are expensive, but have high laser damage thresholds, excellent extinction ratios and broad wavelength ranges.

Chromatic aberrations are caused by dispersion, the variation of a lens's refractive index with wavelength. Because of dispersion, different wavelengths of light come to focus at different points. Chromatic aberration does not appear when monochromatic light is used.

Due to their high extinction ratios, along with their exceptional transmission in the visible spectrum (400 – 700nm), High Contrast Linear Polarizers are an ideal choice for applications involving imaging. Aside from surface flatness and extinction ratio, these plastic substrate polarizers are a high performance and cost-effective alternative to High Contrast Glass Linear Polarizers with more durability than polarizing film. View Product

Cost: Some polarizers require large, very pure crystals, which are expensive, while others are made of stretched plastic, which make them more economical.

In a perfect optical system in the classical theory of optics,[5][6] rays of light proceeding from any object point unite in an image point; and therefore the object space is reproduced in an image space. The introduction of simple auxiliary terms, due to Gauss,[7][8] named the focal lengths and focal planes, permits the determination of the image of any object for any system. The Gaussian theory, however, is only true so long as the angles made by all rays with the optical axis (the symmetrical axis of the system) are infinitely small, i.e., with infinitesimal objects, images and lenses; in practice these conditions may not be realized, and the images projected by uncorrected systems are, in general, ill-defined and often blurred if the aperture or field of view exceeds certain limits.[8]

High Contrast Glass Linear Polarizers offer very high extinction ratios and have exceptional surface flatness for optical grade wavefront qualities. They are anti-reflection (AR) coated to minimize light loss from reflection and achieve a transmission of approximately 25% for randomly polarized visible light (400 – 700nm). High Contrast Glass Linear Polarizers are available in a large variety of sizes. View Product

The aberrations can also be expressed by means of the characteristic function of the system and its differential coefficients, instead of by the radii, &c., of the lenses; these formulae are not immediately applicable, but give, however, the relation between the number of aberrations and the order. Sir William Rowan Hamilton (British Assoc. Report, 1833, p. 360) thus derived the aberrations of the third order; and in later times the method was pursued by Clerk Maxwell (Proc. London Math. Soc., 1874–1875; (see also the treatises of R. S. Heath and L. A. Herman), M. Thiesen (Berlin. Akad. Sitzber., 1890, 35, p. 804), H. Bruns (Leipzig. Math. Phys. Ber., 1895, 21, p. 410), and particularly successfully by K. Schwarzschild (Göttingen. Akad. Abhandl., 1905, 4, No. 1), who thus discovered the aberrations of the 5th order (of which there are nine), and possibly the shortest proof of the practical (Seidel) formulae. A. Gullstrand (vide supra, and Ann. d. Phys., 1905, 18, p. 941) founded his theory of aberrations on the differential geometry of surfaces.[8]

Practical methods solve this problem with an accuracy which mostly suffices for the special purpose of each species of instrument. The problem of finding a system which reproduces a given object upon a given plane with given magnification (insofar as aberrations must be taken into account) could be dealt with by means of the approximation theory; in most cases, however, the analytical difficulties were too great for older calculation methods but may be ameliorated by application of modern computer systems. Solutions, however, have been obtained in special cases.[24] At the present time constructors almost always employ the inverse method: they compose a system from certain, often quite personal experiences, and test, by the trigonometrical calculation of the paths of several rays, whether the system gives the desired reproduction (examples are given in A. Gleichen, Lehrbuch der geometrischen Optik, Leipzig and Berlin, 1902). The radii, thicknesses and distances are continually altered until the errors of the image become sufficiently small. By this method only certain errors of reproduction are investigated, especially individual members, or all, of those named above. The analytical approximation theory is often employed provisionally, since its accuracy does not generally suffice.[8]

The investigations of James Clerk Maxwell[9] and Ernst Abbe[note 1] showed that the properties of these reproductions, i.e., the relative position and magnitude of the images, are not special properties of optical systems, but necessary consequences of the supposition (per Abbe) of the reproduction of all points of a space in image points, and are independent of the manner in which the reproduction is effected. These authors showed, however, that no optical system can justify these suppositions, since they are contradictory to the fundamental laws of reflection and refraction. Consequently, the Gaussian theory only supplies a convenient method of approximating reality; realistic optical systems fall short of this unattainable ideal. Currently, all that can be accomplished is the projection of a single plane onto another plane; but even in this, aberrations always occurs and it may be unlikely that these will ever be entirely corrected.[8]