Aspheric lens

An aspherical lens is a lens having an optically active form deviating from the spherical shape. Due to the higher number of parameters mapping errors can be avoided, which are unavoidable with the spherical lenses. Specifically, you can completely correct the spherical aberration, but the production of glass is considerably more complex than that of a spherical element.

• 3.1 grinding
• 3.2 impression
• 3.3 magnetorheological polishing
• 3.4 Ion beam figuring
• 3.5 Mechanical stress

Form

The shape of rotationally symmetric aspheric lenses is usually specified as a conic section (circle, ellipse, parabola, hyperbola ) plus a power series for higher-order deformations. Not Rotationally symmetrical aspheric lenses can be off-axis cut-outs of such conics, but be freely defined in all directions optical surfaces ( free-form aspheric lenses ).

Formula according to DIN ISO 10110 Optics and photonics - Preparation of drawings for optical elements and systems, Part 12 Aspheric surfaces with:

• Z = sagitta
• R = distance perpendicular to the axis ( height of incidence )
• R = vertex radius
• K = conic constant
• A4, A6, ... = aspherical parameters

The paraxial behavior of the aspherical surface is determined only by the vertex radius R.

Special cases aspherical lenses, the cylindrical lens ( radius of constant curvature in a section plane, infinite radius of curvature in the sectional plane perpendicular thereto ), and the toric lens (two different radii of curvature in two mutually perpendicular cutting planes ).

Calculation of plano-convex lens

Using a plano-convex lens, the shape of the corresponding aspherical surface are relatively easy illustrated. Considering an optical image from infinity with a parallel, monochromatic light through such a lens with the radius of curvature at the height of incidence, resulting in the situation shown in the adjacent figure.

For calculating the aspherical surface of the light beams can be considered to fall parallel to the optical axis on the object side, plane surface of the lens to the height of incidence. They are not refracted on entering the optically denser medium of the lens material having a refractive index as to impinge vertically. These beams to form the image side of the lens in the lens Oberflächenlot the angle and the angle outside the lens. These angles behave as described by Snell's law. The following relations hold:

The optical axis intersect the rays then the angle

For paraxial rays ( ) results in a back focal distance focal length respectively by:

,

Wherein the radius at the apex of the lens on the optical axis.

The arrow height as measured from the principal plane of the lens may then be determined as a function of the height of incidence with the aid of some auxiliary parameters on the basis of and in steps of iteratively:

For the average distance from the vertex of the sphere with the radius on the optical axis:

Finally, the vertex distance from the principal plane results from the difference of average length by the average width for paraxial rays:

Example

The following table shows some example values ​​calculated in this way are, and given the unitless dimensions and length. With increasing height of incidence, the radii of curvature are getting bigger and both the centers and vertices of the corresponding circles to remove the object side further and further from the main level.

Up to a height of incidence of the convex surface 140 of the lens corresponds to ISO 10110-12 (see above) without further aspherical parameters in the higher members of the relatively accurate relationship for a hyperboloid with the conical constant k = -2:

Applications

• Aspherical condenser lenses are used for light collection in projectors and spotlights and here enable a higher light output, because the aperture can be increased without the spherical aberration disturbing.
• Aspheric lenses: by the deviation from the spherical shape can be flatter, thinner, lighter and optically better lenses, especially for long-sighted ( hyperopia ), produce.
• High-quality eyepieces, especially wide angle eyepieces of telescopes and binoculars with image angles up to 70 °, consist of up to 8 partly cemented together lenses, and are sometimes provided with an aspherical surface.
• Zoom ( varifocal ) lenses with variable focal length, such as camera lenses. These are more difficult to calculate and produce, the greater their focal length range is, for the correction of aberrations must be done as a compromise for all adjustable focal lengths. Such systems thus often have many lenses, sometimes more than 15, and they can be realized only in part by aspherical lenses with acceptable imaging errors. It may make economic sense for simpler lenses use aspherical, since cover (see below ) allow this by molding relatively inexpensive produce, and thus correspondingly fewer lenses needed to correct the error sufficiently.
• Photo lenses with high intensity and wide-angle lenses with very large picture angle. If you make the aperture or the angle of the lenses very large, the aberrations grow strong and require a high Korrektionsaufwand. Aspherical surfaces are helpful to correct the error well and at the same time not to let the lens number and the size and weight of the lens grow excessively.
• The aspherical correcting plate of the Schmidt telescope. It eliminates the spherical aberration of the primary mirror almost completely, which otherwise the resolution and the image field diminishes.
• Focusing lenses for diode laser radiation can be aspherical, to cope with the large apertures. An alternative gradient lenses.

Production

The production of aspherical surfaces can be made by a variety of methods:

Grind

Grinding is the oldest, but the most laborious process to produce aspherical glass lenses. For several decades, there are camera lenses with these lenses, but to the production stage of molding techniques, they were limited to very high quality and expensive lenses. Since 2000, the machine technology -based CNC control has evolved to the extent that today ( 2013) the use of CNC machines for production of aspheric lenses is common practice. Well-known machine manufacturers in the German-speaking countries are the companies Satisloh, OptoTech and Schneider Optical Machinery. The CNC machining allows especially the processing of quartz or of optics with large diameters, which can not, or not by means of impression be made ​​in the required quality. They are mainly in the fields of test and measurement, medical technology, laser technology, as well as in the aviation and aerospace industry. Renowned Asphärenhersteller in Germany Zeiss, Jenoptik and asphericon.

Impression

This low cost for mass production method is often used, for example for camera, condenser, as well as for laser pick -up optics in DVD players.

• Aspherical lenses made ​​of plastic can be manufactured very inexpensively by molding. However, for camera lenses their dimensional accuracy and constancy of their properties are not good enough.
• Can be pressed onto a spherical glass lens, a plastic layer with an aspherical surface. The quality of such an element is sufficient for photographic lenses of average quality.
• For high quality camera lenses, a lens is directly connected to a molded aspheric surface produced ( Molding ). But it takes for suitable glasses with not too high transformation temperature, because the material, the ram is only limited temperature resistant. You can not use any optical glass thus.

A magnetorheological polishing

As a magnetorheological polishing (English Magneto Rheological Finishing MRF ) is called a polishing process of optical components such as lenses. The method can also be used for local correction.

Ion beam figuring

Ion Beam Figuring (also known as ion milling ), a surface treatment method in which the material is removed by means of an ion beam, as it were, a sandblaster at the atomic level.

Mechanical stress

The optics can be deformed during grinding by force; it is then spherically ground. The spherical surface is removed from the mold after releasing the tension and so gives the asphere. One example is the Schmidt plate, it is deformed by a negative pressure and then ground flat on one side.

Alternatively can be deformed by a force acting on a spherical surface of an aspherical surface.