Measuring method named after Ernst Abbe used to determine the focal length and the position of the principal planes of a lens singlet or a lens system on the optical axis.
Determination of the focal length of single lenses according to Abbe: To determine the focal length of a single lens, you need an object (light source and slit), a screen and the lens whose focal length is to be determined. The position of the lens is fixed on an optical bench. The object and screen are positioned so that a sharp image is obtained. A further focus is made for an object displaced by d . The focal length f zu results from d , the object size G and the two image sizes B and B',
Lens system: Attached to all lenses rigidly to each other on a tab and defining a reference point on this fixed, is obtained by shifting the object and screen to different focus positions three series of measurements of the distance x to the object, the distance x ' to the image and the image size B . With the image scale the following equations result:
The parameters h , h ' correspond to the distances between the object or image-side main plane and the reference point. This and the focal length f can be obtained from the measurement series by means of a linear regression. f and f 'often have the same amount but a different sign.
The ABBE number is a dimensionless parameter named after Ernst Abbe. also known as the V-number or constringence of a transparent material, is an approximate measure of the material's dispersion (change of refractive index versus wavelength).
The ABBE number is mainly used to characterize and monitor the quality of glasses and polymers used in lens production.
Ray transfer matrix
is a 2x2 matrix describing the effect of an optical element on a laser beam, are used in paraxial optical design
An ABCD Matrix that describes the optical element is formed. The ABCD Matrix is multiplied by the input vector
The result is an output vector that describes the output beam with a new distance from the optical axis and a new angle off the optical axis.
Aberration for lenses made with spherical surfaces
For lenses made with spherical surfaces, rays which are parallel to the optic axis but at different distances from the optic axis fail to converge to the same point. If the center of the image stay in focus an bright, the edges of the field apprear blurry and dimmeter.
Light of different wavelengths are refracted by a lens at different strengths i.e. the distance of the Wavelength of a lens deviates minimally for each color.
Absolute displacement transducer
An absolute displacement transducer measures the distance to an object and supplies a signal proportional to the displacement. These transducers are based on various physical principles.