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where V 1 and V 2 are the Abbe numbers of the materials of the first and second lenses, respectively. Since Abbe numbers are positive, one of the focal lengths must be negative, i.e., a diverging lens, for the condition to be met. The overall focal length of the doublet f is given by the standard formula for thin lenses in contact:
Higher Abbe numbers mean a better lens material, and lower Abbe numbers result in the presence of chromatic aberration (i.e., color fringes above/below or to the left/right of a high contrast object), especially in larger lens sizes and stronger prescriptions (beyond ±4.00D). Generally, lower Abbe numbers are a property of mid and higher index ...
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 ...
A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x).The lens focuses light in the same way as a conventional lens. Gradient-index (GRIN) optics is the branch of optics covering optical effects produced by a gradient of the refractive index of a material.
Refraction of light at the interface between two media of different refractive indices, with n 2 > n 1.Since the velocity is lower in the second medium (v 2 < v 1), the angle of refraction θ 2 is less than the angle of incidence θ 1; that is, the ray in the higher-index medium is closer to the normal.
A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x). The lens focuses light in the same way as a conventional lens. If the refractive index of a medium is not constant but varies gradually with the position, the material is known as a gradient-index (GRIN) medium and is described by gradient index ...
For a single lens surrounded by a medium of refractive index n = 1, the locations of the principal points H and H ′ with respect to the respective lens vertices are given by the formulas = ′ = (), where f is the focal length of the lens, d is its thickness, and r 1 and r 2 are the radii of curvature of its surfaces. Positive signs indicate ...
* σ is the Gaussian standard deviation of the center locations of the same molecule if measured multiple times (e.g. frames of a video). (unit m) * σ PSF is the Gaussian standard deviation of the point spread function, whose FWHM following the Ernst Abbe equation d = λ/(2 N.A.). (unit m) * a is the size of each image pixel. (unit m)