The concept of geodesic curvature applied to optical surfaces

2015 ◽  
Vol 35 (4) ◽  
pp. 388-393 ◽  
Author(s):  
Sergio Barbero
Keyword(s):  
Geodesic Curvature ◽  
Optical Surfaces

Distribution and effects of organic contaminants on optical surfaces - Modeling

1998 ◽  
Author(s):  
Robert Long, Jr. ◽  
Fred Rigby ◽  
Lawrence Grimes
Keyword(s):  
Organic Contaminants ◽  
Optical Surfaces

scholarly journals Pansu–Wulff shapes in ℍ1

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Julián Pozuelo ◽  
Manuel Ritoré
Keyword(s):  
Mean Curvature ◽  
Isoperimetric Problem ◽  
Variational Formula ◽  
Geodesic Curvature ◽  
Vertical Axis ◽  
Singular Part ◽  
Tangent Plane ◽  
Curvature Function ◽  
Invariant Norm ◽  
The First Variation

Abstract We consider an asymmetric left-invariant norm ∥ ⋅ ∥ K {\|\cdot\|_{K}} in the first Heisenberg group ℍ 1 {\mathbb{H}^{1}} induced by a convex body K ⊂ ℝ 2 {K\subset\mathbb{R}^{2}} containing the origin in its interior. Associated to ∥ ⋅ ∥ K {\|\cdot\|_{K}} there is a perimeter functional, that coincides with the classical sub-Riemannian perimeter in case K is the closed unit disk centered at the origin of ℝ 2 {{\mathbb{R}}^{2}} . Under the assumption that K has C 2 {C^{2}} boundary with strictly positive geodesic curvature we compute the first variation formula of perimeter for sets with C 2 {C^{2}} boundary. The localization of the variational formula in the non-singular part of the boundary, composed of the points where the tangent plane is not horizontal, allows us to define a mean curvature function H K {H_{K}} out of the singular set. In the case of non-vanishing mean curvature, the condition that H K {H_{K}} be constant implies that the non-singular portion of the boundary is foliated by horizontal liftings of translations of ∂ ⁡ K {\partial K} dilated by a factor of 1 H K {\frac{1}{H_{K}}} . Based on this we can define a sphere 𝕊 K {\mathbb{S}_{K}} with constant mean curvature 1 by considering the union of all horizontal liftings of ∂ ⁡ K {\partial K} starting from ( 0 , 0 , 0 ) {(0,0,0)} until they meet again in a point of the vertical axis. We give some geometric properties of this sphere and, moreover, we prove that, up to non-homogeneous dilations and left-translations, they are the only solutions of the sub-Finsler isoperimetric problem in a restricted class of sets.

Recent developments in profiling optical surfaces

1993 ◽  
Vol 32 (19) ◽  
pp. 3442 ◽  
Author(s):  
Jean M. Bennett ◽  
Virgil Elings ◽  
Kevin Kjoller
Keyword(s):  
Optical Surfaces ◽  
Recent Developments

In process metrology of aspheric optical surfaces during sub-aperture polishing process

2015 ◽  
Author(s):  
L. M. Pant ◽  
M. P. Singh ◽  
K. K. Pant ◽  
A. Ghosh
Keyword(s):  
Polishing Process ◽  
Optical Surfaces
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