Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Free-form V-groove reflector design with the SMS method in three dimensions

Open Access Open Access

Abstract

The Simultaneous Multiple Surface design method in three dimensions (SMS3D) is applied to the design of free-form V-groove reflectors. The general design problem is how to achieve the coupling of two wavefronts after two reflections at the V-groove, no matter which side of the groove the rays hit first. This paper also explains a design procedure for thin dielectric grooved-reflector substitutes for conventional mirrored surfaces. Some canonical V-groove designs are ray-traced in detail.

©2011 Optical Society of America

Full Article  |  PDF Article
More Like This
Aspheric V-groove reflector design with the SMS method in two dimensions

Dejan Grabovičkić, Pablo Benítez, and Juan C. Miñano
Opt. Express 18(3) 2515-2521 (2010)

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces

Fabian Duerr, Pablo Benítez, Juan C. Miñano, Youri Meuret, and Hugo Thienpont
Opt. Express 20(10) 10839-10846 (2012)

Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

Fabian Duerr, Pablo Benítez, Juan C. Miñano, Youri Meuret, and Hugo Thienpont
Opt. Express 20(5) 5576-5585 (2012)

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 The linear 90° groove reflector 3D view and its front view.
Fig. 2
Fig. 2 Free-form V-groove reflector.
Fig. 3
Fig. 3 (a) In green, ν = constant lines of the V-groove surfaces are such that after a first reflection at either line the second reflection will be at the other line. (b) Vectors at a point of the groove edge-line (G)(v) and contained in the plane perpendicular to its tangent vector t = (G)′(v). The angle α(v) is defined as the one formed by the normal vector of the surfaces (P), NP (0,v), and the plane formed by the ray vectors v i and v o impinging on (G)(v).
Fig. 4
Fig. 4 3D V- groove reflector which reflects a plane into a spherical wavefront. Perspective and front views.
Fig. 5
Fig. 5 LightTools simulation for an asymmetric 3D V-groove design for a plane and a spherical wavefront.
Fig. 6
Fig. 6 LightTools simulation for the symmetric 3D V-groove design coupling two spherical wavefronts.
Fig. 7
Fig. 7 Free from thin dielectric sheet that acts as a TIR reflector.
Fig. 8
Fig. 8 V-groove reflector having a 90° corner as normal sections. Condition for rays having two TIR at the groove sides.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

( v o + v i ) × G '( v ) = 0.
e ( u , v + Δ v ) = P u ( u , v ) N P ( v + Δ v ) N P ( v ) Δ v P ( v + Δ v ) P ( v ) Δ v N P u ( u , v ) .
E ( v ) = 1 u max ( v ) u = 0 u max ( v ) e 2 d u .
v o = v i 2 ( v i N P ( u ) ) N P ( u ) 2 [ v i N Q ( u ) 2 ( v i N P ( u ) ) N P ( u ) N Q ( u ) ] N Q ( u ) .
v o = v i 2 ( v i N Q ( u ) ) N Q ( u ) 2 [ v i N P ( u ) 2 ( v i N Q ( u ) ) N Q ( u ) N P ( u ) ] N P ( u ) .
( N P ( 0 ) N Q ( 0 ) ) [ ( v i N P ( 0 ) ) N Q ( 0 ) ( v i N Q ( 0 ) ) N P ( 0 ) ] = 0.
v o + v i = 2 ( v i t ) t .
( v i v x ) P ( u ) = 0 , ( v i v x ) ( P ( u ) × N P ( u ) ) = 0.
( v x v o ) Q ( u ) = 0 , ( v x v o ) ( Q ( u ) × N Q ( u ) ) = 0.
( v i v x ) Q ( u ) = 0 , ( v i v x ) ( Q ( u ) × N Q ( u ) ) = 0 ,
( v x v o ) P ( u ) = 0 , ( v x v o ) ( P ( u ) × N P ( u ) ) = 0.
| P ( u ) | = 1 , | Q ( u ) | = 1.
N P ( u ) P ( u ) = 0 , N Q ( u ) Q ( u ) = 0.
| N P ( u ) | = 1 , | N Q ( u ) | = 1.
F j ( u ) = F j ( 0 ) + F j ( 0 ) u + ... + F j ( n ) ( 0 ) n ! u n + O ( u n + 1 ) .
F j ( i ) ( h ) = 0.
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved