Abstract

We achieve the analysis and design of optical attenuators with double-prism neutral density filters. A comparative study is performed on three possible device configurations; only two are presented in the literature but without their design calculus. The characteristic parameters of this optical attenuator with Risley translating prisms for each of the three setups are defined and their analytical expressions are derived: adjustment scale (attenuation range) and interval, minimum transmission coefficient and sensitivity. The setups are compared to select the optimal device, and, from this study, the best solution for double-prism neutral density filters, both from a mechanical and an optical point of view, is determined with two identical, symmetrically movable, no mechanical contact prisms. The design calculus of this optimal device is developed in essential steps. The parameters of the prisms, particularly their angles, are studied to improve the design, and we demonstrate the maximum attenuation range that this type of attenuator can provide.

© 2009 Optical Society of America

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References

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  19. V. F. Duma, “Tri-chromatic colorimeter with mix synthesis,” Romanian Patent Request A/00224/31.03.2006, pending.

2008 (2)

Y. Yang, “Analytic solution of free space optical beam steering using Risley prisms,” J. Lightwave Technol. 26, 3576-3583(2008).
[CrossRef]

V. F. Duma, “Theoretical approach on optical choppers for top-hat light beam distributions,” J. Opt. A Pure Appl. Opt. 10, 064008 (2008).
[CrossRef]

2007 (3)

G. García-Torales, J. L. Flores, and R. X. Muñoz, “High precision prism scanning system,” Proc. SPIE 6422, 64220X (2007).
[CrossRef]

W. C. Warger II and Ch. A. DiMarzio, “Dual-wedge scanning confocal reflectance microscope,” Opt. Lett. 32, 2140-2142(2007).
[CrossRef] [PubMed]

V. F. Duma, “Double-prisms neutral density filters: a comparative approach,” Proc. SPIE 6785, 67851W (2007).
[CrossRef]

2006 (1)

2005 (1)

G, Zheng, C. Du, C. Zhou, and C. Zheng, “Laser diode stack beam shaping by reflective two-wedge-angle prism arrays,” Opt. Eng. 44, 044203 (2005).
[CrossRef]

2003 (1)

2002 (1)

2001 (1)

2000 (1)

1998 (1)

Y.-S. Cheng and R.-C. Chang, “Characteristics of a prism-pair anamorphotic optical system for multiple holography,” Opt. Eng. 37, 2717-2725 (1998).
[CrossRef]

1993 (1)

1971 (1)

Bass, M.

M. Bass, Handbook of Optics (McGraw-Hill, 1995).

Chang, R.-C.

Y.-S. Cheng and R.-C. Chang, “Characteristics of a prism-pair anamorphotic optical system for multiple holography,” Opt. Eng. 37, 2717-2725 (1998).
[CrossRef]

Cheng, Y.-S.

Y.-S. Cheng and R.-C. Chang, “Characteristics of a prism-pair anamorphotic optical system for multiple holography,” Opt. Eng. 37, 2717-2725 (1998).
[CrossRef]

DiMarzio, Ch. A.

Du, C.

G, Zheng, C. Du, C. Zhou, and C. Zheng, “Laser diode stack beam shaping by reflective two-wedge-angle prism arrays,” Opt. Eng. 44, 044203 (2005).
[CrossRef]

Duma, V. F.

V. F. Duma, “Theoretical approach on optical choppers for top-hat light beam distributions,” J. Opt. A Pure Appl. Opt. 10, 064008 (2008).
[CrossRef]

V. F. Duma, “Double-prisms neutral density filters: a comparative approach,” Proc. SPIE 6785, 67851W (2007).
[CrossRef]

V. F. Duma, “Tri-chromatic colorimeter with mix synthesis,” Romanian Patent Request A/00224/31.03.2006, pending.

Flores, J. L.

G. García-Torales, J. L. Flores, and R. X. Muñoz, “High precision prism scanning system,” Proc. SPIE 6422, 64220X (2007).
[CrossRef]

Garcia-Torales, G.

García-Torales, G.

G. García-Torales, J. L. Flores, and R. X. Muñoz, “High precision prism scanning system,” Proc. SPIE 6422, 64220X (2007).
[CrossRef]

Ito, T.

Kaneko, T.

Kiyokura, T.

Kothiyal, M. P.

Li, A.

Liu, D.

Liu, L.

Luan, Z.

Muñoz, R. X.

G. García-Torales, J. L. Flores, and R. X. Muñoz, “High precision prism scanning system,” Proc. SPIE 6422, 64220X (2007).
[CrossRef]

Oka, K.

Oseki, T.

Paez, G.

Saito, S.

Sawada, R.

Senthilkumaran, P.

Sirohi, R. S.

Sriram, K. V.

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas (Wiley, 2000).

Strojnik, M.

Sun, J.

Torales, G. G.

Wang, L.

Warger, W. C.

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas (Wiley, 2000).

Yang, Y.

Zheng, C.

G, Zheng, C. Du, C. Zhou, and C. Zheng, “Laser diode stack beam shaping by reflective two-wedge-angle prism arrays,” Opt. Eng. 44, 044203 (2005).
[CrossRef]

Zheng, G,

G, Zheng, C. Du, C. Zhou, and C. Zheng, “Laser diode stack beam shaping by reflective two-wedge-angle prism arrays,” Opt. Eng. 44, 044203 (2005).
[CrossRef]

Zhong, X.

Zhou, C.

G, Zheng, C. Du, C. Zhou, and C. Zheng, “Laser diode stack beam shaping by reflective two-wedge-angle prism arrays,” Opt. Eng. 44, 044203 (2005).
[CrossRef]

Appl. Opt. (5)

Appl. Spectrosc. (1)

J. Lightwave Technol. (1)

J. Opt. A Pure Appl. Opt. (1)

V. F. Duma, “Theoretical approach on optical choppers for top-hat light beam distributions,” J. Opt. A Pure Appl. Opt. 10, 064008 (2008).
[CrossRef]

Opt. Eng. (2)

Y.-S. Cheng and R.-C. Chang, “Characteristics of a prism-pair anamorphotic optical system for multiple holography,” Opt. Eng. 37, 2717-2725 (1998).
[CrossRef]

G, Zheng, C. Du, C. Zhou, and C. Zheng, “Laser diode stack beam shaping by reflective two-wedge-angle prism arrays,” Opt. Eng. 44, 044203 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (2)

V. F. Duma, “Double-prisms neutral density filters: a comparative approach,” Proc. SPIE 6785, 67851W (2007).
[CrossRef]

G. García-Torales, J. L. Flores, and R. X. Muñoz, “High precision prism scanning system,” Proc. SPIE 6422, 64220X (2007).
[CrossRef]

Other (5)

Edmund Optics, Catalog for Optics (Edmunds Optics, Barrington, N.J., 2009).

V. F. Duma, “Tri-chromatic colorimeter with mix synthesis,” Romanian Patent Request A/00224/31.03.2006, pending.

Thorlabs Catalog, Vol. 18 (Thorlabs, Newton, N.J., 2007).

M. Bass, Handbook of Optics (McGraw-Hill, 1995).

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulas (Wiley, 2000).

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Figures (8)

Fig. 1
Fig. 1

Double-prism neutral density filter for solution #1 in the center ( x = 0 ) position: (a) lateral view and (b) view from the top.

Fig. 2
Fig. 2

Extreme positions of the prisms for attenuator #1: (a)  x = l and (b)  x = l .

Fig. 3
Fig. 3

Optical attenuator with neutral density filter for solution #2: (a) lateral view and (b) spot displacement and exit diaphragm.

Fig. 4
Fig. 4

Solution #3 of the double-prism attenuator.

Fig. 5
Fig. 5

Profile of the functioning characteristic τ ( x ) for three solutions of the double-prism attenuator: (a) #1 and (b) #2 and #3.

Fig. 6
Fig. 6

Graphs of (a) absorption coefficient α ( l = x max ) and (b) attenuation range k ( l = x max ) for τ min = 0.1 ; D = 10 mm ; n = 1.517 and for three prism angles of θ 1 = 10 ° , θ 2 = 20 ° , and θ 3 = 30 ° .

Fig. 7
Fig. 7

Graphs of (a) minimum transmission coefficient τ min ( l = x max ) and (b) minimum sensitivity S min ( l = x max ) for D = 10 mm and n = 1.517 and for three pairs of values of α 1 = 0.4 and θ 1 = 10 ° ; α 2 = 0.2 and θ 2 = 20 ° ; and α 3 = 0.1 and θ 3 = 30 ° .

Fig. 8
Fig. 8

Graphs of the error of the transmission coefficient produced by a Δ x = 0.26 μm accumulated positioning error of the two prisms for τ min = 0.1 ; D = 10 mm ; n = 1.517 , and for three pairs of values: α 1 = 0.4 and θ 1 = 10 ° ; α 2 = 0.2 and θ 2 = 20 ° ; and α 3 = 0.1 and θ 3 = 30 ° .

Tables (1)

Tables Icon

Table 1 Characteristic Parameters of Three Possible Configurations of Double-Prism Neutral Density Filters

Equations (27)

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Φ e = Φ i · exp ( α d ) ,
τ = Φ / Φ i ,
d ( x ) = d 0 x tan θ , x [ l , l ] ,
a D + 2 l ,
α = ln τ 0 / d 0 ,
τ ( x ) = τ 0 exp [ α x tan θ ] .
τ max = τ ( l ) = τ 0 exp ( α l tan θ ) τ min = τ ( l ) = τ 0 exp ( α l tan θ ) { τ max = τ 0 C τ min = τ 0 3 / C ,
C = exp ( α D i tan θ ) ;
k = τ max / τ min ,
Δ τ = τ max τ min .
δ ( x ) = 2 x [ n cos θ 1 n 2 sin 2 θ 1 ] sin 2 θ .
D i = D + δ ( l ) ; δ ( l ) = δ max .
d ( x ) = d 0 ( 2 x + δ ) tan θ .
a 2 l + D + δ max .
τ ( x ) = r 1 τ 0 exp [ 2 α r 2 x tan θ ] ,
r 1 = ( D D + δ max ) 2 , r 2 = ( n sin 2 θ 1 n 2 sin 2 θ + cos θ ) cos θ .
τ max = τ ( l ) = r 1 τ 0 1 r 2 C r 2 , τ min = τ ( 0 ) = r 1 τ 0 .
τ = r 1 τ 0 exp [ α r 2 x tan θ ] ,
τ max = τ ( l ) = r 1 τ 0 1 r 2 2 C r 2 2 , τ min = τ ( l ) = r 1 τ 0 .
r 1 > τ 0 / C ,     r 2 > 1 ,
C τ 0 > 1 + ( δ max D ) 4 1
C / τ 0 = exp ( 2 α l tan θ ) .
S max S min = τ max τ min = k ,
Δ τ = τ min ( k 1 ) ,
τ min = r 1 τ 0 = r 1 exp [ α d 0 ] , k = ( C / τ 0 ) r 2 = exp [ 2 α r 2 l tan θ ] .
a = 2 l + D + δ max = d 0 / tan θ .
α ( l ) = 1 ( D + 2 r 2 l ) tan θ ln 1 τ min [ 1 + 2 ( r 2 1 ) l / D ] .

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