Abstract

The design of a partially optically stable (POS) reflector system, in which the exit ray direction and image pose are unchanged as the reflector system rotates about a specific directional vector, was presented in an earlier study by the current group [Appl. Phys. B 100, 883–890 (2010)]. The present study further proposes an optically stable image (OSI) reflector system, in which not only is the optical stability property of the POS system retained, but the image position and total ray path length are also fixed. An analytical method is proposed for the design of OSI reflector systems comprising multiple reflectors. The validity of the proposed approach is demonstrated by means of two illustrative examples.

© 2013 Optical Society of America

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References

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  1. W. J. Smith, Modern Optical Engineering, 3rd ed. (Edmund Industrial Optics, 2001), pp. 91–123.
  2. M. Skop, D. Ben-Ezra, and N. Schweitzer, “Adjustable stabilized reflector for optical communication,” in Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel (IEEE, 1996), pp. 383–386.
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  4. N. Schweitzer, Y. Friedman, and M. Skop, “Stability of systems of plane reflecting surfaces,” Appl. Opt. 37, 5190–5192 (1998).
    [CrossRef]
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    [CrossRef]
  8. Y. Friedman and N. Schweitzer, “Classification of stable configurations of plane mirrors,” Appl. Opt. 37, 7229–7234 (1998).
    [CrossRef]
  9. C. Y. Tsai and P. D. Lin, “Design of optically stable reflector systems and prisms,” Appl. Opt. 47, 4158–4163 (2008).
    [CrossRef]
  10. C. Y. Tsai, “Design of partially optically stable reflector systems and prisms,” Appl. Phys. B 100, 883–890 (2010).
    [CrossRef]
  11. R. P. Paul, Robot Manipulators—Mathematics, Programming and Control (Massachusetts Institute of Technology, 1982).
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    [CrossRef]
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    [CrossRef]

2010 (1)

C. Y. Tsai, “Design of partially optically stable reflector systems and prisms,” Appl. Phys. B 100, 883–890 (2010).
[CrossRef]

2008 (2)

2007 (1)

2006 (1)

1998 (2)

1971 (1)

1960 (1)

1958 (1)

Ben-Ezra, D.

M. Skop, D. Ben-Ezra, and N. Schweitzer, “Adjustable stabilized reflector for optical communication,” in Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel (IEEE, 1996), pp. 383–386.

Chandler, K. N.

Eckhardt, H. D.

Friedman, Y.

Li, W.

Li, X.

Liang, J.

Liang, Z.

Lin, P. D.

Paul, R. P.

R. P. Paul, Robot Manipulators—Mathematics, Programming and Control (Massachusetts Institute of Technology, 1982).

Schweitzer, N.

N. Schweitzer, Y. Friedman, and M. Skop, “Stability of systems of plane reflecting surfaces,” Appl. Opt. 37, 5190–5192 (1998).
[CrossRef]

Y. Friedman and N. Schweitzer, “Classification of stable configurations of plane mirrors,” Appl. Opt. 37, 7229–7234 (1998).
[CrossRef]

M. Skop, D. Ben-Ezra, and N. Schweitzer, “Adjustable stabilized reflector for optical communication,” in Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel (IEEE, 1996), pp. 383–386.

Skop, M.

N. Schweitzer, Y. Friedman, and M. Skop, “Stability of systems of plane reflecting surfaces,” Appl. Opt. 37, 5190–5192 (1998).
[CrossRef]

M. Skop, D. Ben-Ezra, and N. Schweitzer, “Adjustable stabilized reflector for optical communication,” in Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel (IEEE, 1996), pp. 383–386.

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 3rd ed. (Edmund Industrial Optics, 2001), pp. 91–123.

Stewart, G. W.

G. W. Stewart, Introduction to Matrix Computations (Academic, 1973).

Sun, D.

Tsai, C. Y.

Wang, W.

Yoder, P. R.

Zhong, Y.

Appl. Opt. (6)

Appl. Phys. B (1)

C. Y. Tsai, “Design of partially optically stable reflector systems and prisms,” Appl. Phys. B 100, 883–890 (2010).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Express (1)

Other (4)

G. W. Stewart, Introduction to Matrix Computations (Academic, 1973).

W. J. Smith, Modern Optical Engineering, 3rd ed. (Edmund Industrial Optics, 2001), pp. 91–123.

M. Skop, D. Ben-Ezra, and N. Schweitzer, “Adjustable stabilized reflector for optical communication,” in Proceedings of the IEEE 19th Convention of Electrical and Electronics Engineers in Israel (IEEE, 1996), pp. 383–386.

R. P. Paul, Robot Manipulators—Mathematics, Programming and Control (Massachusetts Institute of Technology, 1982).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic illustration of OSI reflector system installed behind converging lens set.

Fig. 2.
Fig. 2.

Ray tracing at flat boundary surface.

Fig. 3.
Fig. 3.

Image-orientation change produced by reflector system comprising two reflectors.

Fig. 4.
Fig. 4.

Schematic illustration of OSI reflector system comprising two reflectors.

Fig. 5.
Fig. 5.

Schematic illustration of OSI reflector system comprising three reflectors.

Equations (33)

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

Ai0=[IiJiKiti]=[IixJixKixtixIiyJiyKiytiyIizJizKiztiz0001].
ni=[nixniyniz0]T=Ai0nii=si[JixJiyJiz0]T.
Pi=[PixPiyPiz1]T=Pi1+i1λi=[Pi1x+i1xλiPi1y+i1yλiPi1z+i1zλi1],
Cθi=i1Tni=si(Jixi1x+Jiyi1y+Jizi1z).
i=[ixiyiz0]T=i12ni(i1Tni)=[i1x+2nixCθii1y+2niyCθii1z+2nizCθi0],
i(ni)i1=I2niniT,
Γ=n0=n(nn)n1n1(nn1)n2i(ni)i12(n2)11(n1)0.
Γ=[a0b0c00]=[a0xb0xc0x0a0yb0yc0y0a0zb0zc0z00001]=Rot(m0,Φ0)[10000δ0000100001],
q0=±m0.
q0=±[m0zS(Φ0/2)1(m0yS(Φ0/2))2C(Φ0/2)1(m0yS(Φ0/2))2m0xS(Φ0/2)1(m0yS(Φ0/2))20]T.
Pnψ=0,
λall=i=1nλi=fbfl,
λallψ=(i=1nλi)ψ=0,
A10=[*0.6*0*0.3*17.9521*0.7416*00001]
A20=[*0.33*0*0.75*41.0159*0.5732*00001],
Γ=[0.06050.85580.513700.85880.30690.410200.50870.41630.753600001].
A30=[*0.8558*0*0.3069*2.0697*0.4163*00001].
Ls=[14.78450.7282·t47.52110.5887·t0.3510·t1]T
A10=[*0.6*0*0.7*30*0.3873*00001],
A20=[*0.52*0*0.85*8*0.0843*00001],
A30=[*0.33*0*0.75*150*0.5732*00001].
Γ=[0.48530.46100.742900.60670.78940.093600.62960.40530.662800001].
A40=[*0.4610*0*0.7894*12.0750*0.4053*00001].
Ls=ds+vs·t=[116.7130+0.3399·t87.09550.9352·t77.61770.0993·t1]T
rii=[Cαi0Sαi00100Sαi0Cαi00001][βi001]=[βiCαi0βiSαi1],
nii=si(riiαi×riiβi)/|riiαi×riiβi|,
nii=si[0100]T.
ni=Ai0nii=si[JixJiyJiz0]T.
Pi=[PixPiyPiz1]T=Pi1+i1λi,
λi=[JixPi1x+JiyPi1y+JizPi1z(Jixtix+Jiytiy+Jiztiz)]Jixi1x+Jiyi1y+Jizi1z.
Rot(m0,Φ0)=[m0x2(1CΦ0)+CΦ0m0xm0y(1CΦ0)m0zSΦ0m0xm0z(1CΦ0)+m0ySΦ0m0xm0y(1CΦ0)+m0zSΦ0m0y2(1CΦ0)+CΦ0m0ym0z(1CΦ0)m0xSΦ0m0xm0z(1CΦ0)m0ySΦ0m0ym0z(1CΦ0)+m0xSΦ0m0z2(1CΦ0)+CΦ0],
m0=[m0xm0ym0z0]=[(δb0zc0y)/(2SΦ0)(c0xa0z)/(2SΦ0)(a0yδb0x)/(2SΦ0)0],
Φ0=atan2{[(δb0zc0y)2+(c0xa0z)2+(a0yδb0x)2]1/2,(a0x+δb0y+c0z1)},

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