Abstract

We demonstrate a simple setup for generating a three-dimensional arbitrary orientation of the polarization vector in a laser focus. The key component is the superposition of a linearly and a radially polarized laser beam, which both can be controlled individually in intensity and relative phase. We exemplify the usefulness of this setup by determining the spatial orientation of a single silver nanorod in three- dimensional space by recording the angle-variable backscattered light intensity.

© 2010 Optical Society of America

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References

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  1. H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. Phys. Soc. 55, 116–128 (1943).
    [CrossRef]
  2. M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986).
    [CrossRef]
  3. Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
    [CrossRef]
  4. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87(2000).
    [CrossRef] [PubMed]
  5. K. S. Youngworth and Thomas G. Brown, “Inhomogenous polarization in scanning optical microscopy,” Proc. SPIE 3919, 75–85 (2000).
    [CrossRef]
  6. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  7. L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
    [CrossRef] [PubMed]
  8. T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343 (2008).
    [CrossRef] [PubMed]
  9. P. Olk, J. Renger, T. Härtling, M. T. Wenzel, and L. M. Eng, “Two particle enhanced nano Raman microscopy and spectroscopy,” Nano Lett. 7, 1736–1740 (2007).
    [CrossRef] [PubMed]
  10. M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Opt. Lett. 21, 1948–1950 (1996).
    [CrossRef] [PubMed]
  11. S. C. Tidwell, D. H. Ford, and W. D. Kimura, “Generating radially polarized beams interferometrically,” Appl. Opt. 29, 2234–2239 (1990).
    [CrossRef] [PubMed]
  12. Here by a four-segment half-wave plate (B. Halle Nachfl. GmbH, Germany) with subsequent spatial cleaning.
  13. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
    [CrossRef]
  14. M. Gu, Advanced Optical Imaging Theory (Springer, 2000).
  15. SNW-A60, 60nm nominal diameter (Blue Nano, USA).
  16. T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless near-field optical microscopy,” J. Microsc. 202-1, 72–76 (2001).
    [CrossRef]
  17. T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2314 (2004).
    [CrossRef]
  18. P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nano particles,” Nano Lett. 8, 1174–1178 (2008).
    [CrossRef] [PubMed]
  19. C. Hafner, Post-Modern Electromagnetics: Using Intelligent MaXwell Solvers (Wiley, 1999).
  20. α-Planfluar, 100×, 1.45, ∞, 0.17 (Carl Zeiss MicroImaging GmbH, Germany).
  21. I. J. Cooper, M. Roy, and C. J. R. Sheppard, “Focusing of pseudoradial polarized beams,” Opt. Express 13, 1066–1071(2005).
    [CrossRef] [PubMed]
  22. N. V. Voshchinnikov and V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
    [CrossRef]
  23. Fig. 3.11, p. 43 in P. Olk, “Optical properties of individual nano-sized gold particle pairs,” Ph.D dissertation (Technische Universität Dresden2008), http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1218612352686-00553.
  24. P. B. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]

2008 (3)

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343 (2008).
[CrossRef] [PubMed]

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nano particles,” Nano Lett. 8, 1174–1178 (2008).
[CrossRef] [PubMed]

Fig. 3.11, p. 43 in P. Olk, “Optical properties of individual nano-sized gold particle pairs,” Ph.D dissertation (Technische Universität Dresden2008), http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1218612352686-00553.

2007 (1)

P. Olk, J. Renger, T. Härtling, M. T. Wenzel, and L. M. Eng, “Two particle enhanced nano Raman microscopy and spectroscopy,” Nano Lett. 7, 1736–1740 (2007).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2314 (2004).
[CrossRef]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

2001 (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless near-field optical microscopy,” J. Microsc. 202-1, 72–76 (2001).
[CrossRef]

2000 (3)

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87(2000).
[CrossRef] [PubMed]

K. S. Youngworth and Thomas G. Brown, “Inhomogenous polarization in scanning optical microscopy,” Proc. SPIE 3919, 75–85 (2000).
[CrossRef]

1999 (1)

C. Hafner, Post-Modern Electromagnetics: Using Intelligent MaXwell Solvers (Wiley, 1999).

1996 (1)

1993 (1)

N. V. Voshchinnikov and V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

1990 (1)

1986 (1)

1972 (2)

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

P. B. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

1943 (1)

H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. Phys. Soc. 55, 116–128 (1943).
[CrossRef]

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87(2000).
[CrossRef] [PubMed]

Brown, Thomas G.

K. S. Youngworth and Thomas G. Brown, “Inhomogenous polarization in scanning optical microscopy,” Proc. SPIE 3919, 75–85 (2000).
[CrossRef]

Christy, R.

P. B. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Cooper, I. J.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Eng, L. M.

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nano particles,” Nano Lett. 8, 1174–1178 (2008).
[CrossRef] [PubMed]

P. Olk, J. Renger, T. Härtling, M. T. Wenzel, and L. M. Eng, “Two particle enhanced nano Raman microscopy and spectroscopy,” Nano Lett. 7, 1736–1740 (2007).
[CrossRef] [PubMed]

Failla, A. V.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343 (2008).
[CrossRef] [PubMed]

Farafonov, V. G.

N. V. Voshchinnikov and V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

Ford, D. H.

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Hafner, C.

C. Hafner, Post-Modern Electromagnetics: Using Intelligent MaXwell Solvers (Wiley, 1999).

Håkanson, U.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2314 (2004).
[CrossRef]

Härtling, T.

P. Olk, J. Renger, T. Härtling, M. T. Wenzel, and L. M. Eng, “Two particle enhanced nano Raman microscopy and spectroscopy,” Nano Lett. 7, 1736–1740 (2007).
[CrossRef] [PubMed]

Hartschuh, A.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343 (2008).
[CrossRef] [PubMed]

Hopkins, H. H.

H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. Phys. Soc. 55, 116–128 (1943).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Kalkbrenner, T.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2314 (2004).
[CrossRef]

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless near-field optical microscopy,” J. Microsc. 202-1, 72–76 (2001).
[CrossRef]

Kimura, W. D.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Mansuripur, M.

Matsumura, K.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Meixner, A. J.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343 (2008).
[CrossRef] [PubMed]

Mlynek, J.

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless near-field optical microscopy,” J. Microsc. 202-1, 72–76 (2001).
[CrossRef]

Mushiake, Y.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Nakajima, N.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Olk, P.

Fig. 3.11, p. 43 in P. Olk, “Optical properties of individual nano-sized gold particle pairs,” Ph.D dissertation (Technische Universität Dresden2008), http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1218612352686-00553.

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nano particles,” Nano Lett. 8, 1174–1178 (2008).
[CrossRef] [PubMed]

P. Olk, J. Renger, T. Härtling, M. T. Wenzel, and L. M. Eng, “Two particle enhanced nano Raman microscopy and spectroscopy,” Nano Lett. 7, 1736–1740 (2007).
[CrossRef] [PubMed]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Ramstein, M.

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless near-field optical microscopy,” J. Microsc. 202-1, 72–76 (2001).
[CrossRef]

Renger, J.

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nano particles,” Nano Lett. 8, 1174–1178 (2008).
[CrossRef] [PubMed]

P. Olk, J. Renger, T. Härtling, M. T. Wenzel, and L. M. Eng, “Two particle enhanced nano Raman microscopy and spectroscopy,” Nano Lett. 7, 1736–1740 (2007).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

Roy, M.

Sandoghdar, V.

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2314 (2004).
[CrossRef]

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless near-field optical microscopy,” J. Microsc. 202-1, 72–76 (2001).
[CrossRef]

Schadt, M.

Sheppard, C. J. R.

Stalder, M.

Tidwell, S. C.

Voshchinnikov, N. V.

N. V. Voshchinnikov and V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

Wenzel, M. T.

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nano particles,” Nano Lett. 8, 1174–1178 (2008).
[CrossRef] [PubMed]

P. Olk, J. Renger, T. Härtling, M. T. Wenzel, and L. M. Eng, “Two particle enhanced nano Raman microscopy and spectroscopy,” Nano Lett. 7, 1736–1740 (2007).
[CrossRef] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and Thomas G. Brown, “Inhomogenous polarization in scanning optical microscopy,” Proc. SPIE 3919, 75–85 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87(2000).
[CrossRef] [PubMed]

Züchner, T.

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343 (2008).
[CrossRef] [PubMed]

Appl. Opt. (1)

Astrophys. Space Sci. (1)

N. V. Voshchinnikov and V. G. Farafonov, “Optical properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993).
[CrossRef]

J. Microsc. (2)

T. Kalkbrenner, M. Ramstein, J. Mlynek, and V. Sandoghdar, “A single gold particle as a probe for apertureless near-field optical microscopy,” J. Microsc. 202-1, 72–76 (2001).
[CrossRef]

T. Züchner, A. V. Failla, A. Hartschuh, and A. J. Meixner, “A novel approach to detect and characterize the scattering patterns of single Au nanoparticles using confocal microscopy,” J. Microsc. 229, 337–343 (2008).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Nano Lett. (3)

P. Olk, J. Renger, T. Härtling, M. T. Wenzel, and L. M. Eng, “Two particle enhanced nano Raman microscopy and spectroscopy,” Nano Lett. 7, 1736–1740 (2007).
[CrossRef] [PubMed]

T. Kalkbrenner, U. Håkanson, and V. Sandoghdar, “Tomographic plasmon spectroscopy of a single gold nanoparticle,” Nano Lett. 4, 2309–2314 (2004).
[CrossRef]

P. Olk, J. Renger, M. T. Wenzel, and L. M. Eng, “Distance dependent spectral tuning of two coupled metal nano particles,” Nano Lett. 8, 1174–1178 (2008).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

P. B. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (2)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett. 86, 5251–5254 (2001).
[CrossRef] [PubMed]

Proc. IEEE (1)

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proc. IEEE 60, 1107–1109 (1972).
[CrossRef]

Proc. Phys. Soc. (1)

H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. Phys. Soc. 55, 116–128 (1943).
[CrossRef]

Proc. R. Soc. London A (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

Proc. SPIE (1)

K. S. Youngworth and Thomas G. Brown, “Inhomogenous polarization in scanning optical microscopy,” Proc. SPIE 3919, 75–85 (2000).
[CrossRef]

Other (6)

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

SNW-A60, 60nm nominal diameter (Blue Nano, USA).

Here by a four-segment half-wave plate (B. Halle Nachfl. GmbH, Germany) with subsequent spatial cleaning.

C. Hafner, Post-Modern Electromagnetics: Using Intelligent MaXwell Solvers (Wiley, 1999).

α-Planfluar, 100×, 1.45, ∞, 0.17 (Carl Zeiss MicroImaging GmbH, Germany).

Fig. 3.11, p. 43 in P. Olk, “Optical properties of individual nano-sized gold particle pairs,” Ph.D dissertation (Technische Universität Dresden2008), http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1218612352686-00553.

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Figures (6)

Fig. 1
Fig. 1

Vectorial construction of the focal polarization for (a) linear polarization, (b) radial polarization, and (c) the sum of both. The light arrows represent the input electric field orientation, and the dark vectors give the direction of the resulting polarization.

Fig. 2
Fig. 2

Experimental implementation of B. Laser light is split by beam splitter BS1 into two arms. The “linear” arm I. contains an appropriate neutral density filter NF, phase delay PD, polarization rotation by a half-wave plate L / 2 , and a telescope to adjust the beam diameter BD. The “radial” arm II. consists of an element for intensity adjustment NF, a device RP generating the radial polarization, and a telescope BD. BS2 recombines the two arms and feeds them into the lens. For the proof of concept, a SNR is positioned in the focus of the lens by a scanning fiber probe. Its backscattered light is collected by the lens and directed via BS3 to a spectrometer.

Fig. 3
Fig. 3

MMP simulations of an Ag [24] nanorod of 125 nm length and 55 nm diameter in homogeneous immersion ( n = 1.52 ), exposed to plane wave excitation ( λ vac = 532 nm , E x , k z ) for various spatial orientations. The images show the near fields, all in the same intensity scale. The simulations provide the energy flux back into the collecting NA.

Fig. 4
Fig. 4

Orientation measurement of the picked particle in the xy plane. The fitted sin 2 curve normalizes the vertical scale and is a guide to the eye, as the beam splitter of the microscope is not perfectly nonpolarizing. The orientation of the SNR long axis projected onto the xy plane is θ opt = ( 105 ± 15 ) ° .

Fig. 5
Fig. 5

Orientation measurement of the picked particle in the ( θ opt ) z plane. The inclination out of the xy plane is φ = ( 35 ± 15 ) ° . The solid curve (bicubic fit) is a guide to the eye and normalizes the vertical scale.

Fig. 6
Fig. 6

Electron micrographs (material contrast) of the particle decorated fiber probe, each image is 1 μm × 1 μm : (a) top view and (b) side view. The coordinates refer to the base of the optical experiment.

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