Abstract

This paper presents a simple method based on the measurement of the 3D intensity point spread function for the quality evaluation of high numerical aperture micro-optical components. The different slices of the focal volume are imaged thanks to a microscope objective and a standard camera. Depending on the optical architecture, it allows characterizing both transmissive and reflective components, for which either the imaging part or the component itself are moved along the optical axis, respectively. This method can be used to measure focal length, Strehl ratio, resolution and overall wavefront RMS and to estimate optical aberrations. The measurement setup and its implementation are detailed and its advantages are demonstrated with micro-ball lenses and micro-mirrors. This intuitive method is adapted for optimization of micro-optical components fabrication processes, especially because heavy equipments and/or data analysis are not required.

© 2014 Optical Society of America

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References

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  1. S. Sinzinger and J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, 2003).
    [Crossref]
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    [Crossref]
  3. R. Leach, Optical Measurement of Surface Topography (Springer, 2011).
    [Crossref]
  4. P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
    [Crossref]
  5. J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
    [Crossref]
  6. D. Malacara, Optical Shop Testing, 3rd ed. (John Wiley and Sons, 2007)
    [Crossref]
  7. F. Charriere, J. Kuhn, T. Colomb, F. Montfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt. 45, 829–835 (2006).
    [Crossref] [PubMed]
  8. M.-S. Kim, T. Scharf, and H. P. Herzig, “Small-size microlens characterization by multi-wavelength high-resolution interference microscopy,” Opt. Express 18, 14319–14329 (2010).
    [Crossref] [PubMed]
  9. J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  14. H. Yang, C.-K. Chao, M.-K. Wei, and C.-P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14, 1197–1204 (2004).
    [Crossref]
  15. J. Braat, S. V. Haver, A. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” Prog. Optics 51, 349–468 (2008).
    [Crossref]
  16. E. Botcherby, R. Juskaitis, M. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281, 880–887 (2008).
    [Crossref]
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    [Crossref] [PubMed]
  20. M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999).
    [Crossref]
  21. T. E. Oliphant, “Python for scientific computing,” Comput. Sci. Eng. 9, 10–20 (2007).
    [Crossref]
  22. M. A. Robertson, S. Borman, and R. Stevenson, “Dynamic range improvement through multiple exposures,” in Proceedings of the International Conference on Image Processing (IEEE, 1999), pp. 159–163.

2011 (2)

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

2010 (1)

2008 (3)

P. Huang, T. Huang, Y. Sun, and S. Yang, “Fabrication of large area resin microlens arrays using gas-assisted ultraviolet embossing,” Opt. Express 16, 3041–3048 (2008).
[Crossref] [PubMed]

J. Braat, S. V. Haver, A. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” Prog. Optics 51, 349–468 (2008).
[Crossref]

E. Botcherby, R. Juskaitis, M. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281, 880–887 (2008).
[Crossref]

2007 (3)

2006 (2)

F. Charriere, J. Kuhn, T. Colomb, F. Montfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt. 45, 829–835 (2006).
[Crossref] [PubMed]

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

2005 (2)

2004 (1)

H. Yang, C.-K. Chao, M.-K. Wei, and C.-P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14, 1197–1204 (2004).
[Crossref]

2002 (1)

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002).
[Crossref] [PubMed]

1993 (1)

P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
[Crossref]

1992 (1)

Albero, J.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Bargiel, S.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Beverage, J. L.

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002).
[Crossref] [PubMed]

Bhatia, A.

M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999).
[Crossref]

Bobroff, N.

Booth, M.

E. Botcherby, R. Juskaitis, M. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281, 880–887 (2008).
[Crossref]

Borman, S.

M. A. Robertson, S. Borman, and R. Stevenson, “Dynamic range improvement through multiple exposures,” in Proceedings of the International Conference on Image Processing (IEEE, 1999), pp. 159–163.

Born, M.

M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999).
[Crossref]

Botcherby, E.

E. Botcherby, R. Juskaitis, M. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281, 880–887 (2008).
[Crossref]

Braat, J.

J. Braat, S. V. Haver, A. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” Prog. Optics 51, 349–468 (2008).
[Crossref]

Brown, C. M.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

Chang, C.

Chao, C.-K.

H. Yang, C.-K. Chao, M.-K. Wei, and C.-P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14, 1197–1204 (2004).
[Crossref]

Charriere, F.

Chiu, C.

Cole, R. W.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

Colomb, T.

Cox, R.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Cuche, E.

Dannberg, P.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Depeursinge, C.

Descour, M. R.

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002).
[Crossref] [PubMed]

Dirksen, P.

J. Braat, S. V. Haver, A. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” Prog. Optics 51, 349–468 (2008).
[Crossref]

Emery, Y.

Firestone, G. C.

Gastinger, K.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Gorecki, C.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Haver, S. V.

J. Braat, S. V. Haver, A. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” Prog. Optics 51, 349–468 (2008).
[Crossref]

Herzig, H. P.

M.-S. Kim, T. Scharf, and H. P. Herzig, “Small-size microlens characterization by multi-wavelength high-resolution interference microscopy,” Opt. Express 18, 14319–14329 (2010).
[Crossref] [PubMed]

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Huang, P.

Huang, T.

Jahns, J.

S. Sinzinger and J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, 2003).
[Crossref]

Janssen, A.

J. Braat, S. V. Haver, A. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” Prog. Optics 51, 349–468 (2008).
[Crossref]

Jiang, L.

Jinadasa, T.

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

Juskaitis, R.

E. Botcherby, R. Juskaitis, M. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281, 880–887 (2008).
[Crossref]

Kim, M.-S.

Kuhn, J.

Leach, R.

R. Leach, Optical Measurement of Surface Topography (Springer, 2011).
[Crossref]

Li, L.

Lin, C.-P.

H. Yang, C.-K. Chao, M.-K. Wei, and C.-P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14, 1197–1204 (2004).
[Crossref]

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (John Wiley and Sons, 2007)
[Crossref]

Marian, A.

Marquet, P.

Miyashita, T.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Montfort, F.

Naessens, K.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Oliphant, T. E.

T. E. Oliphant, “Python for scientific computing,” Comput. Sci. Eng. 9, 10–20 (2007).
[Crossref]

Ottevaere, H.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Passilly, N.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Robertson, M. A.

M. A. Robertson, S. Borman, and R. Stevenson, “Dynamic range improvement through multiple exposures,” in Proceedings of the International Conference on Image Processing (IEEE, 1999), pp. 159–163.

Rosenbluth, A. E.

Rousselot, C.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Sandoz, P.

P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
[Crossref]

Scharf, T.

Shack, R. V.

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002).
[Crossref] [PubMed]

Sinzinger, S.

S. Sinzinger and J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, 2003).
[Crossref]

Stevenson, R.

M. A. Robertson, S. Borman, and R. Stevenson, “Dynamic range improvement through multiple exposures,” in Proceedings of the International Conference on Image Processing (IEEE, 1999), pp. 159–163.

Stumpf, M.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Sun, Y.

Taghizadeh, M.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Thienpont, H.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Tribillon, G.

P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
[Crossref]

Völkel, R.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Wei, M.-K.

H. Yang, C.-K. Chao, M.-K. Wei, and C.-P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14, 1197–1204 (2004).
[Crossref]

Weible, K.

Wilson, T.

E. Botcherby, R. Juskaitis, M. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281, 880–887 (2008).
[Crossref]

Wolf, E.

M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999).
[Crossref]

Woo, H. J.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Yang, H.

H. Yang, C.-K. Chao, M.-K. Wei, and C.-P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14, 1197–1204 (2004).
[Crossref]

Yang, S.

Yi, A. Y.

Zeitner, U. D.

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

Appl. Opt. (3)

Comput. Sci. Eng. (1)

T. E. Oliphant, “Python for scientific computing,” Comput. Sci. Eng. 9, 10–20 (2007).
[Crossref]

J. Micromech. Microeng. (2)

J. Albero, S. Bargiel, N. Passilly, P. Dannberg, M. Stumpf, U. D. Zeitner, C. Rousselot, K. Gastinger, and C. Gorecki, “Micromachined array-type Mirau interferometer for parallel inspection of MEMS,” J. Micromech. Microeng. 21, 065005 (2011).
[Crossref]

H. Yang, C.-K. Chao, M.-K. Wei, and C.-P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14, 1197–1204 (2004).
[Crossref]

J. Microsc. (1)

J. L. Beverage, R. V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002).
[Crossref] [PubMed]

J. Mod. Opt. (1)

P. Sandoz and G. Tribillon, “Profilometry by zero-order interference fringe identification,” J. Mod. Opt. 40, 1691–1700 (1993).
[Crossref]

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

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A: Pure Appl. Opt. 8, S407–S429 (2006).
[Crossref]

Nat. Protoc. (1)

R. W. Cole, T. Jinadasa, and C. M. Brown, “Measuring and interpreting point spread functions to determine confocal microscope resolution and ensure quality control,” Nat. Protoc. 6, 1929–1941 (2011).
[Crossref] [PubMed]

Opt. Commun. (1)

E. Botcherby, R. Juskaitis, M. Booth, and T. Wilson, “An optical technique for remote focusing in microscopy,” Opt. Commun. 281, 880–887 (2008).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Prog. Optics (1)

J. Braat, S. V. Haver, A. Janssen, and P. Dirksen, “Assessment of optical systems by means of point-spread functions,” Prog. Optics 51, 349–468 (2008).
[Crossref]

Other (5)

D. Malacara, Optical Shop Testing, 3rd ed. (John Wiley and Sons, 2007)
[Crossref]

R. Leach, Optical Measurement of Surface Topography (Springer, 2011).
[Crossref]

S. Sinzinger and J. Jahns, Microoptics, 2nd ed. (Wiley-VCH, 2003).
[Crossref]

M. A. Robertson, S. Borman, and R. Stevenson, “Dynamic range improvement through multiple exposures,” in Proceedings of the International Conference on Image Processing (IEEE, 1999), pp. 159–163.

M. Born, E. Wolf, and A. Bhatia, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge U. Press, 1999).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Advantage of investigating aberrations with the 3D Intensity PSF - (a) focus plane images of different aberration examples. Plots are XY cuts in-focus. XY and XZ slices of the evolution of the focused beam around the focal plane: (b) aberration free, (c) spherical aberration, (d) astigmatism (e) higher order aberration (quadrafoil). In all cases, wavefront aberration is 0.2λ RMS. Note that normalized coordinates are used to visualize the effects of aberrations independently of the system NA.

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Fig. 2
Fig. 2 Scheme of the characterization system (a) in transmissive configuration and (b) in reflective configuration. Beam expander BE including spatial filtering, half wave plate (λ/2), polarizer P, beam splitters BS1 and BS2, mirrors M1 and M2, microscope objective MO, tube lens TL and camera CMOS.

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Fig. 3
Fig. 3 Dynamic range enhancement of the camera using three frames with different exposure times. (a) Acquisitions at 1ms, 10ms and 100ms and (b) high dynamic range image obtained from these three frames (intensity plotted in the logarithmic scale).

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Fig. 4
Fig. 4 Measurement of 500μm diameter ball microlens performed with NAobj = 0.45. (a) XY slice (located at the focal plane) and (b) XZ slice of the focal volume.

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Fig. 5
Fig. 5 Ball microlens measurements (a) XZ IPSF slice observed by NAobj = 0.80, (b) same slice drawn in normalized coordinate system and (c) IPSF slice of the same ball microlens observed by NAobj = 0.45 in normalized coordinate system.

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Fig. 6
Fig. 6 PSF analysis of a ball microlens (a) peak intensity and RMS spot radius as a function of axial slices of 3D IPSF and (b) encircled energy plot for the focal plane.

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Fig. 7
Fig. 7 Focus spot response of a 500μm diameter ball microlens in reflection - Measured XZ slice focal spot at (a) the cat’s eye position and (b) the confocal position.

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Fig. 8
Fig. 8 ROC measurement of 500μm diameter ball microlens. (a) Scheme of measuring configuration, (b) XZ-slice of the measured IPSF along the scanned distance, (c) plot of the power passing through virtual pinhole.

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Equations (10)

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I ( u , v , Φ ) ∝ | ∫ 0 1 ∫ 0 2 π P ( ρ , θ ) e i k Φ ( ρ , θ ) e − i 1 2 u     ρ 2 e − i v ρ     cos ( θ − ϕ ) ρ d ρ d θ | 2
P ( ρ , θ ) = P obj ( ρ , θ ) P m ( ρ , θ )
P ( ρ , θ ) = P obj ( ρ , θ ) P m ( ρ , θ ) P obj ( ρ , θ − π )
P m ( ρ , θ ) = { 1 if     ρ < NA m / NA obj 0 otherwise
δ x , y fwhm = 0.51 λ NA
δ z fwhm = 1.4 λ NA 2 .
δ RMS = 1 ∑ i , j I i , j ∑ i , j I i , j | r → i , j − r → 0 | 2
SR = max ( IPSF ( x → , Φ ) max ( IPSF ( x → , Φ = 0 )
SR = max ( IPSF ( x → , Φ ) P tot π NA m 2 λ 2
SR = e − ( σ Φ ) 2

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