Abstract

The study compares three variants of focus sensors designed for the optical topography measurement of rough surface specimens with submicron accuracy. We present a theoretical analysis of the focus sensor principles and the experimental measurements with a single point laser probe. A low coherent illumination beam was provided by a monochromatic laser source and a rotating diffuser, which reduced the speckles generated by the rough surface. The reflected beam was modulated by three specific optical elements (axicon, double wedge prism, four spherical lenses) realized by a spatial light modulator. A digital camera detected the output intensity patterns that were evaluated by the intensity centroid method. The results showed a good coincidence of the surface profiles obtained by the three sensor variants with the root-mean-square deviations below one micron. We discuss the results obtained for several specimens with various surface roughness and compare the differences between the three focus sensor variants.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (2)

G. Maculotti, X. Feng, M. Galetto, and R. Leach, “Noise evaluation of a point autofocus surface topography measuring instrument,” Meas. Sci. Technol. 29(6), 065008 (2018).
[Crossref]

A. Sabatyan and B. Fathi, “High efficiency arrays of any desired optical beams using modified grating based elements,” Opt. Quantum Electron. 50(9), 338 (2018).
[Crossref]

2016 (1)

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).
[Crossref]

2015 (4)

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

Ch.-S. Liu and S.-H. Jiang, “Precise autofocusing microscope with rapid response,” Opt. Lasers Eng. 66, 294–300 (2015).
[Crossref]

M. Šarbort, Š. Řeřucha, M. Holá, Z. Buchta, and J. Lazar, “Self-referenced interferometer for cylindrical surfaces,” Appl. Opt. 54(33), 9930–9938 (2015).
[Crossref]

J. Jang, Y. Yoo, J. Kim, and J. Paik, “Sensor-Based Auto-Focusing System Using Multi-Scale Feature Extraction and Phase Correlation Matching,” Sensors 15(3), 5747–5762 (2015).
[Crossref]

2014 (1)

2010 (2)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

M. K. Kim, “Principles and techniques of digital holographic microscopy,” J. Photonics Energy 1(1), 018005 (2010).
[Crossref]

2008 (1)

2005 (1)

H. Fukatsu and K. Yanagi, “Development of an optical stylus displacement sensor for surface profiling instruments,” Microsyst. Technol. 11(8-10), 582–589 (2005).
[Crossref]

2004 (1)

2002 (1)

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
[Crossref]

2000 (1)

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
[Crossref]

1997 (1)

J. Zhang and L. Cai, “Profilometry using an optical stylus with interferometric readout,” Meas. Sci. Technol. 8(5), 546–549 (1997).
[Crossref]

1994 (1)

1988 (1)

1987 (1)

R. Haberland, “In-Process Optical Metrology For Precision Machining,” Proc. SPIE 0802, 146–149 (1987).
[Crossref]

1984 (1)

Bernet, S.

Brzobohatý, O.

Buchta, Z.

Cai, L.

J. Zhang and L. Cai, “Profilometry using an optical stylus with interferometric readout,” Meas. Sci. Technol. 8(5), 546–549 (1997).
[Crossref]

Cao, W.

W. Y. Yang, W. Cao, T.-S. Chung, and J. Morris, Applied Numerical Methods Using Matlab, (Wiley-Interscience, 2005), Chap. 2.

Chung, T.-S.

W. Y. Yang, W. Cao, T.-S. Chung, and J. Morris, Applied Numerical Methods Using Matlab, (Wiley-Interscience, 2005), Chap. 2.

Cižmár, T.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

O. Brzobohatý, T. Čižmár, and P. Zemánek, “High quality quasi-Bessel beam generated by round-tip axicon,” Opt. Express 16(17), 12688–12700 (2008).
[Crossref]

Cohen, D. K.

de Groot, P.

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

Dholakia, K.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Dirckx, J. J. J.

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).
[Crossref]

Erwin, J. K.

Ettl, S.

G. Häusler and S. Ettl, “Limitation of optical 3D sensors,” in Optical measurement of surface topographyR. Leach, ed. (Springer-Verlag, 2011).

Fathi, B.

A. Sabatyan and B. Fathi, “High efficiency arrays of any desired optical beams using modified grating based elements,” Opt. Quantum Electron. 50(9), 338 (2018).
[Crossref]

Feng, X.

G. Maculotti, X. Feng, M. Galetto, and R. Leach, “Noise evaluation of a point autofocus surface topography measuring instrument,” Meas. Sci. Technol. 29(6), 065008 (2018).
[Crossref]

Fukatsu, H.

H. Fukatsu and K. Yanagi, “Development of an optical stylus displacement sensor for surface profiling instruments,” Microsyst. Technol. 11(8-10), 582–589 (2005).
[Crossref]

Fürhapter, S.

Galetto, M.

G. Maculotti, X. Feng, M. Galetto, and R. Leach, “Noise evaluation of a point autofocus surface topography measuring instrument,” Meas. Sci. Technol. 29(6), 065008 (2018).
[Crossref]

Gee, W. H.

Gerber, R. E.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Haberland, R.

R. Haberland, “In-Process Optical Metrology For Precision Machining,” Proc. SPIE 0802, 146–149 (1987).
[Crossref]

Häusler, G.

G. Häusler and S. Ettl, “Limitation of optical 3D sensors,” in Optical measurement of surface topographyR. Leach, ed. (Springer-Verlag, 2011).

Holá, M.

Jang, J.

J. Jang, Y. Yoo, J. Kim, and J. Paik, “Sensor-Based Auto-Focusing System Using Multi-Scale Feature Extraction and Phase Correlation Matching,” Sensors 15(3), 5747–5762 (2015).
[Crossref]

Jesacher, A.

Jiang, S.-H.

Ch.-S. Liu and S.-H. Jiang, “Precise autofocusing microscope with rapid response,” Opt. Lasers Eng. 66, 294–300 (2015).
[Crossref]

Kim, J.

J. Jang, Y. Yoo, J. Kim, and J. Paik, “Sensor-Based Auto-Focusing System Using Multi-Scale Feature Extraction and Phase Correlation Matching,” Sensors 15(3), 5747–5762 (2015).
[Crossref]

Kim, M. K.

M. K. Kim, “Principles and techniques of digital holographic microscopy,” J. Photonics Energy 1(1), 018005 (2010).
[Crossref]

Kohno, T.

Kothiyal, M. P.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
[Crossref]

Lazar, J.

Leach, R.

G. Maculotti, X. Feng, M. Galetto, and R. Leach, “Noise evaluation of a point autofocus surface topography measuring instrument,” Meas. Sci. Technol. 29(6), 065008 (2018).
[Crossref]

R. Leach, Optical Measurement of Surface Topography, (Springer-Verlag, 2011).

Lewkowicz, J.

Liu, Ch.-S.

Ch.-S. Liu and S.-H. Jiang, “Precise autofocusing microscope with rapid response,” Opt. Lasers Eng. 66, 294–300 (2015).
[Crossref]

Ludeke, M.

Maculotti, G.

G. Maculotti, X. Feng, M. Galetto, and R. Leach, “Noise evaluation of a point autofocus surface topography measuring instrument,” Meas. Sci. Technol. 29(6), 065008 (2018).
[Crossref]

Malacara, D.

D. Malacara, Optical Shop Testing, (Wiley-Interscience, 2007).

Mansuripur, M.

Mazilu, M.

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Meshginqalam, B.

Miura, K.

K. Miura and A. Nose, “Point Autofocus Instruments,” in Optical Measurement of Surface Topography, R. Leach, ed. (Springer-Verlag, 2011).

Miyamoto, K.

Morris, J.

W. Y. Yang, W. Cao, T.-S. Chung, and J. Morris, Applied Numerical Methods Using Matlab, (Wiley-Interscience, 2005), Chap. 2.

Musha, T.

Nose, A.

K. Miura and A. Nose, “Point Autofocus Instruments,” in Optical Measurement of Surface Topography, R. Leach, ed. (Springer-Verlag, 2011).

Ozawa, N.

Paik, J.

J. Jang, Y. Yoo, J. Kim, and J. Paik, “Sensor-Based Auto-Focusing System Using Multi-Scale Feature Extraction and Phase Correlation Matching,” Sensors 15(3), 5747–5762 (2015).
[Crossref]

Ray, S. F.

S. F. Ray, Applied Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging, (Focal, 2002).

Rerucha, Š.

Ritsch-Marte, M.

Sabatyan, A.

A. Sabatyan and B. Fathi, “High efficiency arrays of any desired optical beams using modified grating based elements,” Opt. Quantum Electron. 50(9), 338 (2018).
[Crossref]

A. Sabatyan and B. Meshginqalam, “Generation of annular beam by a novel class of Fresnel zone plate,” Appl. Opt. 53(26), 5995–6000 (2014).
[Crossref]

Šarbort, M.

Singaperumal, M.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
[Crossref]

Sirohi, R. S.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
[Crossref]

Udupa, G.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
[Crossref]

Van der Jeught, S.

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).
[Crossref]

Whitehouse, D. J.

D. J. Whitehouse, Handbook of Surface and Nanometrology, (IOP Publishing, 2003).

Wyant, J. C.

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
[Crossref]

Yanagi, K.

H. Fukatsu and K. Yanagi, “Development of an optical stylus displacement sensor for surface profiling instruments,” Microsyst. Technol. 11(8-10), 582–589 (2005).
[Crossref]

Yang, W. Y.

W. Y. Yang, W. Cao, T.-S. Chung, and J. Morris, Applied Numerical Methods Using Matlab, (Wiley-Interscience, 2005), Chap. 2.

Yoo, Y.

J. Jang, Y. Yoo, J. Kim, and J. Paik, “Sensor-Based Auto-Focusing System Using Multi-Scale Feature Extraction and Phase Correlation Matching,” Sensors 15(3), 5747–5762 (2015).
[Crossref]

Zambuto, J. J.

Zemánek, P.

Zhang, J.

J. Zhang and L. Cai, “Profilometry using an optical stylus with interferometric readout,” Meas. Sci. Technol. 8(5), 546–549 (1997).
[Crossref]

Adv. Opt. Photonics (1)

P. de Groot, “Principles of interference microscopy for the measurement of surface topography,” Adv. Opt. Photonics 7(1), 1–65 (2015).
[Crossref]

Appl. Opt. (5)

J. Photonics Energy (1)

M. K. Kim, “Principles and techniques of digital holographic microscopy,” J. Photonics Energy 1(1), 018005 (2010).
[Crossref]

Meas. Sci. Technol. (3)

G. Maculotti, X. Feng, M. Galetto, and R. Leach, “Noise evaluation of a point autofocus surface topography measuring instrument,” Meas. Sci. Technol. 29(6), 065008 (2018).
[Crossref]

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–314 (2000).
[Crossref]

J. Zhang and L. Cai, “Profilometry using an optical stylus with interferometric readout,” Meas. Sci. Technol. 8(5), 546–549 (1997).
[Crossref]

Microsyst. Technol. (1)

H. Fukatsu and K. Yanagi, “Development of an optical stylus displacement sensor for surface profiling instruments,” Microsyst. Technol. 11(8-10), 582–589 (2005).
[Crossref]

Nat. Photonics (1)

T. Čižmár, M. Mazilu, and K. Dholakia, “In situ wavefront correction and its application to micromanipulation,” Nat. Photonics 4(6), 388–394 (2010).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (2)

S. Van der Jeught and J. J. J. Dirckx, “Real-time structured light profilometry: a review,” Opt. Lasers Eng. 87, 18–31 (2016).
[Crossref]

Ch.-S. Liu and S.-H. Jiang, “Precise autofocusing microscope with rapid response,” Opt. Lasers Eng. 66, 294–300 (2015).
[Crossref]

Opt. Quantum Electron. (1)

A. Sabatyan and B. Fathi, “High efficiency arrays of any desired optical beams using modified grating based elements,” Opt. Quantum Electron. 50(9), 338 (2018).
[Crossref]

Proc. SPIE (2)

J. C. Wyant, “White light interferometry,” Proc. SPIE 4737, 98–107 (2002).
[Crossref]

R. Haberland, “In-Process Optical Metrology For Precision Machining,” Proc. SPIE 0802, 146–149 (1987).
[Crossref]

Sensors (1)

J. Jang, Y. Yoo, J. Kim, and J. Paik, “Sensor-Based Auto-Focusing System Using Multi-Scale Feature Extraction and Phase Correlation Matching,” Sensors 15(3), 5747–5762 (2015).
[Crossref]

Other (8)

G. Häusler and S. Ettl, “Limitation of optical 3D sensors,” in Optical measurement of surface topographyR. Leach, ed. (Springer-Verlag, 2011).

S. F. Ray, Applied Photographic Optics: Lenses and Optical Systems for Photography, Film, Video, Electronic and Digital Imaging, (Focal, 2002).

W. Y. Yang, W. Cao, T.-S. Chung, and J. Morris, Applied Numerical Methods Using Matlab, (Wiley-Interscience, 2005), Chap. 2.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

R. Leach, Optical Measurement of Surface Topography, (Springer-Verlag, 2011).

D. Malacara, Optical Shop Testing, (Wiley-Interscience, 2007).

D. J. Whitehouse, Handbook of Surface and Nanometrology, (IOP Publishing, 2003).

K. Miura and A. Nose, “Point Autofocus Instruments,” in Optical Measurement of Surface Topography, R. Leach, ed. (Springer-Verlag, 2011).

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Figures (9)

Fig. 1.
Fig. 1. The principle of focus sensor. a) Basic setup: beam splitter (BS), microscope objective (MO), specimen (SP), linear stage (LS), modulation element (ME), detector (DET), personal computer (PC). The characteristics of focus sensors with the modulation element represented by b) axicon + lens, c) double wedge prism + lens, d) four lenses.
Fig. 2.
Fig. 2. Computer generated holograms representing a) axicon + Fresnel lens, b) double wedge prism + Fresnel lens, c) four Fresnel lenses. The grayscale colormap from black to white corresponds to the phase modulation from $0$ to $2\pi$ radians.
Fig. 3.
Fig. 3. The evaluation of the output intensity patterns for the focus sensor based on a) axicon + lens, b) double wedge + lens, c) four lenses.
Fig. 4.
Fig. 4. The in-focus detection: a) the measurement configuration, b) the linear interpolation of the dependence curve $\rho (\mathrm {d}z)$ measured at the red point of the specimen surface.
Fig. 5.
Fig. 5. Experimental setup: laser source (LASER), neutral density filter (ND), optical isolator (OI), half-wave plate ($\lambda /2$), focusing lens (FL), polarization-maintaining fiber (PMF), collimator (COL), lenses (L1, L2, L3, L4), rotating diffuser (RD), polarizing beam splitter (PBS), quarter-wave plate ($\lambda /4$), microscope objective (MO), specimen (SP), nano-positioning linear stage (NLS), spatial light modulator (SLM), mirror (M), digital camera (CCD), personal computer (PC). The inset images show the rotating diffuser.
Fig. 6.
Fig. 6. The camera images of the output intensity patterns detected for a) axicon + lens, b) wedge + lens, c) four lenses. The left and right columns correspond to the measurement with the plane mirror and the ground glass specimen with $R_{\mathrm {q}} = 1.1\,$µm, respectively. The rows correspond to the displacement $\mathrm {d}z \in \{-2,0,+2\}$ µm.
Fig. 7.
Fig. 7. The comparison of the dependence curves $\rho (\mathrm {d}z)$. a) The theoretical prediction and the experimental results for the plane mirror. b) The experimental results for the ground glass specimen with $R_{\mathrm {q}} = 1.1\,$µm scanned along the $x$-axis. For clarity, the curves corresponding to the displacement $\mathrm {d}z \in [-5,5]$ µm were displayed only at the points with $2\,$µm spacing. The blue points indicate the values $\rho (0)$ for the displacement $\mathrm {d}z = 0\,$µm, the red points indicate the in-focus value $\rho _0$.
Fig. 8.
Fig. 8. The primary surface profiles measured for the five ground glass specimens and the three tested focus sensors.
Fig. 9.
Fig. 9. The experimental results measured for the five ground glass specimens and the three tested focus sensors: a) surface roughness $P_{\mathrm {q}}$, b) maximum profile height $P_{\mathrm {t}}$, c) RMS deviations between the profile pairs, d) random noise $\sigma _{\mathrm {z}}$.

Equations (13)

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ρ a ( d z ) = ρ a 0 + H a d z = F sin α n n 0 F f N A d z ,
ρ w ( d z ) = ρ w 0 + H w d z = F sin α n n 0 F f N A d z ,
ρ l ( d z ) = ρ l 0 + H l d z = r l + 2 r l F f 2 d z .
T a ( x , y ) = A a exp ( i ϕ a ) = c i r c ( 2 r / D a ) exp [ i ( k r sin α + k r 2 / 2 F ) ] ,
T w ( x , y ) = A w exp ( i ϕ w ) = c i r c ( 2 r / D w ) exp [ i ( k | x | sin α + k r 2 / 2 F ) ] ,
T l ( x , y ) = A l exp ( i ϕ l ) = { c i r c ( 2 r / D l ) exp [ i k r 2 / 2 F ] } [ δ ( x r l , y ) + δ ( x + r l , y ) + δ ( x , y r l ) + δ ( x , y + r l ) ] ,
ρ a = Ω a r I ( x , y ) Ω a I ( x , y ) , Ω a : | r ρ a 0 | 1 2 c a ,
ρ w = 1 2 ( Ω w 1 x I ( x , y ) Ω w 1 I ( x , y ) Ω w 2 x I ( x , y ) Ω w 2 I ( x , y ) ) ,
Ω w 1 : | x ρ w 0 | 1 2 c w , | y | 1 2 d w , Ω w 2 : | x + ρ w 0 | 1 2 c w , | y | 1 2 d w ,
ρ l = 1 4 ( Ω l 1 x I ( x , y ) Ω l 1 I ( x , y ) Ω l 2 x I ( x , y ) Ω l 2 I ( x , y ) + Ω l 3 y I ( x , y ) Ω l 3 I ( x , y ) Ω l 4 y I ( x , y ) Ω l 4 I ( x , y ) ) ,
Ω l 1 : | x ρ l 0 | 1 2 c l , | y | 1 2 d l , Ω l 2 : | x + ρ l 0 | 1 2 c l , | y | 1 2 d l , Ω l 3 : | y ρ l 0 | 1 2 c l , | x | 1 2 d l , Ω l 4 : | y + ρ l 0 | 1 2 c l , | x | 1 2 d l .
d z 0 = d z i + d z i + 1 d z i ρ i + 1 ρ i ( ρ 0 ρ i ) .
σ d z 0 = [ ( ρ i + 1 ρ 0 ) 2 + ( ρ 0 ρ i ) 2 ( ρ i + 1 ρ i ) 2 ( σ d z 2 + ( d z i + 1 d z i ) 2 ( ρ i + 1 ρ i ) 2 σ ρ 2 ) ] 1 / 2 .

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