Abstract

We describe a novel method of noncontact mode area measurement at long distance of 11.25m by borrowing the concept of a circular Dammann grating (CDG). The area of objects can be determined accurately by measuring the circular spectrum diameter of the CDG. This noncontact mode measurement requires neither a large amount of image data nor any pattern recognition approach. The spectrum diameter is derived from simple lens formulas. From the fractional Fourier transform, we find that there exists a linear relationship between the spectrum diameter and the distance traveled by the CDG. Compared with the conventional methods, this technique has the advantages of a simple design with good accuracy of better than 3%, low cost, noncontact mode, and a more compact design. Finally, we present several experimental results demonstrating the effectiveness of this system.

© 2010 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. J. F. Wen and P. S. Chung, “The use of circular Dammann grating for angle measurement,” Appl. Opt. 47, 5197-5200(2008).
    [CrossRef] [PubMed]
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2008 (2)

J. F. Wen and P. S. Chung, “A new circular Dammann grating using Hankel transform,” J. Opt. A: Pure Appl. Opt. 10, 075206 (2008).
[CrossRef]

J. F. Wen and P. S. Chung, “The use of circular Dammann grating for angle measurement,” Appl. Opt. 47, 5197-5200(2008).
[CrossRef] [PubMed]

2007 (3)

2006 (1)

2004 (1)

P. G. Gulden, D. Becker, and M. Vossiek, “Novel optical distance sensor based on MSM technology,” IEEE Sensors J. 4, 612-618 (2004).
[CrossRef]

2003 (2)

B. Culshaw, G. Pierce, and J. Pan, “Non-contact measurement of the mechanical properties of materials using an all-optical technique,” IEEE Sensors J. 3, 62-70 (2003).
[CrossRef]

C. Zhou, J. Jia, and L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174-2176 (2003).
[CrossRef] [PubMed]

2001 (2)

H. Yan, “Image analysis for digital media applications,” IEEE Comput. Graph. Appl. 21, 18-26 (2001).
[CrossRef]

A. Caarullo and M. Parvis, “An ultrasonic sensor for distance measurement in automotive applications,” IEEE Sensors J. 1, 143-147 (2001).
[CrossRef]

2000 (1)

R. Cucchiara, M. Piccardi, and P. Mello, “Image analysis and rule-based reasoning for a traffic monitoring system,” IEEE Trans. Intell. Transp. Syst. 1, 119-130 (2000).
[CrossRef]

1997 (1)

1996 (1)

1995 (2)

1993 (1)

H. M. Ozaktas and D. Mendlovic, “Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163-169 (1993).
[CrossRef]

1992 (1)

1990 (1)

J. N. Mait, “Design of binary-phase and multiphase Fourier gratings for array generation,” J. Opt Soc. Am. A 7, 1514-1528(1990).
[CrossRef]

1985 (1)

A. Yasuda, S. Kuwashima, and Y. Kanai, “Ashipborne-typewave-height mater for oceangoing vessels using microwave Doppler radar,” IEEE J. Ocean. Eng. 10, 138-143 (1985).
[CrossRef]

1977 (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 4, 505-515 (1977).
[CrossRef]

1971 (1)

H. Dammann and K. Gortler, “High-efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

1966 (1)

Becker, D.

P. G. Gulden, D. Becker, and M. Vossiek, “Novel optical distance sensor based on MSM technology,” IEEE Sensors J. 4, 612-618 (2004).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, 1978).

Burckhardt, C. B.

Caarullo, A.

A. Caarullo and M. Parvis, “An ultrasonic sensor for distance measurement in automotive applications,” IEEE Sensors J. 1, 143-147 (2001).
[CrossRef]

Chen, Z. Y.

J. F. Wen, Z. Y. Chen, and P. S. Chung, “A novel distance measurement technique based on optical fractional Fourier transform OECC,” in Opto-Electronics and Communications Conference, 2008, and the 2008 Australian Conference on Optical Fibre Technology, OECC/ACOFT 2008 (IEEE, 2008), pp. 1-2.
[CrossRef] [PubMed]

Chung, P. S.

J. F. Wen and P. S. Chung, “The use of circular Dammann grating for angle measurement,” Appl. Opt. 47, 5197-5200(2008).
[CrossRef] [PubMed]

J. F. Wen and P. S. Chung, “A new circular Dammann grating using Hankel transform,” J. Opt. A: Pure Appl. Opt. 10, 075206 (2008).
[CrossRef]

J. F. Wen and P. S. Chung, “2D optical splitters with polymer optical fiber arrays,” J. Opt. A: Pure Appl. Opt. 9, 723-727(2007).
[CrossRef]

J. F. Wen, S. Y. Law, and P. S. Chung, “Design of circular Dammann grating (CDG) by employing circular spot rotation method,” Appl. Opt. 46, 5452-5455 (2007).
[CrossRef] [PubMed]

S. Zhao, J. F. Wen, and P. S. Chung, “Simple focal-length measurement technique with a circular Dammann grating,” Appl. Opt. 46, 44-49 (2007).
[CrossRef]

S. Zhao and P. S. Chung, “Design of circular Dammann grating,” Opt. Lett. 31, 2387-2389 (2006).
[CrossRef] [PubMed]

J. F. Wen, Z. Y. Chen, and P. S. Chung, “A novel distance measurement technique based on optical fractional Fourier transform OECC,” in Opto-Electronics and Communications Conference, 2008, and the 2008 Australian Conference on Optical Fibre Technology, OECC/ACOFT 2008 (IEEE, 2008), pp. 1-2.
[CrossRef] [PubMed]

Cucchiara, R.

R. Cucchiara, M. Piccardi, and P. Mello, “Image analysis and rule-based reasoning for a traffic monitoring system,” IEEE Trans. Intell. Transp. Syst. 1, 119-130 (2000).
[CrossRef]

Culshaw, B.

B. Culshaw, G. Pierce, and J. Pan, “Non-contact measurement of the mechanical properties of materials using an all-optical technique,” IEEE Sensors J. 3, 62-70 (2003).
[CrossRef]

Dammann, H.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 4, 505-515 (1977).
[CrossRef]

H. Dammann and K. Gortler, “High-efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Dong, B.-Z.

Dorsch, R. G.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Gortler, K.

H. Dammann and K. Gortler, “High-efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

Gu, B. Y.

Gulden, P. G.

P. G. Gulden, D. Becker, and M. Vossiek, “Novel optical distance sensor based on MSM technology,” IEEE Sensors J. 4, 612-618 (2004).
[CrossRef]

Jia, J.

Kanai, Y.

A. Yasuda, S. Kuwashima, and Y. Kanai, “Ashipborne-typewave-height mater for oceangoing vessels using microwave Doppler radar,” IEEE J. Ocean. Eng. 10, 138-143 (1985).
[CrossRef]

Klotz, E.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 4, 505-515 (1977).
[CrossRef]

Kuwashima, S.

A. Yasuda, S. Kuwashima, and Y. Kanai, “Ashipborne-typewave-height mater for oceangoing vessels using microwave Doppler radar,” IEEE J. Ocean. Eng. 10, 138-143 (1985).
[CrossRef]

Law, S. Y.

Liu, L.

Lohmann, A. W.

Mait, J. N.

J. N. Mait, “Design of binary-phase and multiphase Fourier gratings for array generation,” J. Opt Soc. Am. A 7, 1514-1528(1990).
[CrossRef]

Mello, P.

R. Cucchiara, M. Piccardi, and P. Mello, “Image analysis and rule-based reasoning for a traffic monitoring system,” IEEE Trans. Intell. Transp. Syst. 1, 119-130 (2000).
[CrossRef]

Mendlovic, D.

Morrison, R. L.

Ozaktas, H. M.

D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, “Fractional correlation,” Appl. Opt. 34, 303-309 (1995).
[CrossRef] [PubMed]

H. M. Ozaktas and D. Mendlovic, “Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163-169 (1993).
[CrossRef]

Pan, J.

B. Culshaw, G. Pierce, and J. Pan, “Non-contact measurement of the mechanical properties of materials using an all-optical technique,” IEEE Sensors J. 3, 62-70 (2003).
[CrossRef]

Parvis,, M.

A. Caarullo and M. Parvis, “An ultrasonic sensor for distance measurement in automotive applications,” IEEE Sensors J. 1, 143-147 (2001).
[CrossRef]

Piccardi, M.

R. Cucchiara, M. Piccardi, and P. Mello, “Image analysis and rule-based reasoning for a traffic monitoring system,” IEEE Trans. Intell. Transp. Syst. 1, 119-130 (2000).
[CrossRef]

Pierce, G.

B. Culshaw, G. Pierce, and J. Pan, “Non-contact measurement of the mechanical properties of materials using an all-optical technique,” IEEE Sensors J. 3, 62-70 (2003).
[CrossRef]

Vossiek, M.

P. G. Gulden, D. Becker, and M. Vossiek, “Novel optical distance sensor based on MSM technology,” IEEE Sensors J. 4, 612-618 (2004).
[CrossRef]

Wen, J. F.

J. F. Wen and P. S. Chung, “The use of circular Dammann grating for angle measurement,” Appl. Opt. 47, 5197-5200(2008).
[CrossRef] [PubMed]

J. F. Wen and P. S. Chung, “A new circular Dammann grating using Hankel transform,” J. Opt. A: Pure Appl. Opt. 10, 075206 (2008).
[CrossRef]

J. F. Wen and P. S. Chung, “2D optical splitters with polymer optical fiber arrays,” J. Opt. A: Pure Appl. Opt. 9, 723-727(2007).
[CrossRef]

J. F. Wen, S. Y. Law, and P. S. Chung, “Design of circular Dammann grating (CDG) by employing circular spot rotation method,” Appl. Opt. 46, 5452-5455 (2007).
[CrossRef] [PubMed]

S. Zhao, J. F. Wen, and P. S. Chung, “Simple focal-length measurement technique with a circular Dammann grating,” Appl. Opt. 46, 44-49 (2007).
[CrossRef]

J. F. Wen, Z. Y. Chen, and P. S. Chung, “A novel distance measurement technique based on optical fractional Fourier transform OECC,” in Opto-Electronics and Communications Conference, 2008, and the 2008 Australian Conference on Optical Fibre Technology, OECC/ACOFT 2008 (IEEE, 2008), pp. 1-2.
[CrossRef] [PubMed]

Yan, H.

H. Yan, “Image analysis for digital media applications,” IEEE Comput. Graph. Appl. 21, 18-26 (2001).
[CrossRef]

Yang, G. Z.

Yasuda, A.

A. Yasuda, S. Kuwashima, and Y. Kanai, “Ashipborne-typewave-height mater for oceangoing vessels using microwave Doppler radar,” IEEE J. Ocean. Eng. 10, 138-143 (1985).
[CrossRef]

Zalevsky, Z.

Zhang, Y.

Zhao, S.

Zhou, C.

Appl. Opt. (6)

IEEE Comput. Graph. Appl. (1)

H. Yan, “Image analysis for digital media applications,” IEEE Comput. Graph. Appl. 21, 18-26 (2001).
[CrossRef]

IEEE J. Ocean. Eng. (1)

A. Yasuda, S. Kuwashima, and Y. Kanai, “Ashipborne-typewave-height mater for oceangoing vessels using microwave Doppler radar,” IEEE J. Ocean. Eng. 10, 138-143 (1985).
[CrossRef]

IEEE Sensors J. (3)

A. Caarullo and M. Parvis, “An ultrasonic sensor for distance measurement in automotive applications,” IEEE Sensors J. 1, 143-147 (2001).
[CrossRef]

P. G. Gulden, D. Becker, and M. Vossiek, “Novel optical distance sensor based on MSM technology,” IEEE Sensors J. 4, 612-618 (2004).
[CrossRef]

B. Culshaw, G. Pierce, and J. Pan, “Non-contact measurement of the mechanical properties of materials using an all-optical technique,” IEEE Sensors J. 3, 62-70 (2003).
[CrossRef]

IEEE Trans. Intell. Transp. Syst. (1)

R. Cucchiara, M. Piccardi, and P. Mello, “Image analysis and rule-based reasoning for a traffic monitoring system,” IEEE Trans. Intell. Transp. Syst. 1, 119-130 (2000).
[CrossRef]

J. Opt Soc. Am. A (1)

J. N. Mait, “Design of binary-phase and multiphase Fourier gratings for array generation,” J. Opt Soc. Am. A 7, 1514-1528(1990).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (2)

J. F. Wen and P. S. Chung, “A new circular Dammann grating using Hankel transform,” J. Opt. A: Pure Appl. Opt. 10, 075206 (2008).
[CrossRef]

J. F. Wen and P. S. Chung, “2D optical splitters with polymer optical fiber arrays,” J. Opt. A: Pure Appl. Opt. 9, 723-727(2007).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Acta (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 4, 505-515 (1977).
[CrossRef]

Opt. Commun. (2)

H. Dammann and K. Gortler, “High-efficiency in line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312-315 (1971).
[CrossRef]

H. M. Ozaktas and D. Mendlovic, “Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163-169 (1993).
[CrossRef]

Opt. Lett. (2)

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

J. F. Wen, Z. Y. Chen, and P. S. Chung, “A novel distance measurement technique based on optical fractional Fourier transform OECC,” in Opto-Electronics and Communications Conference, 2008, and the 2008 Australian Conference on Optical Fibre Technology, OECC/ACOFT 2008 (IEEE, 2008), pp. 1-2.
[CrossRef] [PubMed]

R. N. Bracewell, The Fourier Transform and its Applications (McGraw-Hill, 1978).

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Figures (9)

Fig. 1
Fig. 1

Transition points in the cross section of the CDG.

Fig. 2
Fig. 2

Schematic diagram of a fractional Fourier transform.

Fig. 3
Fig. 3

Distance and area measurement using the CDG.

Fig. 4
Fig. 4

Measuring area with the diameter of the CDG.

Fig. 5
Fig. 5

Ordinary CDG spectrum.

Fig. 6
Fig. 6

Measurement results with focal length f = 200 mm .

Fig. 7
Fig. 7

Measurement results with focal length f = 250 mm .

Fig. 8
Fig. 8

(a) CDG spectrum for measuring DUT1’s height, (b) CDG spectrum for measuring DUT1’s width.

Fig. 9
Fig. 9

(a) CDG spectrum for measuring DUT2’s height, (b) CDG spectrum for measuring DUT2’s width.

Equations (10)

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A ( x 2 r i ) r i A q J 1 ( 2 π q r i ) .
M ( q ) = 1 q | 2 k = 1 N 1 ( 1 ) k r k J 1 ( 2 π q r k ) + r N J 1 ( 2 π q r N ) | .
n th order : I q = | M ( q ) | 2 = 1 q 2 | 2 k = 1 N 1 ( 1 ) k r k J 1 ( 2 π q r k ) + r N J 1 ( 2 π q r N ) | 2 ,
0 th order : I 0 = [ 2 k = 1 N ( 1 ) k r k + 1 ] 2 .
r k = r k N / 2 + 0.5 ,
η = q = 1 n q I q ,
uni = max { I } min { I } max { I } + min { I } ,
D = f r d .
u ( x F ) = c exp { j k ( f d + L ) · x F 2 2 [ D · ( f d + L ) + f · ( d L ) ] } + t ( x DOE ) exp [ j k f · x DOE · x F D · ( f d + L ) + f · ( d L ) ] d x DOE .
H = 2 L f d f λ T ,

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