Abstract

Because the depth of field (DOF) of lenses is limited, a captured interferogram usually includes a focused region and defocused region simultaneously when the form deviation of the helical tooth flank is measured with laser interferometry. Because of the impact of the interference fringe, the existing autofocusing algorithms are difficult for identifying the focused region of the interferogram directly. This paper proposes a new autofocusing algorithm based on the object image and registration technology. First, the reliability region is evaluated according to the gray level. Then the corresponding pixels in the image sequence are determined with the registration technology. Next, the focused region is judged by comparing the average gray gradients in object images. Based on the characteristics of measured gear and the DOF of lens, an experiment is designed. The experimental results are given to verify the feasibility and accuracy of the proposed autofocusing algorithm.

© 2013 Optical Society of America

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References

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  1. K. S. Choi, S. J. Ko, and J. S. Lee, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827 (1999).
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    [CrossRef]
  3. M. Martorella, F. Berizzi, and B. Haywood, “Contrast maximisation based technique for 2-D ISAR autofocusing,” IEEE Proc. Radar. Sonar. Navigat. 152, 253–262 (2005).
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  5. Y. Sun, S. Duthaler, and B. J. Nelsion, “Autofocusing in computer microscopy: Selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).
  6. P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
    [CrossRef]
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    [CrossRef]
  8. S. P. Fang, L. J. Wang, S. Q. Liu, M. Komori, and A. Kubo, “Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry,” Opt. Eng. 50, 055601 (2011).
    [CrossRef]
  9. L. E. Tenenbaum, Accommodation in Computer Vision (Stanford University, 1970).
  10. S. P. Fang, L. J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2010).

2011

J. W. Feng, Q. C. Yu, N. Lu, and H. M. Feng, “Definition evaluation function of digital image in auto-focusing system,” J. Mech. Electr. Eng. 28, 354–356 (2011).

P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
[CrossRef]

S. P. Fang, L. J. Wang, S. Q. Liu, M. Komori, and A. Kubo, “Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry,” Opt. Eng. 50, 055601 (2011).
[CrossRef]

2010

S. P. Fang, L. J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2010).

2008

2005

M. Martorella, F. Berizzi, and B. Haywood, “Contrast maximisation based technique for 2-D ISAR autofocusing,” IEEE Proc. Radar. Sonar. Navigat. 152, 253–262 (2005).

2004

Y. Sun, S. Duthaler, and B. J. Nelsion, “Autofocusing in computer microscopy: Selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).

2000

1999

K. S. Choi, S. J. Ko, and J. S. Lee, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827 (1999).

Berizzi, F.

M. Martorella, F. Berizzi, and B. Haywood, “Contrast maximisation based technique for 2-D ISAR autofocusing,” IEEE Proc. Radar. Sonar. Navigat. 152, 253–262 (2005).

Choi, K. S.

K. S. Choi, S. J. Ko, and J. S. Lee, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827 (1999).

Corwin, A. D.

Dixon, E. L.

Duthaler, S.

Y. Sun, S. Duthaler, and B. J. Nelsion, “Autofocusing in computer microscopy: Selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).

Fang, S. P.

S. P. Fang, L. J. Wang, S. Q. Liu, M. Komori, and A. Kubo, “Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry,” Opt. Eng. 50, 055601 (2011).
[CrossRef]

P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
[CrossRef]

S. P. Fang, L. J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2010).

Feng, H. M.

J. W. Feng, Q. C. Yu, N. Lu, and H. M. Feng, “Definition evaluation function of digital image in auto-focusing system,” J. Mech. Electr. Eng. 28, 354–356 (2011).

Feng, J. W.

J. W. Feng, Q. C. Yu, N. Lu, and H. M. Feng, “Definition evaluation function of digital image in auto-focusing system,” J. Mech. Electr. Eng. 28, 354–356 (2011).

Filkins, R. J.

Groot, P. D.

Haywood, B.

M. Martorella, F. Berizzi, and B. Haywood, “Contrast maximisation based technique for 2-D ISAR autofocusing,” IEEE Proc. Radar. Sonar. Navigat. 152, 253–262 (2005).

Kenny, K. B.

Ko, S. J.

K. S. Choi, S. J. Ko, and J. S. Lee, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827 (1999).

Komori, M.

P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
[CrossRef]

S. P. Fang, L. J. Wang, S. Q. Liu, M. Komori, and A. Kubo, “Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry,” Opt. Eng. 50, 055601 (2011).
[CrossRef]

S. P. Fang, L. J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2010).

Kubo, A.

S. P. Fang, L. J. Wang, S. Q. Liu, M. Komori, and A. Kubo, “Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry,” Opt. Eng. 50, 055601 (2011).
[CrossRef]

P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
[CrossRef]

S. P. Fang, L. J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2010).

Lee, J. S.

K. S. Choi, S. J. Ko, and J. S. Lee, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827 (1999).

Liu, S. Q.

S. P. Fang, L. J. Wang, S. Q. Liu, M. Komori, and A. Kubo, “Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry,” Opt. Eng. 50, 055601 (2011).
[CrossRef]

Lu, N.

J. W. Feng, Q. C. Yu, N. Lu, and H. M. Feng, “Definition evaluation function of digital image in auto-focusing system,” J. Mech. Electr. Eng. 28, 354–356 (2011).

Martorella, M.

M. Martorella, F. Berizzi, and B. Haywood, “Contrast maximisation based technique for 2-D ISAR autofocusing,” IEEE Proc. Radar. Sonar. Navigat. 152, 253–262 (2005).

Meng, L.

P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
[CrossRef]

Nelsion, B. J.

Y. Sun, S. Duthaler, and B. J. Nelsion, “Autofocusing in computer microscopy: Selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).

Sun, Y.

Y. Sun, S. Duthaler, and B. J. Nelsion, “Autofocusing in computer microscopy: Selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).

Tasimi, K.

Tenenbaum, L. E.

L. E. Tenenbaum, Accommodation in Computer Vision (Stanford University, 1970).

Wang, L. J.

P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
[CrossRef]

S. P. Fang, L. J. Wang, S. Q. Liu, M. Komori, and A. Kubo, “Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry,” Opt. Eng. 50, 055601 (2011).
[CrossRef]

S. P. Fang, L. J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2010).

Yang, P. C.

P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
[CrossRef]

Yazdanfar, S.

Yu, Q. C.

J. W. Feng, Q. C. Yu, N. Lu, and H. M. Feng, “Definition evaluation function of digital image in auto-focusing system,” J. Mech. Electr. Eng. 28, 354–356 (2011).

Appl. Opt.

IEEE Proc. Radar. Sonar. Navigat.

M. Martorella, F. Berizzi, and B. Haywood, “Contrast maximisation based technique for 2-D ISAR autofocusing,” IEEE Proc. Radar. Sonar. Navigat. 152, 253–262 (2005).

IEEE Trans. Consum. Electron.

K. S. Choi, S. J. Ko, and J. S. Lee, “New autofocusing technique using the frequency selective weighted median filter for video cameras,” IEEE Trans. Consum. Electron. 45, 820–827 (1999).

J. Mech. Electr. Eng.

J. W. Feng, Q. C. Yu, N. Lu, and H. M. Feng, “Definition evaluation function of digital image in auto-focusing system,” J. Mech. Electr. Eng. 28, 354–356 (2011).

Microsc. Res. Tech.

Y. Sun, S. Duthaler, and B. J. Nelsion, “Autofocusing in computer microscopy: Selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139–149 (2004).

Opt. Eng.

P. C. Yang, S. P. Fang, L. J. Wang, L. Meng, M. Komori, and A. Kubo, “Correction method for segmenting valid measuring region of interference fringe patterns,” Opt. Eng. 50, 095602 (2011).
[CrossRef]

S. P. Fang, L. J. Wang, S. Q. Liu, M. Komori, and A. Kubo, “Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry,” Opt. Eng. 50, 055601 (2011).
[CrossRef]

Opt. Express

Optik

S. P. Fang, L. J. Wang, M. Komori, and A. Kubo, “Design of laser interferometric system for measurement of gear tooth flank,” Optik 122, 1301–1304 (2010).

Other

L. E. Tenenbaum, Accommodation in Computer Vision (Stanford University, 1970).

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Figures (19)

Fig. 1.
Fig. 1.

(a) Grazing-incidence interferometry. (b) Relationship between the theoretical focused plane and the measured tooth flank.

Fig. 2.
Fig. 2.

(a) Experimental metal plate. (b) Object image of the metal plate. (c) Magnified image of the boundary bc.

Fig. 3.
Fig. 3.

Interferogram of helical gear tooth flank.

Fig. 4.
Fig. 4.

Object image of measured tooth flank.

Fig. 5.
Fig. 5.

Binary mask of interferogram.

Fig. 6.
Fig. 6.

Magnified part of an object image.

Fig. 7.
Fig. 7.

Flow chart of selecting the lower threshold.

Fig. 8.
Fig. 8.

Flow chart of selecting the upper threshold.

Fig. 9.
Fig. 9.

Distribution of gray value in the valid region.

Fig. 10.
Fig. 10.

(a) Grid points of the tooth flank. (b) Simulation tooth image.

Fig. 11.
Fig. 11.

(a) Simulation tooth image and interferogram before the transformation. (b) Simulation tooth image and the interferogram after the transformation.

Fig. 12.
Fig. 12.

Flow chart of the proposed autofocusing algorithm.

Fig. 13.
Fig. 13.

Schematic diagram of the interferometric optical system.

Fig. 14.
Fig. 14.

Relationship between the position of lens and the focused plane.

Fig. 15.
Fig. 15.

Object images (a) the lens is moved to 7.5mm; (b) the lens is moved to 5mm; (c) the lens is moved to 2.5mm; (d) the lens is moved to 0 mm; (e) the lens is moved to 2.5 mm; and (f) the lens is moved to 5 mm.

Fig. 16.
Fig. 16.

Valid region after the reliability evaluation (a) the lens is moved 7.5mm; (b) the lens is moved 5mm; (c) the lens is moved 2.5mm; (d) the lens is moved 0 mm; (e) the lens is moved 2.5 mm; and (f) the lens is moved 5 mm.

Fig. 17.
Fig. 17.

Calculated points in the object image.

Fig. 18.
Fig. 18.

Result of autofocusing algorithm.

Fig. 19.
Fig. 19.

Relative result of autofocusing algorithm.

Tables (4)

Tables Icon

Table 1. Position Relationship of Lens, Focused Plane, and CCD Plane

Tables Icon

Table 2. Thresholds for Every Object Image

Tables Icon

Table 3. Calculation Result of Autofocusing Algorithm

Tables Icon

Table 4. Relative Result of Autofocusing Algorithm

Equations (16)

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

QReli(x,y)={1(white)0(black)ifMaxG(x,y)Minotherwise.
G(k)>G(k).
Pro(k)=Pro(k1)+Δpro,
G(k)G(k1)>GAver/4.
{xI(N×(h25H)+i,w)=NiNx(h,w)+iNx(h+1,w)yI(N×(h25H)+i,w)=NiNy(h,w)+iNy(h+1,w)i=0,1,,N1,
{xI(a,M×b+i)=MiMxI(a,b)+iMxI(a,b+1)yI(a,M×b+i)=MiMyI(a,b)+iMyI(a,b+1)i=0,1,,M1,
FTenengrad=HeightWidthSx(x,y)2+Sy(x,y)2,
ΔLDOF=ΔL1+ΔL2=δFL(Lf)f2+δF(Lf)+δFL(Lf)f2δF(Lf),
B=B×sinβ,
P=[B/ΔLDOF],
{QReli(xI,yI)=1andQReli(xI,yI+1)=1G(xI,yI)G(xI,yI+1)<10,
FGrads=1XYxXyY[G(xI,yI)G(xI,yI+1)]2,
1/f=1/u+1/v,
Δu<ΔLDOF,
{u=u+Δa*i+Δui=0,±1v=vΔa1/f=1/u+1/v,
FRela=FGrads/Fmax,

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