Abstract

A major problem of optical microscopes is their small depth-of-field (DOF), which hinders automation of micro object manipulation using visual feedback. Wavefront coding, a well-known method for extending DOF, is not suitable for direct application to micro object manipulation systems based on visual feedback owing to its expensive computational cost and due to a trade-off between the DOF and the image resolution properties. To solve such inherent problems, a flexible DOF imaging system using a spatial light modulator in the pupil plane is proposed. Especially, the trade-off relationship is quantitatively analyzed by experiments. Experimental results show that, for low criterion resolution, the DOF increases as the strength of the mask increases, while such a trend was not found for high criterion resolution. With high criterion resolution, the DOF decreases as the mask strength increases when high-resolution images are required. The results obtained can be used effectively to find the optimum mask strength given the desired image resolution.

© 2007 Optical Society of America

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References

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  1. S. Nayar, "Shape from focus," IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
    [CrossRef]
  2. H. Cho, Optomechatronics (CRC Press, 2006).
  3. M. Mino and Y. Okano, "Improvement in the optical transfer function of a defocused optical system through the use of shaded apertures," Appl. Opt. 10, 2219-2225 (1971).
    [CrossRef] [PubMed]
  4. J. Ojeda-Castaneda, P. Adres, and A. Diaz, "Annular apodizers for low sensitivity to defocus and to spherical aberration," Opt. Lett. 11, 487-489 (1986).
    [CrossRef] [PubMed]
  5. J. Ojeda-Castaneda, R. Ramos, and A. Noyola-Isgleas, "High focal depth by apodization and digital restoration," Appl. Opt. 27, 2583-2586 (1988).
    [CrossRef] [PubMed]
  6. J. Ojeda-Castaneda, E. Tepichin, and A. Diaz, "Arbitrary high focal depth with a quasioptimum real and positive transmittance apodizer," Appl. Opt. 28, 2666-2670 (1989).
    [CrossRef] [PubMed]
  7. I. De, B. Chanda, and B. Chattopadhyay, "Enhancing effective depth-of-field by image fusion using mathematical morphology," Image Vision Comput. 24, 1278-1287 (2006).
    [CrossRef]
  8. S. Fatikow, J. Seyfried, S. Fahlbusch, A. Buerkle, F. Schmoeckel, and H. Woern, "Intelligent Microrobotic System for Microassembly Tasks," First Int. Conference on Mechatronics and Robotics, St. Petersburg, Russia, 29 May-2 June 2000.
  9. G. Hausler, "A method to increase the depth of focus by two step image processing," Opt. Commun. 6, 38-42 (1972).
    [CrossRef]
  10. E. Dowski and W. Cathey, "Extended depth of field through wave-front coding," Appl. Opt. 34, 1859-1866 (1995).
    [CrossRef] [PubMed]
  11. W. Cathey and E. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002).
    [CrossRef] [PubMed]
  12. J. Gracht, V. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
    [CrossRef]
  13. E. Dowski, R. Cormack, and S. Sarama, "Wavefront coding: jointly optimized optical and digital imaging systems," Proc. SPIE 4041, 114-120 (2000).
    [CrossRef]
  14. S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. Gracht, "High-resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
    [CrossRef]
  15. N. George and W. Chi, "Extended depth of field using a logarithmic asphere," J. Opt. A, Pure Appl. Opt. 5, 157-163 (2003).
    [CrossRef]
  16. Q. Yang, L. Liu, and Jianfeng Sun, "Optimized phase pupil masks for extended depth of field," Opt. Commun. 272, 56-66 (2007).
    [CrossRef]
  17. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A 5, 164-169 (2003).
    [CrossRef]
  18. E. Ben-Eliezer, E. Marom, N. Konforti, and Z. Zalevsky, "Experimental realization of an imaging system with an extended depth of field," Appl. Opt. 44, 2792-2798 (2005).
    [CrossRef] [PubMed]
  19. G. Vdovin and P. Sarro, "Flexible mirror micromachined in silicon," Appl. Opt. 34, 2968-2972 (1995).
    [CrossRef] [PubMed]
  20. J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).
  21. R. Gonzalez and R. Woods, Digital Image Processing (Prentice Hall, 2002).
  22. M. Yamauchi and T. Eiju, "Optimization of twisted nematic liquid crystal panels for spatial light phase modulation," Opt. Commun. 115, 19-25 (1995).
    [CrossRef]

2007

Q. Yang, L. Liu, and Jianfeng Sun, "Optimized phase pupil masks for extended depth of field," Opt. Commun. 272, 56-66 (2007).
[CrossRef]

2006

I. De, B. Chanda, and B. Chattopadhyay, "Enhancing effective depth-of-field by image fusion using mathematical morphology," Image Vision Comput. 24, 1278-1287 (2006).
[CrossRef]

2005

2004

J. Gracht, V. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. Gracht, "High-resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

2003

N. George and W. Chi, "Extended depth of field using a logarithmic asphere," J. Opt. A, Pure Appl. Opt. 5, 157-163 (2003).
[CrossRef]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A 5, 164-169 (2003).
[CrossRef]

2002

2000

E. Dowski, R. Cormack, and S. Sarama, "Wavefront coding: jointly optimized optical and digital imaging systems," Proc. SPIE 4041, 114-120 (2000).
[CrossRef]

1995

1994

S. Nayar, "Shape from focus," IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

1989

1988

1986

1972

G. Hausler, "A method to increase the depth of focus by two step image processing," Opt. Commun. 6, 38-42 (1972).
[CrossRef]

1971

Appl. Opt.

IEEE Trans. Pattern Anal. Mach. Intell.

S. Nayar, "Shape from focus," IEEE Trans. Pattern Anal. Mach. Intell. 16, 824-831 (1994).
[CrossRef]

Image Vision Comput.

I. De, B. Chanda, and B. Chattopadhyay, "Enhancing effective depth-of-field by image fusion using mathematical morphology," Image Vision Comput. 24, 1278-1287 (2006).
[CrossRef]

Int. J. Imaging Syst. Technol.

S. Prasad, T. Torgersen, V. Pauca, R. Plemmons, and J. Gracht, "High-resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

J. Opt. A

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A 5, 164-169 (2003).
[CrossRef]

J. Opt. A, Pure Appl. Opt.

N. George and W. Chi, "Extended depth of field using a logarithmic asphere," J. Opt. A, Pure Appl. Opt. 5, 157-163 (2003).
[CrossRef]

Opt. Commun.

Q. Yang, L. Liu, and Jianfeng Sun, "Optimized phase pupil masks for extended depth of field," Opt. Commun. 272, 56-66 (2007).
[CrossRef]

G. Hausler, "A method to increase the depth of focus by two step image processing," Opt. Commun. 6, 38-42 (1972).
[CrossRef]

M. Yamauchi and T. Eiju, "Optimization of twisted nematic liquid crystal panels for spatial light phase modulation," Opt. Commun. 115, 19-25 (1995).
[CrossRef]

Opt. Lett.

Proc. SPIE

J. Gracht, V. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquisition," Proc. SPIE 5438, 120-129 (2004).
[CrossRef]

E. Dowski, R. Cormack, and S. Sarama, "Wavefront coding: jointly optimized optical and digital imaging systems," Proc. SPIE 4041, 114-120 (2000).
[CrossRef]

Other

S. Fatikow, J. Seyfried, S. Fahlbusch, A. Buerkle, F. Schmoeckel, and H. Woern, "Intelligent Microrobotic System for Microassembly Tasks," First Int. Conference on Mechatronics and Robotics, St. Petersburg, Russia, 29 May-2 June 2000.

H. Cho, Optomechatronics (CRC Press, 2006).

J. Goodman, Introduction to Fourier Optics (Roberts & Company, 2005).

R. Gonzalez and R. Woods, Digital Image Processing (Prentice Hall, 2002).

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Figures (13)

Fig. 1
Fig. 1

(Color online) General configuration of imaging systems.

Fig. 2
Fig. 2

(Color online) Optical setup for the Jones matrix calibration.

Fig. 3
Fig. 3

(Color online) Phase and intensity modulation of the LC-SLM when θ P = 125 ° and θ A = 175 ° .

Fig. 4
Fig. 4

(Color online) Configuration of the optical arrangement of the proposed system. (a) Schematic of the proposed system. (b) Experimental setup of the proposed system.

Fig. 5
Fig. 5

Realization of the desired phase modulation in Fresnel lens form by the LC-SLM. (a) Desired phase modulation; α = 40 , (b) realization in Fresnel lens form; α = 40 , (c) desired phase modulation; α = 100 , and (d) realization in Fresnel lens form; α = 100 .

Fig. 6
Fig. 6

Change of the PSF when a cubic phase mask is applied. (a) PSF without a phase mask. (b) PSF with a phase mask of α = 40 .

Fig. 7
Fig. 7

(Color online) USAF resolution target.

Fig. 8
Fig. 8

(Color online) Definition of I max and I min .

Fig. 9
Fig. 9

Extending the DOF by wavefront-coding with α = 40 : (a) d = 0 , (b) d = 1   mm , (c) d = 0 with tilt.

Fig. 10
Fig. 10

3 mm defocused target and its restored image: (a) α = 0 without a phase mask, (b) α = 40 , (c) α = 100 .

Fig. 11
Fig. 11

MTF measurement results for various mask strengths. (a) Without a phase mask; α = 0 , (b) α = 40 , (c) α = 60 , (d) α = 80 , and (e) α = 100 .

Fig. 12
Fig. 12

(Color online) Plotting the DOF and strength of the phase mask.

Fig. 13
Fig. 13

(Color online) DOF versus the phase mask strength with various criterion frequencies.

Tables (1)

Tables Icon

Table 1 Calibration Results for the LC-SLM

Equations (77)

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x 2 y
x y 2
p ( x p , y p ) = { exp [ i α ( x p 3 + y p 3 ) ] 0 ,   for   | x p | 1 , | y p | 1 .
p ( x p , y p )
x p
y p
M ( u , ψ ) = { ( π 12 | α u | ) 1 / 2    exp ( i α u 3 4 ) | α | 20 u 0 1                                       u = 0 ,
G ( μ , v )
H ( μ , v )
F ( μ , v )
F ( μ , v ) = [ 1 H ( μ , v ) | H ( μ , v ) | 2 | H ( μ , v ) | 2 + K ] G ( μ , v ) ,
{ H ( μ , v ) = { h ( x i , y i ) } G ( μ , v ) = { g ( x i , y i ) } F ( μ , v ) = { f ( x i , y i ) } ,
h ( x i , y i )
g ( x i , y i )
f ( x i , y i )
{ · }
F ( μ , v )
J ( v ) = c   exp [ i ( ϕ o + β ( v ) ) ] × ( f ( v ) i g ( v ) h ( v ) i j ( v ) h ( v ) i j ( v ) f ( v ) + i g ( v ) )
( x out y out ) = P ( θ A ) J P ( θ P ) ( x in y in ) ,
P ( θ )
θ P
θ A
( x in y in ) T
( x out y out ) T
θ P
θ A
5 × 72 × 72 = 25 , 920
θ P
θ A
θ P = 125 °
θ A = 175 °
Contrast   Modulation = I max I min I max + I min .
I max
I min
d = 0
d = 1   mm
d = 0
α = 40
α = 40
3   mm
3   mm
4.5   mm
4.5   mm
4.5   mm
d f
f c
f c = 20 lp / mm
20 lp / mm
2.2   mm
30 lp / mm
45 lp / mm
30 lp / mm
J = 1.3513 exp [ i ( ϕ o + 2.0179 ) ] ( 0.2986 i 0.2055 0.8250 i 0.4323 0.8250 i 0.4323 0.2986 + i 0.2055 )
J = 1.3364 exp [ i ( ϕ o + 1.3260 ) ] ( 0.6495 i 0.2575 0.4672 i 0.5417 0.4672 i 0.5417 0.6495 + i 0.2575 )
J = 1.3533 exp [ i ( ϕ o + 0.3268 ) ] ( 0.9766 i 0.0912 0.0336 i 0.1919 0.0336 i 0.1919 0.9766 + i 0.0912 )
J = 1.3580 exp [ i ( ϕ o + 0.0354 ) ] ( 0.9977 i 0.0103 0.0536 i 0.0217 0.0536 i 0.0217 0.9977 + i 0.0103 )
J = 1.3763 exp [ i ( ϕ o + 0.0226 ) ] ( 0.9977 i 0.0066 0.0448 i 0.0138 0.0448 i 0.0138 0.9977 + i 0.0066 )
θ P = 125 °
θ A = 175 °
α = 40
α = 40
α = 100
α = 100
α = 40
I max
I min
α = 40
d = 0
d = 1   mm
d = 0
α = 40
α = 100
α = 0
α = 40
α = 60
α = 80
α = 100

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