Abstract

The depth of focus of the Gaussian beam is extended by introducing a wavefront phase correction with properly designed diffractive optical elements. Results of the computer simulations show that, compared with other methods, the presented method demonstrates a reduced focal spot size and low sidelobes in a focal domain, within a considerable range of defocusing distances. Experimental results for the visible range diffractive optical element with a focus of 40mm and a depth of focus that extends to 1mm agree with the theory.

© 2006 Optical Society of America

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References

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  1. M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, and V. A. Soifer, "Focusing light into a specified volume by computer-synthesized holograms," Sov. Tech. Phys. Lett. 7, 264-266 (1981).
  2. N. Davidson, A. A. Friesem, and E. Hasman, "Holographic axilens: high resolution and long focal depth," Opt. Lett. 16, 523-525 (1991).
    [CrossRef] [PubMed]
  3. A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The light sword-element: a new diffraction structure with extended depth of focus," J. Mod. Opt. 37, 1283-1286 (1990).
    [CrossRef]
  4. D. Zalvidea and E. E. Sicre, "Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function," Appl. Opt. 37, 3623-3627 (1998).
    [CrossRef]
  5. S. N. Khonina, V. V. Kotlyar and V. A. Soifer, "Calculation of the focusators into a longitudinal line segment and study of a focal area," J. Mod. Opt. 40, 761-769 (1993).
    [CrossRef]
  6. R. Piestun, B. Spector, and J. Shamir, "Pattern generation with an extended focal depth," Appl. Opt. 37, 5394-5398 (1998).
    [CrossRef]
  7. G. Yang, "An optical pickup using a diffractive optical element for a high-density optical disc," Opt. Commun. 159, 19-22 (1999).
    [CrossRef]
  8. H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001).
    [CrossRef]
  9. W. T. Cathey and E. R. Dowski, "Extended depth of field through wave-front coding," Appl. Opt. 34, 1859-1866 (1995).
    [CrossRef] [PubMed]
  10. D. Elkind, Z. Zalevsky, U. Levy, and D. Mendlovic, "Optical transfer function shaping and depth of focus by using a phase only filter," Appl. Opt. 42, 1925-1931 (2003).
    [CrossRef] [PubMed]
  11. A. Flores, M. R. Wang, and J. J. Yang, "Achromatic hybrid refractive-diffractive lens with extended depth of focus," Appl. Opt. 43, 5618-5630 (2004).
    [CrossRef] [PubMed]
  12. M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999).
  13. M. A. Golub, "Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements," J. Opt. Soc. Am. A 16, 1194-1201 (1999).
    [CrossRef]
  14. Holo-Or, Ltd., "DOE-CAD software for design, masks generation, and performance modeling of diffractive optical elements," http://www.holoor.co.il/Website/data/index2.htm.

2004

2003

2001

H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001).
[CrossRef]

1999

M. A. Golub, "Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements," J. Opt. Soc. Am. A 16, 1194-1201 (1999).
[CrossRef]

G. Yang, "An optical pickup using a diffractive optical element for a high-density optical disc," Opt. Commun. 159, 19-22 (1999).
[CrossRef]

1998

R. Piestun, B. Spector, and J. Shamir, "Pattern generation with an extended focal depth," Appl. Opt. 37, 5394-5398 (1998).
[CrossRef]

D. Zalvidea and E. E. Sicre, "Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function," Appl. Opt. 37, 3623-3627 (1998).
[CrossRef]

1995

1993

S. N. Khonina, V. V. Kotlyar and V. A. Soifer, "Calculation of the focusators into a longitudinal line segment and study of a focal area," J. Mod. Opt. 40, 761-769 (1993).
[CrossRef]

1991

N. Davidson, A. A. Friesem, and E. Hasman, "Holographic axilens: high resolution and long focal depth," Opt. Lett. 16, 523-525 (1991).
[CrossRef] [PubMed]

1990

A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The light sword-element: a new diffraction structure with extended depth of focus," J. Mod. Opt. 37, 1283-1286 (1990).
[CrossRef]

1981

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, and V. A. Soifer, "Focusing light into a specified volume by computer-synthesized holograms," Sov. Tech. Phys. Lett. 7, 264-266 (1981).

Bara, S.

A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The light sword-element: a new diffraction structure with extended depth of focus," J. Mod. Opt. 37, 1283-1286 (1990).
[CrossRef]

Born, M.

M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Cathey, W. T.

Davidson, N.

N. Davidson, A. A. Friesem, and E. Hasman, "Holographic axilens: high resolution and long focal depth," Opt. Lett. 16, 523-525 (1991).
[CrossRef] [PubMed]

Dowski, E. R.

Elkind, D.

Flores, A.

Friesem, A. A.

N. Davidson, A. A. Friesem, and E. Hasman, "Holographic axilens: high resolution and long focal depth," Opt. Lett. 16, 523-525 (1991).
[CrossRef] [PubMed]

Gan, F.

H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001).
[CrossRef]

Golub, M. A.

M. A. Golub, "Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements," J. Opt. Soc. Am. A 16, 1194-1201 (1999).
[CrossRef]

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, and V. A. Soifer, "Focusing light into a specified volume by computer-synthesized holograms," Sov. Tech. Phys. Lett. 7, 264-266 (1981).

Hasman, E.

N. Davidson, A. A. Friesem, and E. Hasman, "Holographic axilens: high resolution and long focal depth," Opt. Lett. 16, 523-525 (1991).
[CrossRef] [PubMed]

Jaroszewicz, Z.

A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The light sword-element: a new diffraction structure with extended depth of focus," J. Mod. Opt. 37, 1283-1286 (1990).
[CrossRef]

Karpeev, S. V.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, and V. A. Soifer, "Focusing light into a specified volume by computer-synthesized holograms," Sov. Tech. Phys. Lett. 7, 264-266 (1981).

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar and V. A. Soifer, "Calculation of the focusators into a longitudinal line segment and study of a focal area," J. Mod. Opt. 40, 761-769 (1993).
[CrossRef]

Kolodziejczyk, A.

A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The light sword-element: a new diffraction structure with extended depth of focus," J. Mod. Opt. 37, 1283-1286 (1990).
[CrossRef]

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar and V. A. Soifer, "Calculation of the focusators into a longitudinal line segment and study of a focal area," J. Mod. Opt. 40, 761-769 (1993).
[CrossRef]

Levy, U.

Mendlovic, D.

Piestun, R.

R. Piestun, B. Spector, and J. Shamir, "Pattern generation with an extended focal depth," Appl. Opt. 37, 5394-5398 (1998).
[CrossRef]

Prokhorov, A. M.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, and V. A. Soifer, "Focusing light into a specified volume by computer-synthesized holograms," Sov. Tech. Phys. Lett. 7, 264-266 (1981).

Shamir, J.

R. Piestun, B. Spector, and J. Shamir, "Pattern generation with an extended focal depth," Appl. Opt. 37, 5394-5398 (1998).
[CrossRef]

Sicre, E. E.

D. Zalvidea and E. E. Sicre, "Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function," Appl. Opt. 37, 3623-3627 (1998).
[CrossRef]

Sisakyan, I. N.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, and V. A. Soifer, "Focusing light into a specified volume by computer-synthesized holograms," Sov. Tech. Phys. Lett. 7, 264-266 (1981).

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar and V. A. Soifer, "Calculation of the focusators into a longitudinal line segment and study of a focal area," J. Mod. Opt. 40, 761-769 (1993).
[CrossRef]

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, and V. A. Soifer, "Focusing light into a specified volume by computer-synthesized holograms," Sov. Tech. Phys. Lett. 7, 264-266 (1981).

Spector, B.

R. Piestun, B. Spector, and J. Shamir, "Pattern generation with an extended focal depth," Appl. Opt. 37, 5394-5398 (1998).
[CrossRef]

Sypek, M.

A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The light sword-element: a new diffraction structure with extended depth of focus," J. Mod. Opt. 37, 1283-1286 (1990).
[CrossRef]

Wang, H.

H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001).
[CrossRef]

Wang, M. R.

Wolf, E.

M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Yang, G.

G. Yang, "An optical pickup using a diffractive optical element for a high-density optical disc," Opt. Commun. 159, 19-22 (1999).
[CrossRef]

Yang, J. J.

Zalevsky, Z.

Zalvidea, D.

D. Zalvidea and E. E. Sicre, "Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function," Appl. Opt. 37, 3623-3627 (1998).
[CrossRef]

Appl. Opt.

D. Zalvidea and E. E. Sicre, "Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function," Appl. Opt. 37, 3623-3627 (1998).
[CrossRef]

R. Piestun, B. Spector, and J. Shamir, "Pattern generation with an extended focal depth," Appl. Opt. 37, 5394-5398 (1998).
[CrossRef]

H. Wang and F. Gan, "High focal depth with a pure-phase apodizer," Appl. Opt. 40, 5658-5662 (2001).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

M. A. Golub, "Generalized conversion from the phase function to the blazed surface-relief profile of diffractive optical elements," J. Opt. Soc. Am. A 16, 1194-1201 (1999).
[CrossRef]

J. Mod. Opt.

A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The light sword-element: a new diffraction structure with extended depth of focus," J. Mod. Opt. 37, 1283-1286 (1990).
[CrossRef]

S. N. Khonina, V. V. Kotlyar and V. A. Soifer, "Calculation of the focusators into a longitudinal line segment and study of a focal area," J. Mod. Opt. 40, 761-769 (1993).
[CrossRef]

Opt. Lett.

N. Davidson, A. A. Friesem, and E. Hasman, "Holographic axilens: high resolution and long focal depth," Opt. Lett. 16, 523-525 (1991).
[CrossRef] [PubMed]

Opt. Commun.

G. Yang, "An optical pickup using a diffractive optical element for a high-density optical disc," Opt. Commun. 159, 19-22 (1999).
[CrossRef]

Sov. Tech. Phys. Lett.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, and V. A. Soifer, "Focusing light into a specified volume by computer-synthesized holograms," Sov. Tech. Phys. Lett. 7, 264-266 (1981).

Other

M. Born, and E. Wolf, Principles of Optics (Cambridge University Press, 1999).

Holo-Or, Ltd., "DOE-CAD software for design, masks generation, and performance modeling of diffractive optical elements," http://www.holoor.co.il/Website/data/index2.htm.

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Figures (11)

Fig. 1
Fig. 1

Optical scheme for the design of extended focus DOEs.

Fig. 2
Fig. 2

Phase function of the designed extended focus DOE versus the polar coordinate in its plane. Wavelength is 0.633 μ m , 1 / e 2 diameter of the incident Gaussian beam is 5 mm , focal length of f 0 = 40 mm , and depth of focus of 1 mm . (a) Smooth phase φ ( r ) (bold line) and a best-fit spherical aberration of r 4 (thin line); (b) wrapped phase Φ ( ~ r ) modulo 2 π in the central part of the DOE.

Fig. 3
Fig. 3

Computer-simulated focal intensity distribution versus defocusing distance Δ f  (mm) : (a) our DOE design, (b) focused Gaussian beam; (c) comparison of the DOE (bold curves) and the Gaussian beam (thin curves).

Fig. 4
Fig. 4

Calculated full ( 1 / e 2 ) focal spot size with our DOE design (bold line) and the focused Gaussian beam (thin line).

Fig. 5
Fig. 5

Calculated (FWHM) focal spot size with our DOE design (bold line) and the focused Gaussian beam (thin line).

Fig. 6
Fig. 6

Computer-simulated focal intensity distribution versus defocusing distance Δ f  (mm) : (a) our DOE design, (b) an axilens,[2] (c) comparison of the DOE (bold curves) and the axilens (thin curves).

Fig. 7
Fig. 7

Computer-simulated focal intensity distribution versus defocusing distance Δ f  (mm) : (a) our DOE design, (b) DOE designed for uniform intensity[1] and illuminated by a Gaussian beam, (c) comparison of our DOE design (bold curves) and an existing DOE[1] (thin curves).

Fig. 8
Fig. 8

Arrangement for the experimental investigation of an extended focus DOE with a laser wavelength of 0.633 μm, a focal length of plano–convex lens L of f 0 = 40 mm .

Fig. 9
Fig. 9

Measured focal encircled power as a function of defocusing distance Δ f (thin curve): (a) diaphragm diameter of 60 μ m and (b) diaphragm diameter of 200 μ m . Bold curves, our DOE design; thin curves, the Gaussian beam focused by a standard plano–convex lens. Normalization is done to the maximum encircled power of a standard plano–convex lens.

Fig. 10
Fig. 10

Normalized measured focal intensity distributions from our DOE design versus defocusing distance Δ f  (mm) . Bold curve, the DOE; thin curve, for comparison the Gaussian beam focused by a standard plano–convex lens.

Fig. 11
Fig. 11

Measured full ( 1 / e 2 ) spot size with our DOE design (●) and Gaussian beam focused by a standard plano–convex lens ( ) . Thin lines show trend lines of experimental results.

Tables (1)

Tables Icon

Table 1 Estimates of the Full Focal Spot Size (μm) for the DOE and the Focused Gaussian Beam as a Function of Defocusing Δ f

Equations (149)

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40 mm
1 mm
I 0 ( r )
k ψ 0 ( r )
r D / 2
k = 2 π / λ
1 / e 2
I 0 ( r ) = exp ( 2 r 2 / σ 2 )
ψ 0 ( r )
ψ 0 ( r ) = 0
ψ 0 ( r ) = f 0 ( 1 1 + ( r / f 0 ) 2 )
f 0
f 0
f = f 0 + Δ f
f 0 κ / 2
f 0 + κ / 2
Δ f
1 / e 2
f 0
κ = L 0 [ ( σ max σ f o c ) 2 1 ] 1 / 2 ,
σ f o c
L 0 = π σ foc 2 / λ
σ max
1 / e 2
σ max 2 = σ foc 2 1 + ( Δ f / L 0 ) 2
Δ f
φ ( r )
l ( Δ f )
Δ f
κ / 2
κ / 2
l ( Δ f ) const
φ ( r ) = k [ ψ ( r ) ψ 0 ( r ) ] ,
φ ( r )
ψ ( r )
f ( r ) < f 0
f ( r ) > f 0
Δ f ( r )
r + d r
f ( r ) = f 0 + Δ f ( r )
f ( r + d r ) = f 0 + Δ f ( r + d r )
I 0 ( r ) 2 π r d r = l ( Δ f ) d f .
l ( Δ f ) Δ f r = I 0 ( r ) 2 π r
Δ f ( 0 ) = ± κ 2 , Δ f ( D 2 ) = κ 2 ,
Δ f
l ( Δ f )
Δ f ( r ) = ± κ ( 1 2 e ( r ) e ( D / 2 ) ) ,
e ( r ) = 0 r I 0 ( r ) 2 π r d r .
ψ = s
ψ r = r r 2 + [ f 0 + Δ f ( r ) ] 2 ,
ψ
ψ ( r ) = ψ ( 0 ) 0 r r r 2 + [ f 0 + Δ f ( r ) ] 2 d r
ψ ( 0 ) 0 r r f 0 + Δ f ( r ) d r ,
D / f 0 1
ψ ( r ) = ψ ( 0 ) σ 2 4 ( f 0 + c 1 ) ln ( 1 + f 0 + c 1 c 2 exp ( 2 r 2 σ 2 ) 1 + f 0 + c 1 c 2 )     ,
c 1 = ± κ { 1 2 [ 1 exp ( D 2 2 σ 2 ) ] 1 }     ,
c 2 = ± κ [ 1 exp ( D 2 2 σ 2 ) ] 1    
f ( r ) = f 0 + Δ f ( r )
φ ( r )
ψ ( r )
ψ 0 ( r )
2 π
Φ ( r ) = M o d 2 π [ φ ( r ) ] ,
Mod 2 π
2 π
φ ( r )
φ ( r )
φ ( r )
Φ ( r )
2 π
Φ ( r )
φ ( r )
φ ( r )
r 4
Φ ( r )
0.633 μ m
14 mm
1 / e 2
5 mm
f 0 = 40 mm
1 / e 2
2 σ f o c = 6.4 μ m
κ G a u s s = 0.4 mm
Δ f
2 σ max = 26 μ m
Δ f
Δ f < 0
Δ f > 0
1 / e 2
Δ f
Δ f
Δ f
Δ f
- 1.0
- 0.3 mm
1 / e 2
Δ f
- 1.1 mm
1.5 mm
Δ f
1 / e 2
6 μ m
1 / e 2
16 μ m
1 / e 2
< 26 μ m
κ = 1.0 mm
κ G a u s s = 0.4 mm
M = 16
h ( r )
h ( r ) = M 1 M λ n 1 Φ ( r ) 2 π ,
Φ ( r )
ψ 0 ( r )
14 mm
λ = 0.633 μ m
1 / e 2
f 0 = 40 mm
1.0 mm
60 μm
10X
| Δ f | 0.5 mm
Δ f = 0.0
Δ f = 0.5
1 mm
Δ f
Δ f
Δ f  (mm)
1 / e 2
1 / e 2
0.633 μ m
1 / e 2
5 mm
f 0 = 40 mm
1 mm
φ ( r )
r 4
Φ ( ~ r )
2 π
Δ f  (mm)
1 / e 2
Δ f  (mm)
Δ f  (mm)
f 0 = 40 mm
Δ f
60 μ m
200 μ m
Δ f  (mm)
1 / e 2
( )

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