Abstract

We present and analyze new multifocal optical elements based on an annular distribution of the transmittance. These elements provide selectable number of foci and can be designed to work between two fixed positions or even to provide extended focal depth. The energy of the foci can be modulated through a single parameter that controls the area of each ring. In our study we analyze the quality of the peaks and also the limit number of foci that can be obtained. The properties shown by these elements make them usable in instrumental optics or in ophthalmic optics, as new intraocular implants, where multifocal elements are required. The implementation has been done on a twisted nematic spatial light modulator, thus allowing real time reconfiguration of the element.

© 2008 Optical Society of America

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References

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  1. A. Kolodziejczyk, S. Bara, Z. Jaroszewicz, and M. Sypek, "The light sword optical element -a new diffraction structure with extended depth of focus," J. Mod. Opt. 37, 1283-1286 (1990).
    [CrossRef]
  2. H. Luo and C. Zhou, "Comparison of superresolution effects with annular phase and amplitude filters," Appl. Opt. 43, 6242-6247 (2004).
    [CrossRef] [PubMed]
  3. J. Monsoriu, W. D. Furlan, P. Andrés, and J. Lancis, "Fractal conical lenses," Opt. Express 14, 9077-9082 (2006).
    [CrossRef] [PubMed]
  4. I. Golub, "Fresnel axicon," Opt. Lett. 31, 1890-1892 (2006).
    [CrossRef] [PubMed]
  5. V. F. Canales and M. P. Cagigal, "Pupil filter design by using a Bessel functions basis at the image plane," Opt. Express 14, 10393-10402 (2006).
    [CrossRef] [PubMed]
  6. T. R. M. Sales and G. M. Morris, "Diffractive superresolution elements," J. Opt. Soc. Am. A 14, 1637-1646 (1997).
    [CrossRef]
  7. A. Burvall, K. Kolacz, Z. Jaroszewicz, and A. Friberg, "Simple lens axicon," Appl. Opt. 43, 4838-4844 (2004).
    [CrossRef] [PubMed]
  8. A. Flores, M. Wang, and J. J. Yang, "Achromatic hybrid refractive-diffractive lens with extended focal length," Appl. Opt. 43, 5618-5630 (2004).
    [CrossRef] [PubMed]
  9. J. A. Davis, C. S. Tuvey, O. López-Coronado, J. Campos, M. J. Yzuel, and C. Iemmi, "Tailoring the depth of focus for optical imaging systems using a Fourier transform approach," Opt. Lett. 32, 844-846 (2007).
    [CrossRef] [PubMed]
  10. D. Mas, J. Espinosa, J. Perez, and C. Illueca, "Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus," Opt. Express 15, 17842-17854 (2007).
    [CrossRef] [PubMed]
  11. D. M. Cottrell, J. A. Davis, T. R. Hedman, and R. A. Lilly, "Multiple imaging phase-encoded optical elements written as programmable spatial light modulators," Appl. Opt. 29, 2505-2509 (1990).
    [CrossRef] [PubMed]
  12. J. Leach, G. M. Gibson, M. Padgett, E. Exposito, G. McConell, A. J. Wright, and J. M. Girkin, "Generation of achromatic Bessel beams using a compensated spatial light modulator," Opt. Express 14, 5581-5587 (2006).
    [CrossRef] [PubMed]
  13. C. Iemmi, J. Campos, J. C. Escalera, O. Lopez-Coronado, R. Gimeno, and M. J. Yzuel, "Depth of focus increase by multiplexing programmable diffractive lenses," Opt. Express 14, 10207-10217 (2006).
    [CrossRef] [PubMed]
  14. V. F. Canales, J. E. Oti, and M. P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks," Opt. Commun. 247, 11-18 (2005).
    [CrossRef]
  15. P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, "Visual axial PSF of diffractive trifocal lenses," Opt. Express 13, 2782-2792 (2005).
    [CrossRef] [PubMed]
  16. D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
    [CrossRef]
  17. G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, "Imaging with extended focal depth by means of lenses with radial and angular modulation," Opt. Express 15, 9184-9193 (2007).
    [CrossRef] [PubMed]
  18. J. A. Davis, I. Moreno, and P. Tsai, "Polarization Eigenstates for Twisted-Nematic Liquid-Crystal Displays," Appl. Opt. 37, 937-945 (1998).
    [CrossRef]

2007 (3)

2006 (5)

2005 (2)

V. F. Canales, J. E. Oti, and M. P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks," Opt. Commun. 247, 11-18 (2005).
[CrossRef]

P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, "Visual axial PSF of diffractive trifocal lenses," Opt. Express 13, 2782-2792 (2005).
[CrossRef] [PubMed]

2004 (3)

2003 (1)

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
[CrossRef]

1998 (1)

1997 (1)

1990 (2)

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

D. M. Cottrell, J. A. Davis, T. R. Hedman, and R. A. Lilly, "Multiple imaging phase-encoded optical elements written as programmable spatial light modulators," Appl. Opt. 29, 2505-2509 (1990).
[CrossRef] [PubMed]

Andrés, P.

Bara, S.

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

Burvall, A.

Cagigal, M. P.

Campos, J.

Canales, V. F.

Cottrell, D. M.

Davis, J. A.

Escalera, J. C.

Espinosa, J.

Exposito, E.

Flores, A.

Friberg, A.

Furlan, W. D.

Gibson, G. M.

Gimeno, R.

Girkin, J. M.

Golub, I.

Hedman, T. R.

Hernández, C.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
[CrossRef]

Iemmi, C.

Illueca, C.

D. Mas, J. Espinosa, J. Perez, and C. Illueca, "Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus," Opt. Express 15, 17842-17854 (2007).
[CrossRef] [PubMed]

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
[CrossRef]

Jaroszewicz, Z.

Kolacz, K.

Kolodziejczyk, A.

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, "Imaging with extended focal depth by means of lenses with radial and angular modulation," Opt. Express 15, 9184-9193 (2007).
[CrossRef] [PubMed]

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

Lancis, J.

Leach, J.

Lilly, R. A.

Lopez-Coronado, O.

López-Coronado, O.

Luo, H.

Mas, D.

D. Mas, J. Espinosa, J. Perez, and C. Illueca, "Three dimensional analysis of chromatic aberration in diffractive elements with extended depth of focus," Opt. Express 15, 17842-17854 (2007).
[CrossRef] [PubMed]

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
[CrossRef]

McConell, G.

Mikula, G.

Miret, J. J.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
[CrossRef]

Monsoriu, J.

Moreno, I.

Morris, G. M.

Oti, J. E.

P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, "Visual axial PSF of diffractive trifocal lenses," Opt. Express 13, 2782-2792 (2005).
[CrossRef] [PubMed]

V. F. Canales, J. E. Oti, and M. P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks," Opt. Commun. 247, 11-18 (2005).
[CrossRef]

Padgett, M.

Perez, J.

Pérez, J.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
[CrossRef]

Petelczyc, K.

Sales, T. R. M.

Sypek, M.

G. Mikula, Z. Jaroszewicz, A. Kolodziejczyk, K. Petelczyc, and M. Sypek, "Imaging with extended focal depth by means of lenses with radial and angular modulation," Opt. Express 15, 9184-9193 (2007).
[CrossRef] [PubMed]

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

Tsai, P.

Tuvey, C. S.

Valle, P. J.

Vázquez, C.

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
[CrossRef]

Wang, M.

Wright, A. J.

Yang, J. J.

Yzuel, M. J.

Zhou, C.

Appl. Opt. (5)

J. Mod. Opt. (1)

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

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

D. Mas, J. Pérez, C. Hernández, C. Vázquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
[CrossRef]

V. F. Canales, J. E. Oti, and M. P. Cagigal, "Three-dimensional control of the focal light intensity distribution by analytically-designed phase masks," Opt. Commun. 247, 11-18 (2005).
[CrossRef]

Opt. Express (7)

Opt. Lett. (2)

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Figures (12)

Fig. 1.
Fig. 1.

Limit number of zones in a MFM according to Eq. (14). Bold lines represent the left side of the inequality for two different pupil sizes and the dot line corresponds to the right side of the inequality.

Fig. 2.
Fig. 2.

Axial intensity distribution for different MFMs with the following parameters: λ=λ 0=555 nm, Rp =3.5mm, P 1=1/20 mm-1, Pn =1/25 mm-1, h=0 and with a number rings of n=2 (a), n=5 (b), n=8 (c) and n=9 (d).

Fig. 3.
Fig. 3.

Comparison between phase only MFM and hybrid amplitude and phase modulated MFM (a) Am =1, h=0; (b) Am =1/Pm , h=0.

Fig. 4.
Fig. 4.

Influence of modulating parameter h. (a) h=0; (b) h=hC /9; (c) h=hC /2; (d) h=hC

Fig. 5.
Fig. 5.

Radial MTF at the focal planes (z=20.00, 21.43, 23.08 and 25.00 mm) of a MFM with n=4, P1=50 D, P4=40 D, Rp=3.5 mm. Legend stands for the number of peaks, being p1 the nearest peak and p4 the furthest one.

Fig. 6.
Fig. 6.

Depth of focus provided by MFM with n=1000, λ=λ 0=555 nm, Rp =3.5mm, P 1=1/20 mm-1, Pn =1/25 mm-1, h=hC /3.

Fig. 7.
Fig. 7.

Experimental apparatus for obtaining multifocal distributions: F, laser source; SF, spatial filter; L, imaging lens; ID iris diaphragm; P1, P2 linear polarizers; D1, D2, quarter wave plates; TN-LCD, twisted nematic spatial light modulator; GF gray filter; S screen; C, digital camera.

Fig. 8.
Fig. 8.

Phase mask implemented in the modulator for h=hC /1.8, Rp =6.95 mm, n=4, P 1=1.818 D and Pn =0.4 D.

Fig. 9.
Fig. 9.

(a). Calculated intensity distribution at the theoretical focus of each ring. (b). Real intensity captured with a CCD camera of a phase only MPM (h=hC /1.8) implemented in a TN-LCD. Maximum values of intensity at each plane are shown.

Fig. 10.
Fig. 10.

Phase mask implemented in the modulator for h=hC , Rp =6.95 mm, n=4, P 1=1.818 D and Pn =0.4 D.

Fig. 11.
Fig. 11.

(a). Calculated intensity distribution at the theoretical focus of each ring of a phase only MPM (h=hC ). Maximum values of intensity at each plane are shown.

Fig. 11.
Fig. 11.

(b) Real intensity captured with a CCD camera of a phase only MPM (h=hC ) implemented in a TN-LCD. Maximum values of intensity at each plane are shown.

Equations (29)

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t m ( r ) = A m exp ( j π λ 0 P m r 2 ) with a m 1 r < a m P n P m P 1 m [ 1 , n ]
U ax ( z ) = π j λ z m = 1 n A m ( a m 2 a m 1 2 ) sinc [ 1 2 λ 0 ( λ 0 z λ P m ) ( a m 2 a m 1 2 ) ]
                        exp [ j π 2 λ 0 ( λ 0 z λ P m ) ( a m 2 + a m 1 2 ) ]
P m = P 1 p = 1 m 1 g ( p ) p = 1 n 1 g ( p ) ( P 1 P n ) with g ( p ) > 0
S m = S m 1 + h π P m 1 P m , m 2 , h 0
    S m = π ( a m 2 a m 1 2 ) , S 1 = π a 1 2
a m 2 = m n R p 2 h [ m n i = 1 n 1 n i P i P i + 1 i = 1 m 1 m i P i P i + 1 ]
a m 2 = m n R p 2 h ( n 1 ) ( n m ) m 2 ( P 1 P n )
0 h 2 ( P 1 P n ) R p 2 n ( n 1 ) 2 = h C
U ax ( z ) = 2 λ 0 π j λ z m = 1 n A m 1 b m sinc { 1 b m ( λ 0 z λ P m ) }
exp { j π 2 λ 0 ( λ 0 z λ P m ) ( ( 2 m 1 ) R p 2 n h ( n 1 ) [ 2 m n + 2 m 2 n 2 m 2 1 ] 2 ( P 1 P n ) ) }
b m = 2 λ 0 ( R p 2 n h ( n 1 ) ( n 2 m + 1 ) 2 ( P 1 P n ) )
1 b m ( λ 0 λ z m null P m ) = ξ z m null = λ 0 λ ( P m + b m ξ ) ξ = 1 z m null = λ 0 λ ( P m b m )
z m + 1 null = λ 0 λ ( P m + 1 + b m + 1 )
z m + 1 null z m null 0 P m b m P m + 1 + b m + 1
P 1 P n 2 λ 0 ( n 1 ) 1 R p 2 n h ( n 1 ) ( n 2 m + 1 ) 2 ( P 1 P n ) + 1 R p 2 n h ( n 1 ) ( n 2 m + 3 ) 2 ( P 1 P n )
P 1 P n 2 λ 0 ( n 1 ) 1 R p 2 n h ( n 1 ) 2 2 ( P 1 P n ) + 1 R p 2 n h ( n 2 1 ) 2 ( P 1 P n )
π ( a 2 2 a 1 2 ) = π a 1 2 + h π P 1 P 2 a 2 2 = 2 a 1 2 + h P 1 P 2
π ( a 3 2 a 2 2 ) = π ( a 2 2 a 1 2 ) + h π P 2 P 3 a 3 2 = 2 a 2 2 + h P 2 P 3
                                    a 3 2 = 3 a 1 2 + h 2 P 1 P 2 + h 1 P 2 P 3
a m 2 = m a 1 2 + h i = 1 m 1 m i P i P i + 1
a n 2 = n a 1 2 + h i = 1 n 1 n i P i P i + 1 = R p 2 a 1 2 = R p 2 n h n i = 1 n 1 n i P i P i + 1
a m 2 = m n R p 2 h [ m n i = 1 n 1 n i P i P i + 1 i = 1 m 1 m i P i P i + 1 ]
P i = P 1 i 1 n 1 ( P 1 P n )
P i P i + 1 = [ P 1 i 1 n 1 ( P 1 P n ) ] [ P 1 i n 1 ( P 1 P n ) ] = P 1 P n n 1
a m 2 = m n R p 2 h ( n 1 ) ( P 1 P n ) [ m n i = 1 n 1 ( n i ) i = 1 m 1 ( m i ) ]
a m 2 = m n R p 2 h ( n 1 ) ( n m ) m 2 ( P 1 P n )
h 2 ( P 1 P n ) R p 2 n ( n 1 ) ( n m ) , m
0 h 2 ( P 1 P n ) R p 2 n ( n 1 ) ( n m ) 2 ( P 1 P n ) R p 2 n ( n 1 ) 2 = h C

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