Abstract

A technique based on superresolution by digital holographic microscopic imaging is presented. We used a two dimensional (2-D) vertical-cavity self-emitting laser (VCSEL) array as spherical-wave illumination sources. The method is defined in terms of an incoherent superposition of tilted wavefronts. The tilted spherical wave originating from the 2-D VCSEL elements illuminates the target in transmission mode to obtain a hologram in a Mach–Zehnder interferometer configuration. Superresolved images of the input object above the common lens diffraction limit are generated by sequential recording of the individual holograms and numerical reconstruction of the image with the extended spatial frequency range. We have experimentally tested the approach for a microscope objective with an exact 2-D reconstruction image of the input object. The proposed approach has implementation advantages for applications in biological imaging or the microelectronic industry in which structured targets are being inspected.

© 2006 Optical Society of America

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References

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2004 (1)

2003 (1)

2002 (2)

2001 (2)

1999 (3)

1998 (1)

1997 (1)

1994 (1)

1992 (2)

1987 (1)

1986 (1)

1969 (1)

1967 (1)

1955 (1)

Angell, D.

Bevilacqua, F.

Boyer, K.

Brueck, S. R. J.

Carlsson, T. E.

Chen, X.

Collot, L.

Cox, I. J.

Cuche, E.

Cullen, D.

Depeursinge, C.

Dubois, F.

Garcia, J.

Garcia-Martinez, P.

Gross, M.

Haddad, W. S.

Jüpter, W. P. O.

Kato, J.-I.

Kuei, C.-P.

Kuznetsova, Y.

Le Clerc, F.

Legros, J.-C.

Leith, E. N.

Longworth, J. W.

Lukosz, W.

Massig, J. H.

McPherson, A.

Mendlovic, D.

Mico, V.

Minetti, C.

Mizuno, J.

Monnom, O.

Nilsson, B.

Otha, S.

Rhodes, C. K.

Schnars, U.

Schwarz, C. J.

Shemer, A.

Sheppard, J. R.

Solem, J. C.

Sun, P. C.

Toraldo di Francia, G.

Yamaguchi, I.

Yourassowsky, C.

Zalevsky, Z.

Zhang, T.

Appl. Opt. (7)

J. Opt. Soc. Am. (3)

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

Opt. Express (1)

Opt. Lett. (6)

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Figures (5)

Fig. 1
Fig. 1

Experimental setup. The object is imaged onto the CCD by the microscope lens. Divergence distances for the illumination in both arms, d and d′, are indicated by the broken segments ending with arrows.

Fig. 2
Fig. 2

Synthetic aperture generation.

Fig. 3
Fig. 3

(a) Reference high-resolution image obtained with a 0.42 NA microscope lens and incoherent illumination. (b) Image obtained with a 0.1 NA microscope lens and single-VCSEL (coherent) illumination.

Fig. 4
Fig. 4

(a) Hologram image obtained by illumination with the central VCSEL. The inset shows a magnified portion of the image, in which the fringes can be observed. (b) Image in the corresponding virtual Fourier-transform plane of (a) that underwent a previous multiplication by a spherical phase factor to focus the - 1 order.

Fig. 5
Fig. 5

(a) Image obtained with the 0.1 NA lens and the superresolution approach. (b) Fourier transform of (a) showing the extended synthetic aperture. The dashed circle shows the original aperture.

Equations (6)

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U m , n CCD ( x , y ) = ( f ( - x M , - y M ) exp { j k 2 M d [ ( x - x m ) 2 + ( y - y n ) 2 ] } ) disk ( Δν r ) ,
I m × n CCD ( x , y ) = | ( f ( - x M , - y M ) exp { j k 2 M d [ ( x - x m ) 2 + ( y - y n ) 2 ] } ) disk ( Δν r ) + exp { j k 2 d [ ( x - x m ) 2 + ( y - y n ) 2 ] + j 2 π Q x } | 2 ,
I m , n CCD ( x , y ) = 1 + | ( f ( - x M , - y M ) exp { j k 2 Md [ ( x - x m ) 2 + ( y - y n ) 2 ] } ) disk ( Δvr ) | 2 + [ ( f ( - x M , - y M ) exp { j k 2 Md [ ( x - x m ) 2 + ( y - y n ) 2 ] } ) disk ( Δvr ) ] exp { - j k 2 d [ ( x - x m ) 2 + ( y - y n ) 2 ] - j 2 πQx } + [ ( f * ( - x M , - y M ) exp { - j k 2 Md [ ( x - x m ) 2 + ( y - y n ) 2 ] } ) disk ( Δvr ) ] exp { j k 2 d [ ( x - x m ) 2 + ( y - y n ) 2 ] + j 2 πQx } .
P ˜ 3 ( u , v ) = K { [ f ˜ ( M u + x m λ d , + y n λ d ) FT - 1 { exp [ j k 2 M d ( x 2 + y 2 ) ] } ] circ ( ρ Δν ) } FT - 1 { exp [ - j k 2 d ( x 2 + y 2 ) ] exp [ j k d ( x x m + y y n ) ] } δ ( u + Q , ν ) ,
P ˜ 3 ( u , v ) = K { [ f ˜ ( M u + x m λ d , M ν + y n λ d ) ] circ ( ρ Δν ) } FT - 1 { exp [ j k d ( x x m + y y n ) ] } δ ( u + Q , ν ) .
P ˜ 3 sum ( u , v ) = K { m , n [ f ˜ ( M u + x m λ d , M ν + y n λ d ) circ ( ρ Δν ) ] δ ( u + x m λ d , ν + y n λ d ) } δ ( u + Q , ν ) .

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