Abstract

In this paper we present a new approach providing super resolved imaging at the center of the field of view and yet allowing seeing the remaining of the original field of view with the original resolution. This operation resembles optical zooming while the zoomed and the non zoomed images are obtained simultaneously. This is obtained by taking a single snap shot and using a single imaging lens. The technique utilizes a special static/still coding element and a post processing algorithmic, without any mechanical movements.

© 2005 Optical Society of America

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References

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Appl. Opt. (7)

Applied Optics (1)

D. R. Shafer, "Zoom null lens," Applied Optics, 18, 3863-3870 (1979).
[PubMed]

J. Opt. Soc. Am. (2)

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

Opt. Acta (1)

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Let. (2)

E. C. Tam, "Smart electro optical zoom lens," Opt. Let. 17, 369-371 (1992).
[CrossRef]

D. Y. Zhang, N. Justis and Y. H. Lo, "Integrated fluidic adaptive zoom lens," Opt. Let., 29, 2855-2857 (2004).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

One-dimensional object. The minimal details in the central part are three times finer, than those in the periphery.

Fig. 2.
Fig. 2.

The spatial grating positioned in CTF plane. Its three parts G-1(ν), G0(ν) and G1(ν) are plotted in a folded manner. The period of G0(ν) is three times smaller than the period of G-1(ν) and G0(ν).

Fig. 3.
Fig. 3.

Orthogonality and macro pixels: (a) This is an example for orthogonal coding: in each spectral region there is a macro-pixel with a certain non-zero pixel. (b) After aliasing all nonzero pixel are folded in a non-overlapping way, providing orthogonality. (c) Due to the real realization of the grating the true structure is a bit different than the theory presented in 3(a) and 3(b).

Fig. 4.
Fig. 4.

Spatial effect of the coding mask. (a). Replication of high spectral content. (b). Replication of the low spectral content.

Fig. 5.
Fig. 5.

(a). Sampling high frequency content: S-1(ν) samples are marked with oe-13-24-9858-i001 S1(ν) samples are marked with oe-13-24-9858-i002. (b). The Fourier transform of the grating.

Fig. 6.
Fig. 6.

(a).The experimental setup. (b). The coding Dammann mask that was attached to the imaging lens.

Fig. 7.
Fig. 7.

(a). The non zoomed test object used in simulations: Lena image with high frequency two dimensional barcode pattern at its center. (b). The X3 zoomed test target where one may see the high frequency barcode pattern.

Fig. 8.
Fig. 8.

The obtained result after the digital decoding. One may see the full field of view and the zoomed highly resolved barcode pattern in the center of the field of view.

Equations (19)

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G 1 ( v ) G k ( v ) = δ [ 1 , k ]
I ( ν ) = k = 1 1 S k ( ν ) × G k ( ν ) ν [ 1 3 ν max , 1 3 ν max ]
CCD ( x ) = n = δ ( x nΔx )
CDM A ˜ ( ν ) = n = 1 1 G n ( ν nΔν )
D ( v ) = [ S ( ν ) n = 1 1 G n ( ν nΔν ) ] [ n = δ ( ν n 2 π Δx ) ]
D ( ν ) = S ( ν ) n = 1 1 G n ( ν nΔν ) n = δ ( ν nΔν )
= n = S ( ν nΔν ) [ k = 1 1 G n ( ν ( n + k ) Δν ) ]
R ( ν ) = D ( ν ) CDM A ˜ ( ν ) = { n = S ( ν ν ) [ k = 1 1 G n ( ν ( n + k ) Δν ) ] } [ m = 1 1 G m ( ν mΔν ) ]
= n = S ( ν nΔν ) G n ( ν nΔν ) = S ( ν ) CDM A ˜ ( ν ) downsampling S ( ν )
i L ( x ) = ( s 0 * g 0 ) ( x ) rect ( x L T )
rect ( x L T ) = { 1 x L T 2 0 otherwise
g 0 ( x ) = n = 1 1 a n × δ ( x n L T 2 )
r 1 ( x ) = a 0 f 1 ( x ) + a 1 f 4 ( x )
r 2 ( x ) = a 0 f 2 ( x ) + a 1 f 5 ( x )
r 3 ( x ) = a 0 f 3 ( x ) + a 1 f 6 ( x )
r 4 ( x ) = a 0 f 4 ( x ) + a 1 f 1 ( x )
r 5 ( x ) = a 0 f 5 ( x ) + a 1 f 2 ( x )
r 6 ( x ) = a 0 f 6 ( x ) + a 1 f 3 ( x )
[ r 1 ( x ) r 2 ( x ) r 3 ( x ) r 4 ( x ) r 5 ( x ) r 6 ( x ) ] = [ a 0 0 0 a 1 0 0 0 a 0 0 0 a 1 0 0 0 a 0 0 0 a 1 a 1 0 0 a 0 0 0 0 a 1 0 0 a 0 0 0 0 a 1 0 0 a 0 ] [ f 1 ( x ) f 2 ( x ) f 3 ( x ) f 4 ( x ) f 5 ( x ) f 6 ( x ) ]

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