Abstract

In a previous work done by the authors, it was shown that the superresolution concept based on two moving gratings could be effected by a physical grating attached to the object and a virtual grating. This concept was shown to be very efficient and exhibited features that are helpful in removing some artifacts caused when coherent illumination is used. Furthermore, it simplifies the optical and mechanical modules of the super-resolving system by removing the need for mechanical movement of one grating. However, the system still required the need for moving the first (encoding) grating attached to the input. In this study the encoding grating is replaced by use of a projected grating. This approach simplifies the need for attaching the grating to the input object and thus new applications, such as remote sensing can be considered. The theoretical concept is demonstrated and experimental results are shown.

© 2002 Optical Society of America

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References

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2001

2000

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. (Oxford) 198, 82–87 (2000).
[CrossRef]

1999

1997

1996

1967

1964

1960

A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectra. 9, 204–206 (1960).

1952

M. Francon, “Amélioration de résolution d’optique,” Il Nuovo Cimento Suppl. 9, 283–290 (1952).

Dorsch, R.

Ferreira, C.

Francon, M.

M. Francon, “Amélioration de résolution d’optique,” Il Nuovo Cimento Suppl. 9, 283–290 (1952).

Frohn, J. T.

Garcia, J.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. (Oxford) 198, 82–87 (2000).
[CrossRef]

Kartashev, A. I.

A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectra. 9, 204–206 (1960).

Kiryuschev, I.

Knapp, H. F.

Konforti, N.

Lohmann, A. W.

Lukosz, W.

Marom, Emanuel

Martinez, P. G.

Mendlovic, D.

Paris, D. P.

Shemer, A.

Stemmer, A.

Zalevsky, Z.

Appl. Opt.

Il Nuovo Cimento Suppl.

M. Francon, “Amélioration de résolution d’optique,” Il Nuovo Cimento Suppl. 9, 283–290 (1952).

J. Microsc. (Oxford)

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. (Oxford) 198, 82–87 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Opt. Spectra.

A. I. Kartashev, “Optical systems with enhanced resolving power,” Opt. Spectra. 9, 204–206 (1960).

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Figures (9)

Fig. 1
Fig. 1

Optical system for obtaining an enlarged effective aperture by using the first moving grating and a virtual grating generated by a computer.

Fig. 2
Fig. 2

(a) Desired intensity (autocorrelation) of the input image, (b) intensity (autocorrelation) of the super-resolved image when Dammann-like gratings are used.

Fig. 3
Fig. 3

Optical system for obtaining the projected grating based on two SLM devices.

Fig. 4
Fig. 4

Optical system for obtaining the projected grating based on a moving lens.

Fig. 5
Fig. 5

Optical system for obtaining increased effective aperture by using a projected moving grating at the input plane and a computer-generated virtual grating at the output.

Fig. 6
Fig. 6

Input object used for the experiment.

Fig. 7
Fig. 7

Interference grating that was projected on the input.

Fig. 8
Fig. 8

Low-resolution input object after passing the finite aperture of the optical system.

Fig. 9
Fig. 9

High-resolution reconstructed input object after ssuperresolution based also on the virtual-grating approach as the decoding grating.

Equations (17)

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Uoutx, t=G2x-VtU2x, t]=m Bm exp2πimν0x-Vt×n An  P˜νŨinν-nν0×exp-2πinν0Vtexp2πiνxdν=m,n BmAn  P˜ν×Ũinν-nν0exp2πixν+mν0-nmν0Vtdν,
τ=1/ν0V=dV 1τ-τ/2τ/2 exp-2πiν0Vt×n+mdt=1n+m=00n+m0
Uoutx, t=n=m BnAn  P˜ν+nν0×Ũinνexp2πixνdν=n=m BnAnFT-1P˜ν+nν0Ũinν=FT-1Ũinνn=m BnAnP˜ν+nν0.
Ix, t=|Uoutx, t|2=m,nm,n AnBmAn*Bm*  P˜ν1P˜*ν2×Ũinν1-nν0Ũin*ν2-nν0×exp2πixν1+mν0-ν2-mν0-m-m+n-nVν0tdν1dν2
1τ-τ/2τ/2 Uinx1 tUin*x2 tdt=Uinx1Uin*x1δx1-x2.
Ũinμ1 t= Uinx1 texp-2πixμ1dx1,Ũinμ2 t= Uinx2 texp-2πixμ2dx2,
μ1=ν1-nν0, μ2=ν2-nν0.
ZTalbotn=2L2nλ,
ZTalbotn=2n+1L2λ.
Ux, y=expikziλzexpik2zx2+y2×--Uε, ηexp-i2πλzxε+yηdεdη.
G1x=n=0N-1 An exp2πinν0x,
Ulε, η=Ulε, ηPε, ηexp-ik2Fε2+η2,
Ufx, y=expik2Fx2+y2iλF×-- Ulε, ηPε, η×exp-i2πλFxε+yηdεdη.
Ulε-ε0, η-η0=Ulε-ε0, η-η0Pε-ε0, η-η0×exp-ik2Fε-ε02+η-η02,
exp-ik2Fε-ε02+η-η02=exp-ik2Fε2-2εε0+ε02+η2-2ηη0+η02
Ufx, y=expik2Fx2+y2expik2Fε2+η2iλF×-- Ulε, ηexp-i2πλFεx+ε0+ηy+η0dεdη,
Ufx-ε0, y-η0=expik2Fx-ε02+y-η02ik2Fε2+η2iλF×-- Ulε, ηexp-i2πλFεx+ηydεdη,

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