Abstract

The use of vertical-cavity surface-emitting laser (VCSEL) arrays for implementation of incoherent source superresolution is presented. The method uses an interferometer setup to obtain superresolution in a single step. The novelty of the method relies on the use of a VCSEL array as the light source, which provides a set of coherent sources which are mutually incoherent. The technique accomplishes the transmission of several spatial frequency bands of the object’s spectrum in parallel by use of spatial multiplexing that occurs because of the tilted illumination of the source array. The recording process is done by interference of each frequency band with a complementary set of reference plane waves. After the reconstruction process, the resolution of any optical system can approach the natural λ/2 limit. The benefit of our system is improved modulation speed and hence more rapid image synthesis. Moreover, any desired synthetic coherent transfer function can be realized at ultrafast rates if we simply change the electrical drive of the VCSEL array.

© 2004 Optical Society of America

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References

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Appl. Opt. (4)

J. Mod. Opt. (2)

C. S. Chung and H. H. Hopkins, �??Influence of non-uniform amplitude on PSF,�?? J. Mod. Opt. 35, 1485�??1511 (1988).
[CrossRef]

J. Campos and M. J. Yzuel, �??Axial and extra-axial responses in aberrated optical systems with apodizers Optimization of the Strehl ratio,�?? J. Mod. Opt. 36, 733�??749 (1989).
[CrossRef]

J. Opt. Soc. Am. (3)

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

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

E. Sabo, Z. Zalevsky, D. Mendlovic, N. Konforti, and I. Kiryuschev, �??Superresolution optical system using three fixed generalized gratings: experimental results,�?? J. Opt. Soc. Am. A. 18, 514�??520 (2001).
[CrossRef]

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

Opt. Acta (1)

R. W. Gerchberg, �??Super-resolution through error energy reduction,�?? Opt. Acta 21 709�??720 (1974).
[CrossRef]

Opt. Lett. (3)

Supplementary Material (1)

» Media 1: GIF (260 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup (260 Kbytes). The actual experiment uses five VCSELs lit simultaneously, although the movie presents the lighting of the VCSELs in a time sequence for clarity.

Fig. 2.
Fig. 2.

Test objects of (a) the slit and (b) the resolution test

Fig. 3.
Fig. 3.

(a) Image recorded in the CCD [Eq. (5)] and (b) inverse Fourier transform of (a) performed digitally.

Fig. 4.
Fig. 4.

(a) Superresolved image of the slit and (b) conventional image with a limited aperture.

Fig. 5.
Fig. 5.

(a) Conventional image with a limited aperture (only axial source). (b) Output with the superresolution approach with three sources. (c) Output with the superresolution approach with five sources. (d) High-pass version obtained as for (c) but with the central source turned off.

Equations (15)

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U CCD on− axis ( x ) = f ( x ) sin c ( x Δ ν ) .
f ˜ ( ν ) = m = + f ˜ ( ν ) rect ( ν m Δ ν Δ ν ) .
U ˜ m ( ν ) = f ˜ ( ν m Δ ν ) Rect ( ν Δ ν ) .
U m ( x ) = [ f ( x ) e j 2 π m Δ ν x ] sin c ( x Δ ν ) .
I m ( x ) = [ f ( x ) e j 2 π m Δ ν x ] sin c ( x Δ ν ) + e j 2 π ( m Δ ν + Q ) x 2 =
= 1 + [ f ( x ) e j 2 π m Δ ν x ] sin c ( x Δ ν ) 2
+ [ f ( x ) e j 2 π m Δ ν x ] sin c ( x Δ ν ) × e j 2 π ( m Δ ν + Q ) x
+ [ f * ( x ) e j 2 π m Δ ν x ] sin c ( x Δ ν ) × e j 2 π ( m Δ ν + Q ) x
T ˜ 2 ( ν ) = [ f ˜ ( ν m Δ ν ) rect ( ν Δ ν ) ] * [ f ˜ ( ν m Δ ν ) rect ( ν Δ ν ) ] ,
T ˜ 3 ( ν ) = [ f ˜ ( ν m Δ ν ) × rect ( ν Δ ν ) ] δ ( ν + m Δ ν + Q )
= [ f ˜ ( ν ) × rect ( ν + m Δ ν Δ ν ) ] δ ( ν + Q ) .
T ˜ 4 ( ν ) = [ f ˜ * ( ν ) × rect ( ν m Δ ν Δ ν ) ] δ ( ν Q )
T ˜ 3 Σ ( ν ) = m = [ f ˜ ( ν ) × rect ( ν + m Δ ν Δ ν ) ] δ ( ν + Q ) = f ˜ ( ν ) δ ( ν + Q ) .
T ˜ 3 Σ ( ν ) = { f ˜ ( ν ) [ rect ( ν Δ ν ) m = [ δ ( ν + m Δ ν ) ] ] } δ ( ν + Q ) .
S A ( ν ) = rect ( ν Δ ν ) m = [ δ ( ν + m Δ ν ) ] .

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