Abstract

The Lukosz technique of superresolution by spatial and temporal frequency interaction is extended. The effects of various misalignments and other errors are considered. An implementation of the technique is presented. Experimental results are given.

© 1992 Optical Society of America

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References

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  1. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. 56, 1463–1472 (1966).
    [CrossRef]
  2. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit. II,” J. Opt. Soc. Am. 57, 932–941 (1967).
    [CrossRef]
  3. W. Lukosz, M. Marchand, “Optischen Abbildung unter Überschreitung der Beugungsbedingten Auflösungsgrenze,” Opt. Acta 10, 241–255 (1963).
    [CrossRef]
  4. A. W. Lohmann, D. P. Paris, “Super-resolution for nonbirefringent objects,” Appl. Opt. 3, 1037–1043 (1964).
    [CrossRef]
  5. M. Ueda, T. Sato, M. Kondo, “Superresolution by multiple superposition of image holograms having different carrier frequencies,” Opt. Acta 20, 403–410 (1973).
    [CrossRef]
  6. W. T. Cathey, B. R. Frieden, W. T. Rhodes, C. K. Rushforth, “Image gathering and processing for enhanced resolution,” J. Opt. Soc. Am. A 1, 241–250 (1984).
    [CrossRef]
  7. E. N. Leith, “Small-aperture, high-resolution, two-channel imaging system,” Opt. Lett. 15, 885–887 (1990).
    [CrossRef] [PubMed]

1990 (1)

1984 (1)

1973 (1)

M. Ueda, T. Sato, M. Kondo, “Superresolution by multiple superposition of image holograms having different carrier frequencies,” Opt. Acta 20, 403–410 (1973).
[CrossRef]

1967 (1)

1966 (1)

1964 (1)

1963 (1)

W. Lukosz, M. Marchand, “Optischen Abbildung unter Überschreitung der Beugungsbedingten Auflösungsgrenze,” Opt. Acta 10, 241–255 (1963).
[CrossRef]

Cathey, W. T.

Frieden, B. R.

Kondo, M.

M. Ueda, T. Sato, M. Kondo, “Superresolution by multiple superposition of image holograms having different carrier frequencies,” Opt. Acta 20, 403–410 (1973).
[CrossRef]

Leith, E. N.

Lohmann, A. W.

Lukosz, W.

Marchand, M.

W. Lukosz, M. Marchand, “Optischen Abbildung unter Überschreitung der Beugungsbedingten Auflösungsgrenze,” Opt. Acta 10, 241–255 (1963).
[CrossRef]

Paris, D. P.

Rhodes, W. T.

Rushforth, C. K.

Sato, T.

M. Ueda, T. Sato, M. Kondo, “Superresolution by multiple superposition of image holograms having different carrier frequencies,” Opt. Acta 20, 403–410 (1973).
[CrossRef]

Ueda, M.

M. Ueda, T. Sato, M. Kondo, “Superresolution by multiple superposition of image holograms having different carrier frequencies,” Opt. Acta 20, 403–410 (1973).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Distribution of object spatial frequency spectra in the frequency plane for different diffracted orders of the moving grating. Each spectrum is shifted to cause a selected subband to center on zero spatial frequency. The shadowed area shows the parts of the spectrum that are transmitted through the aperture, which are later to be recombined to restore the original spectrum.

Fig. 2
Fig. 2

Temporal frequency shifting of the light carrying the different spectral pieces enables the different bands to be distinguished from each other: D2, grating; s, object; Im, image plane; ν0, frequency of the incident light; Δν, Doppler shift.

Fig. 3
Fig. 3

Experimental setup for the superresolution system showing object and reference beam paths: s, object; D1, D2, identical diffusers; G1, G2, G3, identical gratings.

Fig. 4
Fig. 4

Temporal frequency shift of light by the motion of a single sheet diffuser generates the spatial–temporal encoding.

Fig. 5
Fig. 5

Experimental result: image formed without reference beam. Vertical resolution is totally lost.

Fig. 6
Fig. 6

Experimental result: image formed with reference beam present. Vertical resolution is restored.

Fig. 7
Fig. 7

Experimental result: image from the situation described in case 8.

Fig. 8
Fig. 8

Experimental result: image from the situation described in case 7.

Equations (18)

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u 1 = δ ( f x ) N ( α , t ) S ( α - f x ) d α exp ( - j 2 π f x x ) d f x ,
u 2 = N ( β , t ) exp ( - j 2 π β x ) d β ,
u 1 u 2 * = N ( α , t ) N * ( β , t ) S ( α ) exp ( j 2 π β x ) d α d β .
u 1 = rect ( f x / Δ f ) N ( α , t ) × S ( α - f x ) d α exp ( - j 2 π f x ) d f x ,
u 2 = N ( β , t ) exp ( - j 2 π β x ) d β .
u 1 u 2 * = rect [ ( α - f x ) / Δ f ] N ( α , t ) N * ( β , t ) × exp [ - j 2 π ( α - β ) x ] d α d β × [ S ( f x ) exp ( - j 2 π f x x ) d f x ] = H ( f x ) S ( f x ) exp ( - j 2 π f x x ) d f x .
N ( α , t ) = T ( α ) exp ( - j 2 π α v t ) exp ( - j π λ d α 2 ) ,
N ( β , t ) = T ( β ) exp [ - j 2 π β ( v t + Δ x ) ] × exp [ - j π λ ( d + Δ d ) β 2 ] ,
N ( α , t ) N * ( β , t ) = T ( α ) T * ( α ) exp [ j 2 π α ( Δ x ) ] × exp [ j π λ ( Δ d ) α 2 ] δ ( α - β ) .
H ( f x ) = rect [ ( α - f x ) / Δ f ] T ( α ) T * ( α ) × exp [ j 2 π α ( Δ x ) ] exp [ j π λ ( Δ d ) α 2 ] d α = rect [ ( α - f x ) / Δ f ] I ( α ) exp [ j 2 π α ( Δ x ) ] × exp [ j π λ ( Δ d ) α 2 ] d α ,
H ( f x ) = rect ( f x / 2 f c ) .
H ( f x ) = rect ( f x / 2 f c ) rect ( f x / 2 f c ) ,
H ( f x ) = rect ( f x / Δ f ) rect ( f x / f c ) .
H ( f x ) = rect ( f x / 2 f c ) exp [ j 2 π f x ( Δ x ) ] .
H ( f x ) = rect ( f x / 2 f c ) exp [ j π λ ( Δ d ) f x 2 ] .
H ( f x ) = rect ( f x / 2 f c ) .
H ( f x ) = rect ( f x ) comb ( f x / f g ) rect ( f x / f c ) .
H ( f x ) = rect ( f x ) comb ( f x / f g ) × exp [ j 2 π f x ( Δ x ) ] rect ( f x / f c ) .

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