Abstract

We propose a resolution enhancement method for mobile small f-number compact imaging systems based on wavefront coding and super-resolution image processing. Wavefront coding increases the focus depth of an optical system and produces point spread functions (PSFs) with similar characteristics at different field and defocus positions. The designed target wavefront is realized as a combination of wavefront errors of each rotationally symmetric lens, without including an additional phase plate. Finally, using one deconvolution filter containing all the characteristics of the PSFs, we achieve high resolution, breaking the diffraction limit of small f-number and the resolution limit of the image sensor by super-resolution image processing.

© 2008 Optical Society of America

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References

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  1. K. Kubala, E. R. Dowski, and W. T. Cathey, "Reducing complexity in computational imaging systems," Opt. Express 11, 2102-2108 (2003).
    [CrossRef] [PubMed]
  2. E. R. Dowski and W. T. Cathey, "Extended depth of field through wavefront coding," Appl. Opt. 34, 1859-1866 (1995).
    [CrossRef] [PubMed]
  3. W. T. Cathey and E. R. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002).

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Figures (12)

Fig. 1.
Fig. 1.

Design procedure

Fig. 2.
Fig. 2.

Initial lens design and spherical aberration

Fig. 3.
Fig. 3.

Spatial frequency response of initial lens design.

Fig. 4.
Fig. 4.

Calculation of target specification

Fig. 5.
Fig. 5.

Characteristics of conventional optical system (a) and Wavefront-coded optical system (b).

Fig. 6.
Fig. 6.

PSFs of conventional optical system (a) and Wavefront-coded optical system (b).

Fig. 7.
Fig. 7.

Final lens design and graph of spherical aberration

Fig. 8.
Fig. 8.

Spatial frequency response of the final lens design

Fig. 9.
Fig. 9.

Process of image restoration

Fig. 10.
Fig. 10.

Final result of SFR

Fig. 11.
Fig. 11.

Image comparison of conventional optical system and wavefront-coded optical system (restored image). Images are magnified from the central region for effective comparison. (a) Image at −15 µm defocused position, (b) best focus position and (c) 15 µm defocused position.

Fig. 12.
Fig. 12.

Image comparison of conventional optical system and wavefront-coded optical system (restored image). Images are magnified from the outer region for effective comparison. (a) Image at −15 µm defocused position, (b) best focus position and (c) 15 µm defocused position.

Tables (1)

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Table 1. Specification of the f-2.0 compact imaging system

Equations (2)

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δ = 4 λ ( F / # ) 2
α = tan 1 ( δ d )

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