Abstract

Diffractive optical elements (DOE) show great promise for imaging optics that are thinner and more lightweight than conventional refractive lenses while preserving their light efficiency. Unfortunately, severe spectral dispersion currently limits the use of DOEs in consumer-level lens design. In this article, we jointly design lightweight diffractive-refractive optics and post-processing algorithms to enable imaging under white light illumination. Using the Fresnel lens as a general platform, we show three phase-plate designs, including a super-thin stacked plate design, a diffractive-refractive-hybrid lens, and a phase coded-aperture lens. Combined with cross-channel deconvolution algorithm, both spherical and chromatic aberrations are corrected. Experimental results indicate that using our computational imaging approach, diffractive-refractive optics is an alternative candidate to build light efficient and thin optics for white light imaging.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (1)

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

2013 (3)

J. Zhou, L. Li, N. Naples, T. Sun, and Y. Y. Allen, “Fabrication of continuous diffractive optical elements using a fast tool servo diamond turning process,” J. Micromech. Microeng. 23, 075010 (2013).
[Crossref]

F. Heide, M. Rouf, M. B. Hullin, B. Labitzke, W. Heidrich, and A. Kolb, “High-quality computational imaging through simple lenses,” ACM Trans. Graphics 32, 149 (2013).
[Crossref]

S. Bernet, W. Harm, and M. Ritsch-Marte, “Demonstration of focus-tunable diffractive moiré-lenses,” Opt. Express 21, 6955–6966 (2013).
[Crossref] [PubMed]

2011 (2)

S. W. Hasinoff and K. N. Kutulakos, “Light-efficient photography,” IEEE Trans. Pattern Analysis and Machine Intelligence 33, 2203–2214 (2011).
[Crossref]

W. Duoshu, C. Luo, Y. Xiong, T. Chen, H. Liu, and J. Wang, “Fabrication technology of the centrosymmetric continuous relief diffractive optical elements,” Physics Procedia 18, 95–99 (2011).
[Crossref]

2008 (2)

L. Yuan, J. Sun, L. Quan, and H.-Y. Shum, “Progressive inter-scale and intra-scale non-blind image deconvolution,” ACM Trans. Graphics 27, 74 (2008).

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphics 27, 73 (2008).
[Crossref]

2007 (2)

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graphics 26, 70 (2007).
[Crossref]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans. Image Processing 16, 2080–2095 (2007).
[Crossref]

2004 (1)

2003 (1)

2001 (1)

1999 (1)

1995 (1)

Agarwala, A.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphics 27, 73 (2008).
[Crossref]

Allen, Y. Y.

J. Zhou, L. Li, N. Naples, T. Sun, and Y. Y. Allen, “Fabrication of continuous diffractive optical elements using a fast tool servo diamond turning process,” J. Micromech. Microeng. 23, 075010 (2013).
[Crossref]

Bernet, S.

Besnerais, G. L.

P. Trouve, F. Champagnat, G. L. Besnerais, G. Druart, and J. Idier, “Design of a chromatic 3d camera with an end-to-end performance model approach,” in “Computer Vision and Pattern Recognition Workshops (CVPRW), 2013 IEEE Conference on,” (IEEE, 2013), pp. 953–960.

Bibikov, S.

A. Nikonorov, R. Skidanov, V. Fursov, M. Petrov, S. Bibikov, and Y. Yuzifovich, “Fresnel lens imaging with post-capture image processing,” in “Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops,” (2015), pp. 33–41.

Cathey, W. T.

Champagnat, F.

P. Trouve, F. Champagnat, G. L. Besnerais, G. Druart, and J. Idier, “Design of a chromatic 3d camera with an end-to-end performance model approach,” in “Computer Vision and Pattern Recognition Workshops (CVPRW), 2013 IEEE Conference on,” (IEEE, 2013), pp. 953–960.

Chen, T.

W. Duoshu, C. Luo, Y. Xiong, T. Chen, H. Liu, and J. Wang, “Fabrication technology of the centrosymmetric continuous relief diffractive optical elements,” Physics Procedia 18, 95–99 (2011).
[Crossref]

Chung, S.-W.

S.-W. Chung, B.-K. Kim, and W.-J. Song, “Detecting and eliminating chromatic aberration in digital images,” in “Image Processing (ICIP), 2009 16th IEEE International Conference on,” (IEEE, 2009), pp. 3905–3908.

Cossairt, O.

O. Cossairt and S. Nayar, “Spectral focal sweep: Extended depth of field from chromatic aberrations,” in “Computational Photography (ICCP), 2010 IEEE International Conference on,” (IEEE, 2010), pp. 1–8.

Dabov, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans. Image Processing 16, 2080–2095 (2007).
[Crossref]

Doskolovich, L.

V. A. Soifer, V. Kotlar, and L. Doskolovich, Iteractive Methods For Diffractive Optical Elements Computation (CRC, 2003).

Dowski, E.

Druart, G.

P. Trouve, F. Champagnat, G. L. Besnerais, G. Druart, and J. Idier, “Design of a chromatic 3d camera with an end-to-end performance model approach,” in “Computer Vision and Pattern Recognition Workshops (CVPRW), 2013 IEEE Conference on,” (IEEE, 2013), pp. 953–960.

Duoshu, W.

W. Duoshu, C. Luo, Y. Xiong, T. Chen, H. Liu, and J. Wang, “Fabrication technology of the centrosymmetric continuous relief diffractive optical elements,” Physics Procedia 18, 95–99 (2011).
[Crossref]

Durand, F.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graphics 26, 70 (2007).
[Crossref]

Egiazarian, K.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans. Image Processing 16, 2080–2095 (2007).
[Crossref]

Elkind, D.

Fergus, R.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graphics 26, 70 (2007).
[Crossref]

Foi, A.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans. Image Processing 16, 2080–2095 (2007).
[Crossref]

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics (Courier Dover Publications, 2012).

Freeman, W. T.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graphics 26, 70 (2007).
[Crossref]

Fursov, V.

A. Nikonorov, R. Skidanov, V. Fursov, M. Petrov, S. Bibikov, and Y. Yuzifovich, “Fresnel lens imaging with post-capture image processing,” in “Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops,” (2015), pp. 33–41.

Gallo, O.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

Gill, P. R.

P. R. Gill and D. G. Stork, “Lensless ultra-miniature imagers using odd-symmetry spiral phase gratings,” in “Computational Optical Sensing and Imaging,” (Optical Society of America, 2013), pp. CW4C–3.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-hill, 2008).

Harm, W.

Harmeling, S.

C. J. Schuler, M. Hirsch, S. Harmeling, and B. Scholkopf, “Non-stationary correction of optical aberrations,” in “Computer Vision (ICCV), 2011 IEEE International Conference on,” (IEEE, 2011), pp. 659–666.

Hasinoff, S. W.

S. W. Hasinoff and K. N. Kutulakos, “Light-efficient photography,” IEEE Trans. Pattern Analysis and Machine Intelligence 33, 2203–2214 (2011).
[Crossref]

Heide, F.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

F. Heide, M. Rouf, M. B. Hullin, B. Labitzke, W. Heidrich, and A. Kolb, “High-quality computational imaging through simple lenses,” ACM Trans. Graphics 32, 149 (2013).
[Crossref]

Heidrich, W.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

F. Heide, M. Rouf, M. B. Hullin, B. Labitzke, W. Heidrich, and A. Kolb, “High-quality computational imaging through simple lenses,” ACM Trans. Graphics 32, 149 (2013).
[Crossref]

Hirsch, M.

C. J. Schuler, M. Hirsch, S. Harmeling, and B. Scholkopf, “Non-stationary correction of optical aberrations,” in “Computer Vision (ICCV), 2011 IEEE International Conference on,” (IEEE, 2011), pp. 659–666.

Hullin, M. B.

F. Heide, M. Rouf, M. B. Hullin, B. Labitzke, W. Heidrich, and A. Kolb, “High-quality computational imaging through simple lenses,” ACM Trans. Graphics 32, 149 (2013).
[Crossref]

Ichioka, Y.

Idier, J.

P. Trouve, F. Champagnat, G. L. Besnerais, G. Druart, and J. Idier, “Design of a chromatic 3d camera with an end-to-end performance model approach,” in “Computer Vision and Pattern Recognition Workshops (CVPRW), 2013 IEEE Conference on,” (IEEE, 2013), pp. 953–960.

Jia, J.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphics 27, 73 (2008).
[Crossref]

Joshi, N.

N. Joshi, C. L. Zitnick, R. Szeliski, and D. Kriegman, “Image deblurring and denoising using color priors,” in “Computer Vision and Pattern Recognition, 2009,” (IEEE, 2009), pp. 1550–1557.
[Crossref]

Kathman, A. D.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test, vol. 62 (SPIE, 2004).

Katkovnik, V.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans. Image Processing 16, 2080–2095 (2007).
[Crossref]

Kim, B.-K.

S.-W. Chung, B.-K. Kim, and W.-J. Song, “Detecting and eliminating chromatic aberration in digital images,” in “Image Processing (ICIP), 2009 16th IEEE International Conference on,” (IEEE, 2009), pp. 3905–3908.

Kitamura, Y.

Kolb, A.

F. Heide, M. Rouf, M. B. Hullin, B. Labitzke, W. Heidrich, and A. Kolb, “High-quality computational imaging through simple lenses,” ACM Trans. Graphics 32, 149 (2013).
[Crossref]

Kondou, N.

Kotlar, V.

V. A. Soifer, V. Kotlar, and L. Doskolovich, Iteractive Methods For Diffractive Optical Elements Computation (CRC, 2003).

Kriegman, D.

N. Joshi, C. L. Zitnick, R. Szeliski, and D. Kriegman, “Image deblurring and denoising using color priors,” in “Computer Vision and Pattern Recognition, 2009,” (IEEE, 2009), pp. 1550–1557.
[Crossref]

Kutulakos, K. N.

S. W. Hasinoff and K. N. Kutulakos, “Light-efficient photography,” IEEE Trans. Pattern Analysis and Machine Intelligence 33, 2203–2214 (2011).
[Crossref]

Labitzke, B.

F. Heide, M. Rouf, M. B. Hullin, B. Labitzke, W. Heidrich, and A. Kolb, “High-quality computational imaging through simple lenses,” ACM Trans. Graphics 32, 149 (2013).
[Crossref]

Levin, A.

A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Trans. Graphics 26, 70 (2007).
[Crossref]

Levy, U.

Li, L.

J. Zhou, L. Li, N. Naples, T. Sun, and Y. Y. Allen, “Fabrication of continuous diffractive optical elements using a fast tool servo diamond turning process,” J. Micromech. Microeng. 23, 075010 (2013).
[Crossref]

Liu, H.

W. Duoshu, C. Luo, Y. Xiong, T. Chen, H. Liu, and J. Wang, “Fabrication technology of the centrosymmetric continuous relief diffractive optical elements,” Physics Procedia 18, 95–99 (2011).
[Crossref]

Liu, J.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

Luo, C.

W. Duoshu, C. Luo, Y. Xiong, T. Chen, H. Liu, and J. Wang, “Fabrication technology of the centrosymmetric continuous relief diffractive optical elements,” Physics Procedia 18, 95–99 (2011).
[Crossref]

Malacara-Hernández, D.

D. Malacara-Hernández and Z. Malacara-Hernández, Handbook of Optical Design (CRC, 2013).

Malacara-Hernández, Z.

D. Malacara-Hernández and Z. Malacara-Hernández, Handbook of Optical Design (CRC, 2013).

Masaki, Y.

Mendlovic, D.

Meyers, M. M.

M. M. Meyers, “Hybrid refractive/diffractive achromatic camera lens,” (August61998). US Patent5,715,091

Miyamoto, M.

Miyatake, S.

Miyazaki, D.

Morimoto, T.

Nakai, T.

T. Nakai and H. Ogawa, “Research on multi-layer diffractive optical elements and their application to camera lenses,” in “Diffractive Optics and Micro-Optics,” (Optical Society of America, 2002), p. DMA2.
[Crossref]

Naples, N.

J. Zhou, L. Li, N. Naples, T. Sun, and Y. Y. Allen, “Fabrication of continuous diffractive optical elements using a fast tool servo diamond turning process,” J. Micromech. Microeng. 23, 075010 (2013).
[Crossref]

Nayar, S.

O. Cossairt and S. Nayar, “Spectral focal sweep: Extended depth of field from chromatic aberrations,” in “Computational Photography (ICCP), 2010 IEEE International Conference on,” (IEEE, 2010), pp. 1–8.

Nikonorov, A.

A. Nikonorov, R. Skidanov, V. Fursov, M. Petrov, S. Bibikov, and Y. Yuzifovich, “Fresnel lens imaging with post-capture image processing,” in “Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops,” (2015), pp. 33–41.

O’Shea, D. C.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test, vol. 62 (SPIE, 2004).

Ogawa, H.

T. Nakai and H. Ogawa, “Research on multi-layer diffractive optical elements and their application to camera lenses,” in “Diffractive Optics and Micro-Optics,” (Optical Society of America, 2002), p. DMA2.
[Crossref]

Ogura, Y.

Pajak, D.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

Petrov, M.

A. Nikonorov, R. Skidanov, V. Fursov, M. Petrov, S. Bibikov, and Y. Yuzifovich, “Fresnel lens imaging with post-capture image processing,” in “Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops,” (2015), pp. 33–41.

Prather, D. W.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, Diffractive Optics: Design, Fabrication, and Test, vol. 62 (SPIE, 2004).

Quan, L.

L. Yuan, J. Sun, L. Quan, and H.-Y. Shum, “Progressive inter-scale and intra-scale non-blind image deconvolution,” ACM Trans. Graphics 27, 74 (2008).

Reddy, D.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

Ritsch-Marte, M.

Rouf, M.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
[Crossref]

F. Heide, M. Rouf, M. B. Hullin, B. Labitzke, W. Heidrich, and A. Kolb, “High-quality computational imaging through simple lenses,” ACM Trans. Graphics 32, 149 (2013).
[Crossref]

Scholkopf, B.

C. J. Schuler, M. Hirsch, S. Harmeling, and B. Scholkopf, “Non-stationary correction of optical aberrations,” in “Computer Vision (ICCV), 2011 IEEE International Conference on,” (IEEE, 2011), pp. 659–666.

Schuler, C. J.

C. J. Schuler, M. Hirsch, S. Harmeling, and B. Scholkopf, “Non-stationary correction of optical aberrations,” in “Computer Vision (ICCV), 2011 IEEE International Conference on,” (IEEE, 2011), pp. 659–666.

Shan, Q.

Q. Shan, J. Jia, and A. Agarwala, “High-quality motion deblurring from a single image,” ACM Trans. Graphics 27, 73 (2008).
[Crossref]

Shirai, N.

Shogenji, R.

Shum, H.-Y.

L. Yuan, J. Sun, L. Quan, and H.-Y. Shum, “Progressive inter-scale and intra-scale non-blind image deconvolution,” ACM Trans. Graphics 27, 74 (2008).

Skidanov, R.

A. Nikonorov, R. Skidanov, V. Fursov, M. Petrov, S. Bibikov, and Y. Yuzifovich, “Fresnel lens imaging with post-capture image processing,” in “Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops,” (2015), pp. 33–41.

Sliusarev, G. G.

G. G. Sliusarev, “Aberration and optical design theory,” Adam Hilger, Ltd., Bristol, England, 672 p. ; Translation 1 (1984).

Soifer, V. A.

V. A. Soifer, V. Kotlar, and L. Doskolovich, Iteractive Methods For Diffractive Optical Elements Computation (CRC, 2003).

Sommargren, G. E.

Song, W.-J.

S.-W. Chung, B.-K. Kim, and W.-J. Song, “Detecting and eliminating chromatic aberration in digital images,” in “Image Processing (ICIP), 2009 16th IEEE International Conference on,” (IEEE, 2009), pp. 3905–3908.

Steinberger, M.

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J. Zhou, L. Li, N. Naples, T. Sun, and Y. Y. Allen, “Fabrication of continuous diffractive optical elements using a fast tool servo diamond turning process,” J. Micromech. Microeng. 23, 075010 (2013).
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N. Joshi, C. L. Zitnick, R. Szeliski, and D. Kriegman, “Image deblurring and denoising using color priors,” in “Computer Vision and Pattern Recognition, 2009,” (IEEE, 2009), pp. 1550–1557.
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P. Trouve, F. Champagnat, G. L. Besnerais, G. Druart, and J. Idier, “Design of a chromatic 3d camera with an end-to-end performance model approach,” in “Computer Vision and Pattern Recognition Workshops (CVPRW), 2013 IEEE Conference on,” (IEEE, 2013), pp. 953–960.

Tsai, Y.-T.

F. Heide, M. Steinberger, Y.-T. Tsai, M. Rouf, D. Pajak, D. Reddy, O. Gallo, J. Liu, W. Heidrich, and K. Egiazarian, “Flexisp: A flexible camera image processing framework,” ACM Trans. Graphics 33, 231 (2014).
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W. Duoshu, C. Luo, Y. Xiong, T. Chen, H. Liu, and J. Wang, “Fabrication technology of the centrosymmetric continuous relief diffractive optical elements,” Physics Procedia 18, 95–99 (2011).
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A. Nikonorov, R. Skidanov, V. Fursov, M. Petrov, S. Bibikov, and Y. Yuzifovich, “Fresnel lens imaging with post-capture image processing,” in “Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops,” (2015), pp. 33–41.

N. Joshi, C. L. Zitnick, R. Szeliski, and D. Kriegman, “Image deblurring and denoising using color priors,” in “Computer Vision and Pattern Recognition, 2009,” (IEEE, 2009), pp. 1550–1557.
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Compared to the imaging pipeline of conventional imaging with well corrected complex refractive lenses (top), our diffractive-refractive computational imaging allows capturing a blurry intermediate image by a super thin phase modulated DOE, and then recovering the sharp image with deconvolution algorithms using cross-channel regularizations. An exemplary blur image (bottom left) and its corresponding recovered image (bottom right) are shown. Insets of the images indicate that our algorithm corrects the residual aberrations and preserves the details.

Fig. 2
Fig. 2

A binary amplitude Fresnel zone plate (top-left) diffracts light into multi-orders (0th, ±1st, ±3rd,…), resulting in a low diffraction efficiency. With continuous phase-only diffractive lens (top-right), the light falls into +1st order could theoretically reach 100%. In practice, multi-level microstructures (bottom) are usually easy to fabricate and approximates the continuous profile very well.

Fig. 3
Fig. 3

Schematic comparisons of a super-thin diffractive optics (top), a diffractive-refractive-hybrid lens (middle), and a simple refractive lens (bottom) for f1 = 50mm (left) and f2 = 25mm (right). The R,G,B colors represent the focal powers for different wavelengths. “+” indicates the focal length for red is longer than that of blue, and “−” for the other way round.

Fig. 4
Fig. 4

Left: Microscopic images of our PZP and phase-coded-aperture lens on a Nikon Eclipse L200N 5X microscope. Right: Real color PSFs captured are shown with their individual RGB components. Note that the axises in the plots denote the pixel domain, and the colorbars indicate the relative intensity.

Fig. 5
Fig. 5

Top of (b–f): The same scene captured by our single PZP (f = 100mm), stacked PZP (f = 50mm), hybrid coded-aperture PZP and refractive lens (f = 50mm), hybrid PZP and refractive lens (f = 50mm), and a simple lens (f = 50mm) respectively. Middle of (b–f): Corresponding deconvolved images for each lens. Bottom of (b–f): R, G and B components of the PSFs for each setup. The scene is projected onto a board by a projector. Note that we only show the same cropped area for cross comparison here. The ground truth image captured by a Canon DSLR is presented for reference (a-2), with the PSNR plot provided (a-1) corresponding to the designs (c–f).

Fig. 6
Fig. 6

Top: Images captured and deconvolved for a text scene with a single PZP (f = 100mm). The teapot and white texts portions show the ability of our algorithms to remove most of the chromatic aberrations. Bottom: Captured and deconvolved images for a flower and book scene with stacked PZPs (f = 50mm). The yellow and green objects are well recovered in the same scene. Note that both scenes are at the same distance from the lenses, and the field of views differ because of the focal lengths.

Fig. 7
Fig. 7

Images captured (a) and deconvolved (b) for a box scene with our diffractive-refractive-hybrid lens (f = 50mm). By introducing a refractive lens, chromatic aberrations are smaller than in the single PZP and stacked PZP cases in Fig. 6. The inverse problem becomes more well-conditioned and shaper images could be recovered.

Fig. 8
Fig. 8

Images captured (a) and deconvolved (b) for a ball scene with our phase-coded-aperture hybrid lens (f = 50mm). By coding the intensity distribution of the PSF, high frequency features as well as colors can be preserved better. Note that the net around the ball is recovered which otherwise would hardly be seen in the blurry image.

Fig. 9
Fig. 9

Images captured (top) and deconvolved (bottom) for the ISO12233 resolution chart with our three designs: (from left to right) hybrid PZP and lens, hybrid phase-coded-aperture PZP and lens, and stacked PZPs. The focal lengths are f = 50mm for each design.

Fig. 10
Fig. 10

Off-axis performance comparison for a simple refractive lens (left), our hybrid PZP lens (center), and stacked PZPs (right). Note that the first row presents the capture images of a black-white checkerboard, while the close-ups illustrate the on-axis and off-axis patches in their green channel, red channel, and blue channel visualization. From the comparison of patch A and patch B, we observe that our designs show better spatial uniformity, despite the chromatic aberration. All the focal lengths are f = 50mm and the full field of view is around 30°.

Fig. 11
Fig. 11

Images of captured (left) and deconvolved (right) for an outdoor scene with our hybrid PZP lens (f = 50mm). The far and near objects vary from around 8m (house) to around 2m (tree) from the lens.

Equations (6)

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η m N = { sin [ π ( ( n 1 ) d λ m ) ] π ( ( n 1 ) d λ m ) } 2 { sin [ π ( ( n 1 ) d λ N ) ] π ( ( n 1 ) d λ N ) } 2 ,
b = Ki + n ,
P c = λ c P ( λ ) d λ ,
i c = arg min i c μ c 2 b c K c i c 2 2 + Γ ( i c ) ,
i m i l i l i m i m / i m i l / i l
Γ ( i c ) = m l D i m i l D i i i m 1 ,

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