Abstract

The purpose of this work is to provide a theoretically grounded assessment on the field of view and bandwidth of a lensless holographic setup. Indeed, while previous works have presented results with super-resolution and field-of-view extrapolation, there are no well-established rules to determine them. We show that the theoretical field of view can be large with a spatial-frequency bandwidth only limited by the wavelength, leading to an unthinkable number of degrees of freedom. To keep a realistic field of view and bandwidth, we propose several practical bounds based on a few setup properties, namely, the noise level and spatiotemporal coherence of the source.

© 2021 Optical Society of America

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  1. O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
    [Crossref]
  2. M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact lensless phase imager,” Opt. Express 25, 4438–4445 (2017).
    [Crossref]
  3. M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact in-line lensfree digital holographic microscope,” Methods 136, 17–23 (2018).
    [Crossref]
  4. C. P. Allier, G. Hiernard, V. Poher, and J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomed. Opt. Express 1, 762–770 (2010).
    [Crossref]
  5. O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
    [Crossref]
  6. S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
    [Crossref]
  7. U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [Crossref]
  8. J. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004).
  9. J. H. Milgram and W. Li, “Computational reconstruction of images from holograms,” Appl. Opt. 41, 853–864 (2002).
    [Crossref]
  10. F. Dubois, O. Monnom, C. Yourassowsky, and J.-C. Legros, “Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies,” Appl. Opt. 41, 2621–2626 (2002).
    [Crossref]
  11. A. Migukin, V. Katkovnik, and J. Astola, “Wave field reconstruction from multiple plane intensity-only data: augmented Lagrangian algorithm,” J. Opt. Soc. Am. A 28, 993 (2011).
    [Crossref]
  12. T. Latychevskaia and H.-W. Fink, “Resolution enhancement in digital holography by self-extrapolation of holograms,” Opt. Express 21, 7726–7733 (2013).
    [Crossref]
  13. W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18, 11181–11191 (2010).
    [Crossref]
  14. J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy,” Sci. Rep. 7, 11777 (2017).
    [Crossref]
  15. Z. Luo, A. Yurt, R. Stahl, A. Lambrechts, V. Reumers, D. Braeken, and L. Lagae, “Pixel super-resolution for lens-free holographic microscopy using deep learning neural networks,” Opt. Express 27, 13581–13595 (2019).
    [Crossref]
  16. T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed. (SPIE, 1997).
  17. F. Soulez, L. Denis, É. Thiébaut, C. Fournier, and C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” J. Opt. Soc. Am. A 24, 3708–3716 (2007).
    [Crossref]
  18. L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, and D. Trede, “In-line hologram reconstruction with sparsity constraints,” Opt. Lett. 34, 3475–3477 (2009).
    [Crossref]
  19. C. Fournier, F. Jolivet, L. Denis, N. Verrier, E. Thiebaut, C. Allier, and T. Fournel, “Pixel super-resolution in digital holography by regularized reconstruction,” Appl. Opt. 56, 69–77 (2016).
    [Crossref]
  20. A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
    [Crossref]
  21. W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light Sci. Appl. 4, e261 (2015).
    [Crossref]
  22. L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929–5935 (2000).
    [Crossref]
  23. A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23, 1227–1235 (2006).
    [Crossref]
  24. F. Soulez, L. Denis, C. Fournier, É. Thiébaut, and C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” J. Opt. Soc. Am. A 24, 1164–1171 (2007).
    [Crossref]
  25. C. Fournier, L. Denis, and T. Fournel, “On the single point resolution of on-axis digital holography,” J. Opt. Soc. Am. A 27, 1856–1862 (2010).
    [Crossref]
  26. D. P. Kelly, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
    [Crossref]
  27. Y. Hao and A. Asundi, “Resolution analysis of a digital holography system,” Appl. Opt. 50, 183–193 (2011).
    [Crossref]
  28. T. E. Agbana, H. Gong, A. S. Amoah, V. Bezzubik, M. Verhaegen, and G. Vdovin, “Aliasing, coherence, and resolution in a lensless holographic microscope,” Opt. Lett. 42, 2271 (2017).
    [Crossref]
  29. J. Zhang, J. Sun, Q. Chen, and C. Zuo, “Resolution analysis in a lens-free on-chip digital holographic microscope,” IEEE Trans. Comput. Imaging 6, 697–710 (2020).
    [Crossref]
  30. N. Chacko, M. Liebling, and T. Blu, “Discretization of continuous convolution operators for accurate modeling of wave propagation in digital holography,” J. Opt. Soc. Am. A 30, 2012–2020 (2013).
    [Crossref]
  31. D. P. Kelly, “Numerical calculation of the Fresnel transform,” J. Opt. Soc. Am. A 31, 755–764 (2014).
    [Crossref]
  32. J.-P. Liu, “Controlling the aliasing by zero-padding in the digital calculation of the scalar diffraction,” J. Opt. Soc. Am. A 29, 1956–1964 (2012).
    [Crossref]
  33. K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17, 19662–19673 (2009).
    [Crossref]
  34. K. Matsushima, “Shifted angular spectrum method for off-axis numerical propagation,” Opt. Express 18, 18453–18463 (2010).
    [Crossref]
  35. S. Odate, C. Koike, H. Toba, T. Koike, A. Sugaya, K. Sugisaki, K. Otaki, and K. Uchikawa, “Angular spectrum calculations for arbitrary focal length with a scaled convolution,” Opt. Express 19, 14268–14276 (2011).
    [Crossref]
  36. H. M. Ozaktas, S. Ö. Arık, and T. Coşkun, “Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform,” Opt. Lett. 36, 2524–2526 (2011).
    [Crossref]
  37. K. Falaggis, T. Kozacki, and M. Kujawinska, “Computation of highly off-axis diffracted fields using the band-limited angular spectrum method with suppressed GIBBS related artifacts,” Appl. Opt. 52, 3288–3297 (2013).
    [Crossref]
  38. T. Kozacki and K. Falaggis, “Angular spectrum-based wave-propagation method with compact space bandwidth for large propagation distances,” Opt. Lett. 40, 3420–3423 (2015).
    [Crossref]
  39. A. Ritter, “Modified shifted angular spectrum method for numerical propagation at reduced spatial sampling rates,” Opt. Express 22, 26265–26276 (2014).
    [Crossref]
  40. T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
    [Crossref]
  41. X. Yu, T. Xiahui, Q. Yingxiong, P. Hao, and W. Wei, “Band-limited angular spectrum numerical propagation method with selective scaling of observation window size and sample number,” J. Opt. Soc. Am. A 29, 2415–2420 (2012).
    [Crossref]
  42. F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981).
    [Crossref]
  43. J. Liang and M. F. Becker, “Spatial bandwidth analysis of fast backward Fresnel diffraction for precise computer-generated hologram design,” Appl. Opt. 53, G84–G94 (2014).
    [Crossref]
  44. G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
    [Crossref]
  45. C.-S. Guo, Y.-Y. Xie, and B. Sha, “Diffraction algorithm suitable for both near and far field with shifted destination window and oblique illumination,” Opt. Lett. 39, 2338–2341 (2014).
    [Crossref]
  46. D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, “Space–bandwidth product adaptation and its application to superresolution: examples,” J. Opt. Soc. Am. A 14, 563–567 (1997).
    [Crossref]
  47. A. Stern and B. Javidi, “Sampling in the light of Wigner distribution,” J. Opt. Soc. Am. A 21, 360–366 (2004).
    [Crossref]
  48. D. Claus, D. Iliescu, and P. Bryanston-Cross, “Quantitative space-bandwidth product analysis in digital holography,” Appl. Opt. 50, H116–H127 (2011).
    [Crossref]
  49. A. W. Lohmann, R. G. Dorsch, D. Mendlovic, C. Ferreira, and Z. Zalevsky, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
    [Crossref]
  50. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
    [Crossref]
  51. D. G. Voelz and M. C. Roggemann, “Digital simulation of scalar optical diffraction: revisiting chirp function sampling criteria and consequences,” Appl. Opt. 48, 6132–6142 (2009).
    [Crossref]
  52. C. J. R. Sheppard and M. Hrynevych, “Diffraction by a half-plane: a generalization of the Fresnel diffraction theory,” Opt. Lett. 16, 1060–1061 (1991).
    [Crossref]
  53. J. W. Goodman, Statistical Optics (Wiley, 2015).
  54. https://doi.org/10.6084/m9.figshare.7998143 .
  55. https://doi.org/10.6084/m9.figshare.7998134 .
  56. https://github.com/FerreolS/COMCI .
  57. E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
    [Crossref]
  58. D. H. Kelly, “Spatial frequency, bandwidth, and resolution,” Appl. Opt. 4, 435–437 (1965).
    [Crossref]

2020 (1)

J. Zhang, J. Sun, Q. Chen, and C. Zuo, “Resolution analysis in a lens-free on-chip digital holographic microscope,” IEEE Trans. Comput. Imaging 6, 697–710 (2020).
[Crossref]

2019 (2)

Z. Luo, A. Yurt, R. Stahl, A. Lambrechts, V. Reumers, D. Braeken, and L. Lagae, “Pixel super-resolution for lens-free holographic microscopy using deep learning neural networks,” Opt. Express 27, 13581–13595 (2019).
[Crossref]

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

2018 (1)

M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact in-line lensfree digital holographic microscope,” Methods 136, 17–23 (2018).
[Crossref]

2017 (3)

2016 (1)

2015 (2)

2014 (4)

2013 (7)

N. Chacko, M. Liebling, and T. Blu, “Discretization of continuous convolution operators for accurate modeling of wave propagation in digital holography,” J. Opt. Soc. Am. A 30, 2012–2020 (2013).
[Crossref]

A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
[Crossref]

T. Latychevskaia and H.-W. Fink, “Resolution enhancement in digital holography by self-extrapolation of holograms,” Opt. Express 21, 7726–7733 (2013).
[Crossref]

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
[Crossref]

K. Falaggis, T. Kozacki, and M. Kujawinska, “Computation of highly off-axis diffracted fields using the band-limited angular spectrum method with suppressed GIBBS related artifacts,” Appl. Opt. 52, 3288–3297 (2013).
[Crossref]

2012 (2)

2011 (5)

2010 (5)

2009 (4)

2007 (2)

2006 (1)

2004 (1)

2002 (2)

2000 (2)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[Crossref]

L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929–5935 (2000).
[Crossref]

1997 (1)

1996 (1)

1994 (1)

1993 (1)

1991 (1)

1981 (1)

F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981).
[Crossref]

1965 (1)

Adams, M.

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed. (SPIE, 1997).

Agbana, T. E.

Allier, C.

Allier, C. P.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

C. P. Allier, G. Hiernard, V. Poher, and J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomed. Opt. Express 1, 762–770 (2010).
[Crossref]

Amoah, A. S.

Arik, S. Ö.

Astola, J.

Asundi, A.

Becker, M. F.

Bezzubik, V.

Bishara, W.

W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18, 11181–11191 (2010).
[Crossref]

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Blu, T.

Braeken, D.

Bryanston-Cross, P.

Chacko, N.

Chen, Q.

J. Zhang, J. Sun, Q. Chen, and C. Zuo, “Resolution analysis in a lens-free on-chip digital holographic microscope,” IEEE Trans. Comput. Imaging 6, 697–710 (2020).
[Crossref]

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy,” Sci. Rep. 7, 11777 (2017).
[Crossref]

Claus, D.

Coskun, A. F.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
[Crossref]

W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18, 11181–11191 (2010).
[Crossref]

Coskun, T.

Debarre, T.

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

Denis, L.

Dinten, J. M.

Donati, L.

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

Dorsch, R. G.

Dubois, F.

Falaggis, K.

Ferreira, C.

Fink, H.-W.

Fournel, T.

Fournier, C.

Goepfert, C.

Gong, H.

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004).

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2015).

Gori, F.

F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981).
[Crossref]

Greenbaum, A.

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light Sci. Appl. 4, e261 (2015).
[Crossref]

A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
[Crossref]

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

Guo, C.-S.

Hao, P.

Hao, Y.

Hennequin, Y.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

Hiernard, G.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Hrynevych, M.

Iliescu, D.

Isikman, S. O.

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Ito, T.

T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
[Crossref]

Javidi, B.

Jolivet, F.

Jueptner, W. P. O.

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed. (SPIE, 1997).

Jüptner, W.

Kakue, T.

T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
[Crossref]

Katkovnik, V.

Kelly, D. H.

Kelly, D. P.

D. P. Kelly, “Numerical calculation of the Fresnel transform,” J. Opt. Soc. Am. A 31, 755–764 (2014).
[Crossref]

D. P. Kelly, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
[Crossref]

Khademhosseini, B.

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Khademhosseinieh, B.

A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
[Crossref]

Koike, C.

Koike, T.

Kozacki, T.

Kreis, T. M.

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed. (SPIE, 1997).

Kujawinska, M.

Lagae, L.

Lambrechts, A.

Latychevskaia, T.

Legros, J.-C.

Li, J.

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy,” Sci. Rep. 7, 11777 (2017).
[Crossref]

Li, W.

Liang, J.

Liebling, M.

Liu, J.-P.

Lohmann, A. W.

Lorenz, D.

Luo, W.

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light Sci. Appl. 4, e261 (2015).
[Crossref]

A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
[Crossref]

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

Luo, Z.

Matsushima, K.

McCann, M. T.

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

McLeod, E.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

Mendlovic, D.

Migukin, A.

Milgram, J. H.

Monnom, O.

Moser, C.

M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact in-line lensfree digital holographic microscope,” Methods 136, 17–23 (2018).
[Crossref]

M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact lensless phase imager,” Opt. Express 25, 4438–4445 (2017).
[Crossref]

Mudanyali, O.

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Murata, S.

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[Crossref]

Odate, S.

Oh, C.

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Oikawa, M.

T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
[Crossref]

Okada, N.

T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
[Crossref]

Onural, L.

Otaki, K.

Ozaktas, H. M.

Ozcan, A.

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light Sci. Appl. 4, e261 (2015).
[Crossref]

A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
[Crossref]

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18, 11181–11191 (2010).
[Crossref]

Oztoprak, C.

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Pham, T.-A.

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

Poher, V.

Reumers, V.

Ritter, A.

Roggemann, M. C.

Rostykus, M.

M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact in-line lensfree digital holographic microscope,” Methods 136, 17–23 (2018).
[Crossref]

M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact lensless phase imager,” Opt. Express 25, 4438–4445 (2017).
[Crossref]

Sage, D.

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

Schnars, U.

Sencan, I.

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Seo, S.

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Sha, B.

Sheppard, C. J. R.

Shimobaba, T.

T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
[Crossref]

K. Matsushima and T. Shimobaba, “Band-limited angular spectrum method for numerical simulation of free-space propagation in far and near fields,” Opt. Express 17, 19662–19673 (2009).
[Crossref]

Soubies, E.

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

Soulez, F.

Stahl, R.

Stern, A.

Su, T.-W.

A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
[Crossref]

W. Bishara, T.-W. Su, A. F. Coskun, and A. Ozcan, “Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution,” Opt. Express 18, 11181–11191 (2010).
[Crossref]

Sugaya, A.

Sugisaki, K.

Sun, J.

J. Zhang, J. Sun, Q. Chen, and C. Zuo, “Resolution analysis in a lens-free on-chip digital holographic microscope,” IEEE Trans. Comput. Imaging 6, 697–710 (2020).
[Crossref]

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy,” Sci. Rep. 7, 11777 (2017).
[Crossref]

Thiebaut, E.

Thiébaut, E.

Thiébaut, É.

Toba, H.

Trede, D.

Tseng, D.

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Uchikawa, K.

Unser, M.

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact in-line lensfree digital holographic microscope,” Methods 136, 17–23 (2018).
[Crossref]

M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact lensless phase imager,” Opt. Express 25, 4438–4445 (2017).
[Crossref]

Vdovin, G.

Verhaegen, M.

Verrier, N.

Voelz, D. G.

Wei, W.

Xiahui, T.

Xie, Y.-Y.

Yamaguchi, Y.

T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
[Crossref]

Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Yasuda, N.

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[Crossref]

Yingxiong, Q.

Yourassowsky, C.

Yu, X.

Yurt, A.

Zalevsky, Z.

Zhang, J.

J. Zhang, J. Sun, Q. Chen, and C. Zuo, “Resolution analysis in a lens-free on-chip digital holographic microscope,” IEEE Trans. Comput. Imaging 6, 697–710 (2020).
[Crossref]

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy,” Sci. Rep. 7, 11777 (2017).
[Crossref]

Zhang, Y.

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light Sci. Appl. 4, e261 (2015).
[Crossref]

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Zuo, C.

J. Zhang, J. Sun, Q. Chen, and C. Zuo, “Resolution analysis in a lens-free on-chip digital holographic microscope,” IEEE Trans. Comput. Imaging 6, 697–710 (2020).
[Crossref]

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy,” Sci. Rep. 7, 11777 (2017).
[Crossref]

Appl. Opt. (11)

J. H. Milgram and W. Li, “Computational reconstruction of images from holograms,” Appl. Opt. 41, 853–864 (2002).
[Crossref]

F. Dubois, O. Monnom, C. Yourassowsky, and J.-C. Legros, “Border processing in digital holography by extension of the digital hologram and reduction of the higher spatial frequencies,” Appl. Opt. 41, 2621–2626 (2002).
[Crossref]

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[Crossref]

C. Fournier, F. Jolivet, L. Denis, N. Verrier, E. Thiebaut, C. Allier, and T. Fournel, “Pixel super-resolution in digital holography by regularized reconstruction,” Appl. Opt. 56, 69–77 (2016).
[Crossref]

L. Onural, “Sampling of the diffraction field,” Appl. Opt. 39, 5929–5935 (2000).
[Crossref]

Y. Hao and A. Asundi, “Resolution analysis of a digital holography system,” Appl. Opt. 50, 183–193 (2011).
[Crossref]

K. Falaggis, T. Kozacki, and M. Kujawinska, “Computation of highly off-axis diffracted fields using the band-limited angular spectrum method with suppressed GIBBS related artifacts,” Appl. Opt. 52, 3288–3297 (2013).
[Crossref]

J. Liang and M. F. Becker, “Spatial bandwidth analysis of fast backward Fresnel diffraction for precise computer-generated hologram design,” Appl. Opt. 53, G84–G94 (2014).
[Crossref]

D. G. Voelz and M. C. Roggemann, “Digital simulation of scalar optical diffraction: revisiting chirp function sampling criteria and consequences,” Appl. Opt. 48, 6132–6142 (2009).
[Crossref]

D. Claus, D. Iliescu, and P. Bryanston-Cross, “Quantitative space-bandwidth product analysis in digital holography,” Appl. Opt. 50, H116–H127 (2011).
[Crossref]

D. H. Kelly, “Spatial frequency, bandwidth, and resolution,” Appl. Opt. 4, 435–437 (1965).
[Crossref]

Biomed. Opt. Express (1)

IEEE Trans. Comput. Imaging (1)

J. Zhang, J. Sun, Q. Chen, and C. Zuo, “Resolution analysis in a lens-free on-chip digital holographic microscope,” IEEE Trans. Comput. Imaging 6, 697–710 (2020).
[Crossref]

Inverse Prob. (1)

E. Soubies, F. Soulez, M. T. McCann, T.-A. Pham, L. Donati, T. Debarre, D. Sage, and M. Unser, “Pocket guide to solve inverse problems with GlobalBioIm,” Inverse Prob. 35, 104006 (2019).
[Crossref]

J. Opt. (1)

T. Shimobaba, T. Kakue, N. Okada, M. Oikawa, Y. Yamaguchi, and T. Ito, “Aliasing-reduced Fresnel diffraction with scale and shift operations,” J. Opt. 15, 075405 (2013).
[Crossref]

J. Opt. Soc. Am. A (13)

X. Yu, T. Xiahui, Q. Yingxiong, P. Hao, and W. Wei, “Band-limited angular spectrum numerical propagation method with selective scaling of observation window size and sample number,” J. Opt. Soc. Am. A 29, 2415–2420 (2012).
[Crossref]

D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, “Space–bandwidth product adaptation and its application to superresolution: examples,” J. Opt. Soc. Am. A 14, 563–567 (1997).
[Crossref]

A. Stern and B. Javidi, “Sampling in the light of Wigner distribution,” J. Opt. Soc. Am. A 21, 360–366 (2004).
[Crossref]

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, C. Ferreira, and Z. Zalevsky, “Space–bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470–473 (1996).
[Crossref]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
[Crossref]

N. Chacko, M. Liebling, and T. Blu, “Discretization of continuous convolution operators for accurate modeling of wave propagation in digital holography,” J. Opt. Soc. Am. A 30, 2012–2020 (2013).
[Crossref]

D. P. Kelly, “Numerical calculation of the Fresnel transform,” J. Opt. Soc. Am. A 31, 755–764 (2014).
[Crossref]

J.-P. Liu, “Controlling the aliasing by zero-padding in the digital calculation of the scalar diffraction,” J. Opt. Soc. Am. A 29, 1956–1964 (2012).
[Crossref]

A. Stern and B. Javidi, “Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields,” J. Opt. Soc. Am. A 23, 1227–1235 (2006).
[Crossref]

F. Soulez, L. Denis, C. Fournier, É. Thiébaut, and C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” J. Opt. Soc. Am. A 24, 1164–1171 (2007).
[Crossref]

C. Fournier, L. Denis, and T. Fournel, “On the single point resolution of on-axis digital holography,” J. Opt. Soc. Am. A 27, 1856–1862 (2010).
[Crossref]

A. Migukin, V. Katkovnik, and J. Astola, “Wave field reconstruction from multiple plane intensity-only data: augmented Lagrangian algorithm,” J. Opt. Soc. Am. A 28, 993 (2011).
[Crossref]

F. Soulez, L. Denis, É. Thiébaut, C. Fournier, and C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” J. Opt. Soc. Am. A 24, 3708–3716 (2007).
[Crossref]

Lab Chip (1)

O. Mudanyali, D. Tseng, C. Oh, S. O. Isikman, I. Sencan, W. Bishara, C. Oztoprak, S. Seo, B. Khademhosseini, and A. Ozcan, “Compact, light-weight and cost-effective microscope based on lensless incoherent holography for telemedicine applications,” Lab Chip 10, 1417–1428 (2010).
[Crossref]

Light Sci. Appl. (1)

W. Luo, A. Greenbaum, Y. Zhang, and A. Ozcan, “Synthetic aperture-based on-chip microscopy,” Light Sci. Appl. 4, e261 (2015).
[Crossref]

Methods (1)

M. Rostykus, F. Soulez, M. Unser, and C. Moser, “Compact in-line lensfree digital holographic microscope,” Methods 136, 17–23 (2018).
[Crossref]

Nat. Photonics (2)

O. Mudanyali, E. McLeod, W. Luo, A. Greenbaum, A. F. Coskun, Y. Hennequin, C. P. Allier, and A. Ozcan, “Wide-field optical detection of nanoparticles using on-chip microscopy and self-assembled nanolenses,” Nat. Photonics 7, 247–254 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Opt. Commun. (1)

F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293–297 (1981).
[Crossref]

Opt. Eng. (1)

D. P. Kelly, “Resolution limits in practical digital holographic systems,” Opt. Eng. 48, 095801 (2009).
[Crossref]

Opt. Express (8)

Opt. Laser Technol. (1)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32, 567–574 (2000).
[Crossref]

Opt. Lett. (6)

Sci. Rep. (2)

A. Greenbaum, W. Luo, B. Khademhosseinieh, T.-W. Su, A. F. Coskun, and A. Ozcan, “Increased space-bandwidth product in pixel super-resolved lensfree on-chip microscopy,” Sci. Rep. 3, 1717 (2013).
[Crossref]

J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, “Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy,” Sci. Rep. 7, 11777 (2017).
[Crossref]

Other (6)

T. M. Kreis, M. Adams, and W. P. O. Jueptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorecki, ed. (SPIE, 1997).

J. Goodman, Introduction to Fourier Optics (Roberts and Company Publishers, 2004).

J. W. Goodman, Statistical Optics (Wiley, 2015).

https://doi.org/10.6084/m9.figshare.7998143 .

https://doi.org/10.6084/m9.figshare.7998134 .

https://github.com/FerreolS/COMCI .

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Figures (13)

Fig. 1.
Fig. 1. Scheme of the setup.
Fig. 2.
Fig. 2. Transformation of the SBP in the Wigner domain after a Fresnel transform.
Fig. 3.
Fig. 3. Space-bandwidth product (light gray) probed by a lensless setup of detector size $\ell$ under a normal illumination ($\theta = 0$). The darker area represents the SBP under paraxial approximation (when the bandwidth of the probed sample is much smaller than $k$).
Fig. 4.
Fig. 4. Scheme of the diffraction by a half plane under illumination with an incidence of $\theta$, as modeled in Section 4.A. The geometrical shadow boundary is at ${x_c}$.
Fig. 5.
Fig. 5. Intensity as a distance from geometrical shadow boundary ${x_c}$ of the diffraction of a half plane at a distance of $z = 250\,\,\unicode{x00B5}{\rm m}$ for an illumination of wavelength $\lambda = 530\;{\rm nm} $ and an incidence ${\theta _1}{= 0^ \circ}$ (gray solid line) and ${\theta _1}{= 30^ \circ}$ (black solid line) both with their upper-bound (dashed lines) computed according to Eq. (31).
Fig. 6.
Fig. 6. Extent of a diffraction pattern boundary is the point where optical path difference between the diffracted wave ${v_d}$ and the illumination wave ${v_i}$ is larger than the coherence length.
Fig. 7.
Fig. 7. Effective bandwidth $B^\prime $ estimated from the extent of the diffraction pattern ${p^ -} + {p^ +}$.
Fig. 8.
Fig. 8. Scheme of the simulated setup where a part of the sample is masked by an opaque screen placed at a distance $t$ of the sensor edge projected in the sample plane along the direction of incident light.
Fig. 9.
Fig. 9. Transmittance (first row) and phase (second row) of the five $20160 \times 20160$ pixel images used to generate test data set. (d) Phase-only USAF-1951 image. (e) Ttransmittance-only binary USAF-1951 image.
Fig. 10.
Fig. 10. Modeling error $E$ as a function of the projected distance $t$ of the opaque screen, for incidence [0°,30°,45°,60°] and a noise level of 20 dB. The bounds given by Eq. (34) ($[37,47,75,113]\,\unicode{x00B5}{\rm m}$, respectively) are indicated by the cross marks.
Fig. 11.
Fig. 11. Modeling error $E$ as a function of the projected distance $t$ of the opaque screen for an incidence of $\theta {= 45^ \circ}$ and noise levels of [6,14,20,26] dBs. The bounds given by Eq. (34) ($[12,32,65,139]\,\unicode{x00B5}{\rm m}$, respectively) are indicated by the cross marks.
Fig. 12.
Fig. 12. Modeling error $E(t)$ as a function of the projected distance $t$ of the opaque screen for an incidence $\theta = - {30^ \circ}$ and coherence lengths of the illumination ${L_c} = [2,20,80]\,\unicode{x00B5}{\rm m}$. The bounds given by Eq. (42) ($[38,113,217]\,\unicode{x00B5}{\rm m}$, respectively) are indicated by the cross marks.
Fig. 13.
Fig. 13. Modeling error $E(t)$ as a function of the projected distance $t$ of the opaque screen for an incidence $\theta = - {30^ \circ}$ and several angular radius $\alpha {= [0.05^ \circ}{,0.07^ \circ}{,0.2^ \circ}]$. The bounds given by Eq. (44) ($[56,160,223]\,\unicode{x00B5}{\rm m}$, respectively) are indicated by the cross marks.

Tables (1)

Tables Icon

Table 1. Parameters Used in All Simulations

Equations (51)

Equations on this page are rendered with MathJax. Learn more.

d = M ( o ) + e ,
M = S C H ,
C ( f ) ( x ) = { f ( x ) i f x D 0 o t h e r w i s e
g ( x ) = o ( x ) exp ( j k x sin ( θ ) ) ,
g ^ ( ω ) = o ^ ( ω k sin ( θ ) ) ,
f ^ ( ω ) = F ( f ) ( ω ) = R 2 f ( x ) e j x ω d x .
w ^ ( ω ) = f ^ A S ( ω ) g ^ ( ω ) ,
f ^ A S ( ω ) = { e + j z k 2 ω 2 i f ω 2 k 2 0 o t h e r w i s e .
f ^ F ( ω ) = e j z 2 k ω 2 .
w = H ( o ) ,
w ( x ) = F 1 ( h ^ A S × o ^ ) ( x ) e j k x sin ( θ ) ,
h ^ A S ( ω ) = { e j z k 2 ω + k sin ( θ ) 2 i f ω + k sin ( θ ) 2 k 2 , 0 o t h e r w i s e .
h A S ( x ) = k z j 2 π ( x 2 + z 2 ) e j k ( x sin ( θ ) + x 2 + z 2 ) .
W F ( x , ω ) = f ^ F ( ω + ω 2 ) f ^ F ( ω ω 2 ) e j ω x d ω
= δ ( ω x k z ) ,
i F = i + z B s k .
ξ i ( x ) = d A r g ( h A S ( x ) ) d x i ,
= k ( x i x 2 + z 2 sin ( θ i ) ) ,
ξ ( x ) = k ( x x 2 + z 2 sin ( θ ) ) .
+ ξ ( x + 2 ) ξ ( x 2 ) d x = 2 k ,
ξ ( x c ) = 0 x c = z tan ( θ ) ,
τ i ( ω ) = d A r g ( h ^ ( ω ) ) d ω i .
z n 2 λ 2 ( n λ 1 1 ) 2 1 ,
λ ( n n 2 ( λ z ) 2 ) 1 .
p i = min ( p i s p a , p i s p e , p i n o i s e ) ,
p i + = min ( p i + s p a , p i + s p e , p i + n o i s e ) .
i = i + p i + p i + .
o ( x 1 , x 2 ) = { 0 i f x 1 0 , 1 o t h e r w i s e .
w ( r , α ) = exp ( j π / 4 ) 1 + cos ( α ) π cos ( θ ) ( cos ( θ + α ) + cos ( θ ) ) × exp ( j k r cos ( α ) ) F ( 2 k r sin ( α 2 ) ) ,
F ( x ) = x exp ( j t 2 ) d t .
| w ( x c + t , x 2 ) | 2 1 + 2 ( r c + t sin ( | θ | ) ) π k t cos ( θ ) .
η ( S N R ) 1 / 2 = max ( σ I 0 , ζ I 0 ) ,
2 ( r c + p i n o i s e sin ( | θ i | ) ) π k p i n o i s e cos ( θ i ) = η ,
p i n o i s e = 2 z k π η 2 cos ( θ i ) + sin 2 ( θ i ) + sin ( | θ i | ) k π η 2 cos 2 ( θ i ) .
μ ( Δ ) = v i ( Δ , t ) v d ( Δ , t ) t v i ( Δ , t ) v i ( Δ , t ) t v d ( Δ , t ) v d ( Δ , t ) t ,
| μ ( Δ ) | | μ 1 ( Δ 1 ) | | μ 2 ( Δ 2 ) | .
γ ( δ , τ ) = v i ( x , t ) v i ( x + δ , t + τ ) x , t v i ( x , t ) v i ( x , t ) x , t .
τ i A B = n z c cos ( θ i ) ,
τ i P B = n c ( z 2 + ( z tan ( θ i ) + Δ i ) 2 + Δ i sin ( θ i ) ) .
μ i ( Δ i ) = γ ( δ i A P , τ i P B τ i A B ) ,
= γ ( Δ i cos ( θ i ) , n c ( z 2 + ( z tan ( θ i ) + Δ i ) 2 z cos ( θ i ) + Δ i sin ( θ i ) ) ) .
p i + s p e = L c n cos 2 ( θ i ) ( 1 + 2 n cos ( θ i ) z L c + sin ( θ i ) ) ,
p i s p e = L c n cos 2 ( θ i ) ( 1 + 2 n cos ( θ i ) z L c sin ( θ i ) ) .
p i = 0.35 λ n tan ( α ) cos ( θ i ) .
p i = 1 π λ n tan ( α ) cos ( θ i ) ,
B i = 2 max ( ξ ( p i ) , ξ ( p i + ) ) ,
R i = 4 π B i = λ n ( p p i 2 + z 2 + sin ( | θ i | ) ) 1 .
( B 2 ) 2 k 2 p 2 p 2 + z 2 + sin ( | θ | ) 1 .
N A i ( x ) = n min ( | x i x i c | + / 2 , p ) min ( x x c + / 2 2 , p 2 ) + z 2 .
d z ( x ) = n λ max ( N A 1 2 ( x ) , N A 2 2 ( x ) ) .
E ( t ) = 10 log 10 r s ( t ) 2 2 10 log 10 r s 2 2 .

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