Abstract

Diffractive lenses fabricated by lithographic methods are one of the most popular image forming optics in the x-ray regime. Most commonly, binary diffractive optics, such as Fresnel zone plates, are used due to their ability to focus at high resolution and to manipulate the x-ray wavefront. We report here a binary zone plate design strategy to form arbitrary illuminations for coherent multiplexing, structured illumination, and wavefront shaping experiments. Given a desired illumination, we adjust the duty cycle, harmonic order, and zone placement to vary both the amplitude and phase of the wavefront at the lens. This enables the binary lithographic pattern to generate arbitrary structured illumination optimized for a variety of applications such as holography, interferometry, ptychography, imaging, and others.

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References

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  21. D. Gabor, “A new microscopic principle,” Nature 161, 777 (1948).
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  22. E. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” Journal of the Optical Society of America 52, 1123–1130 (1962).
    [Crossref]
  23. W.-H. Lee, “Binary synthetic holograms,” Applied optics 13, 1677–1682 (1974).
    [Crossref] [PubMed]
  24. S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
    [Crossref] [PubMed]
  25. W. K. Cheung, P. Tsang, T. Poon, and C. Zhou, “Enhanced method for the generation of binary fresnel holograms based on grid-cross downsampling,” Chinese Optics Letters 9, 120005 (2011).
    [Crossref]
  26. P. W. M. Tsang, “Generation of binary off-axis digital fresnel hologram with enhanced quality,” ICT Express 1, 26–29 (2015).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  29. J. Vila-Comamala, S. Gorelick, E. Färm, C. Kewish, A. Diaz, R. Barrett, V. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Optics Express 19, 175–184 (2011).
    [Crossref] [PubMed]
  30. C. Chang and A. Sakdinawat, “Ultra-high aspect ratio high-resolution nanofabrication for hard x-ray diffractive optics,” Nat. Comm. 5, 4243 (2014).
    [Crossref]
  31. I. Mohacsi, I. Vartiainen, M. Guizar-Sicairos, P. Karvinen, C. Kewish, A. Somogyi, V. Guzenko, E. Müller, E. Färm, M. Ritala, and C. David, “Double-sided diffractive x-ray optics for hard x-ray microscopy,” Optics Express 23, 776 (2015).
    [Crossref]
  32. C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
    [Crossref]

2018 (2)

G. Morrison, F. Zhang, A. Gianoncelli, and I. Robinson, “X-ray ptychography using randomized zone plates,” Optics Express 26, 14915–14927 (2018).
[Crossref] [PubMed]

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Problems 34, 025003 (2018).
[Crossref]

2016 (1)

S. Marchesini, Y.-C. Tu, and H.-t. Wu, “Alternating projection, ptychographic imaging and phase synchronization,” Applied and Computational Harmonic Analysis 41, 815–851 (2016).
[Crossref]

2015 (2)

P. W. M. Tsang, “Generation of binary off-axis digital fresnel hologram with enhanced quality,” ICT Express 1, 26–29 (2015).
[Crossref]

I. Mohacsi, I. Vartiainen, M. Guizar-Sicairos, P. Karvinen, C. Kewish, A. Somogyi, V. Guzenko, E. Müller, E. Färm, M. Ritala, and C. David, “Double-sided diffractive x-ray optics for hard x-ray microscopy,” Optics Express 23, 776 (2015).
[Crossref]

2014 (2)

C. Chang and A. Sakdinawat, “Ultra-high aspect ratio high-resolution nanofabrication for hard x-ray diffractive optics,” Nat. Comm. 5, 4243 (2014).
[Crossref]

M. Eriksson, J. F. van der Veen, and C. Quitmann, “Diffraction-limited storage rings - a window to the science of tomorrow,” J. Synchr. Rad. 21, 837 (2014).
[Crossref]

2013 (2)

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft x-ray spectromicroscopy using ptychography with randomly phased illumination,” Nature communications 4, 1669 (2013).
[Crossref] [PubMed]

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific reports 3, 1927 (2013).
[Crossref] [PubMed]

2012 (1)

C. Xie, X. Zhu, H. Li, L. Shi, Y. Hua, and M. Liu, “Toward two-dimensional nanometer resolution hard x-ray differential-interference-contrast imaging using modified photon sieves,” Optics letters 37, 749–751 (2012).
[Crossref] [PubMed]

2011 (3)

C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

J. Vila-Comamala, S. Gorelick, E. Färm, C. Kewish, A. Diaz, R. Barrett, V. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Optics Express 19, 175–184 (2011).
[Crossref] [PubMed]

W. K. Cheung, P. Tsang, T. Poon, and C. Zhou, “Enhanced method for the generation of binary fresnel holograms based on grid-cross downsampling,” Chinese Optics Letters 9, 120005 (2011).
[Crossref]

2010 (2)

C. Xie, X. Zhu, H. Li, L. Shi, and Y. Wang, “Feasibility study of hard-x-ray nanofocusing above 20 kev using compound photon sieves,” Optics letters 35, 4048–4050 (2010).
[Crossref] [PubMed]

K. A. Nugent, “Coherent methods in the x-ray sciences,” Advances in Physics 59, 1–99 (2010).
[Crossref]

2008 (2)

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, and et al., “Massively parallel x-ray holography,” Nature photonics 2, 560 (2008).
[Crossref]

O. von Hofsten, M. Bertilson, and U. Vogt, “Theoretical development of a high-resolution differential-interference-contrast optic for x-ray microscopy,” Opt. Express 16, 1132–1141 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (1)

2003 (2)

E. D. Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11, 2278–2288 (2003).
[Crossref] [PubMed]

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

1994 (1)

S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]

1993 (1)

L. Vincent, “Morphological grayscale reconstruction in image analysis: applications and efficient algorithms,” IEEE transactions on image processing 2, 176–201 (1993).
[Crossref] [PubMed]

1980 (1)

J. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Optical Engineering 19, 193297 (1980).
[Crossref]

1979 (1)

W.-H. Lee, “Binary computer-generated holograms,” Applied Optics 18, 3661–3669 (1979).
[Crossref] [PubMed]

1978 (1)

E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Applied optics 17, 337–347 (1978).
[Crossref] [PubMed]

1974 (1)

W.-H. Lee, “Binary synthetic holograms,” Applied optics 13, 1677–1682 (1974).
[Crossref] [PubMed]

1962 (1)

E. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” Journal of the Optical Society of America 52, 1123–1130 (1962).
[Crossref]

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161, 777 (1948).
[Crossref] [PubMed]

Altissimo, M.

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

Anderson, E.

Attwood, D.

Bajt, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, and et al., “Massively parallel x-ray holography,” Nature photonics 2, 560 (2008).
[Crossref]

Barrett, R.

C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

J. Vila-Comamala, S. Gorelick, E. Färm, C. Kewish, A. Diaz, R. Barrett, V. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Optics Express 19, 175–184 (2011).
[Crossref] [PubMed]

Barty, A.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, and et al., “Massively parallel x-ray holography,” Nature photonics 2, 560 (2008).
[Crossref]

Behrens, C.

P. Schmüser, M. Dohlus, J. Rossbach, and C. Behrens, Free-Electron Lasers in the Ultraviolet and X-ray Regime (Springer, 2014).
[Crossref]

Bertilson, M.

Bogan, M. J.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, and et al., “Massively parallel x-ray holography,” Nature photonics 2, 560 (2008).
[Crossref]

Boutet, S.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, and et al., “Massively parallel x-ray holography,” Nature photonics 2, 560 (2008).
[Crossref]

Bunk, O.

C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

Businaro, L.

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

Cabrini, S.

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

E. D. Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11, 2278–2288 (2003).
[Crossref] [PubMed]

Cammarata, M.

C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

Cannon, T. M.

E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Applied optics 17, 337–347 (1978).
[Crossref] [PubMed]

Chang, C.

C. Chang and A. Sakdinawat, “Ultra-high aspect ratio high-resolution nanofabrication for hard x-ray diffractive optics,” Nat. Comm. 5, 4243 (2014).
[Crossref]

C. Chang, A. Sakdinawat, P. Fischer, E. Anderson, and D. Attwood, “Single-element objective lens for soft x-ray differential interference contrast microscopy,” Opt. Lett. 31, 1564–1566 (2006).
[Crossref] [PubMed]

Chapman, H. N.

S. Marchesini, S. Boutet, A. E. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, and et al., “Massively parallel x-ray holography,” Nature photonics 2, 560 (2008).
[Crossref]

Chen, P.

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Problems 34, 025003 (2018).
[Crossref]

Cheung, W. K.

W. K. Cheung, P. Tsang, T. Poon, and C. Zhou, “Enhanced method for the generation of binary fresnel holograms based on grid-cross downsampling,” Chinese Optics Letters 9, 120005 (2011).
[Crossref]

Cingolani, R.

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

Cloetens, P.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific reports 3, 1927 (2013).
[Crossref] [PubMed]

Cojoc, D.

E. D. Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, J. Susini, P. Facci, and T. Wilhein, “Diffractive optical elements for differential interference contrast x-ray microscopy,” Opt. Express 11, 2278–2288 (2003).
[Crossref] [PubMed]

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

David, C.

I. Mohacsi, I. Vartiainen, M. Guizar-Sicairos, P. Karvinen, C. Kewish, A. Somogyi, V. Guzenko, E. Müller, E. Färm, M. Ritala, and C. David, “Double-sided diffractive x-ray optics for hard x-ray microscopy,” Optics Express 23, 776 (2015).
[Crossref]

C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

J. Vila-Comamala, S. Gorelick, E. Färm, C. Kewish, A. Diaz, R. Barrett, V. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Optics Express 19, 175–184 (2011).
[Crossref] [PubMed]

De Vittorio, M.

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

Diaz, A.

J. Vila-Comamala, S. Gorelick, E. Färm, C. Kewish, A. Diaz, R. Barrett, V. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Optics Express 19, 175–184 (2011).
[Crossref] [PubMed]

Dierolf, M.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific reports 3, 1927 (2013).
[Crossref] [PubMed]

Dixit, S.

S. Dixit, J. Lawson, K. Manes, H. Powell, and K. Nugent, “Kinoform phase plates for focal plane irradiance profile control,” Optics letters 19, 417–419 (1994).
[Crossref] [PubMed]

Dohlus, M.

P. Schmüser, M. Dohlus, J. Rossbach, and C. Behrens, Free-Electron Lasers in the Ultraviolet and X-ray Regime (Springer, 2014).
[Crossref]

Enders, B.

M. Stockmar, P. Cloetens, I. Zanette, B. Enders, M. Dierolf, F. Pfeiffer, and P. Thibault, “Near-field ptychography: phase retrieval for inline holography using a structured illumination,” Scientific reports 3, 1927 (2013).
[Crossref] [PubMed]

Eriksson, M.

M. Eriksson, J. F. van der Veen, and C. Quitmann, “Diffraction-limited storage rings - a window to the science of tomorrow,” J. Synchr. Rad. 21, 837 (2014).
[Crossref]

Fabrizio, E. D.

Fabrizio, E. Di

E. Di Fabrizio, S. Cabrini, D. Cojoc, F. Romanato, L. Businaro, M. Altissimo, B. Kaulich, T. Wilhein, J. Susini, M. De Vittorio, E. Vitale, G. Gigli, and R. Cingolani, “Shaping x-rays by diffractive coded nano-optics,” Microelectronic engineering 67, 87–95 (2003).
[Crossref]

Facci, P.

Fannjiang, A.

P. Chen and A. Fannjiang, “Coded aperture ptychography: uniqueness and reconstruction,” Inverse Problems 34, 025003 (2018).
[Crossref]

Färm, E.

I. Mohacsi, I. Vartiainen, M. Guizar-Sicairos, P. Karvinen, C. Kewish, A. Somogyi, V. Guzenko, E. Müller, E. Färm, M. Ritala, and C. David, “Double-sided diffractive x-ray optics for hard x-ray microscopy,” Optics Express 23, 776 (2015).
[Crossref]

C. David, S. Gorelick, S. Rutishauser, J. Krzywinski, J. Vila-Comamala, V. Guzenko, O. Bunk, E. Färm, M. Ritala, M. Cammarata, D. Fritz, R. Barrett, L. Samoylova, J. Grünert, and H. Sinn, “Nanofocusing of hard x-ray free electron laser pulses using diamond based fresnel zone plates,” Sci. Rep. 1, 57 (2011).
[Crossref]

J. Vila-Comamala, S. Gorelick, E. Färm, C. Kewish, A. Diaz, R. Barrett, V. Guzenko, M. Ritala, and C. David, “Ultra-high resolution zone-doubled diffractive x-ray optics for the multi-kev regime,” Optics Express 19, 175–184 (2011).
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Figures (4)

Fig. 1
Fig. 1 On axis and off axis Zone plates with order sorting apertures
Fig. 2
Fig. 2 Uniformly redundant array illumination. Top row: desired amplitude, phase at the lens, and at the sample plane complex-HSV representation and amplitude. Following Rows, from top to bottom, W ZP 0, W ZP 1 d c, W ZP 2 h y b, and W ZP 3 g r a t. Columns, from left to right: the zone plate, magnified portion of zone plate, focal plane overview, and the focal spot.
Fig. 3
Fig. 3 Off-axis holographic illumination. Top row: desired amplitude, phase at the lens, and at the sample plane. Following Rows, from top to bottom, W ZP 0, W ZP 1 d c, W ZP 2 h y b, and W ZP 3 g r a t. Columns, from left to right: the zone plate, magnified portion of zone plate, focal plane overview, and the focal spot.
Fig. 4
Fig. 4 Band Limited Random illumination. Top row: desired amplitude, phase at the lens, and at the sample represented in HSV color format with Hue=phase, Value=amplitude, and Saturation=1, and amplitude on the right. Following Rows, from top to bottom, W ZP 0, W ZP 1 d c, W ZP 2 h y b, and W ZP 3 g r a t. Columns, from left to right: the zone plate, magnified portion of zone plate, focal plane overview, and the focal spot.

Tables (1)

Tables Icon

Table 1 The normalized mean square error (nmse), normalized mean square error after morphological opening (nmse-o), relative efficiency, 1/c, and mean power W 2 for the URA, holographic, and bandwidth limited random pytchography zone plates.

Equations (8)

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ZP 0 ( ϕ 0 ) = { 1 , if mod ( ϕ 0 , 2 π ) < π 0 , otherwise ,
ε h ( L , p ) = { L / p , if h = 0 1 h π sin  ( π h L p ) , if | h | > 0
ZP 1 dc ( ϕ w , | W | ) = { 1 , if mod ( ϕ w + ϕ W , 2 π ) < 2 ϕ W , 0 , otherwise
ZP 1 h ( ϕ w , | W | ) = { 1 , if mod ( ϕ w + ϕ W , 4 π ) < 2 π + 2 ϕ W 0 , otherwise
ZP 2 hyb ( ϕ w , | W | ) = { ZP 1 d c ( ϕ w , | W | ) , if | W | > 1 / 2 ZP 1 h ( ϕ w , 2 | W | ) , otherwise
ZP 3 grat ( ϕ w , | W | ) = ZP 0 ( ϕ w ) T ( | W | )
T ( | W | ) = { 1 , if mod ( x / l | W | / 2 , 2 ) < | W | 0 , otherwise
nmse = min c w t r u t h c w Z P O S A 2 w t r u t h O S A 2 ,