Abstract

Coherent modulation imaging (CMI) is a promising technique for online laser beam diagnostics; however, obvious speckle noise is always generated in the reconstruction, seriously degrading the spatial resolution and, accordingly, the accuracy. To solve this problem, both the optical setup of the common CMI and its reconstruction algorithm are slightly modified, and the performance of CMI in laser beam diagnostics can be obviously improved. By adding the second detector to record additional intensity distribution and using it to strengthen the intensity constraint of common CMI algorithm, the speckle noise in the reconstructed image can be distinctively reduced, and thus both the spatial resolution and the measurement accuracy are improved significantly. The feasibility of this proposed method is verified by proof-of-principle experiments.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
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[Crossref]

2016 (2)

X. Pan, S. Veetil, C. Liu, H. Tao, Y. Jiang, Q. Lin, X. Li, and J. Zhu, “On-shot laser beam diagnostics for high-power laser facility with phase modulation imaging,” Laser Phys. Lett. 13(5), 055001 (2016).
[Crossref]

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

2015 (1)

X. He, S. Veetil, C. Liu, S. Gao, Y. Wang, J. Wang, and J. Zhu, “Accurate focal spot diagnostics based on a single shot coherent modulation imaging,” Laser Phys. Lett. 12(1), 015005 (2015).
[Crossref]

2012 (2)

2010 (2)

2009 (1)

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102(1), 018101 (2009).
[Crossref]

2008 (3)

2007 (1)

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

2006 (1)

2004 (1)

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

2003 (2)

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack–Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

J. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref]

2001 (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).

2000 (1)

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

1993 (1)

1991 (1)

R. Lane, “Phase retrieval using conjugate gradient minimization,” J. Mod. Opt. 38(9), 1797–1813 (1991).
[Crossref]

1987 (1)

1986 (1)

1982 (1)

1978 (1)

1972 (1)

R. W. Gerchberg, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–250 (1972).

1952 (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. A 5(6), 843 (1952).
[Crossref]

Aeppli, G.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref]

Almoro, P.

Bahk, S.-W.

Bao, X.

Begishev, I. A.

Bromage, J.

Bunk, O.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref]

Camacho, L.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Chen, B.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref]

Dierolf, M.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref]

Dinapoli, R.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref]

Faulkner, H. M.

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Fienup, J. R.

Gao, M.

J. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref]

Gao, S.

X. He, S. Veetil, C. Liu, S. Gao, Y. Wang, J. Wang, and J. Zhu, “Accurate focal spot diagnostics based on a single shot coherent modulation imaging,” Laser Phys. Lett. 12(1), 015005 (2015).
[Crossref]

García, J.

Gerchberg, R. W.

R. W. Gerchberg, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–250 (1972).

Guizar-Sicairos, M.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref]

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

M. Guizar-Sicairos and J. R. Fienup, “Understanding the twin-image problem in phase retrieval,” J. Opt. Soc. Am. A 29(11), 2367–2375 (2012).
[Crossref]

M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16(10), 7264–7278 (2008).
[Crossref]

He, X.

X. He, S. Veetil, C. Liu, S. Gao, Y. Wang, J. Wang, and J. Zhu, “Accurate focal spot diagnostics based on a single shot coherent modulation imaging,” Laser Phys. Lett. 12(1), 015005 (2015).
[Crossref]

Holler, M.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref]

Imamoto, N.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102(1), 018101 (2009).
[Crossref]

Irwin, D.

Ishikawa, T.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102(1), 018101 (2009).
[Crossref]

Jiang, Y.

X. Pan, S. Veetil, C. Liu, H. Tao, Y. Jiang, Q. Lin, X. Li, and J. Zhu, “On-shot laser beam diagnostics for high-power laser facility with phase modulation imaging,” Laser Phys. Lett. 13(5), 055001 (2016).
[Crossref]

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Kruschwitz, B.

Lane, R.

R. Lane, “Phase retrieval using conjugate gradient minimization,” J. Mod. Opt. 38(9), 1797–1813 (1991).
[Crossref]

Li, X.

X. Pan, S. Veetil, C. Liu, H. Tao, Y. Jiang, Q. Lin, X. Li, and J. Zhu, “On-shot laser beam diagnostics for high-power laser facility with phase modulation imaging,” Laser Phys. Lett. 13(5), 055001 (2016).
[Crossref]

Liesener, J.

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack–Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

Lin, Q.

X. Pan, S. Veetil, C. Liu, H. Tao, Y. Jiang, Q. Lin, X. Li, and J. Zhu, “On-shot laser beam diagnostics for high-power laser facility with phase modulation imaging,” Laser Phys. Lett. 13(5), 055001 (2016).
[Crossref]

Liu, C.

X. Pan, S. Veetil, C. Liu, H. Tao, Y. Jiang, Q. Lin, X. Li, and J. Zhu, “On-shot laser beam diagnostics for high-power laser facility with phase modulation imaging,” Laser Phys. Lett. 13(5), 055001 (2016).
[Crossref]

X. He, S. Veetil, C. Liu, S. Gao, Y. Wang, J. Wang, and J. Zhu, “Accurate focal spot diagnostics based on a single shot coherent modulation imaging,” Laser Phys. Lett. 12(1), 015005 (2015).
[Crossref]

Liu, S.

Liu, Z.

Maeshima, K.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102(1), 018101 (2009).
[Crossref]

Matsuoka, S.

Menzel, A.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref]

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

Micó, V.

Mileham, C.

Moore, M.

Morrison, G. R.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

Müller, E.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref]

Nagahara, L.

J. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref]

Nishino, Y.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102(1), 018101 (2009).
[Crossref]

Osten, W.

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

P. Almoro, G. Pedrini, and W. Osten, “Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field,” Appl. Opt. 45(34), 8596–8605 (2006).
[Crossref]

Pan, X.

X. Pan, S. Veetil, C. Liu, H. Tao, Y. Jiang, Q. Lin, X. Li, and J. Zhu, “On-shot laser beam diagnostics for high-power laser facility with phase modulation imaging,” Laser Phys. Lett. 13(5), 055001 (2016).
[Crossref]

Pedrini, G.

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

P. Almoro, G. Pedrini, and W. Osten, “Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field,” Appl. Opt. 45(34), 8596–8605 (2006).
[Crossref]

Pfeiffer, F.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref]

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).

Raabe, J.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref]

Robinson, I. K.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

Rodenburg, J.

F. Zhang and J. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[Crossref]

Rodenburg, J. M.

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400(6742), 342–344 (1999).
[Crossref]

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. A 5(6), 843 (1952).
[Crossref]

Seifert, L.

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack–Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).

Shen, C.

Stoeckl, C.

Storm, M.

Takahashi, Y.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102(1), 018101 (2009).
[Crossref]

Tan, J.

Tao, H.

X. Pan, S. Veetil, C. Liu, H. Tao, Y. Jiang, Q. Lin, X. Li, and J. Zhu, “On-shot laser beam diagnostics for high-power laser facility with phase modulation imaging,” Laser Phys. Lett. 13(5), 055001 (2016).
[Crossref]

Thibault, P.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321(5887), 379–382 (2008).
[Crossref]

Tiziani, H. J.

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack–Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

Tsai, E. H.

M. Holler, M. Guizar-Sicairos, E. H. Tsai, R. Dinapoli, E. Müller, O. Bunk, J. Raabe, and G. Aeppli, “High-resolution non-destructive three-dimensional imaging of integrated circuits,” Nature 543(7645), 402–406 (2017).
[Crossref]

Vartanyants, I.

J. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities,” Science 300(5624), 1419–1421 (2003).
[Crossref]

Veetil, S.

X. Pan, S. Veetil, C. Liu, H. Tao, Y. Jiang, Q. Lin, X. Li, and J. Zhu, “On-shot laser beam diagnostics for high-power laser facility with phase modulation imaging,” Laser Phys. Lett. 13(5), 055001 (2016).
[Crossref]

X. He, S. Veetil, C. Liu, S. Gao, Y. Wang, J. Wang, and J. Zhu, “Accurate focal spot diagnostics based on a single shot coherent modulation imaging,” Laser Phys. Lett. 12(1), 015005 (2015).
[Crossref]

Vila-Comamala, J.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

Wackerman, C. C.

Wang, J.

X. He, S. Veetil, C. Liu, S. Gao, Y. Wang, J. Wang, and J. Zhu, “Accurate focal spot diagnostics based on a single shot coherent modulation imaging,” Laser Phys. Lett. 12(1), 015005 (2015).
[Crossref]

Wang, Y.

X. He, S. Veetil, C. Liu, S. Gao, Y. Wang, J. Wang, and J. Zhu, “Accurate focal spot diagnostics based on a single shot coherent modulation imaging,” Laser Phys. Lett. 12(1), 015005 (2015).
[Crossref]

Yamakawa, K.

Zalevsky, Z.

Zhang, F.

F. Zhang, B. Chen, G. R. Morrison, J. Vila-Comamala, M. Guizar-Sicairos, and I. K. Robinson, “Phase retrieval by coherent modulation imaging,” Nat. Commun. 7, 13367 (2016).
[Crossref]

F. Zhang and J. Rodenburg, “Phase retrieval based on wave-front relay and modulation,” Phys. Rev. B 82(12), 121104 (2010).
[Crossref]

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75(4), 043805 (2007).
[Crossref]

Zhang, R.

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Figures (7)

Fig. 1
Fig. 1 Setup of (a) common CMI and (b) modified CMI. OL: objective lens, P: pinhole, L1: collimating lens, L2: focusing lens, BS: beam splitter, PM: phase mask, C1: CCD1, C2: CCD2.
Fig. 2
Fig. 2 Flowchart of common CMI (without red dotted square) and modified CMI (with red dotted square).
Fig. 3
Fig. 3 Recorded intensity pattern by (a) CCD C1 and (b) CCD C C2.
Fig. 4
Fig. 4 (a) Phase and (b) intensity obtained by common CMI. (c) Phase and (d) intensity obtained by modified CMI, (e) a photo of the slide taken by a cellphone and (f) intensity of directly imaged glass.
Fig. 5
Fig. 5 Reconstructed focal distribution by (a) common and (b) modified CMI, (c) the focal spot distribution directly recorded by CCD.
Fig. 6
Fig. 6 Recorded intensity pattern by (a) CCD C1 and (b) CCD C2.
Fig. 7
Fig. 7 Reconstructed intensity by (a) common CMI and (b) modified CMI. (c) Intensity of directly imaged USAF target. The bottom three images are enlarged images of the red squares in (a), (b) and (c).

Equations (10)

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p n ( x,y )= F p [ f n ( x,y ),λ, d 2 ]
F p [ f( x,y ),λ,z ]= e jkz jλz f( x,y ) e [ jk ( x 0 x ) 2 + ( y 0 y ) 2 2z ] d x d y .
φ n ( x,y )= F p [ p n ( x,y )M( x,y ),λ,( d 3 d 2 ) ].
ψ n ( x,y )= I C1 φ n ( x,y )/| φ n ( x,y ) |.
ϕ n ( x,y )= F p [ ψ n ( x,y ),λ,( d 3 d 2 ) ].
p ' n ( x,y )= p n ( x,y )+β M * ( x,y ) | M( x,y ) | max 2 [ ϕ n ( x,y ) p n ( x,y )M( x,y ) ].
f ' n ( x,y )= F p [ p ' n ( x,y ),λ, d 2 ]S(x,y).
τ n ( x,y )= F p [ f ' n ( x,y ),λ, d 4 ].
f ¯ n ( x,y )= F p [ I C2 x,y | τ n ( x,y ) | 2 / x,y I C2 τ n ( x,y )/| τ n ( x,y ) |,λ, d 4 ].
f n+1 ( x,y )= f n ( x,y )S(x,y)+δ( f n ( x,y ) f ¯ n ( x,y ) )S(x,y).

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