## Imaging by integrating stitched spectrograms |

Optics Express, Vol. 21, Issue 6, pp. 6783-6793 (2013)

http://dx.doi.org/10.1364/OE.21.006783

Acrobat PDF (1231 KB)

### Abstract

A new diffractive imaging technique called Imaging By Integrating Stitched Spectrograms (IBISS) is presented. Both the data collection and phase retrieval algorithm used in IBISS are direct extensions of frequency resolved optical gating to higher dimensions. Data collection involves capturing an array of diffraction patterns generated by scanning a sample across a coherent beam of light. Phase retrieval is performed using the Principal Components Generalized Projections Algorithm (PCGPA) by reducing the four dimensional data set of images to two remapped two-dimensional sets. The technique is successfully demonstrated using a Helium Neon laser to image a 350μm wide sample with 12μm resolution.

© 2013 OSA

## 1. Introduction

2. 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]

3. K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. **107**(2), 529–534 (2010). [CrossRef] [PubMed]

11. 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] [PubMed]

12. B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. **4**(5), 394–398 (2008). [CrossRef]

16. G. Williams, H. Quiney, B. Dahl, C. Tran, A. G. Peele, K. A. Nugent, M. D. De Jonge, and D. Paterson, “Curved beam coherent diffractive imaging,” Thin Solid Films **515**(14), 5553–5556 (2007). [CrossRef]

17. T. Harada, M. Nakasuji, T. Kimura, T. Watanabe, H. Kinoshita, and Y. Nagata, “Imaging of extreme-ultraviolet mask patterns using coherent extreme-ultraviolet scatterometry microscope based on coherent diffraction imaging,” J. Vac. Sci. Technol. B **29**(6), 06F503 (2011). [CrossRef]

19. D. F. Gardner, B. Zhang, M. D. Seaberg, L. S. Martin, D. E. Adams, F. Salmassi, E. Gullikson, H. Kapteyn, and M. Murnane, “High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination,” Opt. Express **20**(17), 19050–19059 (2012). [CrossRef] [PubMed]

15. D. J. Vine, G. J. Williams, B. Abbey, M. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, G. Peele, and K. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A **80**(6), 063823 (2009). [CrossRef]

20. M. Dierolf, O. Bunk, S. Kynde, P. Thibault, I. Johnson, A. Menzel, K. Jefimovs, C. David, O. Marti, and F. Pfeiffer, “Ptychography & lensless x ray imaging,” Europhys. News **39**(1), 22–24 (2008). [CrossRef]

21. P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy **109**(4), 338–343 (2009). [CrossRef] [PubMed]

*all*of the collected scatter patterns. In ptychography, the wave truncation is achieved by means of a pinhole placed very near the sample being scanned.

## 2. Theory

22. D. Kane, “Principal components generalized projections : a review [ Invited ],” J. Opt. Soc. Am. B **25**(6), A120–A130 (2008). [CrossRef]

23. R. Trebino and D. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. **10**(5), 1101 (1993). [CrossRef]

26. K. DeLong, R. Trebino, J. Hunter, and W. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B **11**(11), 2206–2215 (1994). [CrossRef]

*X*and

*Y*represent the displacement of the sample. The signal immediately after the sample isand the spectrum of this signal isThe camera records the intensity of the spectrum at each scan position (absolute value squared of Eq. (2)):The PCGP algorithm uses Eqs. (1) and (3) as constraints. Equation (1), which is applied in the object domain, is used to obtain the next guess for the beam and sample as well as to construct the guess for the signal immediately after the sample. The constraint from Eq. (3), which is applied in the frequency domain, forces the amplitude of the guess for the spectrogram to be equal to the measured amplitude. Before this constraint is imposed, the error can be estimated in an RMS fashion, by summing the square of the difference between the two amplitudes and taking the square root of the sum.

*x*and

*y*directions to obtain a guess for the collection of spectra:At this point the amplitudes in Eq. (4) are replaced with the measured amplitudes,

^{2}vectors:

*E*with that of

*G*, there is a one to one mapping from the outer product to the object domain signal,

*E*. The object domain signal is produced by first rotating the elements in the rows of the outer product matrix given in Eq. (6) to the left by the row number minus one. The resulting matrix is shown below:

_{sig}*N*columns are the object domain signals which are formed by shifting the sample one through

*N*steps in the

*Y*direction and 0 steps in the

*X*direction. The next

*N*columns are the result of shifting the sample one through

*N*steps in the

*Y*direction and 1 step in the

*X*direction and so on. These columns are reshaped into

*N*by

*N*sub-matrices composing the entire

*N*

^{2}x

*N*

^{2}matrix.

*N*x

*N*elements in Eq. (8) are the beam multiplied by the un-shifted sample (

*X*= 0 and

*Y*= 0). The sub-matrix labeled X = -ΔX, Y = 0 is the beam multiplied by the sample shifted one step to the left in the

*X*direction. The matrix labeled

*X*= 0 and

*Y*= -ΔX is the beam multiplied by the sample shifted one step up in the

*Y*direction. Together the collection of sub-matrices represents the product

27. D. Kane, “Principal components generalized projections: a review,” J. Opt. Soc. Am. B **25**(6), A120–A132 (2008). [CrossRef]

28. K. W. DeLong, R. Trebino, and W. E. White, “Simultaneous recovery of two ultrashort laser pulses from a single spectrogram,” J. Opt. Soc. Am. B **12**(12), 2463 (1995). [CrossRef]

29. D. J. Kane, G. Rodriguez, A. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. B **14**(4), 935–943 (1997). [CrossRef]

*E*(Eq. (8)) from the guess for the beam and sample matrices. From Eq. (8), it can be seen that in each sub-matrix, the sample matrix (

_{sig}*G*) has been circularly shifted, that is, any elements that are shifted beyond the edge of the matrix are wrapped around to the other side. This method generates an accurate representation of

_{sample}*E*when the sample being imaged is isolated (surrounded by a completely opaque material) because the elements of

_{sig}*G*that get wrapped around are either zeros or multiplied by zeros in

_{sample}*E*. This circular shifting also works for imaging periodic samples since the elements of the sample that are wrapped around exactly match the next part of the sample being illuminated as long as the scan distance is some multiple of the sample’s period.

_{beam}*N*is the number of scan positions in one dimension.

## 3. Methods

*square*pinhole (2.) was imaged onto the sample. The sample (3.) was placed on a motorized stage that moved in a plane perpendicular to the beam propagation direction (with 1 µm step size). A Fourier transform lens (L

_{3}), with a focal length of 10 cm, was placed immediately after the sample. The camera was placed at the focus of the Fourier transform lens (4.) and was mounted on a translation stage which moves in the direction of the beam path so that its position could be precisely controlled. The camera is a windowless, USB controlled, CMOS camera with 1024 by 1280 pixels, each of width 5.2µm.

^{2}x64

^{2}. Since this is also the dimensionality of the outer product of the sample and beam matrices, the size of those matrices must be 64x64.

*dX*) be equal to the sampling period of the beam and sample (

*dx)*. Since

*x*and

*y*, the spatial coordinates of the beam and sample, are Fourier transform pairs with

*f*and

_{x}*f*, the spatial frequencies associated with the diffraction patterns, it must be the case that

_{y}*f*can be estimated by

_{x}*x*is the distance from the center of the diffraction pattern, λ is the wavelength, and

_{c}*z*is the focal length of the Fourier transform lens. Combining these equations, we getwhere

*p*is the effective pixel size (5.2µm multiplied by the binning factor of either 16 or 32) and

*N*is the number of scan positions. The focal length of the Fourier transform lens was chosen to be 10cm. With these parameters and a binning factor of 16, Eq. (9) gives a required step size of 11.88µm. The full scan distance, which limits the size of the sample to be imaged, is just the step size multiplied by the number of scan positions.

*D*. To convert this spatial frequency into detector coordinates, we again use the paraxial approximation:The result of substituting Eq. (11) into Eq. (10) is:This is the period of the highest frequency component of the diffraction pattern on the camera. The Nyquist frequency is twice the value of the highest frequency component (twice the reciprocal of Eq. (12):For the L shaped sample that was imaged,

*D*(the size of the sample) = 350µm, and Eq. (13) gives a value of 5.53x10

^{3}m

^{−1}for the Nyquist frequency (

*f*). The actual sampling rate was 1/(2

_{N}*p*) = 6.01x10

^{3}m

^{−1}which is greater than

*f*.

_{N}## 4. Results

## 5. Conclusion

30. B. C. McCallum and J. M. Rodenburg, “Simultaneous reconstruction of object and aperture functions from multiple far-field intensity measurements,” J. Opt. Soc. Am. **10**(2), 231 (1993). [CrossRef]

## Acknowledgments

## References and links

1. | D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. A , 843 (1952). |

2. | 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 |

3. | K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. |

4. | P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. A |

5. | C. A. Larabell and K. A. Nugent, “Imaging cellular architecture with X-rays,” Curr. Opin. Struct. Biol. |

6. | F. Berenguer de la Cuesta, M. P. E. Wenger, R. J. Bean, L. Bozec, M. A. Horton, and I. K. Robinson, “Coherent X-ray diffraction from collagenous soft tissues,” Proc. Natl. Acad. Sci. U.S.A. |

7. | J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. A. M. Neiman, J. J. J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. |

8. | Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express |

9. | R. L. Sandberg, D. A. Raymondson, C. La-O-Vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. |

10. | H. Jiang, C. Song, C. C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C. H. Lu, T. K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. |

11. | 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. |

12. | B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. |

13. | H. M. Quiney, G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. |

14. | G. Williams, H. Quiney, B. Dhal, C. Tran, K. Nugent, A. Peele, D. Paterson, and M. de Jonge, “Fresnel Coherent Diffractive Imaging,” Phys. Rev. Lett. |

15. | D. J. Vine, G. J. Williams, B. Abbey, M. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, G. Peele, and K. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A |

16. | G. Williams, H. Quiney, B. Dahl, C. Tran, A. G. Peele, K. A. Nugent, M. D. De Jonge, and D. Paterson, “Curved beam coherent diffractive imaging,” Thin Solid Films |

17. | T. Harada, M. Nakasuji, T. Kimura, T. Watanabe, H. Kinoshita, and Y. Nagata, “Imaging of extreme-ultraviolet mask patterns using coherent extreme-ultraviolet scatterometry microscope based on coherent diffraction imaging,” J. Vac. Sci. Technol. B |

18. | T. Harada, J. Kishimoto, T. Watanabe, H. Kinoshita, and D. G. Lee, “Mask observation results using a coherent extreme ultraviolet scattering microscope at NewSUBARU,” J. Vac. Sci. Technol. B |

19. | D. F. Gardner, B. Zhang, M. D. Seaberg, L. S. Martin, D. E. Adams, F. Salmassi, E. Gullikson, H. Kapteyn, and M. Murnane, “High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination,” Opt. Express |

20. | M. Dierolf, O. Bunk, S. Kynde, P. Thibault, I. Johnson, A. Menzel, K. Jefimovs, C. David, O. Marti, and F. Pfeiffer, “Ptychography & lensless x ray imaging,” Europhys. News |

21. | P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy |

22. | D. Kane, “Principal components generalized projections : a review [ Invited ],” J. Opt. Soc. Am. B |

23. | R. Trebino and D. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. |

24. | H. Stark, |

25. | R. Trebino, |

26. | K. DeLong, R. Trebino, J. Hunter, and W. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B |

27. | D. Kane, “Principal components generalized projections: a review,” J. Opt. Soc. Am. B |

28. | K. W. DeLong, R. Trebino, and W. E. White, “Simultaneous recovery of two ultrashort laser pulses from a single spectrogram,” J. Opt. Soc. Am. B |

29. | D. J. Kane, G. Rodriguez, A. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. B |

30. | B. C. McCallum and J. M. Rodenburg, “Simultaneous reconstruction of object and aperture functions from multiple far-field intensity measurements,” J. Opt. Soc. Am. |

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(110.0180) Imaging systems : Microscopy

(180.5810) Microscopy : Scanning microscopy

(110.1455) Imaging systems : Blind deconvolution

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: December 11, 2012

Revised Manuscript: February 13, 2013

Manuscript Accepted: February 14, 2013

Published: March 11, 2013

**Virtual Issues**

Vol. 8, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Carson Teale, Dan Adams, Margaret Murnane, Henry Kapteyn, and Daniel J. Kane, "Imaging by integrating stitched spectrograms," Opt. Express **21**, 6783-6793 (2013)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-6-6783

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### References

- D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. A, 843 (1952).
- 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,” Nature400(6742), 342–344 (1999). [CrossRef]
- K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A.107(2), 529–534 (2010). [CrossRef] [PubMed]
- P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from X-ray diffraction data,” Acta Crystallogr. A62(4), 248–261 (2006). [CrossRef] [PubMed]
- C. A. Larabell and K. A. Nugent, “Imaging cellular architecture with X-rays,” Curr. Opin. Struct. Biol.20(5), 623–631 (2010). [CrossRef] [PubMed]
- F. Berenguer de la Cuesta, M. P. E. Wenger, R. J. Bean, L. Bozec, M. A. Horton, and I. K. Robinson, “Coherent X-ray diffraction from collagenous soft tissues,” Proc. Natl. Acad. Sci. U.S.A.106(36), 15297–15301 (2009). [CrossRef] [PubMed]
- J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. A. M. Neiman, J. J. J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A.107(16), 7235–7239 (2010). [CrossRef] [PubMed]
- Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express17(1), 266–277 (2009). [CrossRef] [PubMed]
- R. L. Sandberg, D. A. Raymondson, C. La-O-Vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, H. C. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett.34(11), 1618–1620 (2009). [CrossRef] [PubMed]
- H. Jiang, C. Song, C. C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C. H. Lu, T. K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, and J. Miao, “Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A.107(25), 11234–11239 (2010). [CrossRef] [PubMed]
- 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] [PubMed]
- B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys.4(5), 394–398 (2008). [CrossRef]
- H. M. Quiney, G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys.2(2), 101–104 (2006). [CrossRef]
- G. Williams, H. Quiney, B. Dhal, C. Tran, K. Nugent, A. Peele, D. Paterson, and M. de Jonge, “Fresnel Coherent Diffractive Imaging,” Phys. Rev. Lett.97(2), 025506 (2006). [CrossRef]
- D. J. Vine, G. J. Williams, B. Abbey, M. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, G. Peele, and K. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A80(6), 063823 (2009). [CrossRef]
- G. Williams, H. Quiney, B. Dahl, C. Tran, A. G. Peele, K. A. Nugent, M. D. De Jonge, and D. Paterson, “Curved beam coherent diffractive imaging,” Thin Solid Films515(14), 5553–5556 (2007). [CrossRef]
- T. Harada, M. Nakasuji, T. Kimura, T. Watanabe, H. Kinoshita, and Y. Nagata, “Imaging of extreme-ultraviolet mask patterns using coherent extreme-ultraviolet scatterometry microscope based on coherent diffraction imaging,” J. Vac. Sci. Technol. B29(6), 06F503 (2011). [CrossRef]
- T. Harada, J. Kishimoto, T. Watanabe, H. Kinoshita, and D. G. Lee, “Mask observation results using a coherent extreme ultraviolet scattering microscope at NewSUBARU,” J. Vac. Sci. Technol. B27(6), 3203 (2009). [CrossRef]
- D. F. Gardner, B. Zhang, M. D. Seaberg, L. S. Martin, D. E. Adams, F. Salmassi, E. Gullikson, H. Kapteyn, and M. Murnane, “High numerical aperture reflection mode coherent diffraction microscopy using off-axis apertured illumination,” Opt. Express20(17), 19050–19059 (2012). [CrossRef] [PubMed]
- M. Dierolf, O. Bunk, S. Kynde, P. Thibault, I. Johnson, A. Menzel, K. Jefimovs, C. David, O. Marti, and F. Pfeiffer, “Ptychography & lensless x ray imaging,” Europhys. News39(1), 22–24 (2008). [CrossRef]
- P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy109(4), 338–343 (2009). [CrossRef] [PubMed]
- D. Kane, “Principal components generalized projections : a review [ Invited ],” J. Opt. Soc. Am. B25(6), A120–A130 (2008). [CrossRef]
- R. Trebino and D. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am.10(5), 1101 (1993). [CrossRef]
- H. Stark, Image Recovery : Theory and Application (Academic Press, 1986).
- R. Trebino, Frequency-resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic, 2000).
- K. DeLong, R. Trebino, J. Hunter, and W. White, “Frequency-resolved optical gating with the use of second-harmonic generation,” J. Opt. Soc. Am. B11(11), 2206–2215 (1994). [CrossRef]
- D. Kane, “Principal components generalized projections: a review,” J. Opt. Soc. Am. B25(6), A120–A132 (2008). [CrossRef]
- K. W. DeLong, R. Trebino, and W. E. White, “Simultaneous recovery of two ultrashort laser pulses from a single spectrogram,” J. Opt. Soc. Am. B12(12), 2463 (1995). [CrossRef]
- D. J. Kane, G. Rodriguez, A. Taylor, and T. S. Clement, “Simultaneous measurement of two ultrashort laser pulses from a single spectrogram in a single shot,” J. Opt. Soc. Am. B14(4), 935–943 (1997). [CrossRef]
- B. C. McCallum and J. M. Rodenburg, “Simultaneous reconstruction of object and aperture functions from multiple far-field intensity measurements,” J. Opt. Soc. Am.10(2), 231 (1993). [CrossRef]

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