2,131
Views
1
CrossRef citations to date
0
Altmetric
Reviews

Heterodyne Near Field Speckles: from laser light to X-rays

ORCID Icon, ORCID Icon & ORCID Icon

References

  • Dainty JC. Laser speckle and related phenomena. New York: Springer-Verlag Berlin Heidelberg; 1975.
  • Goodman JW. Speckle Phenomena in Optics. Englewood: Ben Roberts & Company; 2007.
  • Newton I. Optiks. New York: reprinted by Dover Press; 1952.
  • Exner K, Sitzungsber. Kaiserl. Akad. Wiss. 1877;76:522.
  • Exner K, Wiedemanns. Ann. Physik. 1880;9:239.
  • Von Laue M, Sitzungsber. Akad. Wiss. 44 (1914), p. 1144.
  • See, for example, La Mort de Casagemas by Picasso, Pablo (oil on wood, 1901, Musée Picasso, Paris), Il Sole by Pellizza da Volpedo, Giuseppe (oil on canvas, 1904, Galleria Nazionale d’Arte Moderna, Rome), Sole Nascente sul Fiume by Olivero, Matteo (oil on canvas, 1907-1910), Lampada ad Arco by Balla, Giacomo (oil on canvas, 1909-1911, Museum of Modern Art, New York).
  • Interestingly, the eye of the observer itself provides the random medium in these cases. To support this statement, one can perform some convincing experiments. By looking at sunlight through a dense foliage, elongated white light speckles can be observed. Taking pictures of such speckles with a reflex camera is likely to fail, unless e.g. moisture is breathed on the front lens to make its surface irregular.
  • Born M, Wolf E. Priciples of Optics. Oxford: Pergamon Press; 1970.
  • Mandel L, Wolf E. Optical coherence and quantum optics. Cambridge: Cambridge University Press; 1995.
  • Goodman JW. Statistical Optics. New York: John Wiley & Sons, Inc; 2000.
  • De Haas WJ, Koninklighe. Acad. van Wetenschager. 1918;20:1278.
  • Parry G, Some effects of surface roughness on the appearance of speckle in polychromatic light. Opt. Commun. 1974;12:75–46.
  • Brogioli D, Vailati A, Giglio M. Heterodyne near-field scattering. Appl. Phys. Lett. 2002;81:4109–4111.
  • Giglio M, Brogioli D, Potenza MAC, et al. Near field scattering. Phys Chem Chem Phys. 2004;6:1547–1550.
  • Ferri F, Magatti D, Pescini D, et al., Heterodyne near-field scattering: A technique for complex fluids. Phys. Rev. E. 2004;70:041404.
  • Brogioli D, Vailati A, Giglio M. A schlieren method for ultra-low–angle light scattering measurements. Europhys. Lett. 2003;63:220–225.
  • Potenza MAC, Magatti D, Pescini D, et al., Proc. of SPIE Bellingham, WA.2004;5249: 461–470.
  • Potenza MAC, Pescini D, Magatti D, et al. A new particle sizing technique based on near field scattering. Nuclear Physics B (Proc. Suppl.). 2006;150: 334–338.
  • Magatti D, Alaimo MD, Potenza MAC, et al. Dynamic heterodyne near field scattering. Appl Phys Lett. 2008;92:241101.
  • Mazzoni S, Potenza MAC, Alaimo MD, et al. SODI-COLLOID: a combination of static and dynamic light scattering on board the International Space Station. Rev Sci Instrum. 2013;84:043704.
  • Potenza MAC, Manca A, Veen SJ, et al., EPL. 2014;106:68005.
  • Escobedo-Sanchez MA, Rojas-Ochoa LF, Laurati M, et al. Investigation of moderately turbid suspensions by heterodyne near field scattering. Soft Matter. 2017;13:5961–5969.
  • Cremonesi L, Siano M, Paroli B, et al. Near field scattering for samples under forced flow. Rev Sci Instrum. 2020;91:075108.
  • Alaimo MD, Magatti D, Ferri F, et al. Heterodyne speckle velocimetry. Appl Phys Lett. 2006;88:191101.
  • Potenza MAC, Alaimo MD, Pescini D, et al. A new technique for fluid velocimetry based on near field scattering. Opt. Laser Eng. 2006;44:722–731.
  • Alaimo MD, Potenza MAC, Magatti D, et al. Heterodyne speckle velocimetry of Poiseuille flow. J Appl Phys. 2007;102:073113.
  • Siano M, Paroli B, Chiadroni E, et al. Measurement of power spectral density of broad-spectrum visible light with heterodyne near field scattering and its scalability to betatron radiation. Opt Express. 2015;23:32888–32896.
  • Siano M, Paroli B, Chiadroni E, et al., Note: Nanosecond LED-based source for optical modeling of scintillators illuminated by partially coherent X-ray radiation. Rev. Sci. Instrum. 87 (2016), p.126104.
  • Cerbino R, Peverini L, Potenza MAC, et al. X-ray-scattering information obtained from near-field speckle. Nat. Phys. 2008;4:238–243.
  • Lu X, Mochrie SGJ, Narayanan S, et al. X-ray near-field speckle: implementation and critical analysis. J. Synchrotron Rad. 2011;18:823–834.
  • Alaimo MD, Potenza MAC, Manfredda M, et al. Probing the transverse coherence of an undulator X-ray beam using brownian particles. Phys Rev Lett. 2009;103:194805.
  • Alaimo MD, Anania MP, Artioli M, et al. Mapping the transverse coherence of the self amplified spontaneous emission of a free-electron laser with the heterodyne speckle method. Opt Express. 2014;22:30013–30023.
  • Manfredda M, Alaimo MD, Giglio M, et al. Probing transverse coherence with the heterodyne speckle approach: overview and perspectives. Phys Procedia. 2015;62:59–64.
  • Kashyap Y, Wang H, Sawhney K, Phys. Rev. A. 2015;92:033842.
  • Siano M, Paroli B, Manfredda M, et al., Proc. of SPIE. Prague, Czech Republic, 2015.
  • Siano M, Paroli B, Potenza MAC, et al., Proc. of IBIC. IBIC, Barcelona, Spain, 2016.
  • Siano M, Paroli B, Potenza MAC, et al. Characterizing temporal coherence of visible synchrotron radiation with heterodyne near field speckles. Phys. Rev. Accel. Beams. 2017;20: 110702.
  • Mazzoni S, Roncarolo F, Trad G, et al., Proc. of IBIC. Shanghai, China, 2018.
  • Siano M, Paroli B, Potenza MAC, et al., Proc. of IBIC. Malmo, Sweden, 2019.
  • Berujon S, Ziegler E, Cerbino R, et al. Two-dimensional X-ray beam phase sensing. Phys Rev Lett. 2012;108:158102.
  • Berujon S, Ziegler E, Cloetens P. X-ray pulse wavefront metrology using speckle tracking. J. Synchrotron Rad. 2015;22:886–894.
  • Wang H, Kashyap Y, Sawhney K. Speckle based X-ray wavefront sensing with nanoradian angular sensitivity. Opt Express. 2015;23:23310–23317.
  • Seaberg M, Cojocaru R, Berujon S, et al. Wavefront sensing at X-ray free-electron lasers. J. Synchrotron Rad. 2019;26:1115–1126.
  • Sawhney K, Alcock S, Sutter J, et al. Characterisation of a novel super-polished bimorph mirror. J. Phys. Conf. Ser. 2013;425:052026.
  • Berujon S, Wang H, Sawhney KJS. At-wavelength metrology using the X-ray speckle tracking technique: case study of a X-ray compound refractive lens. J. Phys. Conf. Ser. 2013;425:052020.
  • Berujon S, Wang H, Alcock S, et al. At-wavelength metrology of hard X-ray mirror using near field speckle. Opt Express. 2014;22:6438–6446.
  • Wang H, Kashyap Y, Laundy D, et al. J. Synchrotron Rad. 2015;22:925–929.
  • Wang H, Sutter J, Sawhney K. Advanced in situ metrology for x-ray beam shaping with super precision. Opt Express. 2015;23:1605–1614.
  • Kashyap Y, Wang H, Sawhney K. J. Synchrotron Rad. 2016;23:1131–1136.
  • Kashyap Y, Wang H, Sawhney K. Speckle-based at-wavelength metrology of X-ray mirrors with super accuracy. Rev. Sci. Instrum. 2016;87:052001.
  • Wang H, Zhou T, Kashyap Y, et al., Speckle-based at-wavelength metrology of X-ray optics at Diamond Light Source. Proc. of SPIE. 2017;10388:103880I.
  • Zdora M-C, Zanette I, Zhou T, et al. At-wavelength optics characterisation via X-ray speckle- and grating-based unified modulated pattern analysis. Opt Express. 2018;26:4989–5004.
  • Berujon S, Cojocaru R, Piault P, et al. X-ray optics and beam characterization using random modulation: theory. J. Synchrotron Rad. 2020;27:284–292.
  • Berujon S, Cojocaru R, Piault P, et al. X-ray optics and beam characterization using random modulation: experiments. J. Synchrotron Rad. 2020;27:293–304.
  • Morgan KS, Paganin DM, Siu KKW. X-ray phase imaging with a paper analyzer. Appl Phys Lett. 2012;100:124102.
  • Berujon S, Wang H, Sawhney K, Phys. Rev. A. 2012;86:063813.
  • Berujon S, Wang H, Pape I, et al. X-ray phase microscopy using the speckle tracking technique. Appl Phys Lett. 2013;102:154105.
  • Wang H, Berujon S, Pape I, et al. X-ray microscopy using two phase contrast imaging techniques: two dimensional grating interferometry and speckle tracking. J Phys Conf Ser. 2013;463:012042.
  • Zanette I, Zhou T, Burvall A, et al. Speckle-Based X-ray phase-contrast and dark-field imaging with a laboratory source. Phys Rev Lett. 2014;112:253903.
  • Aloision IA, Paganin DM, Wright CA, et al. Exploring experimental parameter choice for rapid speckle-tracking phase-contrast X-ray imaging with a paper analyzer. J. Synchrotron Rad. 2015;22:1279–1288.
  • Zhou T, Zanette I, Zdora M-C, et al. Speckle-based x-ray phase-contrast imaging with a laboratory source and the scanning technique. Opt. Lett. 2015;40:2822–2825.
  • Berujon S, Ziegler E, Phys. Rev A. 2015;92:013837.
  • Wang H, Kashyap Y, Sawhney K. Hard-X-ray directional dark-field imaging using the speckle scanning technique. Phys Rev Lett. 2015;114:103901.
  • Wang H, Berujon S, Herzen J, et al. X-ray phase contrast tomography by tracking near field speckle. Sci Rep. 2015;5:8762.
  • Zanette I, Zdora M-C, Zhou T, et al., PNAS 2015;112:12569–12573.
  • Zdora M-C, Thibault P, Pfeiffer F, et al. Simulations of x-ray speckle-based dark-field and phase-contrast imaging with a polychromatic beam. J Appl Phys. 2015;118:113105.
  • Kashyap Y, Wang H, Sawhney K. Experimental comparison between speckle and grating-based imaging technique using synchrotron radiation X-rays. Opt Express. 2016;24:18664–18673.
  • Zdora M-C, Thibault P, Herzen J, et al., AIP Conf. Proc. 2016;1696:020016.
  • Wang H, Kashyap Y, Sawhney K. Quantitative X-ray dark-field and phase tomography using single directional speckle scanning technique. Appl Phys Lett. 2016;108:124102.
  • Berujon S, Ziegler E. X-ray multimodal tomography using speckle-vector tracking. Phys. Rev. Appl. 2016;5: 044014.
  • Wang H, Kashyap Y, Sawhney K. From synchrotron radiation to lab source: advanced speckle-based X-ray imaging using abrasive paper. Sci Rep. 2016;6:20476.
  • Wang F, Wang Y, Wei G, et al. Speckle-tracking X-ray phase-contrast imaging for samples with obvious edge-enhancement effect. Appl Phys Lett. 2017;111:174101.
  • Zdora M, Thibault P, Rau C, et al. Characterisation of speckle-based X-ray phase-contrast imaging. J. Phys. Conf. Ser. 2017;849:012024.
  • Romell J, Zhou T, Zdora M, et al. Comparison of laboratory grating-based and speckle-tracking x-ray phase-contrast imaging. J Phys Conf Ser. 2017;849:012035.
  • Berujon S, Ziegler E, Phys. Rev. A. 2017;95:063822.
  • Vittoria FA, Endrizzi M, Olivo A. Retrieving the ultrasmall-angle X-ray scattering signal with polychromatic radiation in speckle-tracking and beam-tracking phase-contrast Imaging. Phys. Rev. Appl. 2017;7: 034024.
  • Zdora M-C, Thibault P, Zhou T, et al., Phys. Rev. Lett. 2017;118:203903.
  • Zdora M-C. State of the Art of X-ray speckle-based phase-contrast and dark-field imaging. J Imaging. 2018;4:60.
  • Paganin DM, Labriet H, Brun E, et al., Phys. Rev. A. 2018;98:053813.
  • Zdora M-C, Zanette I, Walker T, et al. X-ray phase imaging with the unified modulated pattern analysis of near-field speckles at a laboratory source. Appl. Opt. 2020;59:2270–2275.
  • Pavlov KM, Paganin DM, Rouge-Labriet H, et al.. Single-shot X-Ray speckle-based imaging of a single-material object. Phys. Rev. Appl. 13:2020; 054023.
  • Tian N, Jiang H, Li A, et al. Influence of diffuser grain size on the speckle tracking technique. J. Synchrotron Rad. 2020;27:146–157.
  • Goodman JW. Introduction to Fourier Optics. Englewood: Ben Roberts & Company; 2007.
  • Paganin DM. Coherent X-ray Optics. Oxford: Oxford University Press; 2006.
  • By virtue of the Huygens-Fresnel principle, et(x, z)= ∫e0(x’) h(x – x’, z) dx’, where h(x,z) = exp(ikz) exp[ik|x|2/(2z)] in paraxial conditions. The convolution kernel h becomes highly oscillatory for |x|>(λz)1/2, thus making the convolution integral vanish. If D≫(λz)1/2, h acts as a Dirac δ-distribution and et(x, z) = e0(x)exp(ikz).
  • Saleh BEA, Teich MC. Fundamentals of Photonics. New York: John Wiley & Sons, Inc; 1991.
  • At variance, the superposition of two laterally-displaced spherical waves as in the Young double-pinhole experiment generates parallel fringes with a fixed spacing. It is equivalent to the interference between two tilted plane waves.
  • Gabor D. A new microscopic principle. Nature. 1948;161:777.
  • Gabor D, Proc. Roy. Soc. London. 1949;197:454.
  • Gabor D, Microscopy by Reconstructed Wave Fronts: II. Proc. Phys. Soc. 1951;64:449.
  • Williams DB, Carter CB. Transmission electron microscopy. New York: Plenum Press; 1996.
  • Kim MK. Principles and techniques of digital holographic microscopy. SPIE Review. 2010;1:018005.
  • Vu X, Hong J, Liu C, et al. Review of digital holographic microscopy for three-dimensional profiling and tracking. Opt Eng. 2014;53:112306.
  • Tahara T, Quan X, Otami R, et al. Digital holography and its multidimensional imaging applications: a review. Microscopy. 2018;67:55–67.
  • Shao Y, Lu X, Konijnenberg S, et al. Spatial coherence measurement and partially coherent diffractive imaging using self-referencing holography. Opt Express. 2018;26:4479–4490.
  • McNulty I, Nucl. Instrum. Methods. Phys. Res. A. 347 (1994), p.170.
  • Eisebitt S, Luning J, Schlotter WF, et al. Lensless imaging of magnetic nanostructures by X-ray spectro-holography. Nature. 2004;432:885–888.
  • Momose A. Recent Advances in X-ray Phase Imaging. Jpn. J. Appl. Phys. 2005;44:6355–6367.
  • Marchesini S, Boutet S, Sakdinawat AE, et al. Massively parallel X-ray holography. Nat Photonics. 2008;2:560–563.
  • Chapman HN, Nugent KA. Coherent lensless X-ray imaging. Nat Photonics. 2010;4:833–839.
  • Gorniak T, Heine R, Mancuso AP, et al. X-ray holographic microscopy with zone plates applied to biological samples in the water window using 3rd harmonic radiation from the free-electron laser FLASH. Opt Express. 2011;19:11059–11070.
  • Martin AV, D’Alfonso AJ, Wang F, et al. X-ray holography with a customizable reference. Nat Commun. 2014;5:4661.
  • Gorkhover T, Ulmer A, Ferguson K, et al. Femtosecond X-ray Fourier holography imaging of free-flying nanoparticles. Nat Photonics. 2018;12:150–153.
  • Medecki H, Tejnil E, Goldberg KA, et al. Phase-shifting point diffraction interferometer. Opt. Lett. 1996;21:1526–1528.
  • Momose A. Phase-sensitive imaging and phase tomography using X-ray interferometers. Opt Express. 2003;11:2303–2314.
  • Leitenberger W, Wendrock H, Bischoff L, et al. Pinhole interferometry with coherent hard X-rays. J. Synchrotron Rad. 2004;11:190–197.
  • Homer P, Rus B, Polan J, Measurements of x-ray laser wavefront profile using PDI technique. Proc. of SPIE. 2007;6702:670211.
  • Malyshev IV, Chkhalo NI, Akhsahalian AD, et al. Surface shape measurement of mirrors in the form of rotation figures by using point diffraction interferometer. J. Mod. Opt. 2017;64:413–421.
  • Takeuchi S, Kakuchi O, Yamazoe K, et al., Visible light point-diffraction interferometer for testing of EUVL optics. Proc. of SPIE 2006;6151:61510E.
  • Wang D, Wang F, Zou H, et al. Analysis of diffraction wavefront in visible-light point-diffraction interferometer. Appl. Opt. 2013;52:7602–7608.
  • Gao F, O’Donoghue T, Wang W. Full-field analysis of wavefront errors in point diffraction interferometer with misaligned Gaussian incidence. Appl. Opt. 2020;59:210–216.
  • Giglio M, Carpineti M, Vailati A. pace Intensity Correlations in the Near Field of the Scattered Light: A Direct Measurement of the Density Correlation Function g(r). Phys Rev Lett. 2000;85:1416–1419.
  • Giglio M, Carpineti M, Vailati A, et al. Near-field intensity correlations of scattered light. Appl. Opt. 2001;40:4036–4040.
  • Trainoff SP, Cannell DS. Physical optics treatment of the shadowgraph. Phys. Fluids. 2002;14: 1340–1363.
  • Cloetens P, Ludwig W, Baruchel J, et al. Holotomography: quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays. Appl. Phys. Lett. 1999;75:2912–2914.
  • Zabler S, Cloetens P, Guigay J-P, et al. Optimization of phase contrast imaging using hard x rays. Rev Sci Instrum. 2005;76:073705.
  • Salditt T, Giewekemeyer K, Fuhse C, et al. Projection phase contrast microscopy with a hard x-ray nanofocused beam: defocus and contrast transfer. Phys Rev B. 2009;79:184112.
  • Van De Hulst HC. Light scattering by small particles. New York: Dover Publications, Inc; 1981.
  • Potenza MAC, Sabareesh KPV, Carpineti M, et al. How to measure the optical thickness of scattering particles from the phase delay of scattered waves: application to turbid samples. Phys Rev Lett. 2010;105:193901.
  • Li WB, Segrè PN, Gammon RW, et al., Physica A 204 (1994), p.399.
  • Berne BJ, Pecora R. Dynamic light scattering. New York: Dover Publications, Inc; 2000.
  • Guo H, Narayanan T, Sztuchi M, et al. Reversible phase transition of colloids in a binary liquid solvent. Phys Rev Lett. 2008;100:188303.
  • Bonn D, Otwinowski J, Sacanna S, et al., Direct Observation of Colloidal Aggregation by Critical Casimir Forces. Phys. Rev. Lett. 2009;103:156101.
  • Veen SJ, Antoniuk O, Weber B, et al. Colloidal aggregation in microgravity by critical casimir forces. Phys. Rev. Lett. 2012;109:248302.
  • Cerbino R, Vailati A. Near-field scattering techniques: novel instrumentation and results from time and spatially resolved investigations of soft matter systems. Curr. Opin. Colloid Interface Sci. 2009;14:416–425.
  • In the far zone, the speckles do not move upon particle motions, but simply fluctuate stochastically in time. This is due to the fact that each speckle in the far field is the result of contributions from the entire illuminated sample, and therefore no correspondence between speckles and particles is possible.
  • Buzzaccaro S, Secchi E, Piazza R. Ghost particle velocimetry: accurate 3D flow visualization using standard lab equipment. Phys Rev Lett. 2013;111:048101.
  • Secchi E, Rusconi R, Buzzaccaro S, et al., Intermittent turbulence in flowing bacterial suspensions. J. R. Soc. Interface. 2016;13:20160175.
  • Eberhard U, Seybold HJ, Secchi E, et al. Mapping the local viscosity of non-Newtonian fluids flowing through disordered porous structures. Sci. Rep. 2020;10:11733.
  • Kuiper GP, Middlehurst BM. Telescopes. Chicago: The University of Chicago Press; 1960.
  • Keller G, Protheroe WM, Barnhart PE, et al., Reprint No. 39. Perkins Observatory, Delaware, 1956.
  • Mikesell AH, Hoag AA, Hall JS. The scintillation of starlight*. J. Opt. Soc. America. 1951;41: 689.
  • Protheroe WM, Contr. Perkins Obs. No. II-4, Delaware, 1955.
  • Gifford F, Mikesell AH, Weather. 19538:195.
  • Mikesell AH, Pub. U. S. Naval Obs. 195517:139.
  • Barnhart PE, Keller G, Mitchell WE, Report TR59-291, Air Force Cambridge Research Center: Bedford, Mass, 1959.
  • Spence JCH. Experimental high-resolution electron microscopy. Oxford: Oxford University Press; 1988.
  • Scherzer O. The theoretical resolution limit of the electron microscope. J. Appl. Phys. 1949;20:20–29.
  • Hashimoto H, Endoh H. Electron Diffraction 1927-1977. Bristol and London: The Institute of Physics; 1978.
  • Krivanek OL. A method for determining the coefficient of spherical aberration from a single electron micrograph. Optik. 1976;45:97.
  • Cerbino R, Peverini L, Potenza MAC, et al. X-ray-scattering information obtained from near-field speckle. Nat. Phys. 2008;4:238–243. [Suppl. Mat].
  • Dubois F, Joannes L, Legros J-C. Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence. Appl. Opt. 1999;38:7085–7094.
  • Dubois F, Minetti C, Monnom O, et al. Pattern recognition with a digital holographic microscope working in partially coherent illumination. Appl. Opt. 2002;41:4108–4119.
  • Dubois F, Novella Requena M-L, Minetti C, et al. Partial spatial coherence effects in digital holographic microscopy with a laser source. Appl. Opt. 2004;43:1131–1139.
  • Dubois F, Callens N, Yourassowsky C, et al. Digital holographic microscopy with reduced spatial coherence for three-dimensional particle flow analysis. Appl. Opt. 2006;45:864–871.
  • Minetti C, Callens N, Coupier G, et al. Fast measurements of concentration profiles inside deformable objects in microflows with reduced spatial coherence digital holography. Appl. Opt. 2008;47:5305–5314.
  • Dubois F, Yourassowsky C, Callens N, et al. Applications of digital holographic microscopes with partially spatial coherence sources. J. Phys. Conf. Ser. 2008;139:012027.
  • Dubois F, Yourassowsky C, Off-axis multispectral digital holographic microscope with partially coherent illumination. Proc. of SPIE. 20128429:84291E.
  • Minetti C, Podgorski T, Coupuier G, et al., Dynamics of vesicle suspension in shear flow between walls by digital holographic microscopy with a spatially reduced coherent source. Proc. of SPIE. 20128429 :84291I.
  • Dohet-Eraly J, Yourassowsky C, El Mallahi A, et al. Quantitative assessment of noise reduction with partial spatial coherence illumination in digital holographic microscopy. Opt. Lett. 2016;41:111–114.
  • Dohet-Eraly J, Yourassowsky C, El Mallahi A, et al., Partial spatial coherence illumination in digital holographic microscopy: quantitative analysis of the resulting noise reduction. Proc. of SPIE. 2016;9890:989004.
  • Manfredda M, Siano M, Paroli B, et al., in preparation.
  • Pfeiffer F, Bunk O, Schulze-Briese C, et al. Shearing interferometer for quantifying the coherence of hard X-ray beams. Phys Rev Lett. 2005;94:164801.
  • Weitkamp T, Diaz A, David C, et al. X-ray phase imaging with a grating interferometer. Opt Express. 2005;12:6296–6304.
  • Pfeiffer F, Bech M, Bunk O, et al. Hard-X-ray dark-field imaging using a grating interferometer. Nat Mater. 2008;7:134–137.
  • Cloetens P, Guigay JP, De Martino C, et al. Fractional Talbot imaging of phase gratings with hard x rays. Opt. Lett. 1997;22:1059–1061.
  • Momose A, Kawamoto S, Koyama I, et al. Demonstration of X-Ray Talbot Interferometry. Jpn. J. Appl. Phys. 2003;42:L866–L868.
  • Guigay J-P, Zabler S, Cloetens P, et al. The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays. J. Synchrotron Rad. 2004;11:476–482.
  • Engelhardt M, Kottler C, Bunk O, et al. The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources. J. Microsc. 2008;232:145–157.
  • Momose A, Yashiro W, Maikusa H, et al. High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron radiation. Opt Express. 2009;17:12540–12545.
  • Yashiro W, Terui Y, Kawabata K, et al. On the origin of visibility contrast in x-ray Talbot interferometry. Opt Express. 2010;18:16890–16901.
  • Salditt T, Kalbfleisch S, Osterhoff M, et al. Partially coherent nano-focused x-ray radiation characterized by Talbot interferometry. Opt Express. 2011;19:9656–9675.
  • Nugent KA. Coherent methods in the X-ray sciences. Adv Phys. 2010;59:1–99.
  • Cipelletti L, Carpineti M, Giglio M. Fractal morphology, spatial order, and pore structure in microporous membrane filters. Langmuir. 1996;12:6446–6451.
  • Manfredda M, Probing synchrotron radiation coherence: the heterodyne speckle approach, Ph.D. thesis, Milan, 2012, https://air.unimi.it/handle/2434/172631
  • Gutt C, Wochner P, Fisher B, et al. Single shot spatial and temporal coherence properties of the SLAC linac coherent light source in the hard X-ray regime. Phys Rev Lett. 2012;108:024801.
  • Lee S, Roseker W, Gutt C, et al. Single shot speckle and coherence analysis of the hard X-ray free electron laser LCLS. Opt Express. 2013;21:24647–24664.
  • Lehmkuhler F, Gutt C, Fischer B, et al. Single shot coherence properties of the free-electron laser SACLA in the hard X-ray Regime. Sci Rep. 2014;4:5234.
  • Geloni G, Saldin E, Schneidmiller E, et al. Transverse coherence properties of X-ray beams in third-generation synchrotron radiation sources. Nucl Instrum Methods Phys Res A. 2008;588:463–493.
  • Paroli B, Potenza MAC, Advances in Physics. X 2(2017), p.978–1004.
  • Geloni G, Serkez S, Khubbutdinov R, et al. Effects of energy spread on brightness and coherence of undulator sources. J. Synchrotron Rad. 2018;25:1335–1345.
  • Thomas C, Dudin P, Hoesch M. Coherence of a near diffraction limited undulator synchrotron radiation source. Opt. Commun. 2016;359:171–176.
  • Paroli B, Chiadroni E, Ferrario M, et al., Asymmetric lateral coherence of betatron radiation emitted in laser-driven light sources. EPL 2015;111::44003.
  • Paroli B, Chiadroni E, Ferrario M, et al. A systematic study of the asymmetric lateral coherence of radiation emitted by ultra-relativistic particles in laser-driven accelerators. Nucl Instrum Methods Phys Res A. 2016;839:1–5.
  • Paroli B, Bravin E, Mazzoni S, et al., A modified two-slit interferometer for characterizing the asymmetric lateral coherence of undulator radiation. EPL 2016;115:14004.
  • Paroli B, Siano M, Potenza MAC. A symmetric lateral coherence allows precise wavefront characterization. EPL. 2018;122:44001.
  • Paroli B, Cirella A, Debrot I, et al. Asymmetric lateral coherence of OAM radiation reveals topological charge and local curvature. J Opt. 2018;20:075605.
  • Paroli B, Siano M, Potenza MAC. The local intrinsic curvature of wavefronts allows to detect optical vortices. Opt Express. 2019;27:17550–17560.
  • Paroli B, Siano M, Teruzzi L, et al. Single-shot measurement of phase and topological properties of orbital angular momentum radiation through asymmetric lateral coherence. Phys. Rev. Accel. Beams. 2019;22: 032901.
  • Paroli B, Siano M, Potenza M. Measuring the topological charge of orbital angular momentum radiation in single-shot by means of the wavefront intrinsic curvature. Appl. Opt. 2020;59:5258–5264.
  • Paroli B, Siano M, Potenza MAC. A composite beam of radiation with orbital angular momentum allows effective local, single-shot measurement of topological charge. Opt Commun. 2020;459:125049.
  • Berto P, Rigneault H, Guillon M. Wavefront sensing with a thin diffuser. Opt. Lett. 2017;42:5117–5120.
  • Gatti A, Magatti D, Ferri F .Three-dimensional coherence of light speckles: theory. Phys Rev. 2008;78:063806. doi:https://doi.org/10.1103/PhysRevA.78.063806.
  • Magatti D, Gatti A, Ferri F .Three-dimensional coherence of light speckles: experiment. Phys Rev.2009;79:053831. doi:https://doi.org/10.1103/PhysRevA.79.053831.