Measurement of power spectral density of broad-spectrum visible light with heterodyne near field scattering and its scalability to betatron radiation

M. Siano; B. Paroli; E. Chiadroni; M. Ferrario; M. A. C. Potenza

doi:10.1364/OE.23.032888

Measurement of power spectral density of broad-spectrum visible light with heterodyne near field scattering and its scalability to betatron radiation

M. Siano, B. Paroli, E. Chiadroni, M. Ferrario, and M. A. C. Potenza

Optics Express
Vol. 23,
Issue 26,
pp. 32888-32896
(2015)
•https://doi.org/10.1364/OE.23.032888

Get Citation
Copy Citation Text
M. Siano, B. Paroli, E. Chiadroni, M. Ferrario, and M. A. C. Potenza, "Measurement of power spectral density of broad-spectrum visible light with heterodyne near field scattering and its scalability to betatron radiation," Opt. Express 23, 32888-32896 (2015)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Get PDF (1173 KB)
Set citation alerts
Save article

Related Topics
Table of Contents Category
- Coherence and Statistical Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Coherence (030.1640)
- Speckle (030.6140)

About this Article
History
- Original Manuscript: October 28, 2015
- Revised Manuscript: November 29, 2015
- Manuscript Accepted: November 29, 2015
- Published: December 14, 2015

Accessible

Open Access

Abstract

We exploit the speckle field generated by scattering from a colloidal suspension to access both spatial and temporal coherence properties of broadband radiation. By applying the Wiener-Khinchine theorem to the retrieved temporal coherence function, information about the emission spectrum of the source is obtained in good agreement with the results of a grating spectrometer. Experiments have been performed with visible light. We prove more generally that our approach can be considered as a tool for modeling a variety of cases. Here we discuss how to apply such diagnostics to broad-spectrum betatron radiation produced in the laser-driven wakefield accelerator under development at SPARC LAB facility in Frascati.

Full Article | PDF Article

OSA Recommended Articles

Analogical optical modeling of the asymmetric lateral coherence of betatron radiation

B. Paroli, E. Chiadroni, M. Ferrario, and M.A.C. Potenza
Opt. Express 23(23) 29912-29920 (2015)

Mapping the transverse coherence of the self amplified spontaneous emission of a free-electron laser with the heterodyne speckle method

Matteo D. Alaimo, Maria Pia Anania, Marcello Artioli, Alberto Bacci, Marco Bellaveglia, Franco Ciocci, Enrica Chiadroni, Alessandro Cianchi, Giuseppe Dattoli, Giampierro Di Pirro, Massimo Ferrario, Giancarlo Gatti, Luca Giannessi, Michele Manfredda, Roberta Martucci, Andrea Mostacci, Bruno Paroli, Alberto Petralia, Vittoria Petrillo, Riccardo Pompili, Marco A.C. Potenza, Marcello Quattormini, Julietta Rau, Daniele Redoglio, Andrea R. Rossi, Luca Serafini, Vincenzo Surrenti, Amalia Torre, Cristina Vaccarezza, and Fabio Villa
Opt. Express 22(24) 30013-30023 (2014)

Nano-particle characterization by using Exposure Time Dependent Spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera

Doriano Brogioli, Fabrizio Croccolo, Valeria Cassina, Domenico Salerno, and Francesco Mantegazza
Opt. Express 16(25) 20272-20282 (2008)

References

View by:
Article Order
|
Year
|
Author
|
Publication

H. Wiedemann, Synchrotron Radiation (Springer-Verlag, 2003).
[Crossref]
E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, “The physics of free electron laser. An introduction,” Phys. Rep. 260, 187–327 (1995).
[Crossref]
S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]
V. Kohn, I. Snigireva, and A. Snigireva, “Measurements of transverse coherence length of hard X-rays from interference fringes,” Phys. Rev. Lett. 85(13), 2745–2748 (2000).
[Crossref]
T. Ditmire, E. T. Gumbrell, R.A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]
D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett 81(22), 4109 (2002).
[Crossref]
J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1975).
[Crossref]
M. D. Alaimo, M. P. Anania, M. Artioli, A. Bacci, M. Bellaveglia, F. Ciocci, E. Chiadroni, A. Cianchi, G. Dattoli, G. Di Pirro, M. Ferrario, G. Gatti, L. Giannessi, M. Manfredda, R. Martucci, A. Mostacci, B. Paroli, A. Petralia, V. Petrillo, R. Pompili, M. A. C. Potenza, M. Quattormini, J. Rau, D. Redoglio, A. R. Rossi, L. Serafini, V. Surrenti, A. Torre, C. Vaccarezza, and F. Villa, “Mapping the transverse coherence of the self amplified spontaneous emission of a free-electron laser with the heterodyne speckle method,” Opt. Express 22(24), 30013–30023 (2014).
[Crossref]
M. D. Alaimo, M. A. C. Potenza, M. Manfredda, G. Geloni, M. Sztucki, T. Narayanan, and M. Giglio, “Probing the transverse coherence of an undulator X-ray beam using brownian particles,” Phys. Rev. Lett. 103, 194805 (2009).
[Crossref]
J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).
R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]
M. Ferrario, D. Alesini, M. Anania, A. Bacci, M. Bellaveglia, O. Bogdanov, R. Boni, M. Castellano, E. Chiadroni, A. Cianchi, S. B. Dabagov, C. De Martinis, D. Di Giovenale, G. Di Pirro, U. Dosselli, A. Drago, A. Esposito, R. Faccini, A. Gallo, M. Gambaccini, C. Gatti, G. Gatti, A. Ghigo, D. Giulietti, A. Ligidov, P. Londrillo, S. Lupi, A. Mostacci, E. Pace, L. Palumbo, V. Petrillo, R. Pompili, A. R. Rossi, L. Serafini, B. Spataro, P. Tomassini, G. Turchetti, C. Vaccarezza, F. Villa, G. Dattoli, E. Di Palma, and L. Giannessi, “SPARC LAB present and future,” Nucl. Instr. Meth. Phys. Res. B 309, 183–188 (2013).
[Crossref]
B. Paroli, E. Chiadroni, M. Ferrario, A. Mostacci, V. Petrillo, M. A. C. Potenza, A. R. Rossi, and L. Serafini, “Coherence properties and diagnostics of betatron radiation emitted by an externally-injected electron beam propagating in a plasma channel,” Nucl. Instr. Meth. Phys. Res. B 355, 217–220, (2015).
[Crossref]
B. Paroli, E. Chiadroni, M. Ferrario, V. Petrillo, M. A. C. Potenza, A. R. Rossi, L. Serafini, and V. Shpakov, “Asymmetric lateral coherence of betatron radiation emitted in laser-driven light sources,” Europhys. Lett. 111, 44003 (2015).
[Crossref]
B. Paroli, E. Chiadroni, M. Ferrario, and M. A. C. Potenza, “Analogical optical modeling of the asymmetric lateral coherence of betatron radiation,” Opt. Express 23(23), 29912–29920 (2015).
[Crossref]
B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, and M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[Crossref]
F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[Crossref]
M. A. C. Potenza, K. P. V. Sabareesh, M. Carpineti, M. D. Alaimo, and M. Giglio, “How to measure the optical thickness of scattering particles from the phase delay of scattered waves: application to turbid samples,” Phys. Rev. Lett. 105, 193901 (2010).
[Crossref]

2015 (3)

B. Paroli, E. Chiadroni, M. Ferrario, A. Mostacci, V. Petrillo, M. A. C. Potenza, A. R. Rossi, and L. Serafini, “Coherence properties and diagnostics of betatron radiation emitted by an externally-injected electron beam propagating in a plasma channel,” Nucl. Instr. Meth. Phys. Res. B 355, 217–220, (2015).
[Crossref]

B. Paroli, E. Chiadroni, M. Ferrario, V. Petrillo, M. A. C. Potenza, A. R. Rossi, L. Serafini, and V. Shpakov, “Asymmetric lateral coherence of betatron radiation emitted in laser-driven light sources,” Europhys. Lett. 111, 44003 (2015).
[Crossref]

B. Paroli, E. Chiadroni, M. Ferrario, and M. A. C. Potenza, “Analogical optical modeling of the asymmetric lateral coherence of betatron radiation,” Opt. Express 23(23), 29912–29920 (2015).
[Crossref]

2014 (1)

M. D. Alaimo, M. P. Anania, M. Artioli, A. Bacci, M. Bellaveglia, F. Ciocci, E. Chiadroni, A. Cianchi, G. Dattoli, G. Di Pirro, M. Ferrario, G. Gatti, L. Giannessi, M. Manfredda, R. Martucci, A. Mostacci, B. Paroli, A. Petralia, V. Petrillo, R. Pompili, M. A. C. Potenza, M. Quattormini, J. Rau, D. Redoglio, A. R. Rossi, L. Serafini, V. Surrenti, A. Torre, C. Vaccarezza, and F. Villa, “Mapping the transverse coherence of the self amplified spontaneous emission of a free-electron laser with the heterodyne speckle method,” Opt. Express 22(24), 30013–30023 (2014).
[Crossref]

2013 (2)

M. Ferrario, D. Alesini, M. Anania, A. Bacci, M. Bellaveglia, O. Bogdanov, R. Boni, M. Castellano, E. Chiadroni, A. Cianchi, S. B. Dabagov, C. De Martinis, D. Di Giovenale, G. Di Pirro, U. Dosselli, A. Drago, A. Esposito, R. Faccini, A. Gallo, M. Gambaccini, C. Gatti, G. Gatti, A. Ghigo, D. Giulietti, A. Ligidov, P. Londrillo, S. Lupi, A. Mostacci, E. Pace, L. Palumbo, V. Petrillo, R. Pompili, A. R. Rossi, L. Serafini, B. Spataro, P. Tomassini, G. Turchetti, C. Vaccarezza, F. Villa, G. Dattoli, E. Di Palma, and L. Giannessi, “SPARC LAB present and future,” Nucl. Instr. Meth. Phys. Res. B 309, 183–188 (2013).
[Crossref]

S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]

2010 (1)

M. A. C. Potenza, K. P. V. Sabareesh, M. Carpineti, M. D. Alaimo, and M. Giglio, “How to measure the optical thickness of scattering particles from the phase delay of scattered waves: application to turbid samples,” Phys. Rev. Lett. 105, 193901 (2010).
[Crossref]

2009 (1)

M. D. Alaimo, M. A. C. Potenza, M. Manfredda, G. Geloni, M. Sztucki, T. Narayanan, and M. Giglio, “Probing the transverse coherence of an undulator X-ray beam using brownian particles,” Phys. Rev. Lett. 103, 194805 (2009).
[Crossref]

2008 (1)

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

2004 (1)

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[Crossref]

2002 (1)

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett 81(22), 4109 (2002).
[Crossref]

2000 (1)

V. Kohn, I. Snigireva, and A. Snigireva, “Measurements of transverse coherence length of hard X-rays from interference fringes,” Phys. Rev. Lett. 85(13), 2745–2748 (2000).
[Crossref]

1996 (2)

T. Ditmire, E. T. Gumbrell, R.A. Smith, J. W. G. Tisch, D. D. Meyerhofer, and M. H. R. Hutchinson, “Spatial coherence measurement of soft X-ray radiation produced by high order harmonic generation,” Phys. Rev. Lett. 77(23), 4756–4759 (1996).
[Crossref] [PubMed]

B. A. Patterson, M. Antoni, J. Courtial, A. J. Duncan, W. Sibbett, and M. J. Padgett, “An ultra-compact static Fourier-transform spectrometer based on a single birefringent component,” Opt. Commun. 130, 1–6 (1996).
[Crossref]

1995 (1)

E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, “The physics of free electron laser. An introduction,” Phys. Rep. 260, 187–327 (1995).
[Crossref]

Alaimo, M. D.

Alesini, D.

Anania, M.

Anania, M. P.

Antoni, M.

Artioli, M.

Bacci, A.

Bellaveglia, M.

Bogdanov, O.

Boni, R.

Bosecke, P.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Brogioli, D.

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett 81(22), 4109 (2002).
[Crossref]

Carpineti, M.

Castellano, M.

Cerbino, R.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Chiadroni, E.

Cianchi, A.

Ciocci, F.

Corde, S.

S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]

Courtial, J.

Dabagov, S. B.

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1975).
[Crossref]

Dattoli, G.

De Martinis, C.

Di Giovenale, D.

Di Palma, E.

Di Pirro, G.

Ditmire, T.

Dosselli, U.

Drago, A.

Duncan, A. J.

Esposito, A.

Faccini, R.

Ferrario, M.

Ferri, F.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[Crossref]

Fitour, R.

S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]

Gallo, A.

Gambaccini, M.

Gatti, C.

Gatti, G.

Geloni, G.

Ghigo, A.

Giannessi, L.

Giglio, M.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[Crossref]

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett 81(22), 4109 (2002).
[Crossref]

Giulietti, D.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

Gumbrell, E. T.

Hutchinson, M. H. R.

Kohn, V.

V. Kohn, I. Snigireva, and A. Snigireva, “Measurements of transverse coherence length of hard X-rays from interference fringes,” Phys. Rev. Lett. 85(13), 2745–2748 (2000).
[Crossref]

Lambert, G.

S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]

Ligidov, A.

Londrillo, P.

Lupi, S.

Magatti, D.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[Crossref]

Malka, V.

S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]

Manfredda, M.

Martucci, R.

Meyerhofer, D. D.

Mostacci, A.

Narayanan, T.

Pace, E.

Padgett, M. J.

Palumbo, L.

Paroli, B.

Patterson, B. A.

Pescini, D.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[Crossref]

Petralia, A.

Petrillo, V.

Peverini, L.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Pompili, R.

Potenza, M. A. C.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[Crossref]

Quattormini, M.

Rau, J.

Redoglio, D.

Robert, A.

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Rossi, A. R.

Rousse, A.

S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]

Sabareesh, K. P. V.

Saldin, E. L.

E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, “The physics of free electron laser. An introduction,” Phys. Rep. 260, 187–327 (1995).
[Crossref]

Schneidmiller, E. A.

E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, “The physics of free electron laser. An introduction,” Phys. Rep. 260, 187–327 (1995).
[Crossref]

Serafini, L.

Shpakov, V.

Sibbett, W.

Smith, R.A.

Snigireva, A.

V. Kohn, I. Snigireva, and A. Snigireva, “Measurements of transverse coherence length of hard X-rays from interference fringes,” Phys. Rev. Lett. 85(13), 2745–2748 (2000).
[Crossref]

Snigireva, I.

V. Kohn, I. Snigireva, and A. Snigireva, “Measurements of transverse coherence length of hard X-rays from interference fringes,” Phys. Rev. Lett. 85(13), 2745–2748 (2000).
[Crossref]

Spataro, B.

Surrenti, V.

Sztucki, M.

TaPhuoc, K.

S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]

Tisch, J. W. G.

Tomassini, P.

Torre, A.

Turchetti, G.

Vaccarezza, C.

Vailati, A.

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett 81(22), 4109 (2002).
[Crossref]

Villa, F.

Wiedemann, H.

H. Wiedemann, Synchrotron Radiation (Springer-Verlag, 2003).
[Crossref]

Yurkov, M. V.

E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, “The physics of free electron laser. An introduction,” Phys. Rep. 260, 187–327 (1995).
[Crossref]

Appl. Phys. Lett (1)

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near field scattering,” Appl. Phys. Lett 81(22), 4109 (2002).
[Crossref]

Europhys. Lett. (1)

Nat. Phys. (1)

R. Cerbino, L. Peverini, M. A. C. Potenza, A. Robert, P. Bosecke, and M. Giglio, “X-ray scattering information obtained from near-field speckles,” Nat. Phys. 4, 238–243 (2008).
[Crossref]

Nucl. Instr. Meth. Phys. Res. B (2)

Opt. Commun. (1)

Opt. Express (2)

Phys. Rep. (1)

E. L. Saldin, E. A. Schneidmiller, and M. V. Yurkov, “The physics of free electron laser. An introduction,” Phys. Rep. 260, 187–327 (1995).
[Crossref]

Phys. Rev. E (1)

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 041405 (2004).
[Crossref]

Phys. Rev. Lett. (4)

V. Kohn, I. Snigireva, and A. Snigireva, “Measurements of transverse coherence length of hard X-rays from interference fringes,” Phys. Rev. Lett. 85(13), 2745–2748 (2000).
[Crossref]

Rev. Mod. Phys. (1)

S. Corde, K. TaPhuoc, G. Lambert, R. Fitour, V. Malka, and A. Rousse, “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85(1), 1103 (2013).
[Crossref]

Other (3)

J. W. Goodman, Statistical Optics (Wiley-Interscience, 2000).

J. C. Dainty, Laser Speckle and Related Phenomena (Springer-Verlag, 1975).
[Crossref]

H. Wiedemann, Synchrotron Radiation (Springer-Verlag, 2003).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.

Click here to see a list of articles that cite this paper

Fig. 1 a) Sketch of the experimental set-up. A collimated broadband source illuminates a colloidal suspension. Each particle scatters a spherical wave (blue) that interferes with the transmitted radiation (red) and the resulting interferogram is acquired with a CCD on a transverse detection plane. b) The optical path difference Δx₂ observed at high angles will be larger than at small angles (Δx₁). This behavior is the analogous of the variation of the optical path of the Michelson’s interferometer arms.

Download Full Size | PPT Slide | PDF

Fig. 2 a) Calculated interferogram for the spherical wave scattered by a single particle. b) Speckle field of a colloidal suspension measured with a CCD.

Download Full Size | PPT Slide | PDF

Fig. 3 Frequency spectra of the halogen 2 lamp (a) and the LED (c) measured with a grating spectrometer. b) and d) are the corresponding temporal coherence factors μ(Δt) obtained by means of Wiener-Khinchine’s theorem.

Download Full Size | PPT Slide | PDF

Fig. 4 Power spectrum of the four white light sources used in experiments (circles). The envelope of the Talbot oscillations is well matched by the theoretical coherence factor C(Δt) (solid curves) given by the product of |μ(Δt)|² (dashed curves) and |C_s(Δt)|² (dotted curves).

Download Full Size | PPT Slide | PDF

Fig. 5 Temporal coherence factors |μ(Δt)|² of the four sources (circles) extracted from the envelope of the Talbot oscillations (see Fig. 4). Dashed curves are the corresponding spatial coherence factors |C_s(Δt)|² and insets are the retrieved spectra.

Download Full Size | PPT Slide | PDF

Tables (1)

Table 1 Comparison of results from the spectrometer and HNFS experiments.

View Table

Equations (3)

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

Γ (Δ x, Δ t) = \frac{〈 E (x, t) E^{*} (x + Δ x, t + Δ t) 〉}{\sqrt{〈 I (x, t) 〉} \sqrt{〈 I (x + Δ x, t + Δ t) 〉}}

S (q) = I (q) T (q) C (q) H (q) + P (q)

C (q) = {| μ (q) |}^{2} {| C_{s} (q) |}^{2}

Light source	FWHM spectrometer (10¹⁴ Hz)	FWHM HNFS experiments (10¹⁴ Hz)
Halogen 1	1.9	2.2
Halogen 2	2.2	2.5
Halogen 3	2.0	2.5
LED	1.2	1.5