OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 27, Iss. 5 — May. 1, 2010
  • pp: 1104–1117

Spectral restoration for femtosecond spectral interferometry with attosecond accuracy

Michael K. Yetzbacher, Trevor L. Courtney, William K. Peters, Katherine A. Kitney, Eric Ryan Smith, and David M. Jonas  »View Author Affiliations


JOSA B, Vol. 27, Issue 5, pp. 1104-1117 (2010)
http://dx.doi.org/10.1364/JOSAB.27.001104


View Full Text Article

Enhanced HTML    Acrobat PDF (613 KB) Open Access





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A spectral restoration algorithm appropriate for the asymmetric and wavelength-dependent linespread of broadband spectrographs with pixelated detectors is presented. The algorithm’s accuracy was tested on spectra of femtosecond pulse pairs with known delays from an actively stabilized interferometer. Using interleaved atomic line spectra, the spectrograph calibration and effective linespread function were retrieved with sub-pixel accuracy. The spectral restoration by Fourier pseudo-deconvolution with the effective linespread function reduced systematic artifacts and allowed recovery of the phase delay to ±2.4 as over a 2 ps range (±0.7 nm path differences over 0.6 mm). The slope delay was determined to within ±20 as and constant (intercept) phase shifts to within ±0.05 rad; these accuracies are limited by Fourier filtering of charge coupled device and interferometer imperfections.

© 2010 Optical Society of America

OCIS Codes
(100.3020) Image processing : Image reconstruction-restoration
(110.4850) Imaging systems : Optical transfer functions
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(320.7100) Ultrafast optics : Ultrafast measurements

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: November 5, 2009
Revised Manuscript: March 5, 2010
Manuscript Accepted: March 5, 2010
Published: April 29, 2010

Citation
Michael K. Yetzbacher, Trevor L. Courtney, William K. Peters, Katherine A. Kitney, Eric Ryan Smith, and David M. Jonas, "Spectral restoration for femtosecond spectral interferometry with attosecond accuracy," J. Opt. Soc. Am. B 27, 1104-1117 (2010)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-5-1104


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. Walker, The Analytical Theory of Light (the Cambridge University Press, 1904).
  2. L. M. Smith and C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of white light in a Michelson interferometer,” Appl. Opt. 28, 3339–3342 (1989). [CrossRef] [PubMed]
  3. J. Schwider and L. Zhou, “Dispersive interferometric profiler,” Opt. Lett. 19, 995–997 (1994). [CrossRef] [PubMed]
  4. J. Schwider and L. Zhou, “Dispersive interferometric profiler: erratum,” Opt. Lett. 20, 945 (1995). [CrossRef] [PubMed]
  5. L. Lepetit, G. Chériaux, and M. Joffre, “Linear techniques of phase measurement by femtosecond spectral interferometry for applications in spectroscopy,” J. Opt. Soc. Am. B 12, 2467–2474 (1995). [CrossRef]
  6. P. de Groot and L. Deck, “Surface profiling by analysis of white-light interferograms in the spatial frequency domain,” J. Mod. Opt. 42, 389–401 (1995). [CrossRef]
  7. P. Sandoz, G. Tribillon, and H. Perrin, “High-resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white-light interferograms,” J. Mod. Opt. 43, 701–708 (1996). [CrossRef]
  8. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses,” Opt. Lett. 21, 884–886 (1996). [CrossRef] [PubMed]
  9. D. N. Fittinghoff, J. L. Bowie, J. N. Sweetser, R. T. Jennings, M. A. Krumbügel, K. W. DeLong, R. Trebino, and I. A. Walmsley, “Measurement of the intensity and phase of ultraweak, ultrashort laser pulses: erratum,” Opt. Lett. 21, 1313 (1996). [CrossRef] [PubMed]
  10. C. Dorrer, “Influence of the calibration of the detector on spectral interferometry,” J. Opt. Soc. Am. B 16, 1160–1168 (1999). [CrossRef]
  11. A. W. Albrecht, J. D. Hybl, S. M. Gallagher Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934–10956 (1999). [CrossRef]
  12. A. W. Albrecht Ferro, J. D. Hybl, S. M. Gallagher Faeder, and D. M. Jonas, “‘Erratum: Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions’ [J. Chem. Phys. 111, 10934 (1999)],” J. Chem. Phys. 115, 5691 (2001). [CrossRef]
  13. C. Dorrer, N. Belabas, J.-P. Likforman, and M. Joffre, “Spectral resolution and sampling issues in Fourier-transform spectral interferometry,” J. Opt. Soc. Am. B 17, 1795–1802 (2000). [CrossRef]
  14. C. Dorrer, N. Belabas, J. P. Likforman, and M. Joffre, “Experimental implementation of Fourier-transform spectral interferometry and its application to the study of spectrometers,” Appl. Phys. B 70, S99–S107 (2000). [CrossRef]
  15. S. K. Debnath, M. P. Kothiyal, and S.-W. Kim, “Evaluation of spectral phase in spectrally resolved white-light interferometry: comparative study of single frame techniques,” Opt. Lasers Eng. 47, 1125–1130 (2009). [CrossRef]
  16. A. A. Michelson and F. G. Pease, “Measurement of the diameter of an Orionis with the interferometer,” Astrophys. J. 53, 249–259 (1921). [CrossRef]
  17. M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436–1438 (2001). [CrossRef]
  18. E. Moon, C. Li, Z. Duan, J. Tackett, K. L. Corwin, B. R. Washburn, and Z. Chang, “Reduction of fast carrier-envelope phase jitter in femtosecond laser amplifiers,” Opt. Express 14, 9758–9763 (2006). [CrossRef] [PubMed]
  19. J. D. Hybl, A. Albrecht Ferro, and D. M. Jonas, “Two dimensional Fourier transform electronic spectroscopy,” J. Chem. Phys. 115, 6606–6622 (2001). [CrossRef]
  20. P. Baum, S. Lochbrunner, and E. Riedle, “Generation of tunable 7-fs ultraviolet pulses: achromatic phase matching and chirp management,” Appl. Phys. B 79, 1027–1032 (2004). [CrossRef]
  21. D. Meshulach, D. Yelin, and Y. Silberberg, “White light dispersion measurements by one- and two-dimensional spectral interference,” IEEE J. Quantum Electron. 33, 1969–1974 (1997). [CrossRef]
  22. M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11, 2183–2189 (2003). [CrossRef] [PubMed]
  23. From the standard deviation of the data in Fig. 6a of , the precision can be estimated as 0.25 fs2.
  24. J. Anderson and I. R. King, “Toward high-precision astrometry with WFPC2. I. Deriving an accurate point-spread function,” Publ. Astron. Soc. Pac. 112, 1360–1382 (2000). [CrossRef]
  25. T. P. Costello and W. B. Mikhael, “One-dimensional comparison of Wiener filtering and Richardson-Lucy methods for sectioned restoration of space-variant digital images,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 49, 518–522 (2002). [CrossRef]
  26. D. A. Fish, J. Grochmalicki, and E. R. Pike, “Scanning singular-value-decomposition method for restoration of images with space-variant blur,” J. Opt. Soc. Am. A 13, 464–469 (1996). [CrossRef]
  27. A. A. Sawchuk, “Space-variant image restoration by coordinate transformations,” J. Opt. Soc. Am. 64, 138–144 (1974). [CrossRef]
  28. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, 1986).
  29. S. B. Howell, Handbook of CCD Astronomy, 2nd ed., Cambridge Observing Handbooks for Research Astronomers (Cambridge U. Press, 2006).
  30. The wavelength axis was given by λ(p)=670 nm+(p−1)⋅0.5 nm/pixel for p=1 through N=512. The pulse spectrum was |e(λ)|2=(λ0/λ)2exp[−(λ−λ0)2/2σ2] withσ2=250 nm2 and λ0=800 nm (a FWHM of ∼75 pixels on the 512 pixel array). The simulated eLSF for each pixel was a convolution of a pixel-centered Gaussian,exp[−(P−p)2/2σ2], where σ=0.53 pixels is constant; a one-sided exponential decay, θ(p−P)exp[−(p−P)/wp]; and a 1-pixel wide pixelation function. The final eLSF was re-positioned with its maximum on the pixel center. The variation in the eLSF was created with the exponential width, wp=2−tanh[(p−(N/2))/40], producing an eLSF FWHM ranging from 2 to 3.4 pixels.
  31. The wavelength axis was given by λ(p)=670 nm+(p−1)⋅0.25 nm/pixel for p=1 through N=1024. The eLSF was constructed in the same way described in note except that σ=0.21 pixels and wp=0.675−(0.125)tanh[(p−(N/2))/200], producing an eLSF FWHM ranging from 1.23 to 1.39 pixels, which was sufficiently undersampled on a grid of 1024 pixels.
  32. J. Reader, “Optimizing Czerny-Turner spectrographs—a comparison between analytic theory and ray tracing,” J. Opt. Soc. Am. 59, 1189–1194 (1969). [CrossRef]
  33. E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1990).
  34. J. R. Janesick, Scientific Charge-Coupled Devices (SPIE, 2001). [CrossRef]
  35. W. H. Steel, Interferometry, Cambridge Monographs on Physics (Cambridge U. Press, 1967).
  36. A. E. Siegman, Lasers (University Science Books, 1986).
  37. F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, 1976).
  38. R. D. Campbell and D. J. Thompson, in Scientific Detectors for Astronomy 2005, J.E.Beletic, J.W.Beletic, and P.Amico, eds. (Springer, 2005), pp. 507–514.
  39. A. Reinheimer, e2v technologies, Tarrytown, NY (personal communication, March 11, 2008).
  40. G. Steinmeyer, “Dispersion oscillations in ultrafast phase-correction devices,” IEEE J. Quantum Electron. 39, 1027–1034 (2003). [CrossRef]
  41. M. Downing, D. Baade, P. Sinclaire, S. Deries, and F. Christen, Proc. SPIE 6276, 627609 (2006). [CrossRef]
  42. A 0.05% sinusoidal ripple with a 14 pixel period is expected on the flatfield from this procedure. This is smaller than the shot noise on the interferograms. In principle, the expected ripple could be divided out of the flatfield, but simulated interferograms show that a 0.05% sinusoidal ripple in the flatfield causes less than 0.5 mrad phase ripple, so this was not done.
  43. G. Norlen, “Wavelengths and energy-levels of Ar-I and Ar-II based on new interferometric measurements in region 3400–9800 A,” Phys. Scr. 8, 249–268 (1973). [CrossRef]
  44. The argon lines used (from ) had the following vacuum wavelengths (in nanometers): 912.547 13, 867.032 50, 852.378 34, 826.679 43, 795.036 27, 763.720 78, 738.601 45, 727.494 00, and 696.735 19.
  45. J. P. De Cuyper and H. Hensberge, “Wavelength calibration at moderately high resolution,” Astron. Astrophys. Suppl. Ser. 128, 409–416 (1998). [CrossRef]
  46. The polynomial was truncated at the quadratic term as the cubic term (predicted by the grating equation) was not well determined. Standard errors for the cubic coefficient, as estimated by least-squares fitting of single calibration spectra, were 30%–150% of its average value(5×10−11 nm/pixel3). In contrast, the quadratic term was determined to within 1%–3% of its value (4.8×10−7 nm/pixel2).
  47. A. W. Fountain, T. J. Vickers, and C. K. Mann, “Factors that affect the accuracy of Raman shift measurements on multichannel spectrometers,” Appl. Spectrosc. 52, 462–468 (1998). [CrossRef]
  48. V. Deckert and W. Kiefer, “Scanning multichannel technique for improved spectrochemical measurements with a CCD camera and its application to Raman-spectroscopy,” Appl. Spectrosc. 46, 322–328 (1992). [CrossRef]
  49. M. Gai, D. Carollo, M. Delbo, M. G. Lattanzi, G. Massone, F. Bertinetto, G. Mana, and S. Cesare, “Location accuracy limitations for CCD cameras,” Astron. Astrophys. 367, 362–370 (2001). [CrossRef]
  50. The standard deviation of the set of calibration constantsc1 is 2.0×10−6 nm/pixel, smaller than the 4.4×10−6 nm/pixel average standard error estimated from the fits to individual spectra. The standard deviation of the set of calibration constants c2 is 2.8×10−9 nm/pixel2, also smaller than the 1.8×10−8 nm/pixel2 average standard error of the fits to individual spectra. This means torsion or forward/backward motion of the CCD relative to the image plane is not detectable within the calibration precision and affects the calibration by less than the standard error of c1 and c2.
  51. K. Burns, K. B. Adams, and J. Longwell, “Interference measurements in the spectra of neon and natural mercury,” J. Opt. Soc. Am. 40, 339–344 (1950). [CrossRef]
  52. The neon lines in are defined by vacuum wave numbers, which were inverted to wavelengths. The six lines used had the following vacuum wavelengths (in nanometers): 703.434 88, 717.591 20, 724.715 93, 744.094 35, 837.990 54, and 849.769 00.
  53. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).
  54. The JILA loop filter was designed by J. L. Hall and T. Brown.
  55. D. J. Jones, E. O. Potma, J. X. Cheng, B. Burfeindt, Y. Pang, J. Ye, and X. S. Xie, “Synchronization of two passively mode-locked, picosecond lasers within 20 fs for coherent anti-Stokes Raman scattering microscopy,” Rev. Sci. Instrum. 73, 2843–2848 (2002). [CrossRef]
  56. M. Metcalf and J. Reid, Fortran 90/95 Explained (Oxford U. Press, 1996).
  57. G. Bönsch and E. Potulski, “Measurement of the refractive index of air and comparison with modified Edlen's formulae,” Metrologia 35, 133–139 (1998). [CrossRef]
  58. J. R. Birge, R. Ell, and F. X. Kartner, in Ultrafast Phenomena XV, P.Corkum, D.Jonas, R.J. D.Miller, and A.M.Weiner, eds. (Springer, 2006), pp. 160–162.
  59. J. H. Seinfeld and S. N. Pandis, Atmospheric Chemistry and Physics: From Air Pollution to Climate Change, 2nd ed. (John Wiley & Sons, 2006).
  60. The magnitude of the largest oscillation in the phase delay error (at ∼2.35 rad/fs for 2 ps delay) gives a change in the real refractive index, Δn, on the order of 10−6. From the Kramers–Kronig relationship, the change in the imaginary portion of the refractive index, Δκ, is approximately equal to Δn. By α=2ωκ/c, the absorption coefficient associated with the Δn from the Δϕ can be found and inverted to an absorption length l=1/α=17 m, several orders of magnitude shorter than that of atmospheric O2 or water vapor (see ).
  61. S. Shaklan, M. C. Sharman, and S. H. Pravdo, “High-precision measurement of pixel positions in a charge-coupled-device,” Appl. Opt. 34, 6672–6681 (1995). [CrossRef] [PubMed]
  62. R.C.Weast and M.J.Astle, eds., CRC Handbook of Chemistry and Physics, 63rd ed. (CRC, 1982).
  63. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am. 55, 1205–1209 (1965). [CrossRef]
  64. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences, 2nd ed. (McGraw-Hill, 1992).
  65. M. Beck, I. A. Walmsley, and J. D. Kafka, “Group delay measurements of optical-components near 800 nm,” IEEE J. Quantum Electron. 27, 2074–2081 (1991). [CrossRef]
  66. J. Kim, J. R. Birge, V. Sharma, J. G. Fujimoto, F. X. Kartner, V. Scheuer, and G. Angelow, “Ultrabroadband beam splitter with matched group-delay dispersion,” Opt. Lett. 30, 1569–1571 (2005). [CrossRef] [PubMed]
  67. P. Hariharan and B. C. Sanders, in Progress in Optics (Elsevier Science, 1996), Vol. XXXVI, pp. 49–128. [CrossRef]
  68. C. Iaconis and I. A. Walmsley, “Self-referencing spectral interferometry for measuring ultrashort optical pulses,” IEEE J. Quantum Electron. 35, 501–509 (1999). [CrossRef]
  69. K. Yamane, Z. G. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, “Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation,” Opt. Lett. 28, 2258–2260 (2003). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Multimedia

Multimedia FilesRecommended Software
» Media 1: PDF (1798 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited