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Volumn 27, Issue 5, 2010, Pages 1104-1117

Spectral restoration for femtosecond spectral interferometry with attosecond accuracy

Author keywords

[No Author keywords available]

Indexed keywords

CHARGE COUPLED DEVICES; ELECTROMAGNETIC PULSE; INTERFEROMETERS; RESTORATION; SPECTROGRAPHS;

EID: 77955694913     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.27.001104     Document Type: Article
Times cited : (18)

References (69)
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    • The wavelength axis was given byλp-=670 nm +(p-1) •0.5 nm/pixel for p=1 through N=512. The pulse spectrum was-e-2=- 0 /-2exp- 0-2/2-2- with-2=250 nm2 and 0=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-Pp-2/2-2-, where-=0.53 pixels is constant; a onesided exponential decay,-λp-λp-exp-λp-λp- /wp-; and a 1λpixel wide pixelation function. The final eLSF was repositioned with its maximum on the pixel center. The variation in the eLSF was created with the exponential width, wp=2?tanh-λp-N/2-/40-, producing an eLSF FWHM ranging from 2 to 3.4 pixels.
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    • The wavelength axis was given byλp-=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 [30] except that-=0.21 pixels and wp=0.675-0.125-tanh- λp -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.
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    • 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
    • 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.
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    • The argon lines used (from [43]) 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.
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    • 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-.
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    • The standard deviation of the set of calibration constants c1 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
    • The standard deviation of the set of calibration constants c1 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.
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    • The neon lines in [51] 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
    • The neon lines in [51] 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.
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    • 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,-n, on the order of 10?6. From the Kramers-Kronig relationship, the change in the imaginary portion of the refractive index,-, is approximately equal to-n. By-=2- /c, the absorption coefficient associated with the-n from the- can be found and inverted to an absorption length l=1/- =17 m, several orders of magnitude shorter than that of atmospheric O2 or water vapor (see [59])
    • 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,-n, on the order of 10?6. From the Kramers-Kronig relationship, the change in the imaginary portion of the refractive index,-, is approximately equal to-n. By-=2- /c, the absorption coefficient associated with the-n from the- can be found and inverted to an absorption length l=1/- =17 m, several orders of magnitude shorter than that of atmospheric O2 or water vapor (see [59]).
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