Applied Spectroscopy, vol. 54, no. 7, July, 2000. (Special issue on generalized 2D correlation spectroscopy)
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Y. Ozaki and I. Noda, Eds. Two-Dimensional Correlation Spectroscopy, AIP Conference proceedings 503, AIP: Melville, 2000.
readily observable in conventional 1D spectra ▪ Sign of cross peaks to determine relative direction of intensity changes and
sequential order of events ▪ Comparison of different spectral data via hetero-correlation
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Generalized 2D Correlation Spectroscopy
Perturbation-based 2D correlation spectroscopy
I. Noda, Appl. Spectrosc., 47, 1329 (1993).
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Reference Literature
1
F(n1,n2 ) m 1
m j 1
~y j (n1) ~y j (n2 )
1
Y(n1,n2 ) m 1
m j 1
~y j (n1) ~z j (n2 )
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Generalized 2D Correlation Formalism
Dynamic spectrum
~y (n,
t)
y(n
,
t
) 0
y(n
)
for Tmin t Tmax otherwise
where
y(n) 1
Tmax y(n , t) dt.
T T max
min Tmin
Fourier transform
Y~1( )
ቤተ መጻሕፍቲ ባይዱ
~y (n 1 , t )
e i t dt
Y~2*( )
~y(n 2 , t)
eit dt
2D correlation spectra
1
F(n1,n2 ) i Y(n1,n2 ) (Tmax Tmin )
0
Y~1( ) Y~2*( )
▪ Generally applicable to a broad range of spectroscopic techniques ▪ Based on a set of spectral data from a system under some perturbation ▪ Either time-dependent or static spectra may be used ▪ Enhance spectral resolution by spreading peaks along the second dimension ▪ Selective development of 2D peaks provides better access to information not
)
for 1 j m otherwise
Discrete Hilbert transform
y(n ) 1
m
m
y j (n )
j 1
m
~z j (n2 ) N jk ~yk (n2 )
k 1
where
0
N jk
1
/
(k
j)
if j k otherwise
2D correlation spectra
d
F(n1, n2) synchronous spectrum Y(n1, n2) asynchronous spectrum
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Practical Computational Method
Discrete spectral sampling
~y j
(n
)
y
j
(n
) 0
y(n
Perturbation
S(t)
Input
I(n)
System
Output
~y (n1,t)
~y(n 2,t) ...
~y (n n ,t)
Comparison of two signals
measured at different n along t
Cross-correlation function
2008年中国科大
Two-Dimensional (2D) Correlation Spectroscopy
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武培怡
复旦大学高分子科学系
1
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Two-Dimensional (2D) Spectroscopy
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Generalized 2D Correlation Spectroscopy
Temperature, pressure, time, concentration, electromagnetic field ……
2D Correlation Spectra
Acquisition of 2D Correlation Spectra
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7
2D Correlation Analysis
5
Book
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Generalized Two-Dimensional Correlation Spectroscopy
Electromagnetic Probe IR, NIR, laser ……
Chemical System
Dynamic Spectra
External Perturbation
(n1,n2) ~y(n1,t) ~y(n2,t')
= F(n1,n2) + i Y(n1,n2)
Synchronous spectrum F(n1,n2) = Similarity of signal dependence on t
Asynchronous spectrum Y(n1,n2) = Dissimilarity of signal dependence on t