Abstract Ž . To increase the sensitivity with which time-resolved Fourier transform infrared FT-IR difference spectra are measured, the detector is often AC-coupled. Thus, the measured interferograms correspond to spectra with both positive and negative intensities. The presence of signed intensities presents problems for the standard Mertz and Forman phase correction methods. The Mertz Signed phase correction method was designed to handle signed intensities, but the smoothing inherent in calculating the phase angles at reduced resolution introduces other errors in AC-coupled spectra produced with this algorithm. These errors are evident as signal remaining along the imaginary axis after phase correction. A new approach to phase correction, the Doubled-Angle method, can directly correct the phases of transient AC-coupled spectra without the w Ž . x need for a DC interferogram M.S. Hutson, M.S. Braiman, Appl. Spectrosc. 52 1998 974 . When this method was applied to the transient AC interferograms measured after photolysis of bacteriorhodopsin, the signal was fully rotated onto the real axis following phase correction. Here, we show that the Doubled-Angle method can be applied to time-resolved difference FT-IR spectra of halorhodopsin, a more demanding biological system due to its intrinsically small differential absorption signals. 

M Shane Hutson

Mark S Braiman

CiteSeerX

Ž .Vibrational Spectroscopy 19 1999 379–383
Application of doubled-angle phase correction method to
time-resolved step-scan FT-IR spectra
M. Shane Hutson, Mark S. Braiman )
Department of Biochemistry and Biophysics Program, UniÕersity of Virginia Health Sciences Center a440, CharlottesÕille, VA 22908, USA
Received 20 July 1998; received in revised form 27 October 1998; accepted 2 November 1998
Abstract
Ž .To increase the sensitivity with which time-resolved Fourier transform infrared FT-IR difference spectra are measured,
the detector is often AC-coupled. Thus, the measured interferograms correspond to spectra with both positive and negative
intensities. The presence of signed intensities presents problems for the standard Mertz and Forman phase correction
methods. The Mertz Signed phase correction method was designed to handle signed intensities, but the smoothing inherent
in calculating the phase angles at reduced resolution introduces other errors in AC-coupled spectra produced with this
algorithm. These errors are evident as signal remaining along the imaginary axis after phase correction. A new approach to
phase correction, the Doubled-Angle method, can directly correct the phases of transient AC-coupled spectra without the
w Ž . xneed for a DC interferogram M.S. Hutson, M.S. Braiman, Appl. Spectrosc. 52 1998 974 . When this method was applied
to the transient AC interferograms measured after photolysis of bacteriorhodopsin, the signal was fully rotated onto the real
axis following phase correction. Here, we show that the Doubled-Angle method can be applied to time-resolved difference
FT-IR spectra of halorhodopsin, a more demanding biological system due to its intrinsically small differential absorption
signals. q 1999 Elsevier Science B.V. All rights reserved.
Keywords: Double-Angle method; FT-IR spectra; Mertz Signed phase correction method
1. Introduction
Interferograms collected in FT-IR spectroscopy
are never perfectly symmetric. Thus, upon Fourier
transformation, a complex result is produced from
the interferogram, i.e.,
FP I d sb n e iu Žn . .Ž . Ž .
A phase correction method is then used to extract the
Ž .intensity information, b n , from this complex repre-
) Corresponding author. Tel.: q1-804-924-5062; Fax: q1-804-
924-5069; E-mail: msb7e@virginia.edu
Ž .sentation of the spectrum. When b n can be as-
sumed to always be positive this is a straightforward
Ž .task. However, if b n is signed then the phase
correction is ambiguous due to the equality:
yA e iu sAe iŽuqp . .Ž .
This is exactly the situation encountered when time-
resolved FT-IR interferograms are collected in an
AC-coupled configuration. AC coupling is typically
employed to improve the sensitivity and accuracy
with which small spectral changes can be measured
and digitized.
0924-2031r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
Ž .PII: S0924-2031 98 00090-3
( )M.S. Hutson, M.S. BraimanrVibrational Spectroscopy 19 1999 379–383380
The Mertz phase correction method assumes that
w xall of the signal intensity is positive 2 . Thus, for
broad negative bands the calculated phase angle is p
radians from the true phase angle. Applying the
phase correction,
Ž .iu n yiwu Žn .qp xB n s b n e PeŽ . Ž .
sb n eyp syb n ,Ž . Ž .
w xproduces a ‘reflected peaks’ pattern 3 .
A modification of the Mertz method, the ‘Mertz
Signed’, was proposed by McCoy and de Haseth for
vibrational circular dichroism spectra with positive
w xand negative bands 3 . Instead of assuming that
Ž .b n )0, the Mertz Signed method assumes that all
true phase angles fall in the range ypr2 to pr2.
Any frequency for which the calculated phase angle
falls outside of this range is assigned to a negative
real intensity. As McCoy and de Haseth showed with
the phase correction of quarterwave platerpolarizer
vibrational circular dichroism spectra, the Mertz
Signed method correctly eliminates the reflection of
w xnegative peaks in spectra with broad bands 3 .
While the Mertz Signed method can properly
correct the phases of difference spectra with broad
features, spectra containing sharp alternating bands
of opposite sign pose a problem. This has been
shown for a set of simulated difference spectra and
the time-resolved step-scan difference spectra of the
w xbacteriorhodopsin photocycle 1 . The problems en-
countered with the Mertz Signed method stem from
using a reduced resolution for the phase calculation.
For differential interferograms, this means that a
discontinuous function is smoothed and intermediate
phase angles are calculated. The restriction placed on
the phase angle range by the Mertz Signed algorithm
restores continuity, but in an incorrect manner, re-
sulting in significant systematic errors.
To solve this problem, we devised the Doubled-
w xAngle phase correction method 1 . In the first step
of the phase calculation, the differential interfero-
Ž .gram D I n is self-convolved, and the result is
truncated. In spectral space, this is equivalent to
squaring the complex spectrum, then reducing its
Ž Ž ..2 i2uresolution. Now, since b n ) 0 and e s
e i2Žuqp ., the phase angle discontinuities have been
eliminated. An advantage of doing the angle dou-
Žbling in interferogram space rather than spectral
.space is that it permits accurate determination of the
Ž .point of Zero Path Difference ZPD of the interfero-
gram. In differential interferograms, the ZPD is not
Ž .necessarily at an extremum of D I d . However, the
ZPD is always at the maximum of the self-convolu-
tion, D ImD I. The Fourier transform can be applied
to D ImD I at reduced resolution without the intro-
duction of intermediate phase angles. Once sin2u X
and cos2u X have been calculated, the half-angle
formulas can be used to find sinu X and cosu X. The
choice between the two possibilities for u X at each
frequency is made on the basis of continuity of the
phase spectrum. This means that when the final
phase corrected spectrum is produced, the bands will
be oriented correctly relative to one another, but the
global orientation is ambiguous. The choice of
whether to ‘flip’ the spectrum must be made on the
basis of some a priori knowledge of the difference
spectrum being measured.
2. Materials and methods
Ž .Purified halorhodopsin hR samples were pre-
pared as described previously from membranes of
w xhalobacteria 4 . The purified hR was washed with a
10 mM HEPES, 50 mM KBr, pHs7 solution sev-
eral times. After concentrating it by centrifugation,
Ž .25 ml ;250 mg of hR were pipetted onto a BaF2
Ž .window 25 mm diameter=2 mm thick . The hR
sample was then dried with a gentle stream of N .2
Once most of the water had been removed from the
sample, a second BaF window was coated around2
its edge with vacuum grease and pressed against the
first to seal the sample. The hR sample is thus in a
nearly saturating KBr solution.
Interferograms were collected on a Bruker IFS-66
FT-IR spectrometer in time-resolved step-scan mode
with a photoconductive HgCdTe detector. The detec-
tor’s preamplifier and the internal digitizer were used
in an AC-coupled configuration throughout. The data
were collected at 16 cmy1 resolution over a 0–3940
cmy1 bandwidth. A long-pass filter was placed in
front of the detector to block the light from the laser
flash and to prevent aliasing. A pulsed, frequency-
q Ž .doubled Nd :YAG laser 532 nm @ 3 Hz was used
to trigger the hR photocycle for the time-resolved
FT-IR measurements. The signals from 20 flashes
( )M.S. Hutson, M.S. BraimanrVibrational Spectroscopy 19 1999 379–383 381
Ž .Fig. 1. Time-resolved step-scan FT-IR measurement of halorhodopsin photoreaction. A The differential interferogram shown was collected
y1 q Ž .at 16 cm resolution over the first 2 ms after a Nd :YAG laser flash see Section 2 for more details . After identification of the ZPD,
Ž . Ž . Ž .Fourier transformation of A yields the complex spectrum shown in B and C .
were averaged at each mirror position to produce
transient differential interferograms at intervals of 25
ms. The 80 interferograms corresponding to delay
times of 25–2000 ms after the flash were averaged to
Ž .produce the higher signal-to-noise-ratio SrN dif-
ferential interferogram shown in Fig. 1.
3. Results and discussion
Fig. 1A shows the time-resolved differential inter-
ferogram obtained from transient signals collected
during the first 2 ms after halorhodopsin photolysis.
After Fourier transformation at 16 cmy1 resolution,
but before phase correction, the spectral information
Ž .is split almost evenly between the real Fig. 1B and
Ž .imaginary Fig. 1C axes.
The Mertz, Mertz Signed and Doubled-Angle
phase correction methods were then applied to this
differential interferogram. For each method, we used
phase spectra calculated at four different resolutions
and then interpolated to the original 16 cmy1 resolu-
tion of the data. In the top 2 panels of Fig. 2, the
phase correction at 16 cmy1 resolution rotates al-
most all of the spectral information onto the real axis
regardless of which method is used, but the calcu-
lated spectra for the three methods are all different.
The Mertz spectrum contains only positive bands
due to the reflection of negative peaks discussed
earlier. The Mertz Signed algorithm actually does a
fine job of flipping the negative bands back to the
correct orientation. The Doubled-Angle method pro-
duces a spectrum very similar to the Mertz Signed
method, except for in the region above 1600 cmy1.
One can see in Fig. 3 that in this region at 16 cmy1
phase resolution, the poor SrN results in an error of
p radian in the phase angle calculated with the
Doubled-Angle method.
However, if the phase resolution is reduced to
improve the SrN ratio, then the error in the Dou-
( )M.S. Hutson, M.S. BraimanrVibrational Spectroscopy 19 1999 379–383382
Fig. 2. Evaluation of three phase correction procedures applied to the time-resolved differential interferogram of the halorhodopsin
photocycle shown in Fig. 1. The real and imaginary spectra after phase correction are shown for each method at four different phase
resolutions.
Žbled-Angle phase calculation is eliminated see e.g.,
Fig. 2, Doubled-Angle correction at 32 cmy1 resolu-
.tion . At the same time, all of the spectral informa-
tion continues to be aligned along the real axis. As
the resolution is reduced even further, the real and
imaginary spectra produced with the Doubled-Angle
Ž y1method change very little See Fig. 2, 64 cm and
y1 .128 cm results .
On the other hand, the story is very different for
the Mertz and Mertz Signed methods. As the resolu-
tion is progressively reduced, more and more spec-
tral information remains imaginary. The Mertz algo-
rithm properly reflects only a subset of the negative
bands as the phase resolution drops towards 128
cmy1, and the Mertz Signed algorithm produces
odd-shaped bands of reduced magnitude along the
( )M.S. Hutson, M.S. BraimanrVibrational Spectroscopy 19 1999 379–383 383
Fig. 3. Phase spectra calculated with the three different phase
correction procedures applied to the time-resolved, differential
interferogram of the halorhodopsin photocycle shown in Fig. 1.
The phase spectra are shown for each method at four different
Ž . Ž .phase resolutions: Mertz dotted , Mertz Signed dashed and
Ž .Doubled-Angle solid . Between yp r2 and p r2, the Mertz and
Mertz Signed algorithms produce the same spectrum. Thus, the
Mertz curve is obscured by the Mertz Signed curve.
real axis. The negative band at ;1435 cmy1 is
actually lost entirely. The phase spectra of Fig. 3
show that although the SrN increases, more inter-
mediate phase angles are calculated with the Mertz
and Mertz Signed methods as the resolution is re-
duced.
We first demonstrated the applicability of the
Doubled-Angle phase correction method to time-re-
solved difference interferograms of bacterio-
Ž . w xrhodopsin bR photoproducts 1 . Halorhodopsin is a
more demanding system for several reasons. First, it
cannot be prepared in a concentration comparable to
bR. Second, its photochemical quantum yield is re-
Ž . w xduced 2–5= 4 . Third, it is more susceptible to
w xirreversible photobleaching at high laser powers 4 .
All of these characteristics play a role in reducing
the absorption changes for hR by a factor of 5–10=
as opposed to bR. The SrN attainable in time-re-
solved difference spectra of halorhodopsin photo-
products is therefore considerably less than the SrN
of similar measurements of bR. We demonstrate here
that the Doubled-Angle phase correction method is
able to properly phase correct even these lower SrN
difference spectra. Only at a phase resolution equal
Ž y1 .to the full spectral resolution 16 cm is this
method unable to produce the correct spectra. As the
phase resolution is reduced towards 128 cmy1, phase
correction by the Doubled-Angle method improves,
while phase correction by the Mertz and Mertz Signed
methods does not. Thus, the Doubled-Angle method
can be used on difference interferograms with mod-
erate SrN, as long as the SrN of the phase angle
calculation is improved by using a reduced phase
resolution.
Acknowledgements
This work was supported by NIH grants GM46854
and GM08323.
References
w x Ž .1 M.S. Hutson, M.S. Braiman, Appl. Spectrosc. 52 1998 974.
w x2 L. Mertz, Transformations in Optics, Wiley, New York, 1965.
w x Ž .3 C. McCoy, J. de Haseth, Appl. Spectrosc. 42 1988 336.
w x4 A.K. Dioumaev, M.S. Braiman, Photochemistry and Photobi-
Ž .ology 66 1997 755.


Application of Doubled-Angle Phase Correction Method to Time-Resolved Step-Scan FT-IR Spectra

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Application of Doubled-Angle Phase Correction Method to Time-Resolved Step-Scan FT-IR Spectra

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