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Polarization Modulation Fourier Transform Infrared Spectroscopy with Digital Signal Processing: Comparison of Vibrational Circular Dichroism Methods JOVENCIO HILARIO, DAVID DRAPCHO, RAUL CURBELO, and TIM OTHY A. KEIDERLING* Department of Chemistry, University of Illinois at Chicago, 845 W. Taylor Street, Chicago, Illinois 60607-7061 (J.H., T.A.K.); and Bio-Rad Laboratories, Digilab Division, 68 Mazzeo Drive, Randolph, Massachusetts 02368 (D.D., R.C.)

Digital signal processing (DSP) has been implemented in a step-scan FT-IR spectrometer in a m odi cation that enables processing of high-frequency polarization modulation signals. In this work, direct comparison is made between vibrational circular dichroism (VC D) spectra measured on the same instrument, with the same samples, under the same conditions, using this new DSP method and a conventional rapid-scan tech nique (employing a lock-in ampli er for demodulation). In this initial test, both techniques generated highquality VCD for solution phase, rigid chiral m olecules such as a pinene and cam phor. Noise and reproducibility of known spectral features, as well as enhancing signal measurability and discrimination, were used as criteria for the selection of optimal DSP measurem ent parameters. Both DSP and rapid-scan VCD methods produced qualitatively reasonable spectra for biologically related molecules such as poly-g -benzyl-L-glutam ate, poly-L-proline, and duplex RNA homopolymer. In most cases, the DSP method had a slight signal-to-noise advantage based on standard deviations of the noise trace data over the rapid-scan measurem ent, but the nal results did depend on the details of the data collection and the phase correction methods inherent in both methods. Index Headings: Fourier-transform vibrational circular dichroism; FT-VCD; Digital signal processing; DSP; Step-scan infrared (IR) spectroscopy; Phase modulation; Biopolymer conformation.

INT RODUCTIO N Since the seminal work of Na e and coworkers 1–3 almost two decades ago, Fourier transform IR (FT-IR ) instruments have become the basis for most polarizationmodulation-based IR measurem ents. This includes linear dichroism (LD), often associated with infrared re ection absorption m easurements of monolayer lms,4 uniaxial deformation of a sample (e.g., polymer stretching),5,6 and vibrational circular dichroism (VC D), a property of chiral molecules typically m easured for solution phase samples.7–9 The original m ethod, sometimes referred to as the double (Fourier and polarization) modulation detection technique, utilized a rapid-scan FT-IR modi ed optically with a linear polarizer and a photoelastic modulator Recieved 3 May 2001; accepted 3 August 2001. * Author to whom correspondence should be sent.

Volume 55, Number 11, 2001

(PEM), placed before the sample. A lock-in ampli er was incorporated after the detector, as well as a pre-amp to demodulate the high-frequency polarization-induced differential absorbance signal. In order to normalize for intensity variations in the instrument (and sample) throughout the spectrum, an independent measurement of transmission was obtained sequentially after (or before) the modulation experiment, and the resulting spectral responses were ratioed in the data processing step. If the rapid-scan interferometric and polarization modulation signals are suf ciently separated in frequency, the lockin output (when set at a very low time constant) produces an interferogram, which can be processed by the FT-IR computer. This scheme requires that the software have som e exibility incorporated for phase correction. Since differential signals intrinsically have two signs (i.e., can be sensibly negative) such a phase correction is best done by transfer of a phase function from some test spectrum for which the relative sign pattern is known. (For this purpose, in the past, we have found it to be convenient to measure the pseudo-CD spectrum produced by a uniaxially stressed piece of ZnSe, usually combined with a polarizer). This reference spectrum must be measured by use of the same electronic pathway, since it is the lockin and other electronic ltering that lead to m uch of the frequency dependent phase shift (or chirp) seen in the polarization modulation interferograms. Calibration of the VCD magnitude is accomplished by measurem ent of a standard compound or by comparison to the signal developed with a multiwave birefringent plate and a polarizer aligned with the m odulator and initial polarizer, respectively.10,11 W hile the rapid-scan method works very well and has been incorporated into a number of successful instruments, 11–17 the restrictions on m odulation and the dif culty of adding yet another modulation source, such as might be envisioned in a dynamic LD experiment, led to the development of a polarization m odulated step-scan FT-IR . With the mirror stopped (relative beam path xed), there is no time-dependent Fourier modulation,

0003-7028 / 01 / 5511-1435$2.00 / 0 q 2001 Society for Applied Spectroscop y

APPLIED SPECTROSCOPY

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and there should not be a need for a frequency-dependent phase correction. Such step-scan m odi ed instruments have been shown to be capable of measuring VCD spectra,14,18–20 but no real advantage for step-scan VCD has yet been demonstrated over rapid-scan measurement for VCD, except for easier access to near-IR VCD (due to avoiding the attenuation of higher rapid-scan Fourier frequencies that is intrinsic to typical lock-in demodulation). On the other hand, with the m irror stopped, measurem ent of the transmission signal becomes problematic, requiring either a DC m easurement or ‘‘phase m odulation’’ (PM ) measurement, the latter facilitated by oscillating a m irror position about the selected step position. Thus, VCD with step-scan has not become routine but has become more useful for LD measurem ents that generate larger differential signals. 21,22 More recently, modi cations of step-scan FT-IR instruments have developed to allow direct digital signal processing (DSP), whereby the full signal from the detector (restricted only by some band-pass ltering) is digitized. 23 The relevant frequency components for the intended m easurement can then be abstracted from this signal by Fourier transforming the time-dependent waveform at each step, identifying the component of interest, and evaluating its intensity. W hen stepped through a range of retardations, these values generate an interferogram of the signal of interest. Such an approach does away with all lock-in ampli ers and their associated restricted dynamic range, nonlinearities, and phase shifts. It also permits multiple modulations to be detected and isolated in a single scan. The cost of accessing these data is that one must step the moving mirror relatively slowly so that full signal development at each step can be captured and the frequency components of interest can be accurately evaluated. Thus, DSP spectra require some time to collect, and samples m ust be stable over the long term to avoid drift or signal decay, which might apodize the spectrum. This is not generally a problem for VCD, which is typically a slow measurem ent. Initial reports of DSP applications utilized software modi cations for step-scan-equipped instruments, but only functioned for low-frequency m odulation. 23 In this paper we report polarization modulation (VCD) spectral results with a new software version that can enable detection of the effect of polarization modulation resulting from a 37 kHz PEM, as well as from PM of the m irror (100s of Hz) and, if desired, could encompass low-frequency modulation due to a sample perturbation. After establishing experimental conditions under which VCD spectra can be measured with a DSP approach, we present comparative spectra obtained on various test m olecules. Sm all m olecules, such as camphor and pinene, have become standards for testing VCD spectrometer capabilities. These molecules have numerous, inherently large bands of varying signs. Camphor has VCD signals ;4 times smaller than a-pinene (in terms of DA/A), which can, in principle, provide a better test of signal-to-noise (S/N) over a wide spectral range in the m id-IR . Signi cantly weaker and noisier VCD signals result from aqueous phase biopolymers. To test and extend the utility of the DSP m ethod for measuring reliable Fourier transform vibrational circular dichroism (FT-V CD) spectra, com1436


parisons for selected peptide and nucleic acid samples are also presented in this report. THEORY AND M ETHO DS The techniques used to perform software demodulation of the signal generated by a photoelastic modulator (PEM) are extensions of m ethods previously applied to demodulation of step-scan phase modulation signals generated by a photo-acoustic detector 23 and to simultaneous demodulation of phase modulation and a low-frequency mechanical strain 24,25 in dynamic polymer stretching m easurem ents. Both of these applications were realized with the Bio-Rad step-scan (896-interferometer) system operating under Win-IR Pro software. Here we describe in detail the process of DSP demodulation of the signals in a VCD measurement that uses relatively high frequency (37 kHz) polarization m odulation in step-scan mode with phase modulation. The interferometer step frequency, phase modulation frequency, and sampling frequency are f St , f PM , and f sa , respectively. These frequencies are controlled by the master clock in the spectrometer, where their exact frequencies are known, and where the phase of f St and f PM are constant relative to the sampling frequency. However, the PEM frequency, f M , cannot be locked to the system clock because the commercial PEM used here is a resonant oscillator whose center frequency can drift with temperature. Consequently, the PEM operates asynchronously. The f M is effectively constant within the entire data-collection period, and its phase is well-behaved within each step of the spectrometer (typically 1 or 2 s), but the PEM phase does vary randomly from step to step with respect to the master clock. The solution to this asynchronous nature is to determine the frequency and phase of the PEM drive from the data collected for the actual experiment. Generally the PEM carrier frequency is present in the signal even without a sample due to residual birefringence and polarization sensitivity in the optical train, and it has strong enough amplitude to be measured directly from the sample data. The VCD-generated signal is convoluted with that basic offset (baseline) signal, which, in principle, can have some consequences on the phase correction of the Fourier transform ed spectrum. For circular dichroism, the polarization modulation signal of interest is present at f M , while for linear dichroism, it would be at 2 f M . 26 The various signals generated due to both m odulations, although widely separated in the frequency domain, each have small bandwidths. To measure these signals by applying the concept of lowpass (minimal Nyquist) sampling would require a sampling frequency higher than 75 kHz. This rate would generate several hundred Mb of data to encompass all of the spectrometer steps required for even a low-resolution measurement. Considering that this data will then require on the order of N k (with k . 1) processing operations, it is highly desirable to reduce the number of samples, N, to be processed for a given experiment. Sam pling can be viewed as a modulation process in which the spectrum of the sampled signal contains periodic repetitions of the base band spectrum of the input signal with a period equal to the sampling frequency f sa . 27 Because the actual signal bandwidth in this exper-

F IG . 1. Im pact of ltering and undersampling on VCD signals. (a) The analog lter bandpasses are shown as trapezoids around the signals (rectangles). (b) With a sampling frequency of 22 kHz, folding points (noted by circles) are created at 11 kHz and at 22 kHz intervals thereafter and sam pling harmonics occur at 44 kHz, etc. as indicated by arrows, (c) resulting in the 37 kHz signal folding to 7 kHz but also reoccurring at ;15, 29, and 37 kHz, etc.

iment is much smaller than the separation of the spectral regions of interest (there are no frequency overlaps by design), a fairly simple analog anti-aliasing lter will allow sampling at a lower rate and prevent folding of noise over the signal bandwidth. In our design, this lter also applies gain to the PEM signal (on the order of 183 the PM signal) to optimize detection of the VCD and effectively provide increased dynamic range to the A-to-D conversion. For the VCD experiment, the signal frequencies, f M and f PM , and lter-pass bands are represented by the rectangles and trapezoids, respectively, shown in Fig. 1. Since the signals are sampled at approximately 22 kHz, folding points will result at 11 kHz and at 22 kHz intervals afterwards. Therefore, signals near 37 kHz will be folded down to ;7 kHz. Replicas of the signal spectra centered at 7 kHz occur at 15 kHz, 29 kHz, 37 kHz, etc. Only the positive frequencies are shown in the spectrum of the sampled signal for simplicity. All other frequency components at frequencies higher than 11 kHz will be ltered out in the DSP process at no cost. The ltering takes place after the demodulation of the desired frequency component for each signal channel. (The ltering integration is implemented by a summation in the discrete time domain.) A portion of the sampled VCD signal from a step near the interferogram center-burst is shown in Fig. 2a. The undersam pled polarization m odulation signal (higher frequency uctuation) and the phase m odulation signal (distorted square wave) can be recognized. A Fourier transform of the time course of this signal generates the frequency m agnitude spectrum displayed in Fig. 2b, which

F IG . 2. (a) A portion of the sampled VCD signal from a step near the interferogram center-burst, showing the 800 Hz phase modulation (PM , distorted square wave) and the undersampled 37 025 Hz polarization modulation (PEM) signals. (b) Power spectrum produced by the Fourier transform of (a). The FT-IR transmission intensity is obtained from the PM fundamental (800 Hz) while the odd harmonics are not processed. The region of the folded PEM frequency around 7400 Hz is expanded in the upper inset, clearly showing the PEM fundamental (VCD signal) appearing at 7419 Hz and the PEM 2nd harmonic (2 f M , linear dichroism signal) at 7384 Hz.

shows the signal generated at the phase modulation frequency (800 Hz) and successively weaker signals at odd harm onics of the PM frequency. The odd harmonics of the PM frequency result from the use of approximately square wave phase m odulation in the Bio-Rad FTS 60A/ 896 spectrometer. Further examination of Fig. 2b also reveals the signal generated by the PEM at 37 025 Hz, which with ltering and undersampling folds down to 7419 Hz when sampled at 22.222 kHz. Residual linear dichroism generated at the second harm onic of the PEM signal (2 f M ) can be obser ved as well, folded down to 7384 Hz. The PM odd harmonics and linear dichroism signals will be ignored in the remainder of this analysis. The PEM frequency can be m easured by determining the position of the m aximum of the magnitude spectrum in a region centered on the nominal (folded) PEM frequency. This method is severely limited by the signal-tonoise ratio (S/N), and in general, the m easured frequency will have large errors. A better m ethod for determining the PEM frequency is measuring the phase of the signal at different times within a step with respect to the phase of the nom inal APPLIED SPECTROSCOPY

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F IG . 3. Phase computational intervals in each data step, indicated with triangular apodization, that are used to compute the PEM frequency, where N is the total number of samp les in the step and M is the width of each interval.

PEM drive frequency f M0 (which we term v0 in rad/s). Then, assuming f M is constant during the step, a corrected, precise average frequency can be calculated. (In a lock-in based experiment, by contrast, the signal is constantly measured and demodulated by m ixing with the instantaneous, but ideally constant, reference signal at the modulation frequency, and their relative phases are determined by maximizing the DC output.) We select three sets of M samples out of the N samples from the rst step of the interferometer scan as shown in Fig. 3 and apodize each set with a triangular window function. We call these samples x n where n is the sample number in the step. We determine the phase error with respect to the nominal PEM frequency v0 for the set of x n samples between N /4 2 M and N /4, (Interval 1) by computing the argument (phase angle) p1 of the discrete Fourier transform (DFT) of x n at an initial estimate for v0 as:

[O ]

F IG . 4. PEM phase vs. sam ple number for the Intervals 1 and 2 shown in Fig. 3. The solid line (slope 5 v0 ) represen ts the initial estimate for the PEM frequency, the dashed line represents the initial estimate (same slope) corrected for p1 (shifted intercept), and the dash-dot line represents the correct frequency and phase of the PEM signal which is determined as vM and p12, respectively, for these two Intervals.

substituting e i(v 1 n1 p12) into Eq. 2, which then uses p3 in Eq. 4 to re ne the estimate of the PEM frequency. (All equations, unless indicated, use v in radians, which is the abscissa of the DFT.) v 3 5 v1 2

N /4

p1 5 arg

N /4 2 M

x n eiv 0n

(1)

where p1 is the average phase in Interval 1; assum ing the phase is linear with time (frequency constant in one step), w e assign p1 as the phase in the m iddle of Interval 1. Figure 4 shows that the actual frequency v M (the slope of the dash-dot line) will be different from the nom inal frequency v 0 of the PEM (slope of the solid line). If w e recom pute the DFT for the sam e samples in Inter val 1 with e i(v 0 n2 p1) , the resulting argum ent would be zero; that is, v0 with phase 2p1 is in phase with the PEM carrier at the center of Interval 1, as indicated by point A in Fig. 4. Now we compute the argument p2 of the DFT of x n over Interval 2 using e i(v 0 n2 p1) , or

[O

N /4 1 M

p2 5 arg

N/4

x n e i(v 0 n2 p1)

]

(2)

With the value of p2, we can compute an estimate of v1, the corrected PEM frequency: v1 5 v0 2

p2 M

(3)

M is selected to m eet the conditions as de ned by Eqs. 6 and 7 below. Using v1 we compute the phase p12 of v1 for zero error in Interval 1. p12 5 (v 0 2 v1 )

1 4 2 2 2 2 p1 N

M

(4)

With p12 we compute the phase error p3, in Interval 3, 1438


p3

1

N 1M 2

(5)

2

Another iteration may be required depending on the value of M used. The order of magnitude of the remnant error can be estimated by evaluating zv3 2 v1z. For Eqs. 3 and 4 to be valid, M m ust be small enough so that p2 , p, and large enough so that p3 , p. The rst condition is met if: zv M 2 v 0zM , p,

then

M ,

f sa z fM 2 f 0 z 2

(6)

where f sa is the sampling frequency. The second condition is met if: zv M 2 v 1z

N ,p 2

(7)

If the second condition is not met, a second iteration in Eq. 3 is required with a larger interval length M 9, to obtain a better estimate of v1 . At the same time, to optimize the convergence of the m easurement of f M , the interval width should be selected so that the spectrum of the apodized signal has a minimal contribution at the PM side band frequency. The spectrum of a signal apodized with a triangular function of time interval M / f sa has zeros at 2k 1 f sa /M, where k 1 is an integer. For the PM frequency f PM we can select M: M 5

2k 1 f sa f PM

(8)

This should zero out the contribution of PM in this interval and result in a better measurem ent of f M . For example, for f sa 5 20 kHz, f M 5 6 kHz, z f M 2 f 0z , 20 Hz, and f PM 5 400 Hz, M can be a multiple of 100, but no larger than 500.

For successive steps, the values of v M and p M m ust be measured using the process above, with v1 5 v M from the previous step. Now only the last iteration will be required, since v M will not have any signi cant drift during the time of one step. This process gives us the best possible determination of the frequency of the PEM-originated signal in each step, thus allowing determination of its m agnitude. Prior to m easurement of the sample spectrum, a calibration procedure is required to determine the spectral phase correction for vPM . In the calibration procedure, a DSP data collection is perform ed to produce a low-resolution interferogram. Demodulation of that signal, Y n , with v PM for each step is performed to obtain the magnitude of the transform for that step and the argument p PM 1, which will be the same for every step and in related experiments, for the step with the maximum magnitude in the scan. The rotation of the complex interferogram with 2p PM 1 gives a real and imaginar y pair of interferograms. The spectrum corresponding to the ‘‘real’’ interferogram is computed with a M ertz phase correction and the resulting phase array is stored for use in computing the spectrum for the ‘‘imaginary’’ interferogram using the same peak location. Next, the areas under the two spectra are computed over the spectral region of interest, and a second rotation, p PM 2, is applied so that the area under the quadrature (imaginary) com ponent is zero. Therefore, the phase for the phase demodulation of any sample is: p PM 5 p PM 1 1 p PM 2

(9)

Once the phase of the PM signal has been determined for a given set of experimental conditions, this parameter is stored for later use with the sample. The phase calibration procedure is automated in the software, from the collection of the calibration data to the calculation of p PM . The phase value is stable for a given instrumental con guration, and it is generally not necessary to recalibrate unless there is a change in the instrum ental measurem ent param eters. EXPERIMENTAL Samples. a-pinene was measured as a neat liquid while camphor was prepared as an ;0.6 M solution in spectrophotometric grade CCl4 . Spectra were collected by placing either neat liquid or solution in a standard variable pathlength cell with KBr windows. Pathlengths were nominally 50 mm and 100 mm for neat and solution samples, respectively. Biopolymer samples included poly-gbenzyl-L-glutamate, dissolved in CHCl3 at approximately 1% (w/v) and m easured in a variable pathlength cell, as well as poly-L-proline and polyC-polyG, which were prepared at concentrations of 25 m g/mL in D 2 O and placed in a cell of our construction consisting of two circular CaF 2 windows separated by a 50-mm Te ony spacer and held in a brass com pression ring. Instrument. VCD measurements were perform ed utilizing a Bio-Rad (Randolph, M A) FTS-60A spectrometer with an 896 interferometer and Win-IR Pro software that provides step-scan and dynamic alignment capabilities. This spectrometer is coupled to a specially constructed external VCD bench, purged with dry air, as schemati-

F IG . 5. Schematic of the UIC FT-VCD spectrometer with signal processin g for DSP and rapid-scan VCD. The external beam emerging from the FTS-60A is directed by a at mirror (M1) onto a spherical (; f /10) focusing mirror. The slowly focused beam passes through the polarizer (P) and modulator (PEM ) and onto the sample (S ) where it diverges again. The beam is collected by a fast (; f /1) ZnSe lens (L) and is focused onto the MCT detector (D ) after passing through an optical bandpass lter (F ). The long path setup was designed for another purpose (magnetic VCD),15 but has proven useful for control of VCD artifacts. The entire spectrometer (FT-IR and external VCD bench) is purged with dry air. The signal collection and processing routines are schem atically represented in the boxes. In rapid-scan mode, separate measu rements of transmission and VCD intensities are made with the polarization modulation signal being demodulated via a lock-in ampli er, while in DSP mode both can be obtained simultaneously and directly by the software with the addition of an analog anti-aliasing lter as described in the text.

cally shown in Fig. 5.11,12,19,28 Infrared intensities were detected with a liquid nitrogen cooled Hg 1 2 x Cd x Te (MCT) detector after passing the beam through an optical bandpass lter (1900 –900 cm 2 1 ) placed directly before the detector. This lter is used to restrict the signal bandpass to the useful mid-IR vibrational region, thereby avoiding folding problems due to undersampling, and additionally helping to avoid saturation and consequent nonlinearity in the transformed spectrum. Alternating left and right circularly (actually elliptically) polarized light was produced by the combination of an Al wire grid polarizer APPLIED SPECTROSCOPY

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on a barium uoride substrate (Cambridge Physical Sciences) in combination with a ZnSe photoelastic m odulator (PEM, Hinds PEM -80) operating at 37 kHz. The nominal PEM operating frequency, which is required by the DSP software, was independently determined by a frequency counter to within 5 Hz and was very stable over a period of weeks as long as the modulator amplitude was not changed. Implementation of DSP-VCD as described in this paper is primarily an issue of software development, which is, in principle, generalizable to any step-scan FT-IR; but implementation of that software is dependent on fast, high precision A-to-D conversion, careful analog ltering, and extensive com putational capability. The actual package used here is now available as an upgrade of the Win-IR Pro software package from Bio-Rad. The personal computer controlling the spectrometer and perform ing the data processing was upgraded to a Pentium III, 733 MHz system with 512 M B of RAM and 40 GB of disk space, and the active analog lter (DSP inset, Fig. 1) was built to purpose by Bio-Rad for VCD or LD applications. For rapid-scan VCD m easurements, the PEM m odulated signal is demodulated with a Stanford M odel 850 lock-in ampli er as indicated in the schematic representation of the FT-VCD electronics (rapid-scan inset, Fig. 5). With this lock-in, which operates internally in a DSP mode, a low output time constant of 300 ms was found to yield an optimal response. Rapid-scan spectral processing required the use of a stored phase correction to be applied to all single-beam interferogram s. These were obtained by previous measurem ent of a stressed ZnSe plate and polarizer pair as described earlier.11,19 The VCD magnitude was determined by calibration with the signal from a CdS m ultiple wave plate–polarizer pair.11 DSP FT-VC D measurements required phase modulation. With phase modulation one can derive an interferogram of the polarization modulation signal at the PEM frequency or one of the v PEM 6 v PM sidebands. For LD signals, the latter method is preferred. However, for small amplitude VCD signals, particularly with biologically relevant samples, the signal derived at the PEM frequency yields the best data. We initially chose a PM frequency of 800 Hz (a condition for which the software parameters allowed 20 000 samples of the waveform at a 45 ms sampling rate for a 1 s step) and a m odulation amplitude of 0.5 l (HeNe reference wavelength). Measurement parameters are, in large part, constrained by the current software package in order to avoid con icts in the highly folded Fourier representation of the frequencies. To the extent possible, they were optimized for m aximal VCD signal and S/N as described in the next section. Due to minor optical m isalignment, m ost test spectra were m easured under less than optimal baseline conditions, which led to an offset probably due to residual birefringence in the optical path. However, this offset had a measurement bene t in that it provided enough integrated signal intensity at the modulation signal to dominate the center-burst area of the interferogram. This normally allowed the software to determine the correct phase directly from the samples themselves and, in most cases, did not require use of a stored phase correction. In speci c instances this ‘‘short-cut’’ could lead to problems, 1440


which are discussed later with presentation of the relevant data. For rapid-scan, the transm ission interferogram and the polarization modulation interferogram normally require separate measurem ents, unless the instrument is enhanced with dual channel signal processing and A-to-D conversion capability. In contrast, DSP detection of phase and polarization modulation allows signals needed to construct both interferogram s to be collected and digitized simultaneously and then processed sequentially using stored data. After Fourier transformation of these two interferogram s, the resultant response spectra (single-beam transmission and polarization modulated spectra) are ratioed to give the raw (uncorrected) VCD spectra (often termed I A C /IDC , re ecting early CD literature).11 Spectra were normally collected at 8 cm 2 1 resolution, and in all cases, each sample was prepared and measured with both rapid-scan and DSP collection m ethods for comparison on exactly the same optical arrangement. In addition, we measured a-pinene VCD as a function of spectral resolution in DSP m ode. Comparison m easurements of the aqueous peptide and nucleic acid samples were also measured with our dispersive VCD instrument11,28 to provide a standardization and a test against accepted band shapes for these more-dif cult-to-measure samples. For each sample, VCD spectra were obtained as the average of 2 blocks of scans, each of which encompassed either 17 m in (sm all rigid organic molecules; total collection time is 34 m in) or 34 min (aqueous, conformationally variable biological polymer molecules; total collection time is 68 min). Additionally, in an attempt to obtain improved spectra for the polypeptide, poly-g-benzyl-L-glutamate (PBLG), throughout the amide I, II, and III regions in the m id-IR (1750 –1300 cm 2 1 ), we m easured spectra for a m uch longer amount of time (total time is ;5 h). In rapid-scanning mode, a single scan set of 1000 symmetric inteferogram s of the PEM signal (I AC ) was collected using in-scan coaddition at an interferometer speed of 10 kHz comprising a collection time of 8.5 min. This choice of collection time was an arti ce dictated by a desire to match the DSP conditions, for which a single asymm etric scan (at 8 cm 2 1 resolution, 1 Hz step speed) required 8.5 m in. Likewise, for every scan set of the PEM signal, a subsequent collection of 64 symmetric coadded interferograms yielded the transmission signal (I DC ). Each was collected with an undersampling of 2 (spectral range of ;7800 cm 2 1 ) which is the usual option for these conditions. Two such scan sets were averaged to produce one rapid-scan block. In both m ethods the raw VCD spectrum is obtained by a direct ratio of the polarization modulation signal to the transm ission signal. The average of the sum of successive scan blocks produced the nal VCD spectrum, while one-half of the difference yielded the noise spectrum. For DSP collection, two 8.5 min asymm etric stepscans (modulated and digitized as described above) collected with an undersam pling ratio of 8 (spectral range 0 –1950 cm 2 1 ) and coadded, constituted one step-scan block, and average VCD and noise spectra were obtained in the same manner. VCD spectra were baseline corrected by subtraction of the subsequently obtained spectra of either an empty cell (for neat liquids) or in the same cell

F IG . 6. Comparison of raw VCD for a-pinene collected at (a) 400 and (b) 800 Hz phase modulation (PM) in DSP mode. In each plot, two successive spectra are presented by solid and dashed lines. Arrows designate regions of variability in the successive scans under 400 Hz PM. At 800 Hz PM, successive scans are practically identical.

with CCl 4 or D 2 O used for the corresponding samples. Since calibration of the DSP was not possible at this time using our multiple (l/4) wave plate–polarizer method,10 due to overload of the electronics under DSP conditions for the ;10 4 larger signal from this calibration method, VCD intensities of DSP-based spectra were norm alized to the conventionally calibrated 10,11 rapid-scan measurements. (In rapid-scan, the lock-in gain is reduced 200fold for the calibration measurement, but the current analog lter has no provision for gain variation.) For measurements of PBLG, two successive scan blocks were collected comprising a time of ;2.5 h each. Each scan block was either the coadded result of 16 DSP step-scans or 16 000 rapid-scans of the polarization m odulation signal (with 256 scans of the transmission signal). Resultant VCD spectra were baseline corrected by subtraction of an identical scan of CHCl 3. The average VCD and noise spectra in both cases comprised a total collection time of ;5 h. RESULTS Parameter Tests. To determine optimal step size, modulation amplitude, and other adjustable parameters, a number of initial tests were carried out with the Win-IR Pro v3.0 software. The frequency of the PM used was the rst variable tested, for which the DSP software allowed a choice of 400 or 800 Hz, but the same num ber of data points (20 000 samples) could be collected with both. To test this we measured a-pinene as a function of PM frequency. Better spectra, in terms of replicating known spectral bandshape and scan-to-scan reproducibility (lower noise) were obtained by use of 800 Hz PM (Fig. 6). As seen in these raw (not calibrated or baseline corrected) VCD in Fig. 6, successive scan blocks collected at 400 Hz PM show more variability at higher wavenumbers (indicated by arrows). In 400 Hz spectra collected for camphor (data not presented), anomalous VCD intensities (compared to other bands in the region) were additionally observed to occur where IR bands of the sample coincided with intense IR bands of the solvent. Because normalization to the transmission intensity

is required to obtain the VCD spectrum, these regions of solvent interference generally have sharply ampli ed noise contributions. Empirically, we found that using a PM of 800 Hz reduced this effect and consequently gave more reproducible spectra with more proportionate intensities. Furthermore, the ratio of the real (in-phase) PM signal to the quadrature (out-of-phase) PM signal at 800 Hz was 2.5 times greater than that obtained at 400 Hz, again implying a more accurate measure of the PM signal and its phase. A key element to the simultaneous measurement of the transm ission with the polarization modulation signal is the use of phase m odulation to develop an AC signal of reasonable S/N whose amplitude at each step is proportional to the interferogram of the transmission. In our previous step-scan VCD tests, using a conventional approach to polarization modulation detection with an external lock-in ampli er, we found that PM led to a distinct degradation in S/N.19 Presumably this is due to overloading or nonlinear response induced in the lock-in. Though tuned to the weak 37 kHz polarization modulation, the lock-in is still subject to the very strong phase modulation signal at its input stage. Furtherm ore, PM is capable of creating potentially interfering sidebands above and below the PEM frequency. Our tests of DSP-based VCD with pinene and camphor were perform ed at a PM of 800 Hz with the PM amplitude selected at either 1.0 l or 0.5 l. As expected, reduction in PM amplitude from 1.0 to 0.5 l produced a decrease in the PM response (transmission signal) by a factor of 2 but did not alter the magnitude of the PEM response (modulation signal). Figure 7a illustrates that by reducing the phase m odulation amplitude, the polarization modulation signal is more detectable to the eye (but is basically the same absolute magnitude), riding on top of the phase modulation signal. With the lower amplitude PM coupled to increased overall signal gain, the dynamic range of the A-to-D conversion can be m ore fully utilized for signals in both band passes, at the PM and PEM frequencies. The effect of PM amplitude variation is passed on to the VCD signal (obtained by the direct ratio of the AC signal to the DC APPLIED SPECTROSCOPY

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F IG . 7. (a) Comparison of the signal from a step near the center-burst collected with a phase modulation (PM) amplitude of 0.5 l (bottom) and 1.0 l (top) in DSP m ode. The sample measured was (1)-camphor. As the PM amplitude (PM frequency 5 800 Hz) is reduced from 1.0 to 0.5 l, the polarization modulation (PEM) signal becomes more apparent riding on top of the PM signal. (b) The subsequent raw VCD spectra for (1)camphor obtained from complete step-scans (513 pts.) as a function of PM amplitude. VCD band features become more intense and sharper at lower PM amplitude due to normalization with a less intense PM spectrum.

signal) in that the m agnitude of the transm ission-normalized VCD was doubled (Fig. 7b) by changing the PM amplitude from 1.0 to 0.5 l. This enhancement was assumed to be useful for detection of weaker VCD signals, but that remains yet to be proven since the corresponding noise traces for pinene and camphor obtained under the two PM amplitudes were not signi cantly different. In summ ary, the increased dynamic range and separability of modulation frequencies that should be possible via DSP detection are borne out in practice. In an effort to have a de ned set of parameters to use for all spectra measured via DSP, we chose a phase m odulation amplitude of 0.5 l. Step size (time) is another variable. For weak signals, we wish to obtain the most precise m easure possible of the PEM frequency component at each step. This should be obtained by collecting the maximum number of samples in the time course of the signal in each step and Fourier transforming those samples to get the most accurate m easure of the amplitude of the components desired. In the Win-IR Pro v3.0 software, the param eter selections are coupled. A choice of longer (time) steps can perm it collection of m ore data points at each step. Since we are primarily interested only in data below 1900 cm 2 1, we can undersample by a factor of 8 (every 8th zero crossing of the HeNe laser interferogram) and thus collect more data points (thereby achieving higher spectral resolution) that re ect only the region of interest for a given total measurement time. (This option is not available or useful with rapid-scan due to the constant velocity of the mirror.) The software used for these tests allowed a step rate of 1 Hz and 20 000 data points sampled at 45 ms spacing (0.9 s total). For biological samples with inherently weaker VCD signals, the ability to collect more points per interferogram m ight be bene cial. We tested this possibility by collecting 40 000 data points per step (0.5 Hz step) and found that there was no measurable difference in the spectra collected with these two step times (under the constraint of a constant total m easurement time). This is consistent with total collection time being the most important variable, since the effective 1442


duty cycle (20 000 data points collected in 0.9 s or 40 000 data points collected in 1.8 s) is the same. The resolution and aperture variables were also tested. For convenience of testing, we chose to use 8 cm 2 1 resolution (scan length), even though spectra for small m olecules are more comm only reported at 4 cm 2 1. To test the capability of DSP to measure FT-VCD at higher resolution, a-pinene was m easured at 2, 4, 8, and 16 cm 2 1 resolution. Naturally, the length of the data collection time scaled linearly with the resolution. As seen in Fig. 8a, use of a standard M ertz phase correction can result in some sign and band shape errors that increase in severity as the spectral resolution is improved. Transfer of a phase correction le that was obtained from the 16 cm 2 1 resolution spectra (Fig. 8a, bottom spectra), which does have the correct VCD sign patterns for the whole spectral region, proved to be a successful m eans of producing qualitatively correct VCD bandshapes for the higher resolution measurem ents as well (Fig. 8b). The choice of 8 cm 2 1 for m easuring comparative VCD spectra was m ade simply to achieve a shorter testing time for each step-scan measurement and, consequently, for each comparative rapid-scan m easurement. All spectra were zero- lled by a factor of 8 to interpolate between the digital data and allow better band shape comparison with other data, such as that obtained from a dispersive spectrometer, which naturally samples the spectrum much more frequently even though its true spectral resolution is low due to the large (8 cm 2 1 effective) slit width used. Such a low-resolution interferogram is suf cient for the broad bands characteristic of the biological samples used in our nal test. Aperture settings corresponding to 8 cm 2 1 (open) and 2 cm 2 1 (resolution at 4000 cm 2 1) were tested. However, having the aperture open produced the same light throughput as 2 cm 2 1 for this VCD experiment, which is not general but rather a design artifact of our instrument. Due to the extremely long focal length (; f /10) used to illuminate the sample (Fig. 5), the polarizer and the sample cell act as the real limiting apertures of the softly focused IR beam. Sample Spectra. Absorbance (bottom) and VCD

F IG . 8. (a) Raw VCD spectra of a-pinene measured at 4, 8, and 16 cm 2 1 resolution. Asterisks in the 4 and 8 cm 2 1 scan s indicate processing problems (sign errors) obtained with the standard Mertz phase correction for that scan . However the low-resolution spectra does retain the correct VCD sign pattern throughout the region. (b) After transfer of the stored phase le from the low-resolution measurem ent to the 4 and 8 cm 2 1 resolution measurem ents, the proper VCD sign pattern is obtained for all scans.

F IG . 9. FT-IR absorbance (bottom), FT-VCD (middle), and FT-VCD noise (top) spectra for a-pinene (neat) collected in rapid-scan and DSP modes. The VCD spectra are the result of a total collection time of 34 min (the average of two successive scan blocks each totaling 17 m in in length) and are baseline subtracted, while the noise traces represent onehalf of the difference between the successive scan blocks. The VCD and noise spectra are stacked in the sam e order: DSP (top) and rapidscan (bottom). The noise spectra ordinate is enlarged to facilitate visible comparison. Identical VCD spectra are obtained with both m ethods and yield essentially comparable noise spectra.

(middle) spectra with a representation of the noise (top) spectra for a-pinene and camphor are presented in Figs. 9 and 10. FT-VC D spectrometer comparisons have generally settled on a-pinene as a standard test sample. It provides easy-to-m easure spectra with multiple transitions over the 900 –1350 cm 2 1 region. As can be seen in Fig. 9, the rapid-scan and DSP spectra for pinene (neat liquid) collected over 34 min are virtually identical and have little noise. In the top traces, the noise amplitudes for each are expanded in scale to facilitate comparison. A standard deviation (s) of 68.9 3 10 2 3 was obtained for both noise traces, revealing that no advantage exists for either method, and, accounting for resolution, the spectra closely m atch literature values. 19 Camphor, on the other hand, has a weaker VCD amplitude than a-pinene (in terms of DA/A) and has more variance in absorbance amplitude, which can provide a tougher instrumental test for VCD spectral measurem ent. For these measurements, ;0.6 M solution of camphor in CCl4 gave absorbances 3–5 times greater than did the apinene sample throughout the characteristic region, which results in each having comparable DA values but added noise for the highly absorbing peaks in camphor. Again, both DSP and rapid-scan FT-VC D results for camphor (Fig. 10) yielded virtually identical spectra, comparable to previous m easurements, 19 reproducing both band shape (width and sign) and intensities (after calibration and normalization). In this case, the noise traces, while very similar in magnitude, gave a slight advantage to the DSP data set, particularly in regions of strong absorption (A ;1). Standard deviations of the noise traces also indicated that DSP gave an advantage (sRAPID 5 60.062 and sD SP 5 60.038) in terms of S/N for successive m easurements. Since DSP requires no lock-in ampli er, thereby eliminating extra electronic variables (lock-in gain, time constants, and tuning), and since high-quality DSP FTVCD spectra can be collected in tens of minutes, it is clear that the DSP method offers a suitable alternative to conventional means of collecting VCD spectra. To look at the potential of DSP FT-VCD for measuring spectra of biopolymers, a comparison of spectra and noise traces obtained with DSP and rapid-scan methods APPLIED SPECTROSCOPY

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F IG . 10. FT-IR absorbance (bottom), FT-VCD (middle), and FT-VCD noise (top) spectra for (1)-camphor (in CCl4 ) collected in rapid-scan and DSP m odes. VCD spectra are corrected for baseline by subtraction of an additional scan of CCl4 in the sam e cell with the same pathlength. More noise is observed in the rapid-scan spectrum for regions where the VCD signal is dominated by large absorbance (A ;1 at ;1450 cm 2 1 , 1040 cm 2 1 ). These regions also show some small differences in the two VCD spectra.

fo r the p olypeptides po ly -g-benzy l-L-glutam ate in CHCl3 , poly-L-proline in D 2 O, and the duplex RNA homopolymer, polyC-polyG, also measured in D 2O, are presented in Figs. 11, 12, and 13. Biopolymers that develop larger VCD signals were chosen for this comparison to effect an initial comparison of these two FT-VCD techniques without the result being overwhelmed by S/N considerations. Furtherm ore, unless this instrument is carefully aligned, it can be subject to absorption artifacts that can distort the spectrum for weak (in terms of DA/A) transitions. Some such effects, due to the current con guration of the UIC FT-VCD spectrometer, are unfortunately evident in the spectra obtained here. Poly-g-benzyl-L-glutamate (PBLG) exhibits a righthanded a-helical conformation in CHCl3 or CDCl 3 with a long persistence length, which results in a quite intense amide I (C5O stretch) and easily detectable amide II (N– H deformation and C–N stretch) VCD bands. 29,30 The DSP and rapid-scan FT-VCD spectra for PBLG with amide I and II bands at ;1660 cm 2 1 and 1510 cm 2 1 , re1444


F IG . 11. FT-IR absorbance (bottom), FT-VCD (middle), and FT-VCD noise (top) spectra for the amide I and II regions of poly-g-benzyl-Lglutamate in CHCl3 collected in rapid-scan and DSP modes. VCD spectra are of the same sample in the same sample cell and are baseline corrected by subtraction of a CHCl 3 spectrum. Total collection time is ;5 h.

spectively, are presented in Fig. 11. These spectra are in agreement with the positive couplet (1, 2 with increasing wavenumber) amide I VCD and negative amide II (shifted below the absorbance) as previously measured with FT-VC D and dispersive VCD for PBLG 29,30 while avoiding the negative artifact (presumably optical in origin 29) to low frequency in the amide I as found in some previous FT-VC D reports.31 W hile DSP and rapid-scan noise traces are very similar for PBLG (s ø 60.16 for both), the resultant bandshapes are impacted by noise and, in the DSP amide I case, further distorted by the phase correction. The amide I shape, with a weak positive component as seen in DSP, matches the dispersive shape better and may again re ect enhanced dynamic range in the DSP-based measurement. The amide III region VCD was even noisier, but was predominantly positive, in agreement with previous results. 29 Turning to a peptide example in aqueous solution, the type II form of poly-L-proline was measured for this comparison because it has a stable structure in D 2 O, develops a long persistence length, and has possibly the

F IG . 12. FT-IR absorbance (bottom), FT-VCD (middle), and FT-VCD noise (top) spectra for poly-L-proline II (in D 2 O) over the amide I region collected in rapid-scan and DSP m odes and compared to a dispersive VCD m easuremen t of the sam e sample at the same resolution (8 cm 2 1 ). Spectra and noise traces are stacked from top to bottom: dispersive, DSP, and rapid-scan.

most intense VCD of any homopolypeptide.32,33 Poly-Lproline II (PLP II), with left-handed helical chirality, displays a characteristic negative couplet amide I (C5O stretch) (Fig. 12), opposite in sign to that seen in a-helices (Fig. 11). This PLP II amide I VCD pattern is similar to the amide I VCD band shape of random coil polypeptides; 32–34 however, the PLP II amide I is more intense and appears at a lower frequency than typical random coils such as poly-L-lysine and poly-L-glutamic acid.34,35 As evident from Fig. 12 (middle), the VCD band shapes in both FT-VC D m easurements are similar, albeit with some variations in intensities. These spectra are slightly distorted from the accepted PLP II form as rem easured with a dispersive instrument (top VCD trace), which is in agreement with published results for PLP II and random coil peptides from our and other laboratories.28,32,34–36 For this comparison, the DSP method had less noise for successive m easurements by about a factor of 2 (sDSP 5 60.012, sRAPID 5 60.022, sD ISPERSIV E 5 60.024) as compared to both rapid-scan and dispersive-based collection,

F IG . 13. FT-IR absorbance (bottom), FT-VCD (middle), and FT-VCD noise (top) spectra for the RNA duplex polyC-polyG (in D 2 O) collected in rapid-scan and DSP modes again compared to a dispersive VCD measu rement of the same samp le. Spectra and noise traces are stacked as in Fig. 12.

but the dispersive VCD signal is somewhat larger than that with FT-VCD (only rapid-scan is calibrated). The RNA homopolymer polyC-polyG forms a regular A-form (right-handed) double helix. The VCD signature for polyC-polyG is that of a positive couplet at ;1690 cm 2 1 , which arises primarily from coupling of the C5O stretching modes of the stacked planar bases. 37,38 Other IR/VCD regions can be accessed, such as the P–O phosphate stretch,39 which give information on polynucleotide backbone stereochemistry; however, solvent choice and concentration in a given sample tend to complicate practical m easurement of spectra over very large wavenumber regions. Again, both FT-VC D measurem ents in Fig. 13 show the expected couplet at ;1690 cm 2 1, but baseline variations obscure the weaker features. It appears that in both cases the baseline drifts to the positive side of zero at lower wavenumbers m aking it dif cult to m easure the very weak negative VCD (1670 –1620 cm 2 1 ) that is seen in the dispersive (upper) spectrum and in previous measurements.37,38 This offset is probably optical in origin (a property of spectrometer alignment) and not due to spectral processing. However, the inconsistency of the two FT-VCD results suggests that one or the other m ay have a slight nonlinearity leading to some photometric inacAPPLIED SPECTROSCOPY

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curacy for the broad components of the spectrum (baseline). In this case the rapid-scan has the edge in terms of the noise (sRA PID 5 60.013, sD SP 5 60.038, sD ISPERSIV E 5 60.017). DISC USSION These comparisons between rapid-scan and DSP m ethods for collecting FT-VC D spectra prove that the DSP method can yield both spectral band shapes and noise levels comparable to its rapid-scan counterpart. Thus, this fully digital process (without lock-in) is realizable and practical. It should be clear that although both types of spectra were carefully m easured and, in particular, common m easurement times were used to elicit sensible comparisons, both m ethods could still be optimized. The DSP spectra measured appear to be m ore limited by optical constraints than by m ethod. For intense spectra from sm all rigid molecules in regions of good baseline, the two FT-VCD methods yield identical results. For weaker VCD signals, the two FT-VCD approaches do not yield identical band shapes, indicating that artifacts were processed differently, either due to non-linearities or phase errors, since identical samples, optics, and detector were used in all cases. In our earlier studies,19 we found that higher S/N rapid-scan spectra can be m easured under what might be called slow-scan conditions, whereby scan rates would be decreased from ;0.30 cm/s (10 kHz) to ;0.03 cm/s (800 Hz). However, in our DSP FT-VC D test of 2 s steps with 40 000 samples vs. 1 s steps with 20 000 samples, each with the same PM and the same total m easurem ent time, we found no difference, which suggests that, with at least 20 000 samples, total m easurement time is the critical issue. In addition, while measuring the PEM frequency signal directly in the DSP process yields the best S/N spectra, it can have potential dif culties with our conventional calibration scheme, which develops a ver y intense oscillating signal.10,11 Despite the large signal levels, we can determine a useful phase correction with a stress plate. However, a VCD calibration curve generated with a m ultiple quarter wave plate and polarizer evidenced a severely distorted interferogram, which is a sign of ampli er overload, and could not be converted to a standard calibration curve.19 The response problem is most likely speci c to our optical or analog (FTS 60A) components, as other Bio-Rad instruments (FTS-6000 based) do not seem to have this same problem. It probably relates to detailed gain pro les in the pre-amp, lter, and analog input stages, which could be modi ed by varying the gain in the PM and PEM signal bandpasses. DSP processing in general yields a greater dynamic range in the demodulation step than one could expect from a conventional lock-in ampli er alone because the analog ltering on the input is designed to give the signals of interest (e.g., PM and PEM based) an optimal amount of gain and to suppress all other out-of-band signals. After input and A-toD conversion, the digital lter can additionally be optimized to extract the maximum information content. However, compared to the rapid-scan experiment, since the transmission and polarization m odulation spectra are there measured sequentially, this DSP dynamic-range advantage may be minor if proper input ltering is used to 1446


prevent overload of the lock-in by out-of-band signals. Additionally, the lock-in gain can be reduced by as much as 10 3 to effectively increase dynamic range between sample and calibration experiments and enable m easurement of these high level signals (where DA is the order of 1.0) without overload of electronics. In the future, such an advantage could also be realized in the DSP mode (if desired) by incorporating a selective (as opposed to xed) gain in the analog signal lter for purposes of calibration and phase determination for VCD. It can further be noted that step-scan VCD with lock-in demodulation, thereby requiring separate m odulated and transmission data collection scans, as in conventional rapid-scan mode, has been shown to be not as good, in terms of S/N, as rapidscan VCD.19 The advantage of VCD spectral collection with an FT instrument as compared to a dispersive (scanning) spectrometer lies in its ability to m easure spectra over an entire spectral region as opposed to collecting one or two IR/VCD active bands in the dispersive case. This can clearly be realized in collecting spectra of the multiple VCD bands of camphor and pinene in the 850 –1500 cm 2 1 region in a single experiment. DSP, by eliminating the need for a lock-in and for separate transmission scans, further simpli ed these measurements. Yet dispersive VCD for measurement of a single broad band remains a quite competitive technique in terms of S/N and band shape delity. Furtherm ore, it is free of the processing dif culties of an FT-based experiment.11,28 Much of the driving force for development of VCD spectroscopy, and indeed any chiro-optical technique, is for biological applications. All important biopolymers are chiral, but the interesting VCD spectra they develop tend to result from chiral coupling of achiral oscillators, either through the vibrational force eld or through space.8,28 These give distinctive VCD patterns, yet for the heteropolymers that are arguably of most importance for conformational analysis, i.e., proteins, the signals are quite weak. Thus sensitivity (S/N) and baseline quality are very important attributes. It appears that DSP-based FT-VCD neither hurts nor helps these conditions; but, with its large dynamic range, DSP may be bene cial for those m easurem ents impacted by sharply interfering absorbance bands through potential increased photometric accuracy in step-scan m easurements. By contrast, the dispersive measurements avoid some of this con ict, and retain very good spectral delity, by the fact that the transmission signal is so much weaker due to detection of a relatively narrow (;8 cm 2 1 ) bandpass at any point in time, which consequently results in less dynamic range requirements than does an interferogram with a large center-burst. CO NCLUSIO N Our results clearly indicate that digital signal processing can successfully be extended to the detection of highfrequency modulation signals as produced in the VCD experiment. All spectra collected are comparable and reproducible in themselves and in relation to previous measurem ents. Examination of the noise traces reveals that qualitatively similar results are obtained with DSP and rapid-scan methods. The spectral noise traces show variations that are the same bandwidth as the VCD bands.

This is a result of the Fourier processing and m ust be carefully examined along with the VCD spectra in order to make valid spectral interpretations. The S/N levels for both FT-VCD m ethods can be considered as roughly equivalent for the large biopolymer signals, as was observed for the sm aller m olecules also m easured here. Both of the current sets of results are superior to stepscan VCD spectra measured with a lock-in ampli er coupled with sequential transm ission m easurement. Thus the DSP approach with simultaneous modulation and transmission spectral m easurement is the better way to obtain step-scan spectra, should that approach be desired. ACK NOW LEDGM ENTS The work at UIC was funded in part by a grant from the Research Corporation and was enabled by provision of software, equipment components, and development assistance through a collaboration at BioRad. 1. L. A. Na e, M. Diem, and D. W. Vidrine, J. Am. Chem. Soc. 101, 496 (1979). 2. L. A. Na e and M. Diem, Appl. Spectrosc. 33, 130 (1979). 3. L. A. Na e and D. W. Vidrine, in Fourier Transform Infrared Spectroscopy, J. R. Ferraro and L. J. Basile, Eds. (Academic Press, New York, 1982), p. 83. 4. A. E. Dowrey and C. Marcott, Appl. Spectrosc. 36, 414 (1982). 5. C. Marcott, Appl. Spectrosc. 38, 442 (1984). 6. R. A. Ingemeny, G. Strohe, and W. S. Veeman, Appl. Spectrosc. 50, 1360 (1996). 7. L. A. Na e, G. S. Yu, X. Qu, and T. B. Freedman, Faraday Discuss. 99, 13 (1994). 8. T. A. Keiderling, in Circular Dichroism: Principles and Applications, N. Berova, K. Nakanishi, and R. A. Woody, Eds. (WileyVCH, New York, 2000), 2nd ed., p. 621. 9. P. L. Polavarapu, Vibrational Spectra: Principles and Applications with Emphasis on Optical Activity, (Elsevier, New York, 1998), Vol. 85. 10. L. A. Na e, T. A. Keiderling, and P. J. Stephens, J. Am. Chem. Soc. 98, 2715 (1976). 11. T. A. Keiderling, in Practical Fourier Transform Infrared Spectroscopy, K. Krishnan and J. R. Ferraro, Eds. (Academic Press, San Diego, 1990), p. 203.

12. P. Malon and T. A. Keiderling, Appl. Spectrosc. 42, 32 (1988). 13. C. C. Chen, P. L. Polavarapu, and S. Weibel, Appl. Spectrosc. 48, 1218 (1994). 14. F. Long, T. B. Freedman, R. Hapanowicz, and L. A. Na e, Appl. Spectrosc. 51, 504 (1997). 15. R. K. Yoo, P. V. Croatto, B. Wang, and T. A. Keiderling, Appl. Spectrosc. 45, 231 (1991). 16. D. Tsankov, T. Eggimann, and H. Weiser, Appl. Spectrosc. 49, 132 (1995). 17. L. A. Na e, X. H. Qu, F. J. Long, and T. B. Freedman, Mikrochim. Acta S14, 803 (1997). 18. C. Marcott, A. E. Dowrey, and I. Noda, Appl. Spectrosc. 47, 1324 (1993). 19. B. Wang and T. A. Keiderling, Appl. Spectrosc. 49, 1347 (1995). 20. F. Long, T. B. Freedman, T. J. Tague, and L. A. Na e, Appl. Spectrosc. 51, 508 (1997). 21. R. A. Palmer, C. J. Manning, J. L. Chao, I. Noda, A. E. Dowrey, and C. Marcott, Appl. Spectrosc. 45, 12 (1991). 22. H. Wang, D. Graff, J. Schoonover, and R. Palmer, Appl. Spectrosc. 53, 687 (1999). 23. D. L. Drapcho, R. Curbelo, E. Y. Jiang, R. A. Crocombe, and W. J. McCarthy, Appl. Spectrosc. 51, 453 (1997). 24. R. Curbelo, U.S. Patent 5-835-213 (1998). 25. R. Curbelo, U.S. Patent 6-020-962 (2000). 26. T. A. Keiderling and P. Malon, Appl. Optics 36, 6141 (1997). 27. A. Oppenheim and R. Schafer, Signal Processing (Prentice Hall, Englewood Cliffs, New Jersey, 1989). 28. T. A. Keiderling, J. Kubelka, and J. Hilario, in Vibratonal Spectroscopy of Polymers and Biological Systems, M. Braiman and V. Gregoriou, Eds. (Marcel Dekker, Amsterdam-New York), in press. 29. P. Malon, R. Kobrinskaya, and T. A. Keiderling, Biopolymers 27, 733 (1988). 30. R. D. Singh and T. A. Keiderling, Biopolymers 20, 237 (1981). 31. E. D. Lipp and L. A. Na e, Biopolymers 24, 799 (1985). 32. R. K. Dukor and T. A. Keiderling, Biopolymers 31, 1747 (1991). 33. R. K. Dukor and T. A. Keiderling, Biospectroscopy 2, 83 (1996). 34. T. A. Keiderling, R. A. G. D. Silva, G. Yoder, and R. K. Dukor, Bioorg. M ed. Chem. 7, 133 (1999). 35. M . G. Paterlini, T. B. Freedman, and L. A. Na e, Biopolymers 25, 1751 (1986). 36. S. C. Yasui and T. A. Keiderling, J. Am. Chem. Soc. 108, 5576 (1986). 37. A. Annamalai and T. A. Keiderling, J. Am . Chem. Soc. 109, 3125 (1987). 38. L. Wang and T. A. Keiderling, Nucleic Acids Res. 21, 4127 (1993). 39. L. Wang, L. Yang, and T. A. Keiderling, Biophys. J. 67, 2460 (1994).

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