Virtual Bioimaging Laboratory

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1 Virtual Bioimaging Laboratory Module: Fourier Transform Infrared (FTIR Spectroscopy and Imaging C. Coussot, Y. Qiu, R. Bhargava Last modified: March 8, 2007 OBJECTIVE... 1 INTRODUCTION... 1 CHEMICAL BASIS OF INFRARED SPECTROSCOPY... 1 IR SPECTROSCOPY INSTRUMENTATION... 3 Continuous Scan Interferometers... 5 Mirror Retardation, Apodization and Spectral Resolution... 6 Computing the Interferogram... 9 SPECTRAL DATA FORMAT AND CHEMICAL ANALYSIS SIGNAL TO NOISE RATIO (SNR IN IR SPECTROSCOPY EXPERIMENTAL PARAMETERS AND DATA ACQUISITION DATA ACQUISITION PARAMETERS: Spectral Resolution Co-addition Sampling Interval and Undersampling REFERENCES: OBJECTIVE The objective of this laboratory is to familiarize the reader with fundamentals of mid-infrared (IR spectroscopy and imaging. INTRODUCTION Infrared spectroscopy is a widely used technique for both qualitative and quantitative analysis, for routine identification of molecular species and their transformations and is strongly emerging in process industries. Since molecular vibrational frequencies are coincident with those of mid-infrared radiation, resonant absorption of specific frequencies is indicative of the presence of those species. Further, the absorption of radiation is a quantitative measure of composition and is easily measured by sophisticated instrumentation. These properties have made IR spectroscopy one of the most common analytical instruments in the world. The most common mode of measuring infrared response of a material as a function of frequency, or IR spectrum, is to use an interferometer based on the design by Albert Michelson and used in the famous Michelson-Morley experiment that helped shape many of the principles of modern optics. In these laboratory notes, we will examine the fundamentals of infrared spectroscopy, instrumentation and data acquisition principles. Subsequently, we will understand the steps to acquire and process data and the special considerations in imaging. Chemical Basis of Infrared Spectroscopy Infrared spectroscopy detects the vibrations characteristic of chemical functional groups in a sample. Specifically, the absorption of mid-infrared light by a vibrating functional group can excite the vibrational mode from a ground state by absorption of the energy at the resonance frequency. To a first approximation, the characteristic absorption is due to the single functional group and total absorption for the peak is related to the abundance of the functional group. Subtle changes and characteristic features can emerge in the wavelength envelope of the absorption feature due to 1

2 specific intra- and inter-molecular interactions (e.g. hydrogen bonding, large scale molecular conformations, local organization (e.g. crystal field splitting or environment, external perturbations and due to measurement parameters. The sensitivity of IR spectroscopy to molecular and structural composition of materials provides it extraordinary usefulness and a rich source of information. The frequency-response curves for any material are referred to as a spectrum (singular or spectra (plural. For example, figure 1 demonstrates the transmittance spectra obtained with different molecules. We will define transmittance more precisely later but, in this figure, note sharp peaks corresponding to specific wavelengths. The reduction in intensity is due to absorption in those wavelengths by specific functional groups. In the first graph, the peaks correspond to the (C-CH 2 -(C and (C-CH 3 groups. Since those groups are present in the two other molecules, the same peaks appear at nearly the same positions. In this manner, IR spectroscopy can be used to identify material composition by identifying specific functional groups present. Charts of functional groups and their characteristic absorptions are available for most organic molecules and medically-relevant species,[1] permitting chemical analysis of a given sample. Note that the units of the abscissa are expressed in both wavelength and wavenumber. Since wavenumber is linearly variant with the energy of incident light, it is commonly employed in IR spectroscopy. Wavenumber is conventionally expressed in cm -1 1 (centimeter inverse and is denoted by!, where" =.! Absorption peaks corresponding to functional groups present in the 3 molecules Figure 1. Transmittance of light obtained using different samples. The sharp decrease in transmittance is due to sample absorbance. The absorbed wavelengths correspond to functional groups present in the sample. [2] 2

3 IR Spectroscopy Instrumentation Nearly all modern IR spectroscopy is performed using a Michelson interferometer to collect timedomain data, which is then converted to frequency domain by the use of a Fourier Transform. Figure 2 illustrates the principle of this interferometer. An Infrared light source emits a broadband beam. The source is typically a stable, heated filament and the emission characteristics can be described by Planck s law. This beam is then divided equally by a beam splitter that allows one to be transmitted and another to be reflected. One beam is then incident on a fixed mirror while the other is incident on a mirror orthogonal to the first one and whose distance to the beam splitter can vary. The beams are reflected back by the mirrors and interfere at the beam splitter. Interference may range from entirely additive (constructive to exactly canceling each other (destructive at specific frequencies. The interference is determined by the ratio of the difference in traveled path and the wavelength of light that is experiencing interference. Fixed Mirror M 1 M 2 From Source To Source B Beam Splitter To Detector Moving Mirror Figure 2. Principle of a Michelson interferometer The process of generating interference patterns that may be detected and how this can be used for spectroscopy can be understood by considering an idealized model of the process. If a source of monochromatic radiation produces an infinitely narrow and perfectly collimated beam and the beamsplitter reflects and transmits exactly 50% of the light, then the path difference between the beams can be given by 2(BM 1 -BM 2. This optical path difference is called the optical retardation or concisely, retardation and usually denoted by the symbol δ. When the mirrors are equidistant from the beamsplitter, the retardation reduces to zero and the beams are perfectly in phase, leading to constructive interference whereby the total intensity is the sum of the intensities of the beams. At this point, all intensity is directed towards the detector and none reaches the source. It can be seen that for monochromatic radiation this condition occurs whenever the optical retardation is exactly a multiple of the wavelength, λ and there is no mechanism to deduce the absolute retardation. By simple symmetry considerations, this is the maximum intensity that can ever reach the detector. Similarly, if the retardation is half a wavelength (implying that a mirror has been moved a distance of λ/4, the combining waves are exactly out of phase leading to destructive interference and no intensity is transmitted to the detector. Once again, it is impossible to distinguish this retardation from a retardation of an integral multiple of the wavelength plus a half wavelength. If the intensity change at the detector is plotted for increasing retardation, it can be seen that maximum values (constructive interference and their corresponding destructively interfering values of 3

4 zero intensity will occur, at a retardation determined by the wavelength of light, in a sinusoidal fashion. Hence, the intensity of light at the detector may be given by (/ 0 (- I = 2 &, # $ * 2./ 1+ cos '! $ * ' % + - (!" I. (2. 1 where I(λ is the intensity of light from the source at a wavelength, λ. The equation above can also be written in terms of the wavenumber,!, which is defined as the reciprocal of the wavelength (in centimeters as (# = 0. 5I(![ 1+ cos( "#!] $ 2 I (2. 2 The resultant intensity at the detector consists of a component that is invariant of the path difference. This is termed the DC-component of the detector signal and merely results in a constant value of the readout signal or an offset. The component of the light intensity from the source that changes with the retardation is termed the AC component of the signal and is given by (# = 0. 5I(! cos( 2"#! I. (2. 3 This sinusoidally modulated component of radiation reaching the detector is called the interferogram and is important for spectroscopic measurements. In practice, beamsplitters do not reflect and transmit exactly 50% of light. Further their performance also changes with the wavelength of light. A wavelength dependent efficiency factor can be incorporated to allow for this beamsplitter efficiency. The response of the detectors and associated electronics may also change the resultant interferogram. The pre-factor and efficiencies may all be accounted for to yield a simple equation for the interferogram that relates the observed intensity at the detector as a function of the retardation by (# = B(! cos( 2"#! I. Comparing this to standard expressions in transform mathematics, it can be seen that I(δ is the cosine Fourier transformation of B (!. The above discussion, however, is valid for a collimated beam of monochromatic wavelength. When the radiation consists of several different wavelengths, for example the constituent wavelengths of a spectral output from a broad band source, it is trivial to observe that all wavelengths will simultaneously add constructively at zero retardation. However, the next larger retardation where a wave adds constructively is at a path difference equal to the wavelength of the radiation. As different wavelengths now add constructively at different retardations, the resultant intensity at the detector for any given retardation is the sum of the intensity of radiation of all component wavelengths at that retardation. Any given retardation contains a non-trivial, but unique, relationship to the spectral profile of the source. Similarly, the retardation for destructive interference of each wavelength depends on the wavelength and the net signal contribution of every wavelength is zero at its characteristic destructive interference retardations. When the source is a continuum, the net interference pattern can be represented by an integral +% I $ B (# = (! ( 2"#! d! &% (2. 4 cos. (2. 5 4

5 10000 Centerburst 9000 Signal 8000 Wings Retardation Figure 3. Interference pattern for a polychromatic source It is also instructive to visually examine the interferogram for a continuum spectral source. Recall that the interference pattern obtained from a monochromatic source was a sinusoid as a function of the optical retardation. Now, consider the interference patterns due to discrete wavelengths of unit magnitude. The observed interferogram is a sum of the interferograms of the individual components and the pattern can be seen to repeat itself after specific intervals. If more lines are summed, the peak intensity is found to decay rapidly while the repetition period becomes longer. By extending the argument to a broad spectral emission from a source, the interference pattern can be expected to decay rapidly and repeat after a very long period. This leads to a typical interferogram for a broadband spectral source as shown in Figure 3. The large amplitude signal is where a majority of signal add constructively and is termed the centerburst. Regions away from the centerburst are small in magnitude and are termed wings. Mathematically, the other half of the cosine pair in the equation above is given by the integral of the even function I(δ such that +% ( = I(! cos( 2#"! d! B " $ 2. ( Hence, using the equation above, a spectral profile may be completely specified by the measured signal as a function of the measured intensity at a known optical retardation. The profile of measured intensity as a function of optical retardation is termed the interferogram. The spectral profile is then computed by measuring the interferogram from zero retardation to an infinitely long retardation at infinitesimally small increments of retardation. It is clear that computation limitations and instrumental considerations require a finite number of discrete measurements or sampling of the interferogram over a finite retardation. This practical consideration dictates that the sampling interval determining the spectral range measured while the finite retardation results in a spectrum of finite resolution. Continuous Scan Interferometers In a common implementation of interferometry, the moving mirror is scanned at a constant velocity v. Consequently, the mirror travels a distance given by vt in a time t. Since the path difference for 5

6 radiation is twice the distance difference between the mirrors, the retardation can be expressed in terms of the velocity and time as! =! 0 + 2vt (2. 7 where, δ 0 is the retardation at the beginning of the observation time. Since the time is set arbitrarily, the point of reference can be taken to be the point of zero retardation. Hence, optical retardation is simply set equal to 2vt. Analogous to velocity of the mirror, a rate of change of optical retardation may be termed the optical velocity, which is always twice the velocity of the moving mirror. The expression for the interferogram, expressed in terms of these directly measurable process parameters reduces to "! #" ( t B( $ cos( % vt$ I = 4 d$ (2. 8 where t is the time after zero retardation. When the sinusoidal variation of the interference pattern of a single wavenumber is compared to a standard expression for a sinusoidal wave [ cos ( 2!ft], the characteristic frequency of the signal due to that wavenumber can be determined. This characteristic frequency of the interferogram, corresponding to a wavenumber,!, is given by f! = 2v!. (2. 9 This frequency of the sinusoidal variation of the interferogram is termed the Fourier frequency corresponding to the wavenumber. Clearly, the Fourier frequency is a function of the scanning velocity. It is also of note that different spectral regions of the spectral profile are encoded by the interferometer at different frequencies. The primary advantage of FT spectroscopy is to allow recording of all wavelengths simultaneously, thereby measuring each wavelength (albeit, in coded manner N times, where N is the number of wavelengths in the band pass. This results in an improvement in the signal to noise ratio (by N 0.5. Further, the precise nature of sampling provides a very accurate wavenumber scale, thus providing high positional fidelity. Last, detectors are responsive optimally to specific modulation frequencies. Hence, interferometer speeds may be selected to provide the optimal detector response. Mirror Retardation, Apodization and Spectral Resolution From equation 2. 8, the spectral profile was determined by integrating the signal from the detector as a function of the retardation around zero to infinitely large retardation. Practically, this is impossible and the measurements can only be carried out for finite time up to a finite retardation. Hence, the spectrum is measured for some points around the centerburst up to a maximum retardation, Δ. The equation relating the spectral profile to the detector output now becomes, +% ( = I(! cos( #"! d! B " $ 2 &% (2. 10 By reducing the integral to the above form, however, the familiar integration limits are lost and comparisons to the theoretical case, where intensity sampling is practically impossible but mathematically tractable solutions are well-known, are very difficult. Alternately, the process of measuring a finite portion of the interferogram may be described as truncating the interferogram by multiplication by a function that is unity between the desired retardation range and zero outside. Mathematically, such a truncation function can be described by A 1 (' $! 1, = #! 0, " ' ( % ' & % (

7 This function is shown graphically below and is termed a boxcar function. 1 -" 0 "! Figure 4. Graphical representation of a Boxcar function. As the Fourier transform of the product of two functions is simply the convolution of the Fourier transforms of the functions, the effect of limited retardation can be compared to the ideal case by examining the effect of the convolution function. Hence, it is instructive to first examine the Fourier transform of the truncation function. The FT of the boxcar truncation function is given by ( ( 2#"! sin " = 2! = 2! sinc 2 2#"! ( #"! A p (2. 12 Graphically, as shown in figure 5, the function (! A resembles a Gaussian peak centered at! = 0 p with positive and negative perturbations that decrease in amplitude at the observation wavenumber is further away from the large peak centered at the origin. Due to the appearance of these side lobes or feet, the function whose FT leads to the production of such lobes is termed an apodization function from the Greek word for feet-apodis. A monochromatic wavenumber,! 1, is represented as a spike in an intensity-wavenumber plot. The same radiation, if detected by interferometry using limited retardation, results in a convolution of the spike with the profile shown in Figure 4 to yield a waveform of the type shown below that is centered at! 1 and extends F( " ! 0 Figure 5. FT of a boxcar function for Δ=0.125 cm. The amplitude and the shape of the central peak are related to the retardation. Other apodization functions may be employed to obtain the spectral profile from a measured interferogram. Some of these, with their resulting full width at half peak heights (FWHH are shown in table 1. 7

8 Table 1. Triangular and Gaussian apodization functions with their Fourier transforms. It is clear that the interferogram can only be measured for a number of points, the frequency of which determines the spectral range measured, and up to a finite retardation, which results in a broadening described the ILS. The broadening also determines whether two close spectral intensities may be distinguishable. For example, consider the case of two closely spaced, infinitely thin spectral intensities to be measured interferometrically as shown in Figure 6. Upon measurement, the lines are broadened by the ILS, assumed to arise from a boxcar apodization in this case, and appear as seen in figure 6. Clearly, if the difference in peak position is more than the breadth of the peak shape as measured by the half-width of the peak, discrimination is easy (top. Where the spacing is comparable to the width of the peaks, resolution of the two distinct intensities is difficult. Since the width of the line shape is dependent on the maximum retardation, it is graphically obvious that the retardation has a determining influence on spectral resolution and that a large retardation is required to distinguish closely spaced spectral lines or to achieve high spectral resolution. To a first approximation, the spectral lines can be readily distinguished if the bands are separated at their first zero crossings. Hence the spectral resolution is equal to the width, which is the reciprocal of the maximum retardation for this apodization function. " 1 " 2 F( " Figure 6. Two Spectral lines whose intensities are measured interferometrically. 8

9 While it is clear that the spectral resolution attainable is proportional to the inverse of the maximum retardation, the actual form of the relationship is more complicated and depends on the resolution criterion itself. It is clear, however, that the retardation determines the spectral resolution and the sampling interval over the course of that retardation determines the spectral range. By using a wider sampling frequency, a smaller spectral region may be examined but the total experimental time is still dependent on the distance the mirror has to travel, i.e. by the retardation. Thus, for rapid scan spectrometers, there is no time advantage for data acquisition to be gained from using a limited spectral range. The advantage lies in acquiring less data and consequently, reducing the time and computation resources required to process and store the data. For step-scan spectrometers, acquiring a smaller spectral range may result in a reduction of acquisition time. This is especially significant if the stabilization time per step is significant compared to the time required to measure the interferometric signal at each retardation. Apodization acts as a smoothing function to suppress systematic modulations. The effect of apodization on spectral accuracy has been discussed. 2 Computing the Interferogram Phase Correction According to the interferogram equation, the even function B (!, need only be measured from the point of zero retardation up to a large enough retardation. In practice, however, it is nearly impossible to start interferogram acquisition at the exact point of absolute zero retardation. Hence, acquisition is initiated a short mirror retardation prior to the vicinity of the zero retardation mirror position. Thus, the origin of the interferogram measurement is a retardation given by "! ( " #! 0 and the interferogram equation is actually of the form I +& ( = B(! cos[ $! (" # " ] d! " % 0 2 (2. 13 ' Sampling electronics, especially filtering electronics for rapid scan spectroscopy, may introduce a further lag in the phase of this AC signal and the resulting signal may be recast in a general form to provide +' ( = B (! cos ( %!$ # "! I 0 $ & 2 (2. 14! d where "! is a wavenumber dependent phase lag in the AC signal arising from optical, sampling and electronic considerations. Usually, this results in an interferogram that is not symmetrical with respect to the point of zero retardation. Comparing with the interferogram equation established previously, a significant effect of the phase lag is to introduce sine components in an otherwise purely cosine function. The interferogram equation above can be recast into a more general form to reflect the presence of both sine and cosine components as I +$ & 2% i!" ( = B(! e d! " # 0 (2. 15 where i is the imaginary number! 1 and constant quantities have been absorbed into the coefficients. Now, to reconstruct the spectral profile, B, from the equation above, the inverse complex transform is required. In this notation, the real part of the complex transform is equivalent to the cosine transform and hence, this component is sometimes also referred to as the real part of the spectrum, Re (! and the component corresponding to the sine transform is called the imaginary part of the spectrum, Im (!. Removing the effects of the imaginary part of the transform, arising due to the phase lag, from the spectrum is termed phase correction. A simple solution is to substitute the true 9

10 spectral intensity with the magnitude of the complex spectral profile, B (!, which introduces nonlinear noise terms. Before discussing phase correction methods, it must be pointed out that the phase lag may be constant in some cases and, at most, a slowly varying function of wavenumber. Hence, it is usually sufficient to calculate the correction at a coarse spectral resolution by using only a few points in the interferogram around the centerburst and then interpolate values to the full spectral resolution. Hence, modern instruments can collect an asymmetric interferogram beginning a short distance prior to the point of zero retardation to provide a short and (approximately symmetric interferogram. While phase correction does not present any complications if the entire interferogram is a symmetrically acquired double sided interferogram, a single sided or asymmetrical interferogram results in the short pre-zero retardation region being accounted for twice. Upon transformation, this would imply that the broad spectral features are twice the magnitude they should be while the finer spectral features are the correct magnitude leading to a gross photometric error. Hence, asymmetrical interferograms are subjected to a correction weighting functions to provide correct sampling. Spectral Data Format and Chemical Analysis Fourier transformation of the interferogram provides a single beam spectrum (SBS(figure 7. Figure 7. Single Beam spectrum obtained after apodization of the interferogram with a triangular function followed by a Fourier Transformation. A common technique employed to keep as much information as possible when Fourier transforming the interferogram to get the SBS consists in extending the interferogram with zeros. This action is called zero-filling or zero-padding. The more points you have in the time-domain, the better the resolution in the spectral domain will be. Therefore, adding zero to the interferogram will lead to a better precision in the spectral domain. Moreover, the fft algorithm widely used to compute the FT is such that it goes faster when the FT is performed on 2 n points and multiplying the number of points by 2 won t increase the processing time by 2. Therefore, the time needed to process the data won t increase much whereas the resolution in the spectral domain will be significantly better. Figure 8 displays two fft performed on a triangular function of originally 128 points and then zero-filled to 1024 points. Having more points leads to more smooth FT, but requires more processing time. 10

11 Less fft points: sharper FT Smoother FT with 1024 points Figure 8. fft performed on a triangular functions of 128 points before and after zero-padding. Notice that once the original function has been zero-padded, there are more points in the fourier transform leading to a smoother plot. The single beam spectrum obtained is the blackbody spectrum of the source, as modified by the spectral response of the instrument, and is often termed the background single beam spectrum. When a sample is placed in the beam path to interact with the light, the single beam spectrum is modified and is referred to as the sample single beam spectrum. By themselves, the two single beam spectra provide indeterminate information if the instrument response is not known. Their ratio, however, provides the effect of sample introduction that is independent of instrument behavior. The ratio of the two single beams is termed the transmittance of the sample and can be calculated by a ratio at every corresponding point as I (! T = (2. 16 I 0 (! Where I 0 is the single beam intensity of the background and I the intensity with the sample in the beam path. Transmittance is usually expressed as a percent and was the most common means to record data for early spectroscopy. The most common method to represent spectra today is to compute the absorbance defined as I A " log( T = " log I 0 (! (! = (2. 17 According to Beer-Lambert s law, absorbance of a sample is directly proportional to the length of light interaction with the sample, b and the number of molecules along the path of the beam or 11

12 concentration of absorbing molecules, c. A constant of proportionality, k, is often employed to mathematically express this law as! I = " k # c #! x where! I is the intensity change over a distance! x in the sample. If we integrate I this over the samples length along the beam propagation direction, we get I ln( I 0 =! k " b" c (2. 18 I(! Therefore, we define absorbance as A(! = " log 10( = a # b# c where I0(! An absorbance signal is displayed on Figure 9. k a =. ln(10 Figure 9. Absorbance of one sample pixel for each wavelength contained in the source. By normalizing against the background spectrum (I 0, we can, if the experiments are made in the same conditions, eliminate the instrumental and atmospheric unwanted contributions. If the concentrations of water vapor and CO 2 are different, peaks will appear around 3500cm -1 and 1630cm - 1 for the water vapor, and around 2350cm -1 and 667cm -1 for the CO 2. It is important to recognize these peaks as arising from experimental environment and not necessarily from the sample. Noise introduced by the detector is also detectable at that point. Figure 9 displayed the absorbance spectrum of one pixel of a sample. You can see that there is a linearly increasing baseline shift. More generally, the detector tends to introduce a linearly increasing error. By performing a baseline correction, one can easily correct this error. Figure 10 displays the absorbance spectrum after the baseline correction, the detector error has been corrected by choosing two points that define the new baseline. 12

13 Figure 10. Absorbance signal of one pixel of the sample once the baseline has been corrected Some noises cannot be corrected that simply. Therefore, one needs to quantify the level of noise for each wavelength. Signal to Noise Ratio (SNR in IR Spectroscopy For a conventional wide beam single element detector in an FTIR spectrometer incorporating a Michelson interferometer, the SNR achieved in time, t, is represented by 3 U SNR = where, ( T " U! ( T $ #"! 1/ 2 NEP t, is the spectral energy density at a given wavenumber,! ; the Noise Equivalent Power (NEP is defined by the ratio of the square root of the detector area, A D, to the measure of it s sensitivity, D* (specific detectivity; Θ is the throughput; "! the spectral resolution and ξ is the spectrometer efficiency. This relation is a measure of the signal to the root-mean-square (rms noise for single beam spectra. The SNR can be considered in the context of two experimental parameters as 1 SNR " #! $ t 2 Where "! is the spectral resolution and t the time over which the data have been acquired. Decreasing the time over which the data are acquired leads to a smaller SNR, hence the practice is to record signal as long as possible without exceeding the dynamic range of the spectrometer. Subsequently the same signal is measured many times and average (termed co-addition. While the signal increases linearly with the time of recording (or the number of spectral data averaged, the noise only increases as the square root of the measure. Hence, the SNR increases as the square root of the time spent in recording data. Studying a dynamic process, however, does not allow extensive averaging as the sample would change during the process and lead to errors. Hence, one option to maintain he data quality is to decrease the spectral resolution. The spectral resolution corresponds to the minimum difference between two wavenumber we will be able to resolve as per some objective measure, for example, Rayleigh Criteria. Since the spectral resolution is generally required based on the problem, flexibility is limited. As a corollary, one must always acquire data at the poorest spectral resolution possible to obtain the highest SNR possible. Since the spectral resolution corresponds to the inverse of the distance traveled by the mirror, a higher spectral resolution requires more time to acquire. For example, a resolution of 0.5 cm -1 means the mirror must travel 2 cm when a resolution of 4 cm -1 13

14 requires the mirror to travel 0.25 cm. Therefore, if the mirror keeps moving at the same speed, it will need more time to acquire data. Then, a better resolution implies a longer measurement time and also a lower SNR if the measurement time is fixed. For unknown samples, a tradeoff has therefore to be found between the experiment time, the spectral resolution and the SNR. To best determine the experimental parameters, we must understand the noise in measurement and determine the level of noise tolerable. Remember that the signal in absorption spectroscopy comes from Beer s law and, hence, cannot be readily change for a sample. Thus, the definition of SNR in absorbance spectra usually involves the measurement of noise. Different notions relative to the SNR such as the Limit Of Detection (LOD and Limit Of Quantitation (LOQ can be introduced in this context. If a signal peak is below a certain level, one won t be able to distinguish it from the noise. Nevertheless, if a peak is too weak, one won t be able to accurately quantify it. Therefore, the LOD corresponds to the value over which a peak has to be to be identified and the LOQ corresponds to the value over which a quantifiable peak has to be. Conventionally, these limits have been defined by IUPAC committees. When expressed in terms of SNRs, their typical values are: LOD=3 and LOQ=10. Hence, if a peak has a value 3 times larger than the noise but less than 10 times the noise, it will be detectable but not quantifiable. If the peak is more than 10 times higher than the average noise value, it will be quantifiable. Limit of Quantitation (LOQ Limit of Detection (LOD Signal to Noise Ratio (SNR Peak B LOQ Peak A LOD Baseline noise Figure 11. The three noise measures (SNR, LOD, LOQ are displayed here on a typical signal.(from Janos Pogany,2005 Now that you are familiar with the basic notions of FTIR, we will describe a few acquisition parameters and go on with the data processing available in the online lab. 14

15 EXPERIMENTAL PARAMETERS AND DATA ACQUISITION Data Acquisition Parameters: The most relevant acquisition parameters in an experiment are the spectral resolution, the number of co-adds, and the undersampling ratio. The laser wavelength of the spectrometer is fixed as are the properties of the source, detector and beamsplitter. The alignment of the optics can change due to the moving parts in the interferometer and the resulting variations can be recognized by users. In this laboratory, we will change the experimental parameters to observe the changes reflected in data quality and data acquisition time. Spectral Resolution We already introduced the spectral resolution "!. In the lab, you will be able to choose between resolutions within 2, 4, 8 and 16 cm -1. As mentioned earlier, a finer resolution, corresponding to a small value of the spectral resolution, will lead to more points in the spectrum to distinguish closer wavenumber contributions, but will also take more time. You will therefore have to find a tradeoff between the resolution you pick and the time over which you can acquire your data. Co-addition We can increase the SNR by performing the same experiment many times and averaging the results. The noise as a function of the number of co-adds. We then get: original _ noise remaining _ noise = N where N is the number of co-adds (number of spectral scans. Acquiring a large number of co-adds will reduce the noise in data but also increase the time over which you acquire the data. In this lab, you will be able to choose between 2, 4 or 8 co-adds and decide which trade-off is the best depending on the sample. For a sample evolving quickly over time, too many co-adds might lead to false observations, hence, care must be exercised to balance noise and distortion. Sampling Interval and Undersampling The interferometer is a discrete device. The data are not acquired continuously but regularly at a! s sampling frequency f s = where c is the sound velocity and! s the wavenumber corresponding to c the sampling frequency. This frequency is defined by a laser of wavenumber! L. As illustrated in Figure 12, each time the laser wave crosses the baseline, a data is acquired. 15

16 Figure 12. Each time the laser wave crosses the baseline, a data is acquired, leading to a sampling of the continuous signal. If the wavelength of the laser decreases, its wavenumber increases. Therefore, the sampling frequency also increases and higher wavenumber values can be identified in the sampled signal without any aliasing problem. We therefore acquire data at a wavenumber! = 2"! since there are two baseline crossings per s period. According to Nyquist, the maximum detectable frequency detectable in a sampled signal corresponds to half the sampling frequency. Therefore, the maximum detectable wavenumber is! s! m = =! L. The laser s wavenumber finally appears to be the maximum detectable wavenumber. If 2 one decides to acquire data at one zero-crossing per period, it will decrease the maximum detectable L 16

17 wavenumber but there will be less data points to Fourier Transform, and the processing will be faster. Nevertheless, if we have, in the light source, wavenumbers superior to the laser s wavenumber, we will get aliasing results. To avoid this, an anti-aliasing filter has been introduced with a cutoff frequency equal to the laser s frequency. Therefore, we can make sure that the resulting signal won t be aliasing, but this may also be useful if you don t need too many points and want to acquire your data fast. If you take an anti-aliasing filter with a smaller cutoff frequency, you will be able to take a smaller sampling frequency. This undersampling ratio is usually within:1, 2, 4 and 8. If the ratio is 4, the sampling frequency and the cutoff frequency of the anti-aliasing filter will both be divided by 4. You will therefore have less data points in a smaller range of wavenumber but you will acquire the data faster. Usually, HeNe lasers are used. Their wavenumber, being 15,798 cm -1, is far over the midinfrared region (from 4000 to 400cm -1. Therefore, dividing the sampling frequency by 2 or 4 will still allow all the wavenumbers in the mid-infrared to be detected. Nevertheless, the anti-aliasing filters are not perfect rectangles with amplitude one. The optical filters used usually have a gain of 0.8 instead of 1; therefore, the cost of this undersampling will be an intensity loss. 17

18 References: [1] Keck Interdisciplinary Surface Science Center, [2] International Union of Cristallography,2002 ww w.iucr.org [3]Bhargava and Levin,Anal Chem 1 Colthup 2 CW Brown 3 Griffiths, P.R.; de Haseth, J.A. Fourier Transform Infrared Spectrometry; Wiley-Interscience: New York,