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Chapter 6 Instrumentation
Chapter 6
Instrumentation
6.1 HISTORY OF INFRARED INSTRUMENTATION Since the discovery of infrared radiation by Sir William Herschel in 1800 [1], a variety of methods have been used to improve the experimental techniques for measuring infrared spectra. In particular, Herschel used a prism and a mercury thermometer to record his observations of heat-based radiation beyond the range of the solar spectrum. Melloni is credited with the construction of the first midinfrared spectrometer in 1833, after his discovery of the transparency of NaCl in the infrared. Excellent references on the early history of vibrational spectroscopy and the minds that shaped the field can be found elsewhere. This chapter will deal in detail with the interferometric methods of capturing infrared radiation. Older monographs treat non-interferometric methods in great detail [2]. 6.1.1 History of FT-IR instrumentation The construction of the first interferometers dates back to 1880. Lord Rayleigh may have constructed an interferometer at that period, but it is Michelson who is credited with the construction of the first operable instrument at that time. The interferometer was used in the measurement of the speed of light in diverse directions. Measurements that took place at was is now Case Western Reserve University showed that there was no detectable difference in the speed of light in either direction. The lack of adequate computing power was the main reason that it took approximately eighty years for the instrument to utilize its full potential as an analytical tool. Ferraro has recently published a very informative account of the history of FT-IR spectroscopy [3]. 105
The first attempts to use interferometric means to measure infrared radiation concentrated in the far infrared region of the spectrum. The operational needs for mechanical precision and computational load are lower in the far-infrared compared to the mid-infrared. Therefore, a lot of the early applications and advancements took place in the field of astronomy where far-infrared spectroscopy is used extensively. One very important recent development that led to the widespread use of infrared spectroscopy as a characterization tool was the introduction of the first Fourier transform infrared spectrometer, the FTS 14, by the Biorad Company of Cambridge, Massachusetts in 1969. Several developments in the 1950s and 1960s contributed to the introduction of this first commercially available instrument. The work of L. Mertz in interferometer design during 1954-56 and the development of data reduction algorithms in 1960-65 are probably the most significant contributors. One historical aspect that should not be overlooked was the role of the NASA contract to Block Engineering for an instrument with ten times the available resolution. The model 1500 (296 in the commercial version) had 0.5 cm-l resolution and a better signal-tonoise (S/N) ratio than the dispersive instruments of the time. Other notable developments were the discovery of the HeNe laser along with the introduction of better infrared detectors, analog-todigital (A/D) converters and minicomputers. In 1966 a one-foot laser with a built-in power supply was available to be used in the first FT-IR spectrometer. In addition, pyroelectric bolometers in the form of the deuterated triglycine sulphate (DTGS) detector also became available. Their major advantage was that their bandwidth was compatible with the rapid-scan frequencies. With respect to computing power there was a remarkable development from the PDP-1 in 1960 to the DG Nova in 1969. After the introduction of this instrument many new instruments from various manufacturers have appeared and tremendous progress has been achieved in the years following 1969. A list of the advancements will undoubtedly include the very small footprint of the modern instruments, quadrature detection with forward and backward scanning, digital signal processing, diagnostic features, low powered aircooled sources, the flexible design of the research-grade instruments, the multiple spectral ranges, the very high spectral resolution, and the tremendous progress in FT-IR software. In addition, one of the most important developments was the 'rediscovery' of step-scan interferometry, a subject that will be extensively dealt with in this book. 106
What is the future of infrared instrumentation? Without a doubt, any technological breakthrough will eventually find its way to a commercial design with time. Improvements in performance, new features and capabilities, usability and (hopefully!) a reduction in cost should all be expected.
6.2 COMPONENTS OF AN FT-IR SPECTROMETER The components of an FT-IR spectrometer primarily include the source interferometer, the source of radiation, the detector and other optical elements (beamsplitters, mirrors, etc.). In addition, data manipulation also takes place in the adjacent computer station. It is beyond the scope of this book to give a detailed account of all the elements involved; instead, an attempt will be made to cover in more detail important components of these designs. 6.2.1 Sources The source of infrared energy in an infrared instrument does not depend on the type of instrumentation used to detect the radiation. Both dispersive instruments and Fourier transformed instruments can use the same types of infrared sources. Therefore, a general overview of the available technology will be reviewed here. The more typical sources are the Globar source and the Nernst glower, even though nichrome coils have also been used in the past. Nichrome coils operate at lower temperatures and therefore have a lower emissivity. Finally, mercury arc lamps are used most frequently for experiments dealing with the far-infrared region of the spectrum. The first two types will be discussed in more detail here. GlobarSource This source is made out of silicon carbide (SiC) and it has metallic leads at the ends which serve as electrodes. The application of electric current results in the generation of heat, which yields radiation at temperatures higher than 1000°C. Water cooling is required for this type of source because the electrodes need to be cooled [4]. This extra level of complexity makes this source less convenient to use and more expensive. Figure 6.1 shows the ratio of the globar source to a 900°C blackbody. 107
Prisms: 4.2. 4.2.
.
NaCI & KBr 0
Ramsey and Alishouse
Q
3.4
s
CsI
Calculated after Silverman
1.8
1.0 0.2
I I i
2.l
6.0 10.0 14.0 18.0 22.0 26.0 30.0 34.0 38.0 Wavelength (m)
Fig. 6.1. Globar versus a 900°C blackbody. (Reproduced from Ref. [7] with permission. Copyright 1968, Pergamon.) I.o
0.9 W 0.8 E 0.7 K 0.6
-255 K Stewart and Richmond
0.
n_
I
1
II 3
I I
5
I I I I 7 9 11 Wavelength (im)
I
I 13
I 15
Fig. 6.2. Spectral emissivity of the globar source. (Reproduced from Ref. [7] with permission. Copyright 1968, Pergamon.)
One other advantage of this source is its high emissivity down to 80 cm - ', making it useful in the far-infrared region of the spectrum. Figure 6.2 shows the spectral emissivity of a typical globar source [5]. These values are only representative and are expected to change considerably with use. Recently, a new low power air-cooled ceramic source has been introduced into the modern FT-IR instruments [6]. This source has the advantage that no watering cooling is necessary, making their instruments portable and easier to maintain. Nernst glowers This infrared source's element is a mixture of yttrium and zirconium oxides and has an emission spectrum that resembles that of a black 108
z
}
3 W
Wavelengt
(m)
Fig. 6.3. Ratio of a Nernst glower to a 900°C blackbody. (Reproduced from Ref. [8] with permission. Copyright 1978, Office of Naval Research.)
body at 1800 K. It is an insulator at room temperature and becomes a conductor after it is preheated. It used to be popular but it has a number of disadvantages, the biggest being its short lifetime and mechanical instability. The spectral characteristics of a Nernst glower versus a 900°C blackbody can be found in Fig. 6.3 [7]. 6.2.2 Infrared detectors One of the most important elements of an infrared spectrometer is the component responsible for the detection of infrared energy. Typically, the description of a detector is not limited to the responsive element which changes the incoming radiation into an electrical signal, but it also includes the physical mounting of the element, like the windows, the apertures, the Dewar flasks, etc. Together, they form what is called a detector [8]. There are two general classes of infrared detectors. One class comprises the thermal detectors and the other class the photon detectors. As the name suggests, thermal detectors operate by sensing fluctuations in the temperature of an absorbing material as a result of exposure to the incoming radiation. The other category, the photon or as often called quantum detectors are sensitive to changes in the quantity of free-charged carriers in the solid, brought by the interaction with the external radiation. 109
Thermal detectors Thermal detectors rely on four different processes to achieve detection of infrared radiation: 1. The bolometric effect. This effect relies on the change in the electrical resistance of the responsive element due to temperature changes produced by the absorbed infrared radiation. This change in resistance is detected by conventional techniques. 2. The thermovoltaic effect. In this case, the heating of the junction between two dissimilar materials produces a measurable voltage across the leads. 3. The thermopneumatic effect. A very common thermal detector, the Golay detector, relies on this phenomenon [9]. In the case of thermopneumatic detectors, a gas-filled chamber that contains an infrared absorbing element is exposed to infrared light. Absorption of energy by the element generates heat, which heats up the gas in the chamber. The consequent increase in the pressure of the gas results in the distortion of a thin flexible mirror on the other end of the sealed gas chamber. This distortion is sensed by an independent optical system. Golay detectors have been extensively used as farinfrared detectors, even though they had problems with their mechanical integrity at one point. Figure 6.4 shows a cross-section of a typical Golay cell [10]. 4. The pyroelectric effect. In this process the radiation increases the temperature of a crystalline material. The result is a change in the electrical polarization of the crystal surface and the generation of an electric field. TARGET: THIN
BSORBING FILM IR TRANSMITTIN WINDOW
ELASTIC MEMBRANE
GAS FILLED CHAMBER Fig. 6.4. Cross-section of the Golay cell. (Reproduced from Ref. [10] with permission. Copyright 1976, Institute of Optics.)
110
Photon detectors The other category of infrared detectors is the quantum or photon detectors. In photon detectors, incident infrared photons result in the production of free charge carriers in the responsive element. No serious temperature change in the element takes place during this process. The above category can be further divided in four underlying processes: 1. Photoconductive effect. The principle behind this effect is that a change in the number of incident photons reaching a semiconducting material changes the number of the free charge carrier in the materials. Since electrical conductivity is directly proportional to the number of these charge carriers, it can be used to deduce the number of incident photons on the semiconductor. 2. Photovoltaic effect. In this case, a change in the number of incident photons on a semiconductor p-n junction results in a change in the voltage generated by the junction. Figures 6.5 and 6.6 show the energy band models for unilluminated and illuminated p-n junctions. 3. Photoelectromagnetic effect. In this case, the separation of the charge takes place via the use of a magnetic field. The charge separation produces a voltage that is directly proportional to the number of incident infrared photons. 4. Photoemissive effect. In this case, an incident photon is absorbed by the surface and gives up its energy to a free electron. This electron can escape the surface and in the case that the surface is in an evacuated chamber equipped with an anode and an eternal circuit, electric current is detected.
Band _.-----------Fermi Level
P-l
n-Region
Unilluminated p-n junction Fig. 6.5. Energy band model for an unilluminatedp-n junction. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.) 111
Conduction Band
h
-'
h f
Illuminated p-n junction Fig. 6.6. Energy band model for an illuminated p-n junction. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
6.3 DETECTOR NOISE
There are several contributors to the noise (the fluctuation in signal intensity for a steady radiation field) of an infrared detector. In infrared spectroscopy, the detector noise is most often much higher than any other noise source. In addition, it has usually a thermal origin. Therefore, the majority of infrared detectors do not operate at room temperature. Johnson noise: this type of noise is generated in resistors due to the random thermal motion of the charge carriers. As the temperature of the element increases there is a concurrent increase in the average kinetic energy of the carriers, which results in an increased electric noise voltage. This is the reason this type of noise is also called thermal noise. Shot or Schottky noise: this is random noise that has to do with the statistical fluctuations of the photon fluxes. It has its origin in the discreteness of electrical charge. Both of the above types of noise are 'white' types of noises. This means that they are independent of the frequency all the way out to the cut-off frequency. Other types of noise exist that are dependent on the frequency of the incoming radiation. The most important of these types is the 1/f noise. Its mechanism is not well understood but, as the name implies, its magnitude is reversibly proportional to the frequency of the radiation. 112
In addition, electronic components associated with the detector contribute to the noise. Pre-amplification is always required for any type of detection system.
6.4 PERFORMANCE OF AN INFRARED DETECTOR The performance of an infrared detector is measured by a set of figures of merit. The responsivity of the detector is the output of the electrical signal to the incident radiation power. The noise equivalent power (NEP) is the level of incident infrared signal that produces a signal-tonoise ratio of one. Detectivity is defined as the reciprocal of the noise equivalent power (NEP). The normalized detectivity D* is a widely used figure-of-merit and it includes the area of the detector and frequency bandwidth of the measurement. Thermal detectors show a 'flat' detectivity response throughout the entire spectral region. In contrast, photon detectors have higher detectivity but over a limited spectral range. Figure 6.7 shows the
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in
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8 10 12 Wavelength (rim)
14
16
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9109 i
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10 10
3 2 10 10 Chopping Frequency (cps)
10
Fig. 6.7. Plots of D* versus wavelength for (a) thermocouple versus (b) an InSb detector. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
113
l
10'
1011
1010
10
9
1081
Wavelength (m)
Fig. 6.8. D*(X) values for a number of commercially available quantum detectors. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
response for a thermocouple detector as compared with the spectral response for an InSb photon detector. In addition, Figure 6.8 shows the plots of the normalized detectivity D* for a collection of commercially available detectors. 6.4.1 MCT detector One of the most widely used infrared detectors is the mercury cadmium telluride (MCT) detector. This is a photon detector which needs to operate at liquid nitrogen temperatures of 77 K. Figure 6.9 shows the spectral response of the commercially available detectors as a function of wavelength. On the other hand, Fig. 6.10 depicts the frequency response of this detector's D*. Essentially, the response is 'flat' from about 103 Hz to 106 Hz. Furthermore, the alloy composition deter114
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t I 6
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8 10 12 14 Wavelength (m)
Fig. 6.9. Plot of detectivity versus wavelength for MCT detectors. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
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Fig. 6.11. MCT detector. Effect of alloy composition to the spectral responsivity characteristics. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
115
x
Fig. 6.12. Wavelength cut-off for an MCT detector versus alloy composition at 77 K (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.).
mines the spectral response of the detector element. Figure 6.11 shows the spectral responsivity for three different alloy compositions (Hg,,CdxTe).
It is evident that manipulation of the alloy composition results in a detector which is tailored to particular needs for wavelength sensitivity. The spectral response of the material is determined by the energy gaps between the various energy levels in the material. Therefore, the energy gap in an MCT alloy is related to the ratio of HgTe to CdTe. Figure 6.12 shows the wavelength cut-off for this ternary alloy system.
6.5 OTHER COMPONENTS 6.5.1 Beamsplitters and mirrors The typical kind of beamsplitters in the mid-infrared region on commercially available instruments is of the germanium (Ge) on potassium bromide (KBr) substrate type. Recently, semiconductor film beam116
t5
D Wavelength (m)
Fig. 6.13. Reflectance of some common metallic films used as mirrors. (Reproduced from Ref. [12] with permission. Copyright 1957, Wissenschaftliche Verlagsgesellschaft mbh.)
splitters for infrared spectrometers have been described which are formed from self-supporting semiconductors, including carbon films. Preferably, the beamsplitters are formed from silicon, germanium, or diamond films [11]. In addition, Figure 6.13 shows the reflectance for some commonly used mirror surfaces in the infrared region [12].
6.6 DISPERSIVE INSTRUMENTS Nowadays, dispersive instruments are used only in selected applications due to the fact that interferometric instruments offer distinct advantages for most applications. However, there are places where dispersive instrumentation is still used when the response at one wavelength or a short range of wavelengths is sought [13]. The basic components of a dispersive spectrometer are the same as in a Fourier transform instrument with the exception of the interferometer. Any differences are within the elements and are the result of the different ways that the source radiation is detected. For instance, sensitive thermocouple detectors are commonplace in dispersive instruments, whereas they are not appropriate for rapid-scanning 117
instruments [14]. In a dispersive instrument a monochromator is used in the place of the interferometer. Before 1950, the monochromator was a rock salt prism for use in the mid-IR region of the electromagnetic spectrum and later was replaced by a diffraction grating. Older monographs provide excellent background information on the operation and maintenance of dispersive infrared instruments and the reader is recommended to consult them [15,16].
6.7 MICHELSON INTERFEROMETER Most commercial interferometers are based on the original Michelson design of 1891 [17]. Interferometers record intensity as a function of optical path difference and the produced interferogram is related to the frequency of the incoming radiation by a Fourier transformation. The principle of a Michelson interferometer is illustrated in Fig. 6.14. The device consists of two flat mirrors, one fixed and one free to move, and a beamsplitter. The radiation from the infrared source strikes the beamsplitter at 45°. The characteristic property of the beamsplitter is that it transmits and reflects equal parts of the radiation. One classic type of beamsplitter, useful in the mid infrared spectral region, consists of a thin layer of germanium (refractive index, n = 4.01) on an infrared transparent substrate (e.g., KBr). The transmitted and reflected beams strike the above described mirrors and are reflected back to the beamsplitter where, again, equal parts are transmitted and reflected. As a consequence, interference occurs at the beamsplitter where the
RADIATIO FROM SOt
MOVING MIRROR I M
BE
TO DETECTOR Fig. 6.14. Block diagram of a Michelson interferometer. 118
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radiation from the two mirrors combine. As shown in Fig. 6.14 when the two mirrors are equidistant from the beamsplitter constructive interference occurs for the beam going to the detector for all wavelengths. In this case, the path length of the two beams in the interferometer are equal and their path difference, called the retardation (6), is zero. The plot of detector response as a function of retardation produces a pattern of light intensity versus retardation, commonly referred to as the interferogram. The interferogram of a monochromatic source is a cosine function. Equation (6.1) describes the above relationship: 1(6) = B(v) cos(27v6)
(6.1)
where v is the wavenumber in cm-l and 6 is the optical path difference, or retardation. The Fourier transform of the above expression is a peak at the frequency of the monochromatic radiation. I is the intensity in the output beam as a function of retardation (6), and B is the intensity as a function of radiation frequency (v). In contrast, the interferogram of a polychromatic source can be considered as the sum of all cosine waves that are produced from monochromatic sources. The polychromatic interferogram has a strong maximum intensity at the zero 119
retardation point where all the cosine components are in phase, as can be seen in Fig. 6.15. This point is also known as the centreburst point [18]. The expression for the intensity of the interferogram of a polychromatic source as a function of retardation is described by Eq. (6.2): 1(6) = [[B(v)[1+ cos(2cv6)]] /2]dv
(6.2)
Thus, in Fourier transform interferometry the data are "encoded" by the interference produced by the retardation and then "decoded" by the Fourier transform to yield the desired intensity signal as a function of frequency (or wavelength).
6.8 ADVANTAGES OF INTERFEROMETRY Two kinds of multichannel advantages exist in Fourier transform interferometry, compared with a dispersive instrument in which only a very narrow band of frequencies is observed at a time. The first-and biggest practical advantage of Fourier transform spectroscopy-is the simultaneous detection of the whole spectrum at once; it is called the Fellgett or multiplex advantage [19,20]. Even though a factor of ca. 2 in signal strength is lost because half of the beam is reflected back to the source, the multichannel advantage is nevertheless 10 4 or higher. That is, theoretically an interferometer can achieve comparable signal-tonoise to a dispersive monochromator 104 faster. In addition, the so-called Jacquinot or 'etendue' advantage exists. This advantage is associated with the increase in source throughput [21]. During dispersive detection the throughput is severely limited by the area of the entrance slit. Even though the interferometer has an entrance aperture of its own, its throughput advantage ranges from 10 to 250 over the infrared frequency range. This was the reason that FTIR spectra of astronomical sources, where very weak astronomical emission sources are present, were produced even before the Fast Fourier Transform (FFT) was invented [22]. A third practical advantage of interferometry is the so-called Connes or registration advantage. Connes advantage stems from the ability of interferometry using a monochromatic source (e.g. a heliumneon (HeNe) laser in today's spectrometers) to accurately and precisely index the retardation, resulting in a superior determination of the 120
retardation sampling position. For example, if the above mentioned HeNe laser ( = 632.8 nm) is used, zero crossings in the visible interferogram occur at intervals of 632.8/2 nm = 0.3164 mm. Because the Nyquist theorem demands at least two sampling points per cycle, the highest infrared frequency that would satisfy the Nyquist criterion is 15,804 cm -l. For mid-IR use, sampling at every other zero-crossing (1 kHeNe intervals) produces a maximum Nyquist frequency of 7902 cm l. Connes advantage allows tremendous reproducibility of interferogram sampling and data storage. This results in full realization of signal-tonoise problems from repeated scans and it is particularly useful for the dynamic experiments that will be discussed later in this book [23,24].
6.9 APODIZATION The amplitude of the side lobes which appear adjacent to absorption bands in the Fourier transform of an interferogram can be drastically reduced if a mathematical manipulation is performed. This treatment is called apodization, from the Greek word ano6os (without feet). This mathematical treatment is necessary because the Fourier transformation is performed over finite limits, even though the theoretical expression for the interferogram's intensity involves infinite limits. Therefore, when the interferogram is truncated, this sudden cut-off results in the appearance of oscillations around the sharp spectral features (absorption bands) in the transform. When the interferogram is multiplied by the apodization function, the transform is essentially free of side lobes. Two of the most popular and effective apodization functions are the triangular and the HappGenzel functions. The amplitude of the first side lobe using triangular apodization is larger than that of the Happ-Genzel function, but the opposite is observed for the subsequent lobes. In general, it can be stated that Happ-Genzel apodization is quite similar to triangular apodization and for most situations they give comparable results [25]. Both types of apodization were used at different times in the work reported in this dissertation. Overall, it can be stated that the biggest drawback of apodization is the worsening of the spectral resolution, since the contributions of the extremes of the interferogram wings are reduced. Therefore, a trade off exists between the reduction in spectral distortion and the worsening of resolution. 121
6.10 RESOLUTION Resolution is defined as the minimum distinguishable spectral interval. The maximum retardation determines the resolution of the scan. The maximum optical resolution achievable by a particular FT-IR spectrometer is given by (Dma) - cm l, where D.ma is the maximum optical path difference attainable by the interferometer. Figure 6.16 shows the effect of different resolution on the appearance of single beam spectra. The spectra shown in this figure have been offset for clarity. Figure 6.16a shows the open-beam background spectrum of the unpurged spectrometer recorded with a resolution of 2 cm - l (Dm~ = 0.5 cm). It is clear that the rotational lines of vapour water are well resolved. In contrast, Fig. 6.16b shows the open-beam spectrum acquired with 16 cm - l resolution (Dm, = 0.0625 cm). Vapour water absorptions are not resolved due to the lower resolution. Dynamic methods have the potential to increase spectral resolution beyond the above limit due to the existence of the possibility of different responses of the components of highly overlapped bands. This possi-
a)
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=
.
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b)
3600
'100
2600
2100
1600
1'0O
600
Wavenumbers Fig. 6.16. (a) Open-beam background, 2 cm-l; (b) open-beam background, 16 cm 1 .
122
bility will be further discussed when dynamic infrared experiments will be presented.
6.11 PHASE CORRECTION The non-ideality of the beamsplitter in a real interferometer results in the introduction of sine components to an interferogram which, in principle, should consist only of cosine components. Equation 6.3 shows the modified relation for the intensity of the interferogram: +o
1(5) =
[[B(v)[l
+ cos(2gv6 + DBS(v))]] / 2]dv
(6.3)
where FBs(V) is the wavelength dependent phase shift introduced by the beamsplitter. Phase correction is the mathematical procedure to remove the sine components from the interferogram. The Fourier transform of a complete double-sided interferogram provides the correct power spectrum, without any phase correction, since the ambiguity does not affect the magnitude. However, when a single-sided interferogram is computed, some knowledge of the phase is required in order to compute the true spectrum [26]. Two of the most popular phase correction routines used in single-sided interferograms are the Mertz algorithm and the Forman algorithm. In the Mertz routine, the largest data point in the interferogram is assigned as the zero retardation point and the amplitude spectrum is calculated with respect to this point. A short double-sided interferogram is measured and its corresponding phase array is used to phase correct the entire single-sided spectrum. The Forman correction is essentially equivalent to the Mertz routine but it is performed in the retardation space [27,28]. Modifications to the Mertz phase correction have appeared in the literature and were originally applied to the vibrational circular dichroism (VCD) spectra [29]. The result of these modifications is that the phase spectrum does not change sign if a quadrant boundary is crossed. As an alternative, a "stored" phase array can be used to produce proper phase correction for the transformed interferograms. This phase array is calculated from a double-sided reference interferogram. The procedure relies on the fact that the beamsplitter phase does not change from scan to scan. 123
6.13 EFFECTS OF MIRROR MISALIGNMENT Mirror misalignment in an interferometer produces a lowering in the energy on the higher energy end of the spectrum (transform). This can be seen in Fig. 6.17 which illustrates three single beam intensities. The degree of alignment varies in these three scans, and this is evident on the high energy portion of the spectrum. These continuous-scan results can be compared to step-scan phase modulation results obtained by dithering the moving mirror with piezoelectric transducers. Continuous-scanFT-IR Most commercially available FT-IR spectrometers use the continuousscan mode of operation, where the moving mirror is scanning at constant velocity. This type of scanning works very well for routine measurements. In the continuous-scan mode of interferometry the laser fringe counter is used to sense the accuracy of the scanning velocity. If a deviation is sensed, correction signals are generated that
Wavenumbers Fig. 6.17. Effect of mirror misalignment on the appearance of single-beam transmission spectra. 124
assure the proper operation (constant velocity). The consequence of this mode of operation is that each infrared wavelength (), is modulated at its own particular Fourier frequency, given by Eq. (6.4): f(k) = 2v/
(6.4)
where v is the mirror velocity. Continuous-scan FT-IR is the technique of choice when static spectral properties are determined. Co-addition of successive scans increases the signal-to-noise ratio (S/N) by a factor proportional to t, where t is the time that the signal is averaged at each collection point. Step-Scan FT-IR In step-scan FT-IR data are collected while the retardation is held constant or is oscillated about a fixed value. Therefore, in order to apply the technique to mid-infrared and shorter wavelength measurements, a method for controlling the retardation and implementing a special sampling rate comparable to that achieved in modern continuous-scan instruments is required. In recent years several different control methods have been reported. However, all of these basically rely on the use of the HeNe laser fringe pattern to generate the control signal and to determine the step size [30]. The biggest advantage of the step-scan mode is the separation of the time of the experiment from the time of the data collection. Two types of experiment are possible with step-scan interferometry. One type is the time-domain or time resolved experiments where data are collected as a function of time at each mirror position. Sorting of the data results in interferograms that contain spectral responses at different times. The event under study must be a repeatable process in order for the experiment to work. The other type of experiment capable with step-scan is the so-called frequency domain or synchronous modulation experiments. In these experiments, there are two ways to modulate the intensity of the infrared radiation in order to generate step-scan interferograms. One way is to use amplitude modulation (AM) which can be achieved by means of a chopper. When a chopper is used for intensity modulation, a lock-in amplifier is used to detect the signal before digitization occurs. The technique has the drawback that the signal is riding on top of a large DC offset, which has to be subtracted before any meaningful data can be obtained. This can be done by either calculating the average 125
value of the interferogram and subtracting it from each sample point before the Fourier transform takes place or by setting the lock-in amplifier offset to zero, far from the interferogram. Even though the latter technique eliminates the problem of reduced dynamic range, the technique is still susceptible to DC drift. Another way to achieve modulation of the radiation is by phase modulation (PM). Phase modulation is achieved in some step-scan instruments by a low amplitude oscillation of the moving mirror along the light path, but any other way of producing phase-difference modulation is acceptable. PM results are superior to AM results by at least a factor of 2 in S/N, when the experiment is detector-noise limited. This improvement stems from the fact that the PM interferogram is essentially the first derivative of the AM interferogram, therefore source intensity fluctuations and other variations of the beam intensity will cancel out [31]. Another parameter associated with PM modulation experiments is the so-called 'phase modulation characteristic' [32]. This refers to the connection between the amplitude of the phase modulation and the wavelength region of maximum modulation efficiency. For the mid-IR region, a PM modulation amplitude of 2 XHeNe (zero-to-peak) is appropriate (maximum modulation at 2300 cm-l). In contrast to the continuous-scan method, the advantages of stepscan operation include the ability, as mentioned above, to apply virtually any modulation frequency to the infrared radiation and to carry out multiple modulation experiments. Since the frequency of modulation is not a function of any retardation velocity (e.g., mirror scan speed), they have no dependence on radiation wavelength. In addition, the use of lock-in amplifier detection or digital signal processors (DSP), provides a high degree of noise rejection, analogous to the Fourier filtering effective in the continuous scan mode. Another advantage of lock-in amplifier or DSP detection is the easy retrieval of the signal phase. This is possible due to the fact that the beamsplitter (instrumental) phase is identical for the in-phase and quadrature (900 out of phase) components of the signal. These components are easily obtained as outputs of a two-phase lock-in amplifier. As a result, not only the magnitude M, but also the phase D can be easily obtained by following Eqs. (6.5) to (6.8): M = (2 + Q2 )1/ 2
(6.5)
D = arctan(Q/I)
(6.6)
126
I=Mcos¢
(6.7)
Q = M sine
(6.8)
The signal-to-noise (S/N) ratio is increased by staying longer at each data collection point. The two modes of operation, step-scan and continuous-scan, should produce identical results under conditions of detector-limited noise. The time resolution of the step-scan technique is limited only by the rise-time of the detector, by the electronics (especially by the A/D converter), and by the signal strength. Therefore, it is capable of measuring various relaxation processes that occur in the sub-microsecond regime and are closely associated with molecularscale phenomena.
6.14 FOURIER TRANSFORMATION AND ITS USE IN FT-IR INSTRUMENTATION The breakthrough in the application of interferometry to spectroscopy came with the discovery by Cooley and Tukey of the fast Fourier transform (FFT) algorithm in 1964 [33]. The FFT procedure takes advantage of several properties of the discrete FT, which is somehow redundant in nature [34]. The FT case can be represented as an nvector (n points interferogram) which must be multiplied by an nxn matrix, each row of which is a discrete representation of a complex sinusoid. The result of the multiplication is an n-vector, which is the transformed spectrum. A straightforward approach requires n2 operations, where operations are complex multiplications followed by complex additions. Since the nxn matrix is highly ordered and cyclical it can be readily factored. IfNis chosen such that it is an integral power of two, then extra advantage may be realized by calculating the FT on a digital computer [35]. As an example, the Fourier transform of a 2048 point vector requires (2048)2, or 4.2 million multiplications. The FFT algorithm reduces this amount to (2048) x log(2048), for a total of 24233 multiplications. Obviously, the great advantage of FFT can be appreciated as the number of data points gets larger and larger. Today's personal computers can calculate an array similar to the one described above in a fraction of one second.
127
REFERENCES 1. W.F. Herschel, Phil. Transact. Roy. Soc., 90 (1800) 284. 2. C.N.R. Rao, Chemical Applications of Infrared Spectroscopy. Academic Press, New York, 1963. 3. J.F. Ferraro, Spectroscopy, 14(2), 1999. 4. W.L. Wolfe and G.J. Zissis, The Infrared Handbook. Office of Naval Research, Department of the Navy, Washington, DC, 1978. 5. J.C. Morris, Comments on the measurement of the emmitance of the globar radiation source. J. Optical Soc. Am. (Washington, DC), 51 (1961) 758. 6. Nicolet Instruments, private communication. 7. W.Y. Ramsey and J.C, Alishouse, A comparison of infrared sources. Infrared Physics (Pergamon, Elmsford, NY), 8 (1968) 143. 8. W.L. Wolfe and G.J. Zissis, The Infrared Handbook. Office of Naval Research, Department of the Navy, Washington, DC, 1978, Chapter 11. 9. M.J.E. Golay, Rev. Scient. Instrum., 18 (1949) 347. 10. M. Hercher, Detectors and Lasers, in: Contemporary OpticalEngineering. The Institute of Optics, Rochester, NY. 1976 11. A. Simon, J. Gast (Bruker Analytische Messtechnik GmbH, Germany. Patent written in German. Application: DE 92-4242440 921216 12. G. Hass and A.F. Turner, in: M. Auwarter (Ed.), Coatings for Infrared Optics. Wissenschaftliche Verlagsgesellschaft mbh, Stuttgart, 1957. 13. I. Noda, A.E. Dowrey and C. Marcott, Appl. Spectrosc., 42 (1988) 203. 14. R. White, Chromatographyl/FourierTransformInfraredSpectroscopy and its Applications. Marcel Dekker, New York, 1990. 15. C.N.R. Rao, Chemical Applications of Infrared Spectroscopy. Academic Press, New York, 1963. 16. A.L. Smith, Applied Infrared Spectroscopy, Fundamentals, Techniques, andAnalytical Problem-Solving. Wiley-Interscience, New York, 1979. 17. A.A. Michelson, Phil. Mag., Ser. 5, 31 (1891) 256. 18. P.R. Griffiths and J.A. de Haseth, Fourier Transform Infrared Spectroscopy. Wiley, New York, NY, pp. 407-425, 1986. 19. P. Fellgett, Thesis, Cambridge University, Cambridge, UK, 1951. 20. P. Fellgett, J. Phys. (Radium), 19 (1958) 187. 21. P. Jacquinot, J. Opt. Soc. Am., 44 (1954) 761. 22. J. Connes and P. Connes, J. Opt. Soc. Am., 56 (1966) 896. 23. J. Connes, Optical Instruments and Techniques. Oriel Press, Paris, 1970. 24. R.A. Palmer, Spectroscopy, 8(2) (1993) 26. 25. A.G. Marshall and F.R. Verdun, FourierTransforms in NMR, Optical, and Mass Spectrometry. Elsevier, Amsterdam, 1990. 26. L. Mertz, InfraredPhys., 7, (1967) 17. 27. M.L. Forman, J. Opt. Soc. Am., 56 (1966) 978. 128
28. 29. 30. 31. 32. 33. 34. 35.
M.L. Forman, W.H. Steel and G.A. Vanasse, J. Opt. Soc. Am., 56 (1966) 59. C.A. McCoy and J.A. de Haseth, Appl. Spectrosc., 42 (1988) 336. R.A. Palmer, Spectroscopy, 8(2) (1993) 26. J. Chamberlain, InfraredPhys., 11 (1971) 25. J. Chamberlain and H.A. Gebbie, Infrared Phys., 11 (1971) 57. J.W. Cooley and J.W. Tukey, Math. Comput., 19 (1965) 297. C.J. Manning, Ph.D. Thesis, Duke University, 1991. M.L. Forman, J. Opt. Soc. Am., 56 (1966) 978.
129
Instrumentation
6.1 HISTORY OF INFRARED INSTRUMENTATION Since the discovery of infrared radiation by Sir William Herschel in 1800 [1], a variety of methods have been used to improve the experimental techniques for measuring infrared spectra. In particular, Herschel used a prism and a mercury thermometer to record his observations of heat-based radiation beyond the range of the solar spectrum. Melloni is credited with the construction of the first midinfrared spectrometer in 1833, after his discovery of the transparency of NaCl in the infrared. Excellent references on the early history of vibrational spectroscopy and the minds that shaped the field can be found elsewhere. This chapter will deal in detail with the interferometric methods of capturing infrared radiation. Older monographs treat non-interferometric methods in great detail [2]. 6.1.1 History of FT-IR instrumentation The construction of the first interferometers dates back to 1880. Lord Rayleigh may have constructed an interferometer at that period, but it is Michelson who is credited with the construction of the first operable instrument at that time. The interferometer was used in the measurement of the speed of light in diverse directions. Measurements that took place at was is now Case Western Reserve University showed that there was no detectable difference in the speed of light in either direction. The lack of adequate computing power was the main reason that it took approximately eighty years for the instrument to utilize its full potential as an analytical tool. Ferraro has recently published a very informative account of the history of FT-IR spectroscopy [3]. 105
The first attempts to use interferometric means to measure infrared radiation concentrated in the far infrared region of the spectrum. The operational needs for mechanical precision and computational load are lower in the far-infrared compared to the mid-infrared. Therefore, a lot of the early applications and advancements took place in the field of astronomy where far-infrared spectroscopy is used extensively. One very important recent development that led to the widespread use of infrared spectroscopy as a characterization tool was the introduction of the first Fourier transform infrared spectrometer, the FTS 14, by the Biorad Company of Cambridge, Massachusetts in 1969. Several developments in the 1950s and 1960s contributed to the introduction of this first commercially available instrument. The work of L. Mertz in interferometer design during 1954-56 and the development of data reduction algorithms in 1960-65 are probably the most significant contributors. One historical aspect that should not be overlooked was the role of the NASA contract to Block Engineering for an instrument with ten times the available resolution. The model 1500 (296 in the commercial version) had 0.5 cm-l resolution and a better signal-tonoise (S/N) ratio than the dispersive instruments of the time. Other notable developments were the discovery of the HeNe laser along with the introduction of better infrared detectors, analog-todigital (A/D) converters and minicomputers. In 1966 a one-foot laser with a built-in power supply was available to be used in the first FT-IR spectrometer. In addition, pyroelectric bolometers in the form of the deuterated triglycine sulphate (DTGS) detector also became available. Their major advantage was that their bandwidth was compatible with the rapid-scan frequencies. With respect to computing power there was a remarkable development from the PDP-1 in 1960 to the DG Nova in 1969. After the introduction of this instrument many new instruments from various manufacturers have appeared and tremendous progress has been achieved in the years following 1969. A list of the advancements will undoubtedly include the very small footprint of the modern instruments, quadrature detection with forward and backward scanning, digital signal processing, diagnostic features, low powered aircooled sources, the flexible design of the research-grade instruments, the multiple spectral ranges, the very high spectral resolution, and the tremendous progress in FT-IR software. In addition, one of the most important developments was the 'rediscovery' of step-scan interferometry, a subject that will be extensively dealt with in this book. 106
What is the future of infrared instrumentation? Without a doubt, any technological breakthrough will eventually find its way to a commercial design with time. Improvements in performance, new features and capabilities, usability and (hopefully!) a reduction in cost should all be expected.
6.2 COMPONENTS OF AN FT-IR SPECTROMETER The components of an FT-IR spectrometer primarily include the source interferometer, the source of radiation, the detector and other optical elements (beamsplitters, mirrors, etc.). In addition, data manipulation also takes place in the adjacent computer station. It is beyond the scope of this book to give a detailed account of all the elements involved; instead, an attempt will be made to cover in more detail important components of these designs. 6.2.1 Sources The source of infrared energy in an infrared instrument does not depend on the type of instrumentation used to detect the radiation. Both dispersive instruments and Fourier transformed instruments can use the same types of infrared sources. Therefore, a general overview of the available technology will be reviewed here. The more typical sources are the Globar source and the Nernst glower, even though nichrome coils have also been used in the past. Nichrome coils operate at lower temperatures and therefore have a lower emissivity. Finally, mercury arc lamps are used most frequently for experiments dealing with the far-infrared region of the spectrum. The first two types will be discussed in more detail here. GlobarSource This source is made out of silicon carbide (SiC) and it has metallic leads at the ends which serve as electrodes. The application of electric current results in the generation of heat, which yields radiation at temperatures higher than 1000°C. Water cooling is required for this type of source because the electrodes need to be cooled [4]. This extra level of complexity makes this source less convenient to use and more expensive. Figure 6.1 shows the ratio of the globar source to a 900°C blackbody. 107
Prisms: 4.2. 4.2.
.
NaCI & KBr 0
Ramsey and Alishouse
Q
3.4
s
CsI
Calculated after Silverman
1.8
1.0 0.2
I I i
2.l
6.0 10.0 14.0 18.0 22.0 26.0 30.0 34.0 38.0 Wavelength (m)
Fig. 6.1. Globar versus a 900°C blackbody. (Reproduced from Ref. [7] with permission. Copyright 1968, Pergamon.) I.o
0.9 W 0.8 E 0.7 K 0.6
-255 K Stewart and Richmond
0.
n_
I
1
II 3
I I
5
I I I I 7 9 11 Wavelength (im)
I
I 13
I 15
Fig. 6.2. Spectral emissivity of the globar source. (Reproduced from Ref. [7] with permission. Copyright 1968, Pergamon.)
One other advantage of this source is its high emissivity down to 80 cm - ', making it useful in the far-infrared region of the spectrum. Figure 6.2 shows the spectral emissivity of a typical globar source [5]. These values are only representative and are expected to change considerably with use. Recently, a new low power air-cooled ceramic source has been introduced into the modern FT-IR instruments [6]. This source has the advantage that no watering cooling is necessary, making their instruments portable and easier to maintain. Nernst glowers This infrared source's element is a mixture of yttrium and zirconium oxides and has an emission spectrum that resembles that of a black 108
z
}
3 W
Wavelengt
(m)
Fig. 6.3. Ratio of a Nernst glower to a 900°C blackbody. (Reproduced from Ref. [8] with permission. Copyright 1978, Office of Naval Research.)
body at 1800 K. It is an insulator at room temperature and becomes a conductor after it is preheated. It used to be popular but it has a number of disadvantages, the biggest being its short lifetime and mechanical instability. The spectral characteristics of a Nernst glower versus a 900°C blackbody can be found in Fig. 6.3 [7]. 6.2.2 Infrared detectors One of the most important elements of an infrared spectrometer is the component responsible for the detection of infrared energy. Typically, the description of a detector is not limited to the responsive element which changes the incoming radiation into an electrical signal, but it also includes the physical mounting of the element, like the windows, the apertures, the Dewar flasks, etc. Together, they form what is called a detector [8]. There are two general classes of infrared detectors. One class comprises the thermal detectors and the other class the photon detectors. As the name suggests, thermal detectors operate by sensing fluctuations in the temperature of an absorbing material as a result of exposure to the incoming radiation. The other category, the photon or as often called quantum detectors are sensitive to changes in the quantity of free-charged carriers in the solid, brought by the interaction with the external radiation. 109
Thermal detectors Thermal detectors rely on four different processes to achieve detection of infrared radiation: 1. The bolometric effect. This effect relies on the change in the electrical resistance of the responsive element due to temperature changes produced by the absorbed infrared radiation. This change in resistance is detected by conventional techniques. 2. The thermovoltaic effect. In this case, the heating of the junction between two dissimilar materials produces a measurable voltage across the leads. 3. The thermopneumatic effect. A very common thermal detector, the Golay detector, relies on this phenomenon [9]. In the case of thermopneumatic detectors, a gas-filled chamber that contains an infrared absorbing element is exposed to infrared light. Absorption of energy by the element generates heat, which heats up the gas in the chamber. The consequent increase in the pressure of the gas results in the distortion of a thin flexible mirror on the other end of the sealed gas chamber. This distortion is sensed by an independent optical system. Golay detectors have been extensively used as farinfrared detectors, even though they had problems with their mechanical integrity at one point. Figure 6.4 shows a cross-section of a typical Golay cell [10]. 4. The pyroelectric effect. In this process the radiation increases the temperature of a crystalline material. The result is a change in the electrical polarization of the crystal surface and the generation of an electric field. TARGET: THIN
BSORBING FILM IR TRANSMITTIN WINDOW
ELASTIC MEMBRANE
GAS FILLED CHAMBER Fig. 6.4. Cross-section of the Golay cell. (Reproduced from Ref. [10] with permission. Copyright 1976, Institute of Optics.)
110
Photon detectors The other category of infrared detectors is the quantum or photon detectors. In photon detectors, incident infrared photons result in the production of free charge carriers in the responsive element. No serious temperature change in the element takes place during this process. The above category can be further divided in four underlying processes: 1. Photoconductive effect. The principle behind this effect is that a change in the number of incident photons reaching a semiconducting material changes the number of the free charge carrier in the materials. Since electrical conductivity is directly proportional to the number of these charge carriers, it can be used to deduce the number of incident photons on the semiconductor. 2. Photovoltaic effect. In this case, a change in the number of incident photons on a semiconductor p-n junction results in a change in the voltage generated by the junction. Figures 6.5 and 6.6 show the energy band models for unilluminated and illuminated p-n junctions. 3. Photoelectromagnetic effect. In this case, the separation of the charge takes place via the use of a magnetic field. The charge separation produces a voltage that is directly proportional to the number of incident infrared photons. 4. Photoemissive effect. In this case, an incident photon is absorbed by the surface and gives up its energy to a free electron. This electron can escape the surface and in the case that the surface is in an evacuated chamber equipped with an anode and an eternal circuit, electric current is detected.
Band _.-----------Fermi Level
P-l
n-Region
Unilluminated p-n junction Fig. 6.5. Energy band model for an unilluminatedp-n junction. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.) 111
Conduction Band
h
-'
h f
Illuminated p-n junction Fig. 6.6. Energy band model for an illuminated p-n junction. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
6.3 DETECTOR NOISE
There are several contributors to the noise (the fluctuation in signal intensity for a steady radiation field) of an infrared detector. In infrared spectroscopy, the detector noise is most often much higher than any other noise source. In addition, it has usually a thermal origin. Therefore, the majority of infrared detectors do not operate at room temperature. Johnson noise: this type of noise is generated in resistors due to the random thermal motion of the charge carriers. As the temperature of the element increases there is a concurrent increase in the average kinetic energy of the carriers, which results in an increased electric noise voltage. This is the reason this type of noise is also called thermal noise. Shot or Schottky noise: this is random noise that has to do with the statistical fluctuations of the photon fluxes. It has its origin in the discreteness of electrical charge. Both of the above types of noise are 'white' types of noises. This means that they are independent of the frequency all the way out to the cut-off frequency. Other types of noise exist that are dependent on the frequency of the incoming radiation. The most important of these types is the 1/f noise. Its mechanism is not well understood but, as the name implies, its magnitude is reversibly proportional to the frequency of the radiation. 112
In addition, electronic components associated with the detector contribute to the noise. Pre-amplification is always required for any type of detection system.
6.4 PERFORMANCE OF AN INFRARED DETECTOR The performance of an infrared detector is measured by a set of figures of merit. The responsivity of the detector is the output of the electrical signal to the incident radiation power. The noise equivalent power (NEP) is the level of incident infrared signal that produces a signal-tonoise ratio of one. Detectivity is defined as the reciprocal of the noise equivalent power (NEP). The normalized detectivity D* is a widely used figure-of-merit and it includes the area of the detector and frequency bandwidth of the measurement. Thermal detectors show a 'flat' detectivity response throughout the entire spectral region. In contrast, photon detectors have higher detectivity but over a limited spectral range. Figure 6.7 shows the
10
lA
I I
E
in
8
1_1_~~~' N~I
I
1~~,___
i.. 2
4
6
8 10 12 Wavelength (rim)
14
16
18
9109 i
10 X
10 10
3 2 10 10 Chopping Frequency (cps)
10
Fig. 6.7. Plots of D* versus wavelength for (a) thermocouple versus (b) an InSb detector. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
113
l
10'
1011
1010
10
9
1081
Wavelength (m)
Fig. 6.8. D*(X) values for a number of commercially available quantum detectors. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
response for a thermocouple detector as compared with the spectral response for an InSb photon detector. In addition, Figure 6.8 shows the plots of the normalized detectivity D* for a collection of commercially available detectors. 6.4.1 MCT detector One of the most widely used infrared detectors is the mercury cadmium telluride (MCT) detector. This is a photon detector which needs to operate at liquid nitrogen temperatures of 77 K. Figure 6.9 shows the spectral response of the commercially available detectors as a function of wavelength. On the other hand, Fig. 6.10 depicts the frequency response of this detector's D*. Essentially, the response is 'flat' from about 103 Hz to 106 Hz. Furthermore, the alloy composition deter114
I
I
10 M
10
2
Z
1
M
9
0
- 10
4
,
t I 6
I
I'
I
1(6
8 10 12 14 Wavelength (m)
Fig. 6.9. Plot of detectivity versus wavelength for MCT detectors. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
..
. _
1 10 2 10 RF
109 2 -
-8
In
. . ... . . .. '
I
........
2
103
..
.
I ~{J· I
10 4
1
..
I~~ I{
105
{ II~
106
107
Frequency (Hz)
Fig. 6.10. Plot of D* versus frequency for an MCT detector. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
W W C 0..
i.
10
a:
IB\
.
C
i
t
O
C:
- Spectral Response
is a Function of x I
i 6
l 8
l 10
I 12
, 14
i 16
l 18
Wavelength (. m)
Fig. 6.11. MCT detector. Effect of alloy composition to the spectral responsivity characteristics. (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.)
115
x
Fig. 6.12. Wavelength cut-off for an MCT detector versus alloy composition at 77 K (Reproduced from Ref. [4] with permission. Copyright 1978, Office of Naval Research.).
mines the spectral response of the detector element. Figure 6.11 shows the spectral responsivity for three different alloy compositions (Hg,,CdxTe).
It is evident that manipulation of the alloy composition results in a detector which is tailored to particular needs for wavelength sensitivity. The spectral response of the material is determined by the energy gaps between the various energy levels in the material. Therefore, the energy gap in an MCT alloy is related to the ratio of HgTe to CdTe. Figure 6.12 shows the wavelength cut-off for this ternary alloy system.
6.5 OTHER COMPONENTS 6.5.1 Beamsplitters and mirrors The typical kind of beamsplitters in the mid-infrared region on commercially available instruments is of the germanium (Ge) on potassium bromide (KBr) substrate type. Recently, semiconductor film beam116
t5
D Wavelength (m)
Fig. 6.13. Reflectance of some common metallic films used as mirrors. (Reproduced from Ref. [12] with permission. Copyright 1957, Wissenschaftliche Verlagsgesellschaft mbh.)
splitters for infrared spectrometers have been described which are formed from self-supporting semiconductors, including carbon films. Preferably, the beamsplitters are formed from silicon, germanium, or diamond films [11]. In addition, Figure 6.13 shows the reflectance for some commonly used mirror surfaces in the infrared region [12].
6.6 DISPERSIVE INSTRUMENTS Nowadays, dispersive instruments are used only in selected applications due to the fact that interferometric instruments offer distinct advantages for most applications. However, there are places where dispersive instrumentation is still used when the response at one wavelength or a short range of wavelengths is sought [13]. The basic components of a dispersive spectrometer are the same as in a Fourier transform instrument with the exception of the interferometer. Any differences are within the elements and are the result of the different ways that the source radiation is detected. For instance, sensitive thermocouple detectors are commonplace in dispersive instruments, whereas they are not appropriate for rapid-scanning 117
instruments [14]. In a dispersive instrument a monochromator is used in the place of the interferometer. Before 1950, the monochromator was a rock salt prism for use in the mid-IR region of the electromagnetic spectrum and later was replaced by a diffraction grating. Older monographs provide excellent background information on the operation and maintenance of dispersive infrared instruments and the reader is recommended to consult them [15,16].
6.7 MICHELSON INTERFEROMETER Most commercial interferometers are based on the original Michelson design of 1891 [17]. Interferometers record intensity as a function of optical path difference and the produced interferogram is related to the frequency of the incoming radiation by a Fourier transformation. The principle of a Michelson interferometer is illustrated in Fig. 6.14. The device consists of two flat mirrors, one fixed and one free to move, and a beamsplitter. The radiation from the infrared source strikes the beamsplitter at 45°. The characteristic property of the beamsplitter is that it transmits and reflects equal parts of the radiation. One classic type of beamsplitter, useful in the mid infrared spectral region, consists of a thin layer of germanium (refractive index, n = 4.01) on an infrared transparent substrate (e.g., KBr). The transmitted and reflected beams strike the above described mirrors and are reflected back to the beamsplitter where, again, equal parts are transmitted and reflected. As a consequence, interference occurs at the beamsplitter where the
RADIATIO FROM SOt
MOVING MIRROR I M
BE
TO DETECTOR Fig. 6.14. Block diagram of a Michelson interferometer. 118
Un
Z l
M UI
U C I
I~
$---------
_
I
. .
Z'
U
'
0X o
Qc
I
"o00
SZS9
s=a
i2
-at 0
s TA POINTS
sea
s
5
7Z'-
75
Fig. 6.15. Typical interferogram showing centre-burst region.
radiation from the two mirrors combine. As shown in Fig. 6.14 when the two mirrors are equidistant from the beamsplitter constructive interference occurs for the beam going to the detector for all wavelengths. In this case, the path length of the two beams in the interferometer are equal and their path difference, called the retardation (6), is zero. The plot of detector response as a function of retardation produces a pattern of light intensity versus retardation, commonly referred to as the interferogram. The interferogram of a monochromatic source is a cosine function. Equation (6.1) describes the above relationship: 1(6) = B(v) cos(27v6)
(6.1)
where v is the wavenumber in cm-l and 6 is the optical path difference, or retardation. The Fourier transform of the above expression is a peak at the frequency of the monochromatic radiation. I is the intensity in the output beam as a function of retardation (6), and B is the intensity as a function of radiation frequency (v). In contrast, the interferogram of a polychromatic source can be considered as the sum of all cosine waves that are produced from monochromatic sources. The polychromatic interferogram has a strong maximum intensity at the zero 119
retardation point where all the cosine components are in phase, as can be seen in Fig. 6.15. This point is also known as the centreburst point [18]. The expression for the intensity of the interferogram of a polychromatic source as a function of retardation is described by Eq. (6.2): 1(6) = [[B(v)[1+ cos(2cv6)]] /2]dv
(6.2)
Thus, in Fourier transform interferometry the data are "encoded" by the interference produced by the retardation and then "decoded" by the Fourier transform to yield the desired intensity signal as a function of frequency (or wavelength).
6.8 ADVANTAGES OF INTERFEROMETRY Two kinds of multichannel advantages exist in Fourier transform interferometry, compared with a dispersive instrument in which only a very narrow band of frequencies is observed at a time. The first-and biggest practical advantage of Fourier transform spectroscopy-is the simultaneous detection of the whole spectrum at once; it is called the Fellgett or multiplex advantage [19,20]. Even though a factor of ca. 2 in signal strength is lost because half of the beam is reflected back to the source, the multichannel advantage is nevertheless 10 4 or higher. That is, theoretically an interferometer can achieve comparable signal-tonoise to a dispersive monochromator 104 faster. In addition, the so-called Jacquinot or 'etendue' advantage exists. This advantage is associated with the increase in source throughput [21]. During dispersive detection the throughput is severely limited by the area of the entrance slit. Even though the interferometer has an entrance aperture of its own, its throughput advantage ranges from 10 to 250 over the infrared frequency range. This was the reason that FTIR spectra of astronomical sources, where very weak astronomical emission sources are present, were produced even before the Fast Fourier Transform (FFT) was invented [22]. A third practical advantage of interferometry is the so-called Connes or registration advantage. Connes advantage stems from the ability of interferometry using a monochromatic source (e.g. a heliumneon (HeNe) laser in today's spectrometers) to accurately and precisely index the retardation, resulting in a superior determination of the 120
retardation sampling position. For example, if the above mentioned HeNe laser ( = 632.8 nm) is used, zero crossings in the visible interferogram occur at intervals of 632.8/2 nm = 0.3164 mm. Because the Nyquist theorem demands at least two sampling points per cycle, the highest infrared frequency that would satisfy the Nyquist criterion is 15,804 cm -l. For mid-IR use, sampling at every other zero-crossing (1 kHeNe intervals) produces a maximum Nyquist frequency of 7902 cm l. Connes advantage allows tremendous reproducibility of interferogram sampling and data storage. This results in full realization of signal-tonoise problems from repeated scans and it is particularly useful for the dynamic experiments that will be discussed later in this book [23,24].
6.9 APODIZATION The amplitude of the side lobes which appear adjacent to absorption bands in the Fourier transform of an interferogram can be drastically reduced if a mathematical manipulation is performed. This treatment is called apodization, from the Greek word ano6os (without feet). This mathematical treatment is necessary because the Fourier transformation is performed over finite limits, even though the theoretical expression for the interferogram's intensity involves infinite limits. Therefore, when the interferogram is truncated, this sudden cut-off results in the appearance of oscillations around the sharp spectral features (absorption bands) in the transform. When the interferogram is multiplied by the apodization function, the transform is essentially free of side lobes. Two of the most popular and effective apodization functions are the triangular and the HappGenzel functions. The amplitude of the first side lobe using triangular apodization is larger than that of the Happ-Genzel function, but the opposite is observed for the subsequent lobes. In general, it can be stated that Happ-Genzel apodization is quite similar to triangular apodization and for most situations they give comparable results [25]. Both types of apodization were used at different times in the work reported in this dissertation. Overall, it can be stated that the biggest drawback of apodization is the worsening of the spectral resolution, since the contributions of the extremes of the interferogram wings are reduced. Therefore, a trade off exists between the reduction in spectral distortion and the worsening of resolution. 121
6.10 RESOLUTION Resolution is defined as the minimum distinguishable spectral interval. The maximum retardation determines the resolution of the scan. The maximum optical resolution achievable by a particular FT-IR spectrometer is given by (Dma) - cm l, where D.ma is the maximum optical path difference attainable by the interferometer. Figure 6.16 shows the effect of different resolution on the appearance of single beam spectra. The spectra shown in this figure have been offset for clarity. Figure 6.16a shows the open-beam background spectrum of the unpurged spectrometer recorded with a resolution of 2 cm - l (Dm~ = 0.5 cm). It is clear that the rotational lines of vapour water are well resolved. In contrast, Fig. 6.16b shows the open-beam spectrum acquired with 16 cm - l resolution (Dm, = 0.0625 cm). Vapour water absorptions are not resolved due to the lower resolution. Dynamic methods have the potential to increase spectral resolution beyond the above limit due to the existence of the possibility of different responses of the components of highly overlapped bands. This possi-
a)
Ca
E M Mt U e
=
.
'A
b)
3600
'100
2600
2100
1600
1'0O
600
Wavenumbers Fig. 6.16. (a) Open-beam background, 2 cm-l; (b) open-beam background, 16 cm 1 .
122
bility will be further discussed when dynamic infrared experiments will be presented.
6.11 PHASE CORRECTION The non-ideality of the beamsplitter in a real interferometer results in the introduction of sine components to an interferogram which, in principle, should consist only of cosine components. Equation 6.3 shows the modified relation for the intensity of the interferogram: +o
1(5) =
[[B(v)[l
+ cos(2gv6 + DBS(v))]] / 2]dv
(6.3)
where FBs(V) is the wavelength dependent phase shift introduced by the beamsplitter. Phase correction is the mathematical procedure to remove the sine components from the interferogram. The Fourier transform of a complete double-sided interferogram provides the correct power spectrum, without any phase correction, since the ambiguity does not affect the magnitude. However, when a single-sided interferogram is computed, some knowledge of the phase is required in order to compute the true spectrum [26]. Two of the most popular phase correction routines used in single-sided interferograms are the Mertz algorithm and the Forman algorithm. In the Mertz routine, the largest data point in the interferogram is assigned as the zero retardation point and the amplitude spectrum is calculated with respect to this point. A short double-sided interferogram is measured and its corresponding phase array is used to phase correct the entire single-sided spectrum. The Forman correction is essentially equivalent to the Mertz routine but it is performed in the retardation space [27,28]. Modifications to the Mertz phase correction have appeared in the literature and were originally applied to the vibrational circular dichroism (VCD) spectra [29]. The result of these modifications is that the phase spectrum does not change sign if a quadrant boundary is crossed. As an alternative, a "stored" phase array can be used to produce proper phase correction for the transformed interferograms. This phase array is calculated from a double-sided reference interferogram. The procedure relies on the fact that the beamsplitter phase does not change from scan to scan. 123
6.13 EFFECTS OF MIRROR MISALIGNMENT Mirror misalignment in an interferometer produces a lowering in the energy on the higher energy end of the spectrum (transform). This can be seen in Fig. 6.17 which illustrates three single beam intensities. The degree of alignment varies in these three scans, and this is evident on the high energy portion of the spectrum. These continuous-scan results can be compared to step-scan phase modulation results obtained by dithering the moving mirror with piezoelectric transducers. Continuous-scanFT-IR Most commercially available FT-IR spectrometers use the continuousscan mode of operation, where the moving mirror is scanning at constant velocity. This type of scanning works very well for routine measurements. In the continuous-scan mode of interferometry the laser fringe counter is used to sense the accuracy of the scanning velocity. If a deviation is sensed, correction signals are generated that
Wavenumbers Fig. 6.17. Effect of mirror misalignment on the appearance of single-beam transmission spectra. 124
assure the proper operation (constant velocity). The consequence of this mode of operation is that each infrared wavelength (), is modulated at its own particular Fourier frequency, given by Eq. (6.4): f(k) = 2v/
(6.4)
where v is the mirror velocity. Continuous-scan FT-IR is the technique of choice when static spectral properties are determined. Co-addition of successive scans increases the signal-to-noise ratio (S/N) by a factor proportional to t, where t is the time that the signal is averaged at each collection point. Step-Scan FT-IR In step-scan FT-IR data are collected while the retardation is held constant or is oscillated about a fixed value. Therefore, in order to apply the technique to mid-infrared and shorter wavelength measurements, a method for controlling the retardation and implementing a special sampling rate comparable to that achieved in modern continuous-scan instruments is required. In recent years several different control methods have been reported. However, all of these basically rely on the use of the HeNe laser fringe pattern to generate the control signal and to determine the step size [30]. The biggest advantage of the step-scan mode is the separation of the time of the experiment from the time of the data collection. Two types of experiment are possible with step-scan interferometry. One type is the time-domain or time resolved experiments where data are collected as a function of time at each mirror position. Sorting of the data results in interferograms that contain spectral responses at different times. The event under study must be a repeatable process in order for the experiment to work. The other type of experiment capable with step-scan is the so-called frequency domain or synchronous modulation experiments. In these experiments, there are two ways to modulate the intensity of the infrared radiation in order to generate step-scan interferograms. One way is to use amplitude modulation (AM) which can be achieved by means of a chopper. When a chopper is used for intensity modulation, a lock-in amplifier is used to detect the signal before digitization occurs. The technique has the drawback that the signal is riding on top of a large DC offset, which has to be subtracted before any meaningful data can be obtained. This can be done by either calculating the average 125
value of the interferogram and subtracting it from each sample point before the Fourier transform takes place or by setting the lock-in amplifier offset to zero, far from the interferogram. Even though the latter technique eliminates the problem of reduced dynamic range, the technique is still susceptible to DC drift. Another way to achieve modulation of the radiation is by phase modulation (PM). Phase modulation is achieved in some step-scan instruments by a low amplitude oscillation of the moving mirror along the light path, but any other way of producing phase-difference modulation is acceptable. PM results are superior to AM results by at least a factor of 2 in S/N, when the experiment is detector-noise limited. This improvement stems from the fact that the PM interferogram is essentially the first derivative of the AM interferogram, therefore source intensity fluctuations and other variations of the beam intensity will cancel out [31]. Another parameter associated with PM modulation experiments is the so-called 'phase modulation characteristic' [32]. This refers to the connection between the amplitude of the phase modulation and the wavelength region of maximum modulation efficiency. For the mid-IR region, a PM modulation amplitude of 2 XHeNe (zero-to-peak) is appropriate (maximum modulation at 2300 cm-l). In contrast to the continuous-scan method, the advantages of stepscan operation include the ability, as mentioned above, to apply virtually any modulation frequency to the infrared radiation and to carry out multiple modulation experiments. Since the frequency of modulation is not a function of any retardation velocity (e.g., mirror scan speed), they have no dependence on radiation wavelength. In addition, the use of lock-in amplifier detection or digital signal processors (DSP), provides a high degree of noise rejection, analogous to the Fourier filtering effective in the continuous scan mode. Another advantage of lock-in amplifier or DSP detection is the easy retrieval of the signal phase. This is possible due to the fact that the beamsplitter (instrumental) phase is identical for the in-phase and quadrature (900 out of phase) components of the signal. These components are easily obtained as outputs of a two-phase lock-in amplifier. As a result, not only the magnitude M, but also the phase D can be easily obtained by following Eqs. (6.5) to (6.8): M = (2 + Q2 )1/ 2
(6.5)
D = arctan(Q/I)
(6.6)
126
I=Mcos¢
(6.7)
Q = M sine
(6.8)
The signal-to-noise (S/N) ratio is increased by staying longer at each data collection point. The two modes of operation, step-scan and continuous-scan, should produce identical results under conditions of detector-limited noise. The time resolution of the step-scan technique is limited only by the rise-time of the detector, by the electronics (especially by the A/D converter), and by the signal strength. Therefore, it is capable of measuring various relaxation processes that occur in the sub-microsecond regime and are closely associated with molecularscale phenomena.
6.14 FOURIER TRANSFORMATION AND ITS USE IN FT-IR INSTRUMENTATION The breakthrough in the application of interferometry to spectroscopy came with the discovery by Cooley and Tukey of the fast Fourier transform (FFT) algorithm in 1964 [33]. The FFT procedure takes advantage of several properties of the discrete FT, which is somehow redundant in nature [34]. The FT case can be represented as an nvector (n points interferogram) which must be multiplied by an nxn matrix, each row of which is a discrete representation of a complex sinusoid. The result of the multiplication is an n-vector, which is the transformed spectrum. A straightforward approach requires n2 operations, where operations are complex multiplications followed by complex additions. Since the nxn matrix is highly ordered and cyclical it can be readily factored. IfNis chosen such that it is an integral power of two, then extra advantage may be realized by calculating the FT on a digital computer [35]. As an example, the Fourier transform of a 2048 point vector requires (2048)2, or 4.2 million multiplications. The FFT algorithm reduces this amount to (2048) x log(2048), for a total of 24233 multiplications. Obviously, the great advantage of FFT can be appreciated as the number of data points gets larger and larger. Today's personal computers can calculate an array similar to the one described above in a fraction of one second.
127
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M.L. Forman, W.H. Steel and G.A. Vanasse, J. Opt. Soc. Am., 56 (1966) 59. C.A. McCoy and J.A. de Haseth, Appl. Spectrosc., 42 (1988) 336. R.A. Palmer, Spectroscopy, 8(2) (1993) 26. J. Chamberlain, InfraredPhys., 11 (1971) 25. J. Chamberlain and H.A. Gebbie, Infrared Phys., 11 (1971) 57. J.W. Cooley and J.W. Tukey, Math. Comput., 19 (1965) 297. C.J. Manning, Ph.D. Thesis, Duke University, 1991. M.L. Forman, J. Opt. Soc. Am., 56 (1966) 978.
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