A spectral feature at 4, cm -1 spectral location represents a transition between two molecular levels separated by twice the energy of a transition with spectral signature at 2, cm Once an interferogram is collected, it needs to be translated into a spectrum emission, absorption, transmission, etc.
The process of conversion is through the Fast Fourier Transform algorithm. The discovery of this method by J. Cooley and J. Tukey in , followed by an explosive growth of computational power at affordable prices, has been the driving force behind the market penetration of FT-IR instruments.
A number of steps are involved in calculating the spectrum. Instrumental imperfections and basic scan limitations need to be accommodated by performing phase correction and apodization steps. These electronic and optical imperfections can cause erroneous readings due to different time or phase delays of various spectral components. Apodization is used to correct for spectral leakage, artificial creation of spectral features due to the truncation of the scan at its limits a Fourier transform of sudden transition will have a very broad spectral content.
FT-IRs are capable of high resolution because the resolution limit is simply an inverse of the achievable optical path difference, OPD. Table 2 shows the relationship between resolution expressed in wavenumbers and in nanometers, as is customary in dispersive spectroscopy.
Following, we talk about three significant advantages that FT-IR instruments hold over dispersive spectrometers , but first we compare the two instruments. In a dispersive spectrometer, wavenumbers are observed sequentially, as the grating is scanned.
In an FT-IR spectrometer, all the wavenumbers of light are observed at once. However, the optimum spectral ranges for these kinds of systems tend to be much shorter than FT-IRs and therefore the two techniques are mostly complementary to each other. FTIR instruments do not require slits in the traditional sense to achieve resolution. Therefore, much higher throughput with an FTIR can be achieved than with a dispersive instrument. This is called the Jacquinot Advantage. In reality there are some slit-like limits in the system, due to the fact that one needs to achieve a minimum level of collimation of the beams in the two arms of the interferometer for any particular level of resolution.
This translates into a maximum useable detector diameter and, through the laws of imaging optics, it defines a useful input aperture. Spectral resolution is a measure of how well a spectrometer can distinguish closely spaced spectral features. In a 2 cm -1 resolution spectrum, spectral features only 2 cm -1 apart can be distinguished.
The interferograms of light at cm -1 and cm -1 can be distinguished from each other at values of 0. A collimated, monochromatic light source will produce an interferogram, in the form of a sinusoid, at the detector. When the light intensity of the interferogram changes from one maximum to the next, the optical path difference between the two legs in the interferometer will change by exactly 1 wavelength of the incoming radiation.
Then we can find the wavelength through the formula:. There is, however, an important practical difficulty. We need to keep the velocity Vm constant at all times, and we need to know what this velocity is with a high degree of accuracy.
An error in the velocity value will shift the wavelength scale according to 1. Fluctuations in Vm have a different effect; they manifest themselves as deviations of the interferogram from a pure sine wave that in turn will be considered as a mix of sinusoids.
In other words, we will think that there is more than one wavelength in the incoming radiation. Since the manufacture of an interferometrically-accurate drive is extremely expensive, FT-IR designers added an internal reference source into the interferometer to solve the drive performance problem.
A HeNe laser emits light with a wavelength which is known to a very high degree of accuracy and which does not significantly change under any circumstance. The laser beam parallels the signal path through the interferometer and produces its own interferogram at a separate detector. This signal is used as an extremely accurate measure of the interferometer displacement optical path difference.
This was just a theoretical example. The signal from the interfering beams of the HeNe is monitored by a detector. What is observed is a sinusoidal signal. The average value is the same as we would see if the beam was not divided and interference produced.
The sinusoid oscillates about this value. The average signal level is called zero level. A high precision electronic circuit produces a voltage pulse when the HeNe reference sinusoid crosses zero level. By use of only positive zero crossings, the circuitry can output one pulse per cycle of the reference interferogram, or use all zero crossings for two pulses per cycle of this interferogram.
The latter case is often called oversampling. There is a fundamental rule called the Nyquist Theorem which can be paraphrased to state that a sinusoid can be restored exactly from its discrete representation if it has been sampled at a frequency at least twice as high as its own frequency. In practice, the FFT math runs into difficulties close to the theoretical limit. That is why we say 1. The FT-IR principle of operation is very different from that of dispersive instruments.
Many aspects of this relatively new approach are counter intuitive to those of us weaned on dispersive techniques, starting of course with the funny wavenumber units that go the wrong way!
Figure 5a shows a typical optical layout of external optics relative to a dispersive monochromator. Figure 5b shows the same for an FT-IR spectrometer. The main optical feature of the FT-IR is that there are no focusing elements inside the instrument; it works with parallel beams. Dispersive instruments from the input slit to an output slit are self-contained in the sense that major spectral characteristics are not highly dependent on how the input slit is illuminated or how the light emitting from the output slit is collected.
Manipulating the light with external optics adds or reduces stray light and other optical aberrations. This is not the case with FT-IRs. External optics are as important for proper functioning of the instrument as their internal parts.
Figure 6 shows on a larger scale a simplified scanning Michelson interferometer coupled with a source and a detector. Suppose first that the source is a monochromatic point source and therefore the beam entering the interferometer rays ' is perfectly parallel. With motion of the scanning mirror, the detector will register an interferogram - a sequence of constructive and destructive interactions between two portions of the beam in the interferometer.
The further the scanning mirror is traveling, the longer the interferogram and the higher the spectral resolution that can be achieved. In real life, point sources as well as purely parallel beams, do not exist. A finite size source produces a fan of parallel beams inside the interferometer.
A marginal beam, ', of this fan is shown in Figure 6. This beam will be focused at some distance from the center of the detector. To be exact it will be focused into a ring if the source has a round shape. Now the simple picture we had before becomes much more complex since interference conditions will be different for the beams ' and '.
At ZPD, both beams ' and ' are at constructive interference conditions and the whole detector will sense a high level of intensity. But while the scanning mirror moves away from ZPD, the next condition of constructive interference will happen sooner for beam ' than for beam '. As a result, different parts of the detector will see different phases of the interference pattern: a maximum in the center will be surrounded by a ring of minimum intensity, then a ring at maximum intensity again, etc.
The farther the scanning mirror moves, the tighter this ring pattern becomes, so the detector will see an average level of intensity, and the distinct interference pattern recorded for the collimated input will be smeared.
To get it back, we need to have just one fringe across the detector when the ring pattern is the tightest, in other words, when the OPD has its maximum value.
The function of external optics for FT-IRs is not only to collect and collimate light, but also to provide a certain acceptance angle in the system according to the resolution formula:. To be able to perform calculations for FT-IR auxiliary optics we will need first to revisit some basic optical ideas. Consider light collected by a lens onto a focal spot or emitted by a source placed in the focal plane of a lens.
The solid angle of the cone of rays collected from the source, or alternately directed onto the focal spot, is given by:. The intensity of the absorbance will correlate to the quantity of functionality present in the sample. For instance, we utilize FTIR for quantitative analysis for characterizing the amount of water in an oil sample and the degree of oxidation and nitration of an oil. We have even developed a method for characterizing how paraffinic or naphthenic an oil sample is. Proper FTIR analysis is only as good as the ability to introduce and observe the energy from a particular matrix.
Fortunately we have many sample preparation and introduction techniques available in the laboratory to properly analyze the sample. In the early days of infrared spectroscopy, the only available method of analysis was transmission. For analysis by transmission, the sample needed to be made translucent to the laser and infrared energy, by directly inserting the sample in the optical path, casting a thin film on a salt crystal, or mixing a powder version of the sample with a salt and casting.
Today, however we have the ability to not only use transmission techniques, but reflectance techniques as well. Because of the ability to focus and manipulate the incident beam with optics, we generally rely on variations of ATR Attenuated Total Reflectance techniques to introduce and observe the energy.
ATR involves using a phenomenon of internal reflectance to propagate the incident energy. The sample is made to make contact with the crystal at the top such that energy interaction occurs at the crystal and sample interface where the bounce positions are located.
Typically the more bounce positions, the larger the energy transfer and thus better spectral response , however single bounce systems are used when a very small area needs to be analyzed. Interaction of the infrared beam with the sample when introduced via Attenuated Total Reflectance multi bounce. For liquid and paste samples we will typically use a HATR Horizontal Attenuated Total Reflectance multi bounce technique which will involve placing the sample on a crystal plate or trough in the horizontal position such that gravity acts to make the intimate contact with the cell.
As a result, a maximum intensity signal is observed by the detector. This situation can be described by the following equation:. In contrast, when OPD is the half wavelength or half wavelength add multiples of wavelength, destructive interference occurs because crests overlap with troughs. Consequently, a minimum intensity signal is observed by the detector. These two situations are two extreme situations. So the intensity of the signal should be between maximum and minimum.
Since the mirror moves back and forth, the intensity of the signal increases and decreases which gives rise to a cosine wave. The plot is defined as an interferogram. When detecting the radiation of a broad band source rather than a single-wavelength source, a peak at ZPD is found in the interferogram. At the other distance scanned, the signal decays quickly since the mirror moves back and forth.
The interferogram is a function of time and the values outputted by this function of time are said to make up the time domain. The time domain is Fourier transformed to get a frequency domain, which is deconvolved to product a spectrum. The first one who found that a spectrum and its interferogram are related via a Fourier transform was Lord Rayleigh. He made the discover in But the first one who successfully converted an interferogram to its spectrum was Fellgett who made the accomplishment after more than half a century.
Fourier transform, named after the French mathematician and physicist Jean Baptiste Joseph Fourier, is a mathematical method to transform a function into a new function. The following equation is a common form of the Fourier transform with unitary normalization constants:. The following equation is another form of the Fourier transform cosine transform which applies to real, even functions:. The following equation shows how f t is related to F v via a Fourier transform:.
The math description of the Fourier transform can be tedious and confusing. An alternative explanation of the Fourier transform in FTIR spectrometers is provided here before we jump into the math description to give you a rough impression which may help you understand the math description. The interferogram obtained is a plot of the intensity of signal versus OPD. A Fourier transform can be viewed as the inversion of the independent variable of a function.
Thus, Fourier transform of the interferogram can be viewed as the inversion of OPD. Inverse centimeters are also known as wavenumbers. After the Fourier transform, a plot of intensity of signal versus wavenumber is produced. Such a plot is an IR spectrum.
Although this explanation is easy to understand, it is not perfectly rigorous. The wave functions of the reflected and transmitted beams may be represented by the general form of:. The resultant wave function of their superposition at the detector is represented as:.
The physically measured information recorded at the detector produces an interferogram, which provides information about a response change over time within the mirror scan distance. Therefore, the interferogram obtained at the detector is a time domain spectrum. This procedure involves sampling each position, which can take a long time if the signal is small and the number of frequencies being sampled is large.
The ratio of radiant power transmitted by the sample I relative to the radiant power of incident light on the sample I 0 results in quantity of Transmittance, T. Absorbance A is the logarithm to the base 10 of the reciprocal of the transmittance T :. Step 1 : The first step is sample preparation. About 2 mg of sample and mg KBr are dried and ground. The particle size should be unified and less than two micrometers. Then, the mixture is squeezed to form transparent pellets which can be measured directly.
For liquids with high boiling point or viscous solution, it can be added in between two NaCl pellets. Then the sample is fixed in the cell by skews and measured. Then the solution is injected into a liquid cell for measurement. Gas sample needs to be measured in a gas cell with two KBr windows on each side. The gas cell should first be vacuumed. Then the sample can be introduced to the gas cell for measurement. Step 2: The second step is getting a background spectrum by collecting an interferogram and its subsequent conversion to frequency data by inverse Fourier transform.
We obtain the background spectrum because the solvent in which we place our sample will have traces of dissolved gases as well as solvent molecules that contribute information that are not our sample. The background spectrum will contain information about the species of gases and solvent molecules, which may then be subtracted away from our sample spectrum in order to gain information about just the sample.
Step 3: Next, we collect a single-beam spectrum of the sample, which will contain absorption bands from the sample as well as the background gaseous or solvent. Step 5: Data analysis is done by assigning the observed absorption frequency bands in the sample spectrum to appropriate normal modes of vibrations in the molecules. Despite of the powerfulness of traditional FTIR spectrometers, they are not suitable for real-time monitoring or field use.
So various portable FTIR spectrometers have been developed. Below are two examples.
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