Fourier transform IR (FTIR) machine for textile application

Editor's Notes

• #6: The interferogram is converted to a spectrum by Fourier transformation. The resultant Fourier Transform of the time shifted signal. Note how the higher frequency components revolve in complex plane faster than the lower frequency components. f (t) = cos(6πt) e−πt2  oscillates at 3 Hz The mathematics behind Fourier Transform The main idea behind Fourier transform is that : Any continuous signal in the time domain can be represented uniquely and unambiguously by an infinite series of sinusoids. What does this mean? It means that, If we have a signal and this signal is generated by some function x(t) then we can come up with another function f(t) such that : Image for post So, It doesn't matter how strong the signal is, we can find a function like f(t) which is a sum of an infinite series of sinusoids that will actually represent the signal perfectly. Now, the question that arises now is, How do we find the coefficients here in the above equation because these are the values that would determine the shape of the output and thus the signal. Image for post So, to get these coefficients we use Fourier transforms and the result from Fourier transform is a group of coefficients. So, we use X(F) to denote the Fourier coefficients and it is a function of frequency which we get by solving the integral such that : Image for post The tricky part in this integral is actually the i which denotes a complex number. So, we probably remember that i² = -1 or i = √-1. It also might help to remember that the form of a complex number is a + ib . So, It has a real and imaginary part. Also, when we actually solve the above integral, we get these complex numbers where a and b correspond to the coefficients that we are after. We do have however three problems that we need to deal with : How to deal with i. How to deal with discrete signals. So, let’s start with the second one.
• #8: infrared region which has a longer wavelength and a lower frequency than visible light, and is measurable in a sample when submitted to infrared radiation (IR).
• #9: The energy associated with such stretching vibrations is close to that of infrared light,
• #10: A dipole moment arises in any system in which there is a separation of charge. They can, therefore, arise in ionic bonds as well as in covalent bonds. Dipole moments occur due to the difference in electronegativity between two chemically bonded atoms. A bond dipole moment is a measure of the polarity of a chemical bond between two atoms in a molecule. It involves the concept of electric dipole moment, which is a measure of the separation of negative and positive charges in a system. The bond dipole moment is a vector quantity since it has both magnitude and direction. An illustration describing the dipole moment that arises in an HCl (hydrochloric acid) molecule is provided below. For a molecule to be IR active there must be a change in dipole moment as a result of the vibration that occurs when IR radiation is absorbed. Dipole moment is a vector quantity and depends on the orientation of the molecule and the photon electric vector. The dipole moment changes as the bond expands and contracts. The absorption band of water molecule due to symmetrical stretching appears at 3,652 cm-1, and that due to asymmetric stretching appears at 3,756 cm-1. Atmospheric warming occurs because CO2 absorbs infrared light in asymmetric, and so acts as a greenhouse gas.
• #13: FTIR analysis measures the range of wavelengths in the infrared region that are absorbed by a material. This is accomplished through the application of infrared radiation (IR) to samples of a material. The sample’s absorbance of the infrared light’s energy at various wavelengths is measured to determine the material’s molecular composition and structure. A simple device called an interferometer is used to identify samples by producing an optical signal with all the IR frequencies encoded into it. The signal can be measured quickly. Then, the signal is decoded by applying a mathematical technique known as a mapping of the spectral information. The resulting graph is the spectrumFourier transformation. This computer-generated process then produces which is then searched against reference libraries for identification.
• #14: tional energy levels of the ground (lowest) electronic energy state. This is in contrast to absorption of the energetically more powerful visible and ultraviolet radiation, which induces transitions between vibrational and rotational energy levels of different electronic levels.
• #20: pyroelectric detectors that respond to changes in temperature as the intensity of IR radiation falling on them varies. An ideal beam-splitter transmits and reflects 50% of the incident radiation. For the mid-IR region, 2−25 μm (5,000–400 cm−1), the most common source is a silicon carbide element heated to about 1,200 K (Globar).
• #21: Testing Process Step 1: Place sample in FTIR spectrometer. The spectrometer directs beams of IR at the sample and measures how much of the beam and at which frequencies the sample absorbs the infrared light. The sample needs to be thin enough (10 microns)for the infrared light to transmit through.  Reflectance techniques can be used on some samples and no damage is done to the sample.   Step 2: The reference database houses thousands of spectra, so samples can be identified. The molecular identities can be determined through this process.