Model Michelson interferometry, Zero Path Difference (ZPD) centerburst, ATR evanescent wave penetration depth ($d_p$), characteristic functional group vibrational bands, and analytical QA/QC testing lab economics.
Pro-forma cash flow statement modeling $95k CapEx, annual desiccant/laser replacement reserves, diamond crystal refurbishments, and 10% discount rate hurdle.
| Period | Revenue ($) | OpEx ($) | EBITDA ($) | Free Cash Flow ($) | Discounted FCF ($) | Cumulative FCF ($) |
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Unlike dispersive spectrometers that measure each wavelength sequentially, a Fourier-Transform Infrared (FTIR) spectrometer passes broadband radiation through a Michelson Interferometer. A beam splitter divides radiation between a fixed mirror and a moving mirror driven by an air-bearing carriage:
At Zero Path Difference (ZPD, δ = 0), all wavelengths constructively interfere simultaneously, generating an intense central spike known as the centerburst. A co-axial 632.8 nm Helium-Neon (HeNe) laser monitors mirror position with sub-nanometer precision, providing the Connes advantage of superior wavenumber accuracy across the entire spectrum.
Attenuated Total Reflectance (ATR) bypasses laborious sample preparation (such as KBr pellets) by pressing the solid or liquid sample directly onto an internal reflection crystal with high refractive index ($n_1$). Above the critical angle $\theta_c = \arcsin(n_2/n_1)$, an evanescent wave decays exponentially into the sample:
Because $d_p$ is proportional to wavelength ($\lambda = 1/\bar{\nu}$), the evanescent field penetrates roughly three times deeper at $1000\text{ cm}^{-1}$ ($d_p \approx 1.6\ \mu\text{m}$) than at $3000\text{ cm}^{-1}$ ($d_p \approx 0.5\ \mu\text{m}$). This wavelength dependence naturally strengthens low-frequency fingerprint bands relative to transmission spectra.
The choice of ATR internal reflection element dictates chemical compatibility, mechanical durability, and spectral window:
Quantitative analysis in FTIR converts transmission $\%T$ into Absorbance $A = -\log_{10}(T/100)$, which scales linearly with analyte concentration $c$ and effective pathlength $d_{\text{eff}} = 2 d_p$:
Test your understanding of infrared vibrational transitions, ATR crystal physics, and interferometry.