ATR Correction Calculator
Calculate ATR penetration depth across the mid-infrared range for any ATR crystal material. Understand how crystal choice and measurement geometry affect your ATR-FTIR spectra.
How ATR Correction Works
In ATR-FTIR spectroscopy, the evanescent wave penetrates deeper into the sample at longer wavelengths (lower wavenumbers). This wavelength dependence means that an uncorrected ATR spectrum has relatively stronger bands at low wavenumbers compared to a transmission FTIR spectrum of the same compound. ATR correction compensates for this effect by scaling the spectrum, making it comparable to transmission data for library matching and quantitative analysis.
The key parameter is the depth of penetration (dp) — the distance at which the evanescent wave intensity drops to 1/e of its surface value. This depth depends on four variables: the wavelength of light, the crystal refractive index, the sample refractive index, and the angle of incidence.
Depth of Penetration Formula
The Harrick equation
λ— wavelength of infrared light (= 10,000 / wavenumber in μm)
n1 — refractive index of the ATR crystal
n2 — refractive index of the sample
θ— angle of incidence (typically 45°)
Total internal reflection requires sinθ > n2/n1. If this condition is not met, the evanescent wave does not form and ATR measurement is not possible.
Calculate ATR Penetration Depth
Choose your crystal material and measurement parameters to see penetration depth across the spectral range.
PARAMETERS
Typical: 1.3 (water), 1.5 (organics), 1.7 (inorganics)
Most ATR accessories use 45°
dp at 1000 cm⁻¹
2.005 µm
dp at 3000 cm⁻¹
0.668 µm
Max dp
5.013 µm
Min dp
0.501 µm
PENETRATION DEPTH vs WAVENUMBER
Diamond| Wavenumber (cm⁻¹) | Wavelength (μm) | dp (μm) |
|---|---|---|
| 4000◆ | 2.50 | 0.501 |
| 3900 | 2.56 | 0.514 |
| 3800 | 2.63 | 0.528 |
| 3700 | 2.70 | 0.542 |
| 3600 | 2.78 | 0.557 |
| 3500◆ | 2.86 | 0.573 |
| 3400 | 2.94 | 0.590 |
| 3300 | 3.03 | 0.608 |
| 3200 | 3.13 | 0.627 |
| 3100 | 3.23 | 0.647 |
| 3000◆ | 3.33 | 0.668 |
| 2900 | 3.45 | 0.691 |
| 2800 | 3.57 | 0.716 |
| 2700 | 3.70 | 0.743 |
| 2600 | 3.85 | 0.771 |
| 2500◆ | 4.00 | 0.802 |
| 2400 | 4.17 | 0.835 |
| 2300 | 4.35 | 0.872 |
| 2200 | 4.55 | 0.911 |
| 2100 | 4.76 | 0.955 |
| 2000◆ | 5.00 | 1.003 |
| 1900 | 5.26 | 1.055 |
| 1800 | 5.56 | 1.114 |
| 1700 | 5.88 | 1.180 |
| 1600 | 6.25 | 1.253 |
| 1500◆ | 6.67 | 1.337 |
| 1400 | 7.14 | 1.432 |
| 1300 | 7.69 | 1.542 |
| 1200 | 8.33 | 1.671 |
| 1100 | 9.09 | 1.823 |
| 1000◆ | 10.00 | 2.005 |
| 900 | 11.11 | 2.228 |
| 800 | 12.50 | 2.506 |
| 700 | 14.29 | 2.865 |
| 600 | 16.67 | 3.342 |
| 500◆ | 20.00 | 4.010 |
| 400 | 25.00 | 5.013 |
Frequently Asked Questions
What is ATR correction?
ATR correction compensates for the wavelength-dependent penetration depth in ATR-FTIR spectra. Because the evanescent wave penetrates deeper at lower wavenumbers, bands in that region appear disproportionately strong compared to a transmission spectrum. ATR correction multiplies the absorbance at each wavenumber by the wavenumber value, approximating what the transmission spectrum would look like. This is essential for spectral library searching against transmission reference databases.
How is depth of penetration calculated?
The depth of penetration (dp) is calculated using the formula: dp = λ / (2π · n₁ · √(sin²θ − (n₂/n₁)²)), where λ is the wavelength of IR light, n₁ is the crystal refractive index, n₂ is the sample refractive index, and θ is the angle of incidence. At 1000 cm⁻¹ with a diamond crystal (n=2.4), 45° incidence, and a typical organic sample (n=1.5), dp is approximately 1.66 µm.
Why does ATR penetration depth depend on wavenumber?
Penetration depth depends on wavenumber because the evanescent wave's decay length is proportional to the wavelength of the infrared light. Lower wavenumbers correspond to longer wavelengths, so the evanescent wave extends further into the sample. This means a band at 500 cm⁻¹ samples roughly eight times more material than a band at 4000 cm⁻¹, causing the lower-wavenumber band to appear relatively stronger in the uncorrected ATR spectrum.
Does crystal choice affect penetration depth?
Yes. The crystal's refractive index directly affects penetration depth. Germanium (n=4.0) produces the shallowest penetration (~0.65 µm at 1000 cm⁻¹), making it ideal for highly absorbing samples. Diamond and ZnSe (both n=2.4) give deeper penetration (~1.66 µm), suitable for most routine analyses. Silicon (n=3.4) falls in between. A shallower penetration depth means less interaction with the sample but avoids spectral saturation for strongly absorbing materials.
RELATED GUIDES
ATR-FTIR Crystal Guide
Crystal properties directly affect penetration depth — compare diamond, ZnSe, germanium, and silicon.
ATR vs Transmission FTIR
Why ATR correction matters for comparing spectra across techniques.
Troubleshooting Guide
Diagnose and fix common ATR-FTIR problems — weak spectra, distorted peaks, and more.