Basic aspects of ATR theory

As shown in Sec. 6.4 radiation is totally reflected at the boundary between a medium with a refractive index n and a medium with lower refractive index ni if it hits this boundary with an incident angle greater than the critical angle 6 ,. = arcsin(/72//J ). The reflected radiation energy penetrates the boundary as a so-called evanescent wave. The penetration depth dp is the thickness within which the intensity decreases to 1/e of the intensity at the boundary (see Fig. 6.5-2). It is a function of the refractive indices n and H2, the incident angle 0, and the wavelength A (in vacuum). With ri2 = ri2/n  

The penetration depth should he discussed separately from the effective thickness de. The latter is the thickness needed in normal transmission measurements to achieve the same absorbance as measured with one internal reflection. The effective thickness can be calculated theoretically (Harrick, 1979). The results show for randomly polarized radiation and for sample thicknesses greater than dp that the effective thickness is proportional to the penetration depth. The wavelength dependence of the refractive indices can usually be neglected. So we arrive at  

Regarding Eq. 6.5-1 it is obvious that the absorbance is proportional to the wavelength. This is different from normal transmission spectro.scopy. For an incident angle of 45 ° Eq. 6.5-2 can be simplified to  

The angle of incidence to the surface of total reflection should be somewhat (more than 5°) greater than the critical angle. Otherwi.se nonlinearity of the absorbance, band shifts and other difficulties may occur. 

---