Terahertz frequency waves are highly sensitive to the changes in matter composition and can provide characteristic properties of enamel and dentine within teeth. 

For an electromagnetic wave with electric field amplitude E0(ω) that is incident with a parallel slab of media l, thickness d, refractive index n(ω), and absorption coefficient k(ω) the amplitude ET(ω) of the transmitted wave through the media is given by:

T(ω) is the complex transmission coefficient that is related to the Fresnel transmission coefficients and reflected coefficients of the slab.  The time domain signals ET(t) and reflected field ER(t) are defined as:

Equations (2) and (3) are used to provide a basis relationship for obtaining time and frequency domain images in terahertz imaging.  Using equations (1)-(3), experimental information can be expressed in various forms such as spectroscopically resolved images of transmission, reflection, phase, absorption coefficient and refractive index.

Using the above theory, Zinov et al. acquired images of teeth in vitro. Portions of the enamel were demineralised in hydroxyethyl cellulose gel containing lactic acid.  The THz images are processed in the time domain using a Thz 50fs pump-probe that generates a THz pulse with a wavelength of 800nm.  The transmission images at various frequencies are depicted below.

There is a clear distinction between enamel and dentine areas that are due to the change of the complex refractive index between the two materials.   There is also a notable increase in resolution with increase of frequency.   Another factor that leads to increase of resolution is the relative intensity of the incident T-ray. 

The transmission spectra of three locations within a demineralised tooth are graphed below:

The spectrum labeled “A” characterizes a demineralised spot with reference to a healthy spot while “B” and “C” are spectra of two different dentine locations with reference to a healthy spot.  There is a clear distinction between the signals between 0.5 and 1.5 THz due to the changes in carbonate composition.  The difference between “B” and “C” is due to the natural variations between the same type of tooth tissue. 

In summary, THz imaging can be used to as a non-invasive and non-ionizing solution to provide high sensitivity information for monitoring the development of demineralization and possibly the cause of dental disease.