A fast, accurate technique for the three-dimensional characterisation of terahertz beams is presented. Using gold-on-glass resolution targets the beam profile, depth of focus and astigmatism of a quantum cascade laser-based imaging system have been measured.ª2007 Optical Society of America OCIS codes: 110.4850 (Optical transfer functions); 140.3070 (Infrared and far-infrared lasers) IntroductionThe terahertz portion of the electromagnetic spectrum has long been identified as a spectral region that is well-suited to a range of security applications including stand-off imaging of concealed weapons and sensing of chemical and biological agents. This suitability stems from the transparency of many non-polar materials such as fabrics, plastics and paper to terahertz radiation, coupled with the molecularly-specific absorption features that many chemical compounds (e.g. illicit drugs and explosives) exhibit at terahertz frequencies.Owing to the lack of affordable multi-element sensing arrays with good sensitivity at terahertz frequencies, the majority of imaging systems demonstrated to date adopt a configuration in which the terahertz beam is focused onto a sample, which is then raster-scanned in two orthogonal directions to yield a two-dimensional image. Under these circumstances, the resolution of the system is dictated by the spatial characteristics of the focused beam. In the case of stand-off imaging, particular attention must also be paid to the beam characteristics away from the focal plane since exact positioning of the object under inspection can rarely be guaranteed in practice. Specifically, a large depth of focus and low astigmatism are essential for such applications. A need therefore exists for techniques that can quickly and accurately quantify the spatial properties of focused terahertz beams in three-dimensions. Furthermore, since the emission from terahertz quantum cascade lasers with sub-wavelength cavity dimensions has been shown to be non-Gaussian in profile [1], such techniques must also allow quantification of non-Gaussian beams.The simplest beam profiling technique involves sampling the beam by use of a detector and focal-plane aperture. However, this has the drawback of requiring large optical powers or a sensitive detection scheme for high-resolution sampling. Multi-element pyroelectric or bolometric arrays provide a convenient means of profiling terahertz beams, but these are expensive and provide only moderate sensitivity (~250 nW/pixel), thus also demanding large optical powers. The most commonly-used profiling technique involves scanning a knife-edge across the beam in two orthogonal directions [2]. By performing a fit to the resulting step response function (SRF) one can extract a Gaussian full-width-at-half-maximum (FWHM). However, this method does not allow simple quantification of non-Gaussian beam sizes. Differentiation of the SRF yields the line spread function of the beam, but also greatly amplifies noise in the data when high-resolution sampling is employed.In this paper, we demonst...