When illuminated by a plane wave, continuously self-imaging gratings (CSIGs) produce a field whose intensity profile is a propagation- and wavelength-invariant biperiodic array of bright spots. In the case of an extended and incoherent source, we show that CSIGs produce multiple images of the source. The fundamental properties of these gratings will be derived. In particular, methods to assess the image quality in angle of CSIGs will be introduced. It turns out that this new type of pinhole-array camera works on the same principle as diffractive axicons, which are known to produce wavelength-invariant nondiffracting beams. The formalism developed for CSIGs will be also extended to axicons. CSIGs and axicons both produce focal lines and can be robust in field, in compensation of a trade-off with the resolution. They also offer interesting properties in terms of compactness, achromaticity and long depth of focus for imaging systems. However, compared to classical imaging systems, they produce degraded images and an image processing is necessary to restore these images. Experimental images obtained with these components in the visible and infrared spectral ranges will be presented.© (2007) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.