An InfraRed (IR) cooled camera is generally composed by an optical block (warm lenses outside a dewar) and a detection block (a cooled focal plane array inside the dewar). A minimalist approach to design a compact and robust camera consists in giving the dewar an imaging function by replacing the cold pupil by a Diffractive Optical Element (DOE). In this paper we present different DOE that can be used to design the camera. We present first a pinhole camera that validates this approach but that is limited in radiometric performances and in angular resolution. We replace then the pinhole by a continuously self-imaging DOE, such as the diffractive axicon, to improve both the radiometric performances and the angular resolution. Finally, the MALDA 1 is introduced to improve the performances of the axicon. Diffraction effects and Talbot effect under polychromatic light are exposed for such DOE and two different design rules are derived from those effects to allow the design of a compact camera with dimensions compatible with the size of an industrial dewar. Experimental prototypes are presented and radiometric performances are compared and show the best performances for the MALDA.