A two-dimensional (2D) diffraction pattern is an image representing the diffraction intensity distribution over the detected area. For data evaluations of various materials characterization, such as phase identification, stress, texture, and crystal size, this distribution is further converted into the intensity distribution over 2θ or γ angles. For many applications, especially phase analysis and structure refinement, it is crucial for the two-dimensional (2D) pattern to have a large 2θ range sufficient to cover as many diffraction rings as necessary. The 2θ range covered by a 2D detector is determined by the size of the detector active area and the detector distance from the sample. In order to expand the 2θ coverage with a given 2D detector, one may collect several 2D frames at various swing angles and then merge the multiple frames, or scan the 2D detector over the desired 2θ range during the data collection. This paper introduces the geometry and algorithms to produce accurate 2D diffraction patterns with expanded 2θ coverages from multiple images or scanned images.