We will present a fundamental solution of the constructive interference-problem of waves in two dimensions (also known as fringe patterns). Such problems are known from quantum physics and optics. In case of two one-dimensional waves with same frequency but different phases and different amplitudes, the solution of their resulting superposition or interference is well known. We will generalize this solution to two dimensions. In case of two dimensions the waves can not only be described by their phases, amplitudes and frequencies, also geometric properties pop up since in two dimensions an infinite number of additional degrees of freedom exists. The wave equations will be given in a traditional Clifford-valued tensor form. We will solve this problem in a hybrid matrix geometric algebra setting by mapping the traditional tensor expressions to Clifford numbers in conformal space. This Clifford number representation of two-dimensional waves can be used to solve the interference-problem linearly. Future work will consist of the generalization from 2D to multi-dimensional waves.
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