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We propose a method to experimentally demonstrate contextuality with a family of tests for qudits. The experiment we propose uses a qudit encoded in the path of a single photon and its temporal degrees of freedom. We consider the impact of noise on the effectiveness of these tests, taking the approach of ontologically faithful non-contextuality. In this approach, imperfections in the experimental set up must be taken into account in any faithful ontological (classical) model, which limits how much the statistics can deviate within different contexts. In this way we bound the precision of the experimental setup under which ontologically faithful non-contextual models can be refuted. We further consider the noise tolerance through different types of decoherence models on different types of encodings of qudits. We quantify the effect of the decoherence on the required precision for the experimental setup in order to demonstrate contextuality in this broader sense.