A genre of low-cost and high-performance sensors for measuring the irradiation angle is proposed via a working mechanism of the physical design and mathematical modeling. A dexterous mechatronic design, together with a gray-box modeling approach, was used to deploy the and cosine effects of sensors in a way that could measure the irradiation angle accurately. Two pairs of identical photodiodes, mounted symmetrically on four facets of an inverted pyramid, yielded currents under the uniform irradiation that would map to the irradiation angle mathematically. A sensor prototype was calibrated in a controlled indoor environment via a celebrated test bed and also tested outdoor under direct solar irradiation, where the manufacturing and assembly errors were compensated for by the gray-box modeling approach. It was shown that the sensor prototype had advantages over others in terms of the synergy of accurate angle measurement, low cost, compact size, sensitivity to light, and wide sensing range.
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Liu et al. (2012) studied this question.
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