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The diagonal representation and optical equivalence theorem are the E. C. G.Sudarshan's mid 20th century adventures in non-classical optics. It basicallydeals with a quantum mechanical description of photons to explain the quantumproperties of light. Inspired by Sudarshan's pioneering work we try to explainthe every minute mathematical details of his paper "Equivalence ofsemi-classical and quantum mechanical descriptions of statistical light beams".In this article we are going to go through some of the basics in developingquantum optics, then land up in E.C.G's original work and try to present it asrigorous as possible. We show some of its important applications in variousclasses of physics problems.

A sincere tribute to E.C.G Sudarshan's phenomenal contribution toward quantum theory of optical coherence