Traditional branches of optics describe the behavior of light from different points of view (geometrical, wave and energetic). All of them were logically united in the famous book Principles of Optics by M. Born and E. Wolf, first published in 1969. However, over the past 60 years, optics has changed radically: the invention of the laser led to the emergence of new branches of optics (coherence optics, holography, optics of ultra-fast laser pulses, etc.) and mathematical tools of modern physical theories (quantum mechanics, electronics and microwave technology, etc.) were applied to new presentations of traditional branches of optics. At the same time, in mathematical and physical theories, a heuristic approach based on plausible reasoning (modeling, analogies, dualities etc.) and a first principal method were developing. This work unites the traditional and modern branches of optics into a single theory by using modern mathematical tools and a heuristic approach.
