There's a problem with our understanding of Persian armies, which is that there are no surviving Persian sources describing those armies in any detail. Our best internal evidence are the reliefs and remains found in major palace sites like Persepolis, but they do not give us a full sense of the size, armament, tactics, or development of the Achaemenid Persian army. For much of this history, we are forced to use Greek sources, with all of the problems that entails.

For example, Herodotos' famously exaggerated account of the army of Xerxes is actually the most detailed description of a Persian armed force to survive from the Classical period. If we want to understand how this army functioned, we have to use this source, and try to make sense of it in light of what little other evidence there is.

An unfortunate result of the paucity of Persian sources is that we really only hear of what Persian armies looked like and how they functioned if Greeks came into contact with them. This only happened in a few distinct phases of Greek history: the Persian Wars in the early 5th century BC, the March of the Ten Thousand and the Spartan war against Persia in the early 4th century BC, and the campaign of Alexander. There were contacts and clashes in the intervening periods, but it is only in these periods of major armed conflict that the Greeks bothered to describe to us what their Persian opponents actually brought to the field.

Our understanding of the Persian army, then, is patchy. Worse, our understanding of its development in response to internal and external crises is pretty much non-existent. While Persian armies are described differently in the different periods of Greco-Persian conflict, we can't tell if the difference is due to structural changes in the Persian army (and if so, what triggered them) or if it is merely the result of different Greek experiences. To name just one example: unlike the Persians who came to Greece with Xerxes, the army that fought the Ten Thousand in 401 BC seems to have included no Persian heavy infantry, and never engaged the Greeks in hand-to-hand combat. Is this because the Persians abandoned their heavy spear infantry and increasingly relied on missile troops and cavalry? Or is it simply because they saw no need to risk a direct engagement with an army that could easily be harrassed to destruction?

Anything that looks like a genuine development in response to foreign threats (such as the increasing use of heavily armoured cavalry and Persian spear infantry) is invariably very poorly attested and hotly debated. We hear of scythed chariots for the first time in 401 BC, but we have no idea when they were invented or what tactical purpose they were intended to serve. The only thing we can say with certainty is that the Persians made increasing use of Greek mercenaries to flesh out their field armies - but the traditional view that this was because they lacked good native heavy infantry is debatable, given that they also hired Cretan archers, Thracian peltasts and cavalry, and mercenaries of many other kinds. The role of the Persian Empire as an equal-opportunity employer suggests that the sheer availability of Greek mercenaries was a bigger factor in their popularity than their tactical abilities.

The consequence of the bad source base and the myriad uncertainties is that there is still no authoritative scholarly work on the Achaemenid Persian army. Even cutting-edge scholarship often leans heavily on a couple of illustrated, semi-popular guides to the subject (by David Head and Nicholas Sekunda). The only dedicated monograph is Kaveh Farrokh's Shadows in the Desert: Ancient Persia at War (2007), and I haven't had a proper look at this book in 7-8 years so I hesitate to recommend it. I'm not sure if it is even possible to write a comprehensive study of the Achaemenid Persian armed forces; much will always depend on plausibility, educated guesses and speculation.