The Athenian Empire was not extensive or culturally diverse enough to be a 'real' empire, it fits the description of a thalassocracy more so. Why is it called the Athenian Empire? Who coined the term? Should it be seen as a legitimate empire?
The source you want is: Ian Morris and Walter Scheidel, eds. The Dynamics of Ancient Empires: State Power from Assyria to Byzantium (Oxford 2009). Morris wrote Chapter 4, "The Greater Athenian State," and it is fantastic. I can summarize it a bit here, but you really should just go get your hands on it and read it.
He starts by noting that the Athenian "empire" of the 5th century is very odd as far as empires go. It was small-scale, contained a relatively small population, didn't last very long, and was culturally homogeneous (nearly all Greek, and nearly all Ionian Greek specifically).
In general, Morris argues that Athens should not be called an Empire and should not be compared with other classic examples (Rome, Persia, Han China). He suggests that in the 5th century, Greece was undergoing a next phase of state formation, during which process individual polis city-states were being co-opted into larger political structures. Athens was one such example (he uses the Spartan and Syracusan systems as comparanda). He imagines this greater state formation as being, at its basic, an expansion of central power (usually at the expense of somebody somewhere), and that the entity we call the Athenian Empire was really just a very capital-intensive iteration of this expansion. He imagines that, given time, Athens may have become a true multi-ethnic 'empire' (perhaps via conquest of Egypt, Carthage, or Sicily -- which they did indeed attempt in 415). Without such conquests, he finds a distinct lack of "foreignness" between rulers and ruled.
Now the meat:
"...the Athenians were turning themselves from an egalitarian citizen community into the stratified, horizontally segregated layers of a military and administrative ruling class, standing above the laterally insulated communities of subjected poleis." (139)
Breaking this down, we can isolate:
Athens was, then, "becoming home to a ruling elite interested in extracting taxes, maintaining the peace, and defending itself." He identifies categories of evidence for the "empire" as the Greater Athenian State. Economically, Athens quickly moved to consolidate the "Delian League's" finances in her own hands. The tribute of the cities was a form of centralized direct taxation, a concept which Athens innovated; the port of Athens, Piraeus, became the central market of Greece, either organically or by subtle coercion. The 1% duty on imports/exports at Piraeus was another form of taxation. Finally, the Coinage Decree of Klearchos. It stipulated that all coinage in the Empire had to be Athenian coins, and be standard Athenian weights. Personally I think this move was meant to simplify the collection of tribute, not to quash the cultural expression of the cities. The coinage evidence suggests that the decree was never heeded anyway.
Administratively, the development of a central ruling structure. The Athenians developed a system of archai ("managers" or something), including archontes, Athenians resident in the cities with some kind of administrative power; episkopoi, with some kind of oversight powers (see Aristophanes Birds 1021ff); and phrourarchoi, military garrisons (see Arist. Wasps 235-37). Phratries probably belong in this category, as well -- it's unclear exactly what was going on, but they were Athenian citizen settlements in the territories of the cities.
Culturally, Athens took steps to centralize (but I don't believe they were actively out to simplify or eliminate the identities of the cities; that is for another topic). As I said, it is clear that Athens was to be the "capital" of the Greater Athenian State, adorned with the best architecture in Greece and the cultural heart. A sort of "religious politics" was being played out -- famously, de Polignac has argued that early Greek city-states defined their territory by placing their major sanctuary on the periphery, then establishing regular cult and procession to that periphery. The act itself established "ownership" of the land in between. We can see this sort of thing happening between Argos and the Heraion, Corinth and Isthmia/Perachora, or Athens and Eleusis. Interestingly, for the Greater Athenian State it was in reverse. Athens was the sanctuary, not on the periphery but centralized, and the subject cities were the periphery. By compelling them to travel to Athens to participate in centralized religious activity, they were re-enacting that early Archaic ideological marking of territory. The cities had to provide a cow and a panoply in the procession of the Great Panathenaia, and were also forced to provide a tithe ("first-fruits") to Demeter at Eleusis.
Anyway, that's a terrible summary. Go read the chapter! It's great!
(NOTE - HAVE NOT FINISHED, WILL FINISH IN A FEW HOURS, still to do part on the level of autonomy of the allies - what control the Athenians really had over the members of the league, the cultures of the empire, and a comparison to other 'empires' of the classical world. Then a verdict can be made on whether it is a 'real' empire.)
Thucydides, an Athenian general who began to write his 'History of the Peloponnesian War' is our main ancient source for the period, and is praised for his 'scientific method' in his history, looking beyond the superstition and exaggerations of his contemporaries, such as Herodotus. That is not to say that his work is perfect, but I would recommend reading further into Thucydides for more information.
The language in Thucydides, and other sources, such as epigraphic evidence, appear to change over the time period. We see a shift from "Athens and her allies" in earlier Athenian inscriptions, to "Athens and the cities which she rules" in later inscriptions. So what has happened?
Following the defeat of the Persian invasion by land and sea, the Hellenic League, a league under Spartan hegemony formed to defend against the Persians had won victory. The question was now - what next? Being the relatively insular and isolationist power that they were, the Spartans saw no use in further pursuing the war, but rather favouring to return to their hegemony over the Peloponnesus. The Athenians had built by this time, in response to the threat of the Persian, a powerful navy which had displayed its prowess and skill at battles off Salamis and at Mycale. The Athenians, unlike the Spartans, were willing to see the war against the Persians to its conclusion and take the war into Asia. The Ionians, seeing this, pushed the Athenians, as their kinsmen and liberators, become their leaders. The suffering of the Greeks at the hands of the Spartan general Pausanias furthered this desire, as the Greeks knew that despite their defeat, the Persians would surely return.
Thus, the 'Delian League' was formed under Athenian hegemony. The league's "professed objective being to retaliate for their sufferings by ravaging the King's country" (Thucydides 1.96.1) - the king in this instance being Darius of Persia. The league upon its establishment won the favour of the allies. The tribute levels payed by the allies, assessed by Aristides, an Athenian general, earned him the the nickname 'Aristides the Just/Fair'. The common treasury of the League was established at Delos, a culturally significant place for the Ionian people and the island after which the league was name. Some states, such as Naxos, Chios, Lesbos and others chose to contribute ships to the war effort instead. Decisions were made with the consent of the allies in general congress at Delos. Thucydides says that "initially the Athenians commanded autonomous allies." (1.97.1)
However, it was on the framework of the Delian League that the so-called Athenian Empire was built. Over a period of approximately fifty years, Athenian power grew and it is this process which is considered the transition from the Delian League to an Athenian Empire. It is important to note, however, that it is not the case that Athens set out to establish an empire from the League's very beginning. The allies began to lose their autonomy- and there are many reasons for this.
Now lets step back from the story for a minute to answer the question which I am reading as; was the Athenian Empire really an empire - not least because I do not quite understand the question in the title, although I'll be happy to answer any follow up questions if i can. An empire (and I just looked it up) can be defined as:
an extensive group of states or countries ruled over by a single monarch, an oligarchy, or a sovereign state.
Ruled over seems to me like the key term - that the state which does the 'ruling over' has control over their subject states, that they can influence their decision, and have power over them and that the subjects have experienced a loss of autonomy - their control over their own affairs has waned. In this sense, I certainly consider the Athenian Empire to be an empire.
Back to Athens. Athens did well in their military campaigns against the Persian - in a way, too well and I'll mention why in a minute. Under Cimon, an Athenian general, was behind much of this success, winning victories in Thrace at Eion, and in the Aegean at Carystus due to fears of their medising (aiding the Persians). The war was taken into Asia, campaigning in Caria and in the highlight of Cimon's military career, a great and decisive victory over the Persians on land and sea at the battle of Eurymedon in southern Anatolia in c.468 BC.
The first reason for the growing power of Athens over her allies was this. By now several states were questioning the need for a Delian League at all - after all the Persians no longer presented a threat to many, especially those of the Aegean. Naturally, Athens, enjoying the new wealth from the war spoils and the payment of their citizens who fought the war, did not want to let go of its hegemony. Naxos, one of the largest islands of the Aegean, was likely the first major state to revolt from the Delian League in c.472 BC. What Athens did now was the beginning of a much longer process - upon the defeat of the Naxians, their fleet was confiscated from them and they became the first tribute-paying subject state. This was by no means the last revolt, and the Athenian desire to retain her position among the allies was a factor in the road to an empire.
Secondly, an important process was under way - and this time it was the fault of the allies which contributed to their loss of autonomy. The process, sometimes referred as the transmutation of tribute involved the voluntary surrender of the allies' fleets. As the options for the Delian League contributions were to provide a certain number of ships or to pay tribute, the allies had to make a decision. At first many states did provide ships, but as time went on, many decided to voluntarily give up their ships; it just was not worth it. Not only did they have to send men away for months at a time at a significant cost, but to pay tribute was cheaper. As time went on, therefore, the Athenians were able to sustain a larger and larger navy, while the allies held an increasingly smaller navies. So much so that of the 100+ members of the Delian League by 450, only 3 were contributing ships; the large islands off the coast of Asia minor- Lesbos, Chios and Samos.
The third reason for the shift to an Athenian Empire was not do to with external politics or the politics of the Delian League but those of Athens. Under the guidance of Cimon, the Athenian state grew wealthy and powerful. The navy, the institution which was the fundamental basis of Athenian power, was manned and rowed by the thetes, the poorest of the four non-slave Athenian classes. As the navy grew in strength, so did they, because if they did not row, then Athens was no longer a power. This was the birth of a purer democracy. Cimon's aristocratic domestic policy fell out of favour and he was exiled, and Ephialtes and Pericles began to bring reform to the institutions of Athenian government. This shift in internal power also led to a change in foreign policy to a more 'hawkish' and aggressive one, as happens when it benefits the rowers and lower classes, who got a lot of the benefits of the empire through payment of jurors, the Periclean building programme, their share of war spoils and so forth. As they pushed for further expansion, more empire building, the Athenians were all too willing to push their own agenda, even if it was at the detriment of the members of their Delian League.
I have presented the growth of the Delian League and Athenian power, and the reasons the Delian League became increasingly more under Athenian control. Next answer, which i shall write up likely in the next few hours, will explain the specific decrees and changes made, which deprived the allies of their autonomy and thus make a judgement on the state of Athenian control over the members of the Delian League.
Before I reply, I just want to check; do you mean the Athenian empire of the 5th century BC?
For others who are thinking of answering, do not let me dissuade you- while I can give some insight into the topic, I am no expert.