The Emperor Eye (天帝の眼（エンペラーアイ）Enperaa Ai) is a term referring to the eyes with the observational ability to accurately predict the future. The user has the ability to predict the movements of the opponents.
The Emperor Eye enables its user to see another person's body with extreme detail, such as breathing, muscle movements or muscle contractions, body tension, rhythm, sweat, etc. allowing the user to predict future movements. It can be awakened by observing people and their muscle movements, which is how Kuroko acquired his Quasi-Emperor Eye. So far, the four known users have all shown to have great observational skills and court awareness. Akashi being able to see other players' potentials as well as their strengths and weaknesses, Kuroko being able to notice other peoples' habits and behavior patterns, and lastly Kise who has to observe others in order to copy their movements perfectly. Even though we haven't seen much, Gold was able to see that Murasakibara had a large defensive range and Akashi had an Emperor Eye as well. The Emperor Eye is shown to be one of the most powerful skills as it can change the outcome of the match completely. It is also noted that the Emperor Eye is as powerful as its user, as it is stated that Akashi is not strong because he has the Emperor Eye, but is strong because he knows how to use it.
All of the users have developed their Emperor Eyes in different ways. Akashi has acquired his by long-term observation of the Teikō team as it's vice-captain and then eventually captain. His eyes were forcefully awakened fully when his second persona emerged during his one-on-one match against Murasakibara. Unlike Akashi, Kuroko has acquired his eye ability with long-term observation in a slower pace. However, it was not until the latter began developing his Misdirection that his eyes began to develop observation skills. In order to use Misdirection, Kuroko needed to observe others which led to his eye development. Furthermore, Kise's ability of copy and Perfect Copy has led him to develop his eyes as well. Kise needs to observe the movements of others around him and analyze their moves in order to use his Perfect Copy. Lastly, how Gold specifically developed his eyes is currently unknown, but it can be assumed he acquired them through the rigorous training he went through while developing his other moves.
Akashi's Emperor Eye/Complete Emperor EyeThe Emperor Eye is the other Akashi's signature ability. He developed this due to his long-term observation of the Teikou team. Akashi uses his eyes as a base to develop other skills such as ankle break, but also to strengthen his other moves such as passes and steals. His ankle break is a move in which Akashi dribbles with high speed to make the opponent player fall on the ground, strengthening his image of an emperor. Akashi uses the Emperor Eye to see the weak points in the opposing players movements and body posture in order to make them fall to the ground. Due to being awakened to its full ability early, Akashi is the only player who has the most experience and knowledge on how to use his Emperor Eye, making full use of his eyes. When Akashi enters the Zone, his Emperor Eye's prediction ability increase greatly, allowing him to stop Kagami from executing Meteor Jam. Even Akashi's real personality can use the Eye, however he comments that it'd be against the wishes of its true owner.
During the game between Team Vorpal Sword and the Jabberwocks, both of Akashi's personalities thought that the Emperor Eye was inferior to Gold's Belial Eye. However, the other personality that was created then thought otherwise. Stating that the Emperor Eye isn't inferior but rather incomplete because the two had split apart. In order to stop Nash Gold Jr., the other Akashi decided to vanish and transfer his full skill to Akashi, enabling him to use the true power of the Emperor Eye. With his Complete Emperor Eye, Akashi obtained a power that was equal to or possibly greater than Nash. Akashi was now able to predict further into the future by perceiving the best pattern of his opponent's entire movement. This resulted in Akashi stealing the ball from Gold.
Kise's "Copy" of the Emperor Eye
Kise doesn't necessarily have but can "copy" Akashi's Emperor Eye with the help of the Perfect Copy, though it has been noted that while it is not 100% accurate like Akashi's, it's still good enough to predict the future with astonishing accuracy. He also combined it with either Murasakibara's blocking for the absolute defense or Aomine's agility for the ultimate ankle breaker.
Kise's copying ability requires him to observe others which is what led him to develop his eye ability of observing other players movements and copying them. In fact, he gains the Emperor Eye's abilities because he needed to develop his eyes. However, unlike Akashi and Kuroko, Kise's eyes do not see into the future or predict it but are only able to copy the movements of others. Also, his basketball experience is short compared to his former teammates, another reason why his copied version of the Emperor Eye is not 100% like Akashi's. This makes Kise's predicting capabilities the lowest compared to Akashi and Kuroko because it is copying that he capitalizes.
Kuroko's Quasi-Emperor Eye
Kuroko's Emperor Eye is referred to as "Quasi-Emperor Eye" (疑似的「天帝の眼（エンペラーアイ）」 Gijiteki Enperaa Ai) as it can only predict the movements of Kuroko's teammates rather than the opponents. Kuroko developed his Emperor Eye by observing his teammates, instead of opponents. It is due to Misdirection that Kuroko had began observing people and started to develop his eye ability. It is only after discovering Misdirection that the latter began developing his eyes.
With the development of his misdirection, Kuroko needed to observe his teammates' behavior and movement patterns to further improve his passing ability. Because of this Kuroko was able to notice their habits, movements and body language, allowing him to predict further into the future even faster than Akashi's Emperor Eye, which is enhanced with his Zone. Due to his trust in his teammates and long-term observation, he is able to surpass Akashi's Emperor Eye in terms of how far into the future he can see. The only downside to this is that he is unable to predict his opponents' movements, thus a teammate is required for aid. This makes Kuroko's predicting capabilities the highest and most accurate compared to Akashi and Kise.
Gold's Demon Eye
Gold has sharp observational capabilities to predict the movements of others to some degree. However, Gold only uses his Eye as a last resort, whenever he feels that Jabberwock has been pushed back into a corner. According to Gold, his Eye is his trump card.
Even though Gold's Eye is similar to Akashi's Emperor Eye it's mechanics are different and is known as the Demon Eye. The Demon Eye is capable of predicting further into the future than Akashi's Emperor Eye. Unlike Akashi's Emperor Eye which predicts the future of who he is facing in a 1-on-1 situation, Gold's Demon Eye predicts the future of everyone's movements on the court whether it's an opponent or a teammate. Gold's Demon Eye is even shown to have the capacity to intimidate and scare his opponents - the presumed reason for it's name. Gold uses his eyes as a base to develop other skills such as the ankle break, and also to strengthen his other moves such as his shooting and passing. The Demon Eye is considered to be on a higher level than Akashi's Emperor Eye, making Gold the biggest threat on the court and even more difficult to defeat.
However, it's disadvantage surfaced when faced against Akashi's Complete Emperor Eye. While the Demon Eye allowed Nash to predict the movements of everyone on the court, Akashi states that it is the ONLY thing that he is doing. To beat Nash's Demon Eye, Akashi had to look further into the future. Akashi managed to do this by perceiving Nash's best pattern from his entire movement. His eyes (Complete Emperor Eye) now possessed a power equal to or superior to Nash's Demon Eye .This resulted in Akashi stealing the ball from Nash.