The Doubling of Clara and Olimpia
Authors will often present characters in doubles in order to allow parallels and comparisons. Clara and Olimpia can be treated as doubles in The Sandman, especially as they are seen through the eyes of Nathanael, and this creates an ironic tone due to the reality of Olimpia as an automaton. Nathanael professes ardent love to both, but also expects total silence and attention from them. He receives this only from Olimpia, since she cannot speak and likely cannot understand as well as Clara, who is portrayed as caring, intelligent and even outspoken. Because this, Nathanael believes Clara is less valuable as a woman and transfers his proposal of marriage to Olimpia, even calling Clara an automaton. This is especially ironic, as he calls her this for expressing her views, something that true automatons like Olimpia are unable to do.
Nathanael's Mother's (Lack of) Presence
Nathanael, Clara, and Lothar seem to keep Nathanael's preoccupation with Coppelius and ensuing mental illness a secret from his mother. However, as his mother was an adult at the time of Nathanael's childhood fear, she is someone whose point of view it would be useful to have in order to clarify the situation. Furthermore, it should be remembered that Nathanael, Clara, and Lothar are all young (university age) throughout Nathanael's mental illness, and it is perhaps due to a lack of adult guidance surrounding that situation (as well as the duel, Nathanael's abrupt switch in romantic partners, and more) that could benefit greatly from adult, especially parental, guidance. Ironically, in protecting Nathanael's mother from the situation, the young characters do not protect themselves or spare her the grief caused by the loss of her son.
Clara and Lothar's Responses to Nathanael
The most pronounced irony in the story, if one takes it at face value, is Clara and Lothar's lack of belief in Nathanael's childhood story, as demonstrated in the first and second letters of the story. They attempt to convince him that the problems with Coppelius and Coppola stem only from his mind and childish fears, but along with the reveal of Olimpia's nature as an automaton, the reader finds out that Coppelius really is the same as Coppola and that he really was attempting to steal others' eyes to examine their functioning. The irony is lost, however, if one reads the story as warped beyond any reality.
Social Response to Olimpia
Hoffmann broadens the irony surrounding Olimpia's role in the story by commenting on her success in society. For the same reasons she was successful with Nathanael - that is, being unwaveringly attentive, demonstrated by yawning less frequently than other women at tea parties - she is accepted and well-liked. This social commentary reveals the comical nature of the standards of etiquette people to which held each other, especially women, at the time. Hoffmann forwards this parody by noting that after the reveal of Olimpia's true nature, it became vogue to yawn often at parties and even for women to express themselves to their husbands, demonstrating that society people still did not feel comfortable together but were able to change their customs for propriety's sake.