Star Trek: Deep Space Nine S05 E16 Doctor Bashir, I Presume?

"At the edge of the Final Frontier, the Universe's greatest mystery is about to unfold."

Stardate: Unknown. Dr. Bashir is selected to be the model for the next-generation of Emergency Medical Hologram (EMH). But he balks when his parents are invited to the station to be interviewed by the EMH programmer, Dr. Zimmerman. There is a dark secret in his family that he's afraid that his parents will reveal.