Two men stole cash and jewellery valued at a five-figure total from a property in Balado, Perth and Kinross, on June 17.
Police said the 76-year-old occupier was left shaken by the raid, which occurred between 1pm and 2pm.
Detective inspector Paul Riley said: “The e-fit shows an image of a man described as being in his 20s, of thin build, with brown eyes, short brown hair and a ‘goatee’-type beard. At the time of the incident he was wearing a blue hooded top and blue jeans.
“We are also keen to trace a second man in connection with the incident, who is described as being around 18, with a tanned complexion, who was wearing a grey/blue hooded top.
“I am appealing to any members of the public who recognise the man shown in the e-fit picture, or anyone who has information regarding the other individual, to call Police Scotland on 101 or provide information anonymously through Crimestoppers on 0800 555 111.”
He added: “I am also keen to trace any persons who were passing through the area on the A977 between 1pm and 2pm on Wednesday June 17 in a vehicle that is fitted with a CCTV system that may have recorded the surrounding areas.”
A three-figure sum of cash stolen in the robbery included Turkish lira, police said.