The attack, near Shotts, North Lanarkshire, happened last September at a remote house.
It featured in last night's edition of Crimewatch with actors playing the roles of the attacker and victim.
The reconstruction showed the gunman burst into the woman's home and hold a gun at her head. The man, who was wearing tights over his head, subjected her to a sexual assault.
Speaking to the Evening Times earlier this week the woman, who cannot be named, said: "The guy just appeared, then started demanding money. That's when I felt the gun at the side of my head.
"It was just a nightmare. You never really think it would be something that would happen to you."
Detectives from the Specialist Crime Division took part in last night's programme.
Police said they believed the woman was "specifically targeted" by her attacker, possibly because she lived in such a remote location.
The reconstruction showed him fleeing the scene in a green BMW car found abandoned later that day at Plains, near Airdrie.
Police described the suspect as 5ft 8in to 5ft 10in, stocky with a noticeable beer belly.
He was wearing a khaki green army-style jumper with patches on the elbows. He was also wearing heavy boots.
Detectives said the victim did not require hospital treatment but had been left traumatised by her ordeal.
Detective Chief Inspector Gary Church, who is leading the investigation said: "We are hopeful that the reconstruction will jog someone's memory and give us the vital piece of information we require."
The appeal will stay on the Crimewatch website - www.bbc.co.uk/crimewatch until the attacker is arrested.
Anyone with information is asked to contact police on 101.