The attack happened at a farm near Shotts, in North Lanarkshire, at 08:30 on 5 September.
The 32-year-old victim did not require hospital treatment but was left traumatised by the experience.
A reconstruction of the attack will be played on Crimewatch, to be broadcast on Wednesday at 21:00 on BBC One.
The victim was in her home when a man entered and threatened her with a firearm.
He tied her up and demanded she hand over money. He then subjected her to a sexual assault.
The man fled in the family's BMW car, which was found later that day abandoned near to Plains, Airdrie, North Lanarkshire.
The suspect is described as between 5ft 8in and 5ft 10in tall with a stocky build and had tights over his face.
At the time of the attack he was wearing a khaki green army style jumper with patches on the elbows and heavy boots. He is also described as having a noticeable beer belly.
Officers working on the case will take part in Crimewatch and a reconstruction will be broadcast as well as an interview with the victim, which will be played and voiced by actors in order to protect her identity.
Speaking ahead of the programme, Det Ch Insp Garry Church, who is leading the investigation, said: "Our initial public appeal in November was very positive and the public, especially those in the local area, have been extremely helpful.
"However we are now turning to Crimewatch to help to identify the man responsible for this terrifying attack on a woman in her own home.
"We are very hopeful that the reconstruction and our direct appeal will jog someone's memory and give us the vital piece of information we require to catch the man responsible."
The BBC's Crimewatch programme will feature an appeal later to find an armed man who tied up, robbed and sexually assaulted a woman in her home.