The 32-year-old victim was at home around 8:30am on Thursday, 5 September when a man entered and threatened her with a gun, before he tied her up and demanded money. He then sexually assaulted her, leaving her “traumatised”.
He fled in a BMW car which was later found abandoned.
The woman did not require hospital treatment, police said.
The man officers are trying to trace is around 5ft 8in with a stocky build. He was wearing tights to cover his face, a green army-style jumper with patches on the elbows, and heavy boots. Police said he also had a “noticeable beer belly”.
The attack happened at a farm in Salsburgh, near Shotts, North Lanarkshire, but details have only been released now after officers carried out “sensitive and covert inquiries”.
The car was found in the nearby village of Plains.
Officers spoke to motorists in Plains yesterday to see if anyone remembered anything from 5 September which could help the investigation.
Police Scotland Detective Inspector David McFall said: “The victim of this terrifying but thankfully rare incident has been left traumatised by the events which took place in her home. In the nine weeks since the incident took place we have carried out extensive and sensitive inquiries to identify the person responsible for this attack which has meant we were not in a position to go public until today with details of the assault and robbery.
“However, I would like to reassure the public that I have no doubt this was a specifically targeted attack on the family.
“I am particularly keen to speak to anyone who saw the stolen black BMW on the morning of Thursday September 5 driving from Salsburgh to the Plains area.
“I would also like to speak to anyone who has any information on this attack or who can identify the man responsible.
“I would ask people who live or work near to Salsburgh to get in touch if they remember anyone suspicious in their area around 5 September 2013.”
DI McFall said police spoke to more than 100 motorists yesterday on the road where the BMW was abandoned.
He said: “We do believe there was a targeted attack on the individual concerned and there’s nothing to suggest that there’s any risk to any other person. That’s been drawn from the extensive inquiries that have been carried out since the incident
occurred in September.
“What we’re hoping to do is encapsulate any individual who has possibly seen the car in situation here or the person who has brought it here or anyone acting suspiciously round about it, more importantly the person that was described as being the person responsible.”