Adrian Wyllie, 56, confessed after human anatomy expert, Professor Sue Black, and her team at Dundee University revealed "compelling similarities" between Wyllie's hand and that of the perpetrator, seen in a number of images.
Wyllie, of Lossiemouth, had denied the charges, and the matter had been due to go to trial before he confessed and pled guilty.
He abused a two-year-old girl and had more than 1600 indecent images of young children on his laptop and six video clips of children being abused, a court heard.
Wyllie appeared at Elgin Sheriff Court on Thursday.
Fiscal depute Alison Wylie had told the court police were directed to Wyllie after receiving intelligence child abuse material was being accessed from a computer IP address at his home.
A search of his home was carried out, and computers and other equipment seized, including a hard drive, a laptop and discs.
Wyllie admitted he owned the laptop and when asked what was on it, he said "all sorts". He claimed he had accessed a number of websites out of curiosity.
Ms Wylie said police found 1625 images, mostly of girls aged from one to 13 years.
Just weeks before a trial was due to take place, Wyllie pled guilty to taking or permitting the taking of indecent photos or pseudo-photos of children at a house in Lossiemouth over a two-year period. He also admitted using lewd, indecent practices and behaviour towards a two-year-old girl and repeatedly abusing her
Sentencing was deferred until November 14 and Wyllie was denied bail.