A wealthy antiques dealer has been jailed for at least 24 years for strangling his seven-year-old daughter.
"Deceitful and manipulative" Robert Peters, 56, researched child killers online but kept his murderous plans secret from authorities, the Old Bailey heard.
Last November, the former Israeli soldier throttled Sophia with a dressing gown cord while alone with her at his £1 million family home in Wimbledon, south-west London.
When she woke up and asked what he was doing, Peters said "sorry" but carried on anyway.
Afterwards, he called 999 to report what he had done and the little girl was rushed to hospital, but died the following day.
The killing came just over a month after depressed Peters was found not to be a risk by a Merton child protection team, despite two attempts to kill himself in 2017.
Jailing him for life with a minimum term of 24 years, Mr Justice Edis said: "This was a determined pre-mediated killing in which there was an intention to kill.
"It is impossible to imagine the last few conscious minutes of that child's life. She was a lovely little girl who loved her parents and thought that they loved her.
"Asleep in bed, she no doubt felt safe and believed that, should she need it, she had the protection of her father.
"Her shock and bewilderment to find that he was set on her death amounted, in my judgment, to an intentional act of cruelty over and above the killing itself.
"I do not think the defendant intended to wake her up but, when she did, he carried on anyway, now knowing that the death would not be a painless and oblivious event."
Peters, who had been cheating on his wife, was "deceitful and manipulative, calculating and disingenuous" in the way he hid his plans to kill, the judge said.
He added: "This was a premeditated crime carefully thought through and relentlessly executed."
Earlier, Sophia's mother, Krittiya Peters, said in a statement: "Sophia was a beautiful, loving, active, adventurous, brave and outgoing girl. She loved to dance and sing.
"I would give anything I have to be able to bring my daughter back.
"I could not believe what happened to Sophia. Initially I did not know what to think but knew Robert should never have hurt her."
At first, Mrs Peters, who was in court, said she was "worried and concerned" about her husband's mental health.
But she added: "Now I no longer worry about him. I don't care about him as he killed our beautiful daughter.
"I always think to myself 'If Robert was ill, why didn't he kill himself? Why did he kill my innocent daughter?
"I wish if only Robert had permanently left and set up home with his mistress, I would still have (Sophia)."
The court had heard that Peters had recently ended a two-and-a-half-year affair with a married Home Office official he met online.
He was also worrying about his finances and claimed his Kensington-based oriental antiques business was going bankrupt, even though he drove a Jaguar car and had money in the bank.
In the months before the killing, he searched the internet for "serial killers", "treatment of child killers in prison" and "premeditated murder".
He chose his opportunity to kill Sophia before she was due to return to her £5,000-a-term boarding school after the half-term break.
Peters waited until his wife had gone out before he woke Sophia up in bed by tying a cord around her neck and throttling her for up to half an hour.
Mr Justice Edis said the Old Bailey was not the forum to investigate the "efficiency or effectiveness" of the assessment of Peters before the killing, but said the evidence showed it was not a "rushed or hurried effort".
He said Peters' brother had called the defendant "duplicitous" and his behaviour towards the Merton home treatment team only illustrated it.
The defendant, who admitted murder on the third day of his Old Bailey trial, gave away no emotion as he was sent down.
Detective Inspector Helen Rance, of Scotland Yard, said: "The death of a child is something no family should have to go through, but the fact that Sophia Peters died at the hands of her own father makes it truly dreadful.
"Sophia was a loving and much-loved child whose loss has devastated all who knew her from her family through to her school friends and teachers. I hope that the conclusion of the judicial process will be of some comfort to all those so terribly affected by her death."
An NSPCC spokesman said: "This is a desperately sad case in which a young girl's life was cut brutally short by her own father.
"Cases where a young child is murdered in these horrific circumstances are mercifully rare but we know that abuse and neglect take place every day in too many homes across the country, each damaging a child's future. We all have a duty to look out for their welfare."