The officers - Sergeant Sheree Bissett, 52,  Sergeant Emily Metcalfe, 37, Senior Constable Leah Wilson, 41, and Constable Aaron Abela, 33 - were overcome with emotion in the dock as Judge Gregory Woods proclaimed them not guilty of perjury.

After hearing three weeks of testimony, Judge Woods found the Crown's case - that each officer had given false evidence to the 2012 Police Integrity Commission inquiry into Mr Salter's death - had not been proved beyond reasonable doubt.

At the centre of each of the officers' accounts was the claim that Constable Abela had tried to restrain Mr Salter when he was shot in the back and killed by Sergeant Bissett in his father's Lakemba home on the morning of November 18, 2009.

While none of the officers gave evidence in the trial, the court heard Sergeant Bissett told the Police Integrity Commission she fired her gun because, upon entering the kitchen, she saw Adam Salter "struggling" with Constable Abela and believed he was about stab the officer.

In evaluating the veracity of the eyewitness accounts, he said the rapid unfolding of events in the kitchen that morning was "confusing, dramatic, noisy and stressful" and "made it difficult for most if not all witnesses accurately to observe and recount what occurred".

During the trial, the court heard the four officers arrived at the Salters' home on Wangee Road in Lakemba just before 9am, responding to a radio call-out triggered by Adrian Salter's triple zero call that his son was stabbing himself in the chest with a kitchen knife.

By the time the officers arrived - in pairs, at 8.55am and 8.57am - Adam Salter was lying on the floor of the small kitchen as two ambulance officers treated his wounds and bandaged his chest.

But less than 10 minutes after the police had entered the home, Sergeant Bissett had shot Mr Salter though the heart, using her glock pistol.

In the intervening minutes, Adam Salter had jumped off the floor and moved to the sink, retrieved the knife and once again began stabbing himself.

In acquitting the officers, Judge Woods said the absence of CCTV footage was an "important consideration in my mind".

Although he could not be certain, he said he believed "Constable Abela did move towards Adam Salter and probably attempted to restrain him".

This finding, he said, was based on the "central weakness of the Crown case" that Constable Abela remained "rooted to the spot near the refrigerator and did not move", which could not be reconciled with the evidence of ambulance officers in the kitchen.

Namely, it contradicted the evidence of ambulance officer Megan Coolahan's evidence.

She recalled seeing Constable Abela "ducking" across the room shortly before the shot was fired.

"I cannot rule out the real possibility that Abela did in fact make physical contact after he moved, and that he did attempt, albeit briefly, to physically restrain Adam."

However, the crucial blow to the Crown case was dealt by Judge Woods' finding that a "significant aspect of Adrian Salter's evidence is mistaken".

The Crown built its case around Adrian Salter's evidence that he was the last person to have had any contact with Adam before he was shot.

Describing Adrian Salter "as a beacon of light" crown prosecutor Nanette Williams characterised his version as so materially at odds with the accounts of the four officers that "if the police are right then Mr Adrian Salter is either fundamentally mistaken or he is lying".

Mr Salter told the court he was instructed to leave the kitchen area by police shortly after they arrived at his home.

However, he rushed back into the room once he saw Adam trying to retrieve the knife but was brushed aside by his son, and tripped over the ambulance equipment moments before Adam was shot.

Though he was motivated by love and concern for his son, Adrian Salter's distress "may well have made it difficult for him to perceive the swiftly moving events with complete clarity and accuracy," Judge Woods said.

"It is entirely possible, indeed probable, that when he fell over in a tangle of ambulance service equipment he may not have seen what other witnesses, particularly the accused, say they observed."

He also rejected the Crown's central thesis that the officers had "got their heads together" and fabricated their version of the events shortly after Mr Salter was shot, accepting the defence counsel's claim there was "extremely limited time available for possible collusion."

The court heard Sergeant Bissett shouted "Taser, Taser, Taser" before firing her gun, but she told the commission her decision to use her gun was deliberate.

Judge Woods noted the trial was not concerned with an evaluation of Sergeant Bissett's use of force.

However, that issue was addressed in a 2011 coronial inquest, in which Deputy State Coroner Scott Mitchell said "it was more likely than not" that she had mistakenly grabbed her gun instead of her Taser.

The inquest made no recommendations about criminal prosecution, and Sergeant Bissett has never been charged with any form of homicide over Mr Salter's death.