Faced with an eerie image that becomes dreadfully familiar during RTÉ’s uncommonly powerful documentary on Ireland’s humanitarian response to the migrant crisis, it takes a moment to understand what is happening.

A camera mounted to a naval officer’s helmet lunges forward, seemingly fixed on an inanimate object, perhaps a lifebuoy, while the lens is obscured by sea spray or shrouded in fog. We hear a hard, insistent thud. The point of view, surreally detached, belongs to somebody performing emergency CPR. You feel it, rather than see it: the moment a life is being saved, or lost.

Even the title of this extraordinary programme, The Crossing (Monday, RTÉ One, 9.35pm), can hit you in different ways: as a gesture of stark dispassion, with a true documentary’s insistence on impartial details behind the search-and-rescue procedure around the defining crisis of our times; or as a muted kind of poetry, fitting for the namesake of the vessel, the LÉ Samuel Beckett, in which people follow careful routine while grimly aware that lives depend on it.

One rare and essential skill of this documentary is the ability to bring some clarity to chaos. “They’ve never seen the water before and they panic,” explains O’Donovan. “It’s the people who are not screaming you have to get to first.” It’s unclear how many drowning people the crew have seen before, or how to gauge their level of panic, but they each present fascinating figures, generally calm and contemplative in later reflection, insistent and frustrated during rescue. “Starboard chamber has deflated,” somebody reports, matter of factly, then, as the bodies tumble into the sea, “They’re all starting to go now. That f***ing starboard side.”

It takes cool heads to respond to drowning: the irrational behaviour of those overboard – hoarding flotation devices, in one instance – is the consequence of acting on instinct; the rescuers must ignore their own. “You don’t go into the water,” insists a bluff petty officer Dave O’Leary, who, seeing a drowning woman and child, does precisely that. In that mission, 112 people were saved of 120. The crew consider it a defeat.

The Crossing grazes against another paradox, which is how we see migrants in different circumstances. The political and social failure around the crisis is not to regard migrants as people, but reduce them to grainy images or statistics. For rescuers, though, it is necessary to see them first as a task, otherwise it would be overwhelming. “You keep hauling them out, dead or alive, as fast as you can,” says O’Donovan, and as the crew speak to camera, you often get an uneasy sense that they are finally processing such trauma in front of your eyes, sometimes choking on emotion. The documentary doubles as counselling. O’Leary’s self-recrimination, that he batted away the hand of a dying man’s brother while he struggled to save him, is beyond heart breaking, as is director Judy Kelly’s decision to show the moment.

The promised level of personal access here is indeed extraordinary, and deeply harrowing – from the psychology of the rescuers, to the hideous conditions of the boats and even the details of the smuggling economy – but it never appears exploitative, largely because the programme is so well structured: it conveys insights without the need to editorialise.

Pay attention and you’ll see the subtle, shaping hand of Kelly and editor Guy Montgomery, but otherwise theirs is a skill that is even more rare, and one that is sadly deserting documentaries: they are invisible.

Thanks to their efforts, the crisis is much harder to ignore, if no easier to solve. It is a dismal testament to human nature that, among almost 800 survivors who very narrowly escaped death, religious sectarianism is aggressively reasserted on-board, and a measure of the diabolical cynicism of smugglers that such European Union-sanctioned rescue missions are now part of their sales pitch. “We were told we’d be picked up,” says one young man, plucked from a sinking dinghy, as though it was all part of the service. In other even-handed interviews with various refugees, that is not the general feeling. “No matter what, don’t leave your country,” says a young Sudanese woman, Lielit, in tears, having risked rape and death during her uncertain journey. And when a grateful Barrymamadou Gallé, one of only 19% of refugees to have found asylum, is asked if he would make the crossing again, he answers, unhesitatingly, “No.”

At the end of its mission, having saved more than 2,000 people, among the 15,512 rescued by the Irish Defence Forces, O’Donovan, long in experience and short on illusion, does not anticipate any new wave of caution. “Whether we’re there or not, they will put to sea.” This was not, finally, a documentary on the crew of the LÉ Samuel Beckett, but a clear-sighted documentary on desperation. As the poet Warsan Shire put it:

“you have to understand,

that no one puts their children in a boat

unless the water is safer than the land.”