Yet, it is also one of the most controversial. Made with the backing of the regime, it was considered by many to be Nazi propaganda and copies were seized by military authorities after the Second World War.

Berlin had been awarded the Olympics in 1931, before Hitler came to power. When he became German Chancellor in 1933, he demanded that they should be on the grandest scale ever seen.

The film which recorded them for posterity was to be of equal grandeur. In charge of production was one Helene Riefenstahl. Better known as Leni, she had been responsible for the propaganda film Triumph of the Will which depicted the 1934 Nazi rally at Nuremberg.

Riefenstahl was described in one newspaper as "the slim, dark haired, dark eyed tense young woman who is a friend of the Führer".

She was already renowned as an actress and filmmaker and in February 1936, she was even featured on the cover of Time Magazine. 

She claimed that she had been asked to make Olympia by Carl Diem, the administrator charged with organising the Berlin Games.

In fact, all cinematic matters in the Third Reich fell within the clutches of the notorious Dr Joseph Goebbels, the Nazi Minister for Propaganda. Goebbels was not an admirer of Riefenstahl but even he admitted that "she is a woman who knows what she wants".

Riefenstahl had one vital card to play. Her work had the personal approval of Hitler himself.

Preparations for shooting the film began in 1935, almost a year before the Games themselves. The contract specified that "Riefenstahl will direct the overall administration and production of this film".

The budget was to be 1.5 million reichmarks. Riefenstahl herself was to be paid a quarter-of-a-million.

Her production team were lodged at a castle in Spandauer Berg in West Berlin. This was only a few minutes walk from most of the key venues.

They shot a great deal of footage during training sessions in the months before the Games. This was edited into the final film.

Riefenstahl and her crew wanted unusual angles and constructed rostrums, moving platforms and dug pits to ensure they were able to shoot the images they needed.

Her vision for the opening of the film featured the ruins of the Athenian Parthenon and gliding images across statues of antiquity. As the music soared, the statues were transformed into real-life athletes, throwing the discus and javelin. With a change of tempo, women were shown dancing in a sequence of rhythmic exercises with the ocean as a backdrop. This sequence was filmed some months after the Games.

Their movements mixed through to the flames of an Olympic fire. This revealed a dark haired youth standing at an altar, ready to light a Torch.

The 1936 Games were the first to feature a Torch Relay from Ancient Olympia but the impressive sequences which open the film were not shot there. A civil servant called Kostas Kondyllis was the first man to carry the Olympic Torch, but he is not seen in the film.

Riefenstahl was dissatisfied with the material that she had shot. It was said that her cameramen had even missed the vital moment when the flame burst into life.

A few miles down the road, Riefenstahl and her crew had come across Anatol Dobriansky.

He had just carried the Torch and was persuaded to accompany the crew to Delphi.

The ruins at the archaeological site made a wonderful backdrop for what Riefenstahl had in mind. The Torchbearer even ran through the Ancient Stadium where the Delphic Games had been staged in antiquity.

The finished film showed very little of the actual Torch Relay. Enthusiastic crowds were shown watching an exchange of Torches but progress through Bulgaria, Yugoslavia, Austria and Czechoslovakia was depicted by animated sequences.

Finally, an aerial shot of the great stadium in Berlin announced the arrival in the Olympic city as a giant bell tolled its message to the youth of the World.

For the Opening Ceremony, Riefenstahl positioned no fewer than 36 cameras around the stadium.

Hitler was to open the Games using the prescribed words laid down in the Olympic Charter.

It was one moment which could not be "re-shot" so to guard against a malfunction at the vital moment, two cameras were positioned to capture his very short speech which opened the Games.

A few minutes before the ceremony began, SS guards tried to remove her cameras but Riefenstahl remonstrated with them and her equipment remained in position.

After Hitler's declaration, a salute of guns and the mass release of pigeons, the film switches to the Brandenburg Gate as the Torchbearer carrying the burning flame, escorted by eight runners, runs towards the stadium.

The final runner, Fritz Schilgen, emerged from the stadium entrance in a dramatic moment of cinema. He ran past the assembled teams to light the cauldron at the far end of the stadium.

The opening sequence ended with the flame burning as the choir sang an Olympic hymn, conducted by the composer Richard Strauss. It was said that the only time Strauss ever set foot in a cinema was to see himself on screen.

For the athletic competitions, Riefenstahl arranged for camera pits to be positioned at strategic points on the field. Although officials demanded that many be removed, those which remained yielded stunning footage. So too did a huge 600 millimetre lens on one of the cameras, the first of its kind.

Riefenstahl wrote later: "Never before had cameramen been allowed to work so close to the athletes.

"There were great struggles before the International Olympic Committee (IOC) finally gave its permission. Even then, there were daily arguments with the competition judges.

"A downright war had to be fought in order to get the shots. But it was worth the fight."

The close-ups of the great Jesse Owens are among the most memorable images in Olympic history.

Covering the marathon demanded tremendous logistical planning. The final sequence lasted some 14 minutes and represented the most extensive coverage of a marathon race seen up until that time.

Riefenstahl had even arranged to borrow an airship from the Luftwaffe to film the rowing at Grunau. The officials in charge of competition there turned this down too.

There were also shots of athletes relaxing in the Village and running into the lake after a sauna.

The finale of the film featured diving which provided the most memorable footage and assumed an almost balletic quality.

When the searchlights pierced the sky above the Olympic Stadium at the close of the Games, an image re-created in the studio for the film, Riefenstahl knew her task was only just beginning.

It was estimated that 400,000 metres of film had been shot. Every day the raw footage known as "rushes" had been viewed and a full written report came back so that where necessary and possible, close-ups and other scenes might be re-filmed.

Even cataloguing the rushes had been a remarkable exercise in logistics.

The music was added in post-production by Herbert Windt, a popular composer who had also written for Triumph of the Will.

A number of versions in different languages were recorded. The German voice was Dr Paul Laven, regarded as one of the pioneers of sports broadcasting in the country.

BBC broadcaster Howard Marshall provided the commentary in English.

At last, in the spring of 1938, the film was completed. The premiere in Berlin was scheduled for Hitler's 49th birthday.

The film was divided into two parts, Fest der Volker, the Festival of the People, and Fest der Schoenheit, the Festival of Beauty. It ran to some 3 hours, 38 minutes.

The UFA Palast am Zoo cinema was festooned with swastikas and decorations designed by Albert Speer.

Hitler presented Riefenstahl with a bouquet and a Greek envoy came forward with an olive branch from Olympia.

Henry McLemore of the United Press wrote in the Hollywood Citizen News of "the best film I have ever seen".

Schweizervolk said: "It is in the truest sense of the word, an Olympian film."

The film was honoured in France, Sweden and Greece. At the Venice Film Festival it won the Coppa Mussolini.

Later in the year, Riefenstahl sailed on the liner Europa to America to promote the film.

As she arrived, news came from Germany of Kristallnacht. This was the infamous "night of broken glass" when Nazi gangs attacked Jewish homes and synagogues.

A joint council of the American Jewish Congress and the Jewish Labor Committee announced that they would picket any cinema which showed what they called "this Fascist picture".

They circulated a telegram to American film distributing companies:

"SEEKING YOUR COOPERATION TO STOP POSSIBLE SHOWING THE NAZI OLYMPIC FILM BROUGHT TO THIS COUNTRY BY LENI RIEFENSTAHL. THE PRODUCTION IS PART OF A NAZI PROPAGANDA ATTACK ON AMERICAN INSTITUTIONS AND DEMOCRACY".

Distributors in the US refused to screen the film but there was at least one American who remained enthusiastic about the picture.

At the 1939 IOC Session in London, Avery Brundage suggested that a diploma be awarded to Riefenstahl for her work. "Because it was the sporting film which best served the Olympic cause," he claimed.

This was seconded by Francois Pietri with the support of the Marquis de Polignac and Francois Pietri who were said to express "at the same time their hearty approval".

It turned out to be the last award that Olympia would receive.

After the war, the film was actually banned and Riefenstahl was questioned. She denied ever having been a member of the Nazi party, but many prints of the film were impounded by the allied authorities.

In 1958, Diem wrote to Hans Blank, director of the German film board in Wiesbaden, asking that the ban be lifted. His letter suggested that the "justified criticism of national socialism time of terror should not be dragged in here, but the Games should be respected as an oasis of honour".

He was supported by IOC chancellor Otto Mayer.

"This excellent film will give useful publicity to the idea of the Olympic Games," Mayer said. "This film is the best presentation of the Olympic Games ever shown.

"The IOC simply asks the censorship board to give the film a certificate and that nothing may stand in the way of a successful reissue."

In time, Riefenstahl regained possession of some of the negatives of the film and retained the rights. It seems remarkable now but when the original contract had been drawn up, the IOC had not taken steps to ensure it had a claim on the rights.

So it was that in 1965, Brundage, by now IOC President, was forced to write to Riefenstahl.

"We should very much like to have a copy of your wonderful film of the 1936 Games for our archive," he said.

"We should be prepared to buy a copy. Would you therefore pass on our order to the salesman negotiating for the lowest price since our reserves for this purpose are very limited. But we really do need this film."

By the 1980s, the film was again being shown.

When Lausanne staged an "Olympic Week" for the first time in 1982, the programme included a showing of Olympia alongside another famous movie with an Olympic theme - Chariots of Fire.

The late Monique Berlioux, at the time a senior IOC official, said: "Riefenstahl’s work is much more than a mere record of athletic achievement. It has become a worldwide symbol of the close bond between art and sport."

Riefenstahl herself lived to the age of 101 but her legend lives on. In the 2016 film Race which told the story of the Berlin Games, she was portrayed by the Dutch actress Carice Van Houten.