When the Spawr Optical Research Co. of Corona, Calif., applied for a license to export 10 laser mirrors to the Soviet Union four years ago, the application was turned down by the U.S. government because the lasers and copper mirrors could be used as anti-satellite weapons in space.

Rejection of his application didn't stop Walter Spawr, president of Spawr Optical, from shipping about 50 laser mirrors to a laser research laboratory in Moscow.

Testimony in U.S. District Court in Los Angeles last year showed that Spawr deliberately understated the value of his high-energy laser mirrors to the Customs Service, and then shipped the mirrors to firms in Switzerland and West Germany, which he said was their final destination.

In Switzerland and Germany, a West German named Wolfgang Weber, who was a business associate of Spawr, reconsigned the mirrors to Moscow.

Intelligence sources told the court in Los Angeles that the mirrors already may have been used in tests of Soviet anti-satellite weapons, where lasers were used to burn holes in aircraft to blow them up.

Spawr was convicted of violating the Export Administration Act and given a 10-year suspended sentence on condition he serve six months in jail. His company was fined $100,000.

The Spawr case spotlights a steadily rising effort by the Soviet Union to pry away the secrets of American high technology by means they rarely used in the Cold War years of the '50s and '60s.

The Soviets, offering huge sums of money for lasers, fiber optics and computers, bribing company officials and using European middleman and dummy Polish, Hungarian and Romanian corporations, are conducting an unprecedented assault on the industries of America.

"The Russian targets are no longer weapons and strategy," FBI Director William H. Webster told The Washington Post. "The emphasis is now on technology, and they will go to any lengths to get it."

Lasers have military uses in space; fiber optics can be used to make small, secret communications devices. Computers have thousands of military and intelligence applications.

The FBI says at least 1,000 of the 2,800 Soviet and East European diplomats in the United States are "known or suspected" intelligence officers whose assignment is at least in part the acquisition of high technology.

Also, 2,500 Soviet engineers and scientists visit this country every year on trade missions, which may be another way of saving that at least some of them are here to steal industrial secrets.

At no time in its history has the FBI had a larger, more active counterintelligence operation. Of the 7,800 agents in its 59 field offices, as many as 2,000 are engaged full-time in counterintelligence.

Their task isn't easy, mostly because it's corporate and not Pentagon secrets the Soviets are after. In California's high-technology Silicon Valley, more than 500 companies have access to classified information. Nationwide, 11,000 companies have the same access.

At least five times, the Soviets have been able to bribe American company officials to assist them in buying instruments on the export control list. Swiss and German middlemen also have been bribed by the Soviets to buy controlled American devices.

Usually, sheer greed is involved. Says a federal official: "We haven't come across a case yet that involved ideological espionage. The sales to the Russians have always been for money."

The top Soviet targets are microelectronics and computers. Last year, a Belgian, Marc Andre DeGeyter, offered a $500,000 bribe to an official of Software A.G. in Reston, Va., to steal a coded computer program for the Soviets. The program would allow the Russians instant inventory control at any military base, no matter how large or complex. DeGeyter got a four-month jail sentence.

DeGeyter's case was unusual because he was caught before anything found its way into Soviet hands.

Two years ago, two top officials of I.I. Industries in San Jose, Calif., were found guilty of violating the same law after federal agents discovered they had shipped more than $1 million in computer machinery to the Soviet Union without a license by selling it to a West German businessman, who forwarded it to Moscow.

The first shipment was through a phantom company in Montreal, which sent it to Zurich and then Moscow. The next three shipments went to a fictitious company in Kansas City, where the computer machinery was crated with air conditioners and washing machines and sent through Germany and The Netherlands to Moscow.

Almost as high as computers on the Soviet want list are lasers and fiber optics. Laser and fiber optics parts have been carried out of the United States in East European diplomatic pouches. The FBI has investigated at least 30 cases in which the Soviets offered bribes to buy lasers and fiber optics that were on the export control list.

Federal agents often learn of illegal technology exports while they are in progress. A favorite federal tactic is to intercept an illegal shipment and substitute something meaningless. At least twice, federal agents packed computer machinery boxes with sand that was then transshipped to Europe on its way to Moscow.

So heavy is the traffic between the United States and the Soviet Union that the Commerce Department, which administers the export control law, is now in the counterintelligence business.

Not only does staid old Commerce have its own agents, but it also has a stable of informers whom it sometimes pays out of its own informer fund. Who are its informers? People in the export business, people working at air freight companies, people working on the docks in New York and San Francisco.

"It's hard to say these cases are on the increase, but in 1980 we closed twice as many cases as we closed the previous year," said Sharon Connolly, director of the enforcement division of the Commerce Department's Office of Export Administration. "If these cases are not on the increase, we're certainly hearing more about them."