To Richard C. Pembrook, a dovish doctor in this city of submariners, the summit meeting between President Reagan and Soviet leader Mikhail Gorbachev was worthwhile because "most of the problems in the world are caused by insufficient communication."

To Donna D'Amico, a hawkish technical aide at the Electric Boat division of General Dynamics down the street, the Geneva talks were good because they gave Reagan a chance to show Gorbachev he is determined to develop "Star Wars" as a space-defense system that "might protect everybody . . . . if a character like Libyan strongman Muammar Qaddafi got the bomb."

D'Amico and Pembrook were sitting in separate booths of Norm's Diner Friday morning, looking at the summit from opposing perspectives. "I'm not a peace person," she said firmly, adding that despite the new Soviet leadership, "the Russians haven't changed their tune." The cardiovascular specialist, by contrast, said that he opposed the president's Strategic Defense Initiative (SDI) and thought the Russians were eager to change their economy "from missiles to wheat production."

But both found signs of hope in what has happened and both praised Reagan's handling of the meeting.

So did the overwhelming majority of other voters interviewed in sites from here to Austin and from New York City to Chicago and Waterloo, Iowa.

The grass-roots reporting by The Washington Post -- while constituting no scientific poll -- strongly suggested that Reagan has improved his already high reputation for personal leadership and united a broad spectrum of American opinion behind his approach to arms control and U.S.-Soviet relations.

Overwhelmingly, those interviewed said they thought Reagan was sincere in seeking arms control and, by narrower margins, said they were hopeful that Geneva would not just ease tensions between the superpowers but eventually move toward reductions in nuclear arsenals on both sides.

There were skeptics like Mike Blain, 26, the owner of two Austin sandwich shops, who said, "I can't imagine either one cutting back on arms. They both want to be top dog."

But many more agreed with the Rev. Robert Leverenz, a Methodist minister in Cedar Falls, Iowa, and chairman of the local Citizens for Peace. "The fear of nuclear annihilation has gone down," he said, "if only a fraction."

Reagan went into the summit with historically high levels of public support. The presummit Washington Post-ABC News poll showed two-thirds of those questioned approved his handling of the presidency in general and relations with the Soviet Union in particular.

Because of that high standing and the relatively low advance expectations of concrete accomplishments in Geneva, Richard B. Wirthlin, the president's pollster, said the day before the summit began that he doubted success or failure would change Reagan's standing "by more than 3 or 4 points."

Yet only 48 percent of those in the presummit Post-ABC News poll said they thought Reagan had done "as much as he should" to limit the arms race. Interviewing in five states Friday showed continuing skepticism on that point, but the comments volunteered on Reagan's performance -- from both past critics and supporters -- indicated warmer appreciation of his efforts.

Waterloo television executive Harry Slife, a staunch Republican who had fretted about Reagan's policies in Lebanon and Grenada in earlier interviews with The Post, said, "We were all worried if the old guy Reagan had it in him. You just have to be impressed with his performance. Both sides could have come out frowning, rather than smiling."

Penny Russman, a 45-year-old graduate student in library sciences at Wesleyan University in Middletown, Conn., is as opposed to "Star Wars" as many others on that liberal campus. But "the one thing I like about Reagan," she said, "is his civility, and it may be that served a very positive function with Gorbachev. It helped start the process, and maybe somebody else can come along to finish it."

The sense that a real breakthrough in arms control is still distant is heightened by voters' growing sense that Reagan really is determined to pursue SDI, the president's proposed space-based missile defense system.

Friday's interviews confirm presummit polls that showed most Americans are willing to make the trade-off Reagan has refused -- scrapping "Star Wars" for deep cuts in offensive weapons. Down the line, that could cause problems for him if he is seen as an intransigent leader blocking the pathway to disarmament.

For now, however, Gorbachev apparently has not sold most Americans on that view of the president. And paradoxically, the more the Russians criticize "Star Wars," the more Americans seem to think there may be something to it.

"I'm for it," said 28-year-old Mike Hajdan, a drug wholesaler in Connecticut. "The Russians know we're ahead of them on this, and I'd hate to see us stop and them get ahead."

Hajdan was having mid-morning coffee at Tami's restaurant in Colchester with his friend and fellow-salesman, Don Rahl. Rahl pointed out that Colchester was a likely aiming point for Soviet missiles, lying halfway between the submarine pens in Groton and the Pratt & Whitney aircraft-engine plant in East Hartford. "I'd like to see us have a defensive shield up there," he said. "Just like in football: dee-fense beats offense."

Although a "Star Wars" defense is years and perhaps decades distant and some scientists say it can never be guaranteed, Reagan's assiduous promotion of the idea has given it an appeal to many people.

Jim Bocanegra, 21, a part-time security guard and photography student at the University of Texas, said, "Treaties are broken all the time. If they start nuking us and we had the space weapons, at least we'd be able to stop them."

That argument is important, because Gorbachev -- at least in these interviews -- did not dissipate the suspicion and uncertainty about Soviet intentions.

More people than not were ready to credit him with sincere intentions on arms control, but a significant number agree with New York City flower vendor Walter Korzeniewski, who said: "I think he's bluffing."

Vince Zamora, 21, a sales clerk in an electronics store in Chicago's Loop, said, "I wouldn't turn my back on Gorbachev. He's evil." And Erhard Konerding, a librarian at Wesleyan, said, "It's refreshing to see a Russian who is smiling, but it's scary too. A lot of people may be suckered into thinking he's a moderate liberal."

Wirthlin argued before the summit that Reagan's high support level and Gorbachev's enigmatic reputation gave Reagan "a latitude of action" that few other presidents have enjoyed in dealing with the Russians. These interviews confirm Wirthlin's view.

Although most would use "Star Wars" as a bargaining chip, there was little vehement condemnation of Reagan for sticking to his guns. And some of the agreements dismissed as "cosmetic" by the pundits in Geneva seemed welcome to Americans back home.

The Post-ABC News presummit poll showed 66 percent favored annual summits, and the scheduling of further Reagan-Gorbachev meetings in 1986 and 1987 was cheering news to many. Stewart Fleischmann, 28, a Scotch Plains, N.J., lawyer, said, "If you know your enemy, you are less likely to act impulsively . . . . Summits help dispel the view that . . . the other guy is an ogre."

Cultural exchanges also have their grass-roots fans, including Joe Cerreto, a Colchester, Conn., pharmacist, whose daughter and her high-school classmates are about to make a vacation trip to the Soviet Union. "I think it's great," he said. "We don't understand the Russians at all."

But a customer listening to Cerreto expressed skepticism. "When the visits are done," said 57-year-old retired state employe David Slonim, "the Russians will still be in their bunkers, with the keys to their missiles in their hands, and our Air Force guys will be running test missions every day. So what changes?"

But back in Groton, 21-year-old Navy missile fire control technician Bart Pendergast, assigned to the USS Alabama, said he could see a value in Soviet-American meetings.

Pendergast favors "Star Wars" because "they the Russians are a little worried about what we might develop . . . and every missile of theirs we can stop, is a good deal."

But he also likes the idea of Soviet-American meetings, because "you've got to put your feelings out front, dealing with other people. Otherwise, they put their thoughts into your minds, and you put yours into theirs, and neither one really knows what the other's thinking."

By pushing "Star Wars" and at the same time "putting his feelings out front," Reagan pleased Bart Pendergast -- and most others in these interviews.