The military commanders at Supreme Headquarters Allied Powers Europe (SHAPE) think they have the goods on the Soviet Union's dark designs in Europe: secret aerial photographs from American spy satellites clearly reveal military deployments that can only have offensive, as distinct from defensive, purposes.

Publication of this evidence, they believe, might work wonders on European public opinion and, in turn, on parliamentary votes on defense spending. A bigger European effort could conceivably silence a growing number of American critics who threaten to pull out American troops if the European allies are unwilling to take on a larger share of the NATO burden.

Yet the Reagan administration, which has not hesitated to use similar aerial photos as evidence in seeking public support and congressional funds for its policies in Central America and the Caribbean, has steadfastly refused to make this evidence public.

Why? Gen. Bernard Rogers, the Supreme Allied Commander in Europe, would like to know. He has been told that publication of these photographs could compromise U.S. intelligence gathering, but he is puzzled by the "nuance" between aerial surveillance from fixed-wing aircraft over Nicaragua and spy-satellite surveillance of Warsaw Pact deployment. Rogers is a Rhodes scholar, a combat veteran and a former Army chief of staff. He understands the problem of the intelligence gatherers.

But he also believes profoundly in the business of balancing risks. And the "basic challenge we face in this alliance," he told me in the course of a long interview, is "to convince the people, particularly in Western Europe, that there is a threat to their freedom."

Rogers sees two ominous trends. One is a widening Soviet advantage in conventional military power along the European front. The other is a growing temptation among "serious people, not just kooks" to think in terms of pacifism, neutralism, accommodation. "I'm convinced that the time has come -- or passed -- for the common good of collective defense to have a little give on the part of the intelligence community," he says.

Even if Rogers is wrong, the runaround he has been getting from Washington is a commentary on the Reagan administration's management of national security affairs. He has been pressing what he thinks is an important case at the highest levels of the U.S. government and even getting a sympathetic hearing for almost four years. What he has not been getting is anything in the nature of a considered response reflecting a serious effort to make a choice between risks and opportunities.

Instead, intelligence technicians have been bottling up useful and damning evidence at a time when, (a)Europeans are regularly falling short in meeting NATO commitments, (b)the Soviets are moving ahead in sheer numbers of tanks, helicopters and other armaments, and (c)Sen. Sam Nunn (D-Ga.) is using his considerable prestige to round up Senate support for drawing down U.S. forces if the Europeans don't do more in their own behalf.

Rogers believes this would be the "unraveling" of the alliance. He sees hard-pressed and in many cases shaky European coalition governments under heavy pressure for social welfare spending. So he would try to strengthen their hand with public opinion.

Many Europeans seriously doubt the numbers -- or even the existence -- of the Soviet intermediate-range ballistic missiles that constitute the rationale for the hard-won alliance agreement to deploy countervailing U.S. missiles in Western Europe. Rogers says the spy photos would show the sites and even the Soviet missiles, unmistakably.

The European man on the street, he contends, does a lot of wishful thinking about the purely defensive posture of Warsaw Pact forces. "You can show the offensive nature of the Warsaw Pact if you can show the massive amounts of prepositioned river-crossing equipment, the massive amount of prepositioned (petroleum) pipeline and their ability to lay that pipeline up to 90 kilometers a day."

He has tested his theory. With the permission of Defense Secretary Caspar Weinberger, he did a slide show for a select group of European Cabinet ministers: "You could hear the breath being sucked in when they saw the pictures for the first time."

Few American authorities question his analysis. The debate is over what to do. And the remedy of choice, increasingly, is to think in terms of threats that the United States will simply walk away from the problem. Rogers makes a good case that before it comes to that, the administration ought to lay out its best evidence of the Soviet threat that the admiistration talks so much about, and see how the Europeans respond.