Let me first start by saying I haven't found anything in my literature about specific cases of reconstructing what satellites could detect. So my answer here is speculative. Part of the problem is that it concerns very sensitive data. To the present day, the methods of intelligence agencies to reconstruct what the other side may have photographed from the sky or space is probably still a guarded kitchen secret.

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However, in more general terms, the ''reverse engineering'' of the reconnaissance and intelligence activities of the adversary form a basic function of what is called Counterintelligence. Protecting sensitive information, whether by restricting access to documents, or by camouflaging military sites and locations, is the first line of defense against a hostile intelligence effort. Counterintelligence staff during the Cold War typically tried to identify potential objects of interest to an adversary, try to work out how the adversary might try to get to it, and compile lists of what information could be obtained where and who had access to it. If a leak has been discovered, a damage assessment follows, which includes trying to reconstruct how the adversary succeeded and what information they may have obtained.

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Whether it is a colonel defecting to the other side, carrying under his arm a stash of photocopies of classified documents, or a spy plane flying over a military installation to take pictures, in both cases the job of counterintelligence was to assess the damage and what information exactly ended up in enemy hands. The core business of Cold War counterintelligence was to determine what the other side knew or didn't know.

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Tracking spy planes and monitoring their activities would be useful to learn what the adversary is looking for, although in case of the U-2 spy planes, they took bizarre flying routes to obscure their purpose and to test variation in response times between different sectors of the Soviet air space.

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With the launch of the unironically named CORONA satellite program, it became virtually impossible for Soviet counterintelligence to exactly assess what the Americans might see on that, or rather, where they're looking at. For instance, in 1959 the KGB informed the Soviet leaders that their experts estimated that these satellites could ''effectively photograph sectors of the Earth 50-90 km in width and with a range of 150000 km''.

Another problem that the KGB reported was the lack of knowledge on the American satellite orbits and radio frequency. Nevertheless, the KGB stressed the need to try to combine the resources of the GRU (Military intelligence) to place these satellites under surveillance. Several weeks later, the head of Soviet military industry in the Central Committee of the Communist Party reported that it was only possible to determine the path of the US spy satellite by capturing its radio signals, the responsibility of the KGB's 4th ''Special Section''. This section was merged in 1959 into the larger ''Operational-Technical Department'' of the KGB.

In a similar fashion, US Naval intelligence and the CIA kept track of the small Soviet sea trawlers and, if possible, submarines going near the US coast to intercept signals, and the US Air Force monitored the flights of Soviet strategic bombers over North America. Later during the Cold War, the US deployed the SR-71 Blackbird, flying at such extreme altitude with enormous speeds that it could map a 100,000 square miles per hour. If it was picked up by Soviet radar at all, there was probably little hope of really reconstructing what it might have been photographing.

So my answer is speculative at best, and I welcome everyone with more detailed knowledge to add to it. I think that especially in the very beginning, between 1956 and 1961, the Soviets tried to figure out where the Americans were flying and what this meant in terms of intelligence. After 1961, both sides probably attempted to monitor eachothers reconnaissance activities as best as they could, by learning satellite orbits for example, but the capabilities of such tools became so powerful and wide-ranging that it was probably virtually impossible to determine precisely what the other side had been photographing. At the same time, experienced counterintelligence veterans in the Cold War could probably guess what the adversary was looking for. After the nuclear treaties of 1968, 1970 and 1972, it was even agreed on that both sides more or less used these reconnaissance tools to verify eachothers promises on nuclear missiles. But in short, yes, I think you could speak of ''reverse engineering'' spy flights, but not in such great detail as you would do in actual reverse engineering.

It may be difficult to get specific literature on this but here are some things you could look at:

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For more general literature on the purpose and mission of counterintelligence:

William R. Johnson, Thwarting Enemies at Home and Abroad: How to Be a Counterintelligence Officer (Washington 2009).

Nigel West, Historical Dictionary of International Intelligence (Oxford 2006)

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Some works on technical espionage during the Cold War:

Matthew Aid, Secret Sentry: The Untold History of the National Security Agency (New York 2009) [Unlike the title suggests, its not an ''untold'' history...]

James Bamford, Body of Secrets: Anatomy of the ultra secret National Security Agency (New York 2002)

Paul Lashmar, Spy Flights of the Cold War (Stroud, England, 1996)

Robert Jackson, High Cold War (Yeovil, 1998)

There is more literature on spy flights during the Cold War, but much of it focusses only on the American side. Soviet archives remain closed.