To uncover this hidden idea for a poem the writers each have their own unique method. As for me, the idea for the poem evolves when an idea from a photograph is confronted with an obviously unrelated, disparate idea from a text (mythology or science) until the two conflicting ideas are reconciled as a totally new, surprising, and workable one. This method was easy for me to come by. As an attorney I was trained to reconcile disparate views, to do exactly what a metaphor does for a living. It's not a mystery that so many practicing lawyers write poetry. Lawyer Poets And That World We Call Law, James R. Elkins, Editor (Pleasure Boat Studio Press. Also, Off the Record, An Anthology of Poetry by Lawyers, edited by James R. Elkins, Professor of Law, University of West Virginia.
The efficacy of this method for getting ideas is documented at length by Wayne Barker, MD. who, in his Brain Storms: A Study of Human Spontaneity, on page 15 writes:
If we can endure confrontation with the unthinkable, we may be able to fit together new patterns of awareness and action. We might, that is, have a fit of insight, inspiration, invention, or creation. The propensity for finding the answer, the lure of creating or discovering the new, no doubt has much to do with some people's ability to endure tension until something new emerges from the contradictory and ambiguous situation.
Likewise, Douglas R. Hofstadter, in his Godel, Escher, Bach: An Eternal Golden Braid writes on page 26:
One of the major purposes of this book is to urge each reader to confront the apparent contradiction head on, to savor it, to turn it over, to take it apart, to wallow in it, so that in the end the reader might emerge with new insights into the seemingly unbreachable gulf between the formal and the informal, the animate and the inanimate, the flexible and the inflexible.