The actor posted a photo to Instagram moments ago ... a profile shot from the trial -- and, given the emotion etched on his face, seems like it was taken just as the realization his legal troubles were at an end dawned on him.

Baldwin writes, "There are too many people who have supported me to thank just now. To all of you, you will never know how much I appreciate your kindness toward my family."

Alec seems focused on gratitude right now instead of slamming the prosecutors ... though he'd seemingly be justified in doing so given the grounds on which the case was dismissed.

As we reported ... the judge in Baldwin's case dismissed the prosecution's case -- with prejudice, so it cannot be brought again -- after finding law enforcement had concealed evidence that prevented the actor from preparing his defense.

A police investigator -- Marissa Poppell -- testified her superiors had directed her to create a report documenting how cops had received ammunition ... and, then file it under a different case number. This made it so the evidence wasn't available to the defense.

Judge Mary Marlowe Sommer ruled the concealment of the evidence irrevocably damaged Baldwin's case, and the only proper sanction was to dismiss with prejudice.

The revelation was so distressing to one prosecutor, she abruptly resigned when she found out what happened.