No. A military judge does not have the authority to issue a “judicial reprimand” as a form of punishment, either during sentencing or as a separate post-trial action. The power to impose punishment at a court-martial rests exclusively with the court-martial panel (the jury) or with the military judge if the accused has elected a trial by judge alone. The judge’s role is to preside over the trial, rule on legal matters, and instruct the panel on the law.
The authorized punishments that a court-martial can adjudge are specifically listed in the Rules for Courts-Martial. These include confinement, forfeitures of pay, a reduction in rank, and a punitive discharge. A “reprimand” is an authorized punishment, but it must be part of the sentence that is formally adjudged by the panel or the judge at the conclusion of the trial. A judge cannot unilaterally add a reprimand to the sentence later on.
Similarly, the convening authority has the power of clemency—they can reduce a sentence—but they cannot add to it. If the court-martial did not adjudge a reprimand as part of the sentence, the convening authority cannot add one during their post-trial action. The concept of a judge issuing an independent reprimand does not exist in the military justice system; punishment can only be imposed as part of the formal sentence of the court.