The preschooler, Belle Thomas, and her 1-year-old brother, Preston, are standing still, looking straight into the camera lens and smiling. It’s picture-perfect, and the photographer is ready.

Click.

Just then, a 6-foot-1, two-term former president of the United States strides into the frame. In a few seconds, the photo shoot is over, and the photos are no longer of the siblings alone.

That’s how Barack Obama inadvertently became part of a family’s moment early Monday morning at the Tidal Basin in Washington.

The family was elated to have him as an interloper, the parents said.

“What! Barack Obama is in my picture?” exclaimed Belle, 4, the preschooler, during the joyous aftermath, when her parents, grandparents, and the family photographer, Briana Inell, realized that Mr. Obama had indeed been part of four or five frames.

The photographer had not planned it that way.

“I was trying to frame my picture, make sure that the Washington Monument is on the left and the blossoms are on the right, and the babies are in the center,” Ms. Inell said on Wednesday.

In the moment, Ms. Inell — who has been taking photos during peak cherry blossom season for the last 10 years — did not even notice as Mr. Obama entered the frame.