Aldrin took very few photographs of Armstrong on the lunar surface but this image of him back in the LM after the moonwalk is the first “helmet-free” photograph of a man on the Moon.

The members of the Apollo 11 crew conducted themselves with a cool-even laconic-professionalism throughout the mission, to the general despair of newspaper headline writers. Once the more difficult and novel aspects of the flight had been successfully completed, however, a change of mood became evident.
The photograph shows a tired and elated Armstrong smiling with satisfaction after regaining the cabin of the LM following his and Aldrin’s exploration of the lunar surface.

From the mission transcript before the liftoff from the Moon:

114:22:23 McCandless (Mission Control): We’d like to say from all of us down here in Houston and really from all of us in all the countries in the entire world, we think that you’ve done a magnificent job up there today. Over.
114:22:46 Armstrong: Thank you very much.
114:22:48 Aldrin: It’s been a long day.