Nasa experts are continuing to analyse pictures of the Discovery shuttle in a bid to confirm the vehicle's heatshield tiles have sustained no serious damage.
High quality images of Discovery are being analysed
The agency has suspended all future orbiter flights until it can find an effective way to stop foam sliding off the vehicle's external tank on launch.
The images taken from the International Space Station suggest Discovery has suffered no major harm on its lift-off.
Nasa chief, Dr Mike Griffin, said the shuttle looked to be "a clean bird".
But the work to inspect Discovery's external surfaces is expected to go on for another few days yet.
And part of Friday has been set aside for astronauts to take a closer look at "areas of interest" - places on the tiled surface which may have chips or nicks.
The concern about Discovery's structural integrity stems from video footage of Tuesday's spectacular launch that showed foam falling about the vehicle a few minutes into its ride to orbit.
Before arriving at the space station, Discovery performed an unprecedented 360-degree flip. It allowed the crew on the ISS the chance to train long lenses on the vehicle's underside.
The digital images were sent down to Nasa's Johnson Space Center in Houston, Texas, for engineers to work over.
All together: Docking occurred over the South Pacific
"The team is employing all of their tools to go look at that. The team has a lot of information. They have a lot of data. And we'll work to understand that," flight operations manager John Shannon said during a media briefing.
"Some good news is, it looks like all of the foam loss that we had from the tank did not hit the orbiter."
Discovery's docking with the ISS was completed at 0718 EDT (1218 BST; 1118 GMT) above the South Pacific just west of Chile.
The ISS crew, American John Phillips and Russian Sergei Krikalev, warmly greeted Discovery's seven-member team, led by Commander Eileen Collins.
Work was immediately started to allow the 15 tonnes of supplies ferried up by the shuttle to be moved across to the station.
SHUTTLE RETURN TO FLIGHT
Mission known as STS-114
Discovery's 31st flight
17th orbiter flight to ISS
Payload: Raffaello Multi-Purpose Logistics Module
Lift-off: 1039 EDT, 26 July
Location: Kennedy Space Center, Launch Pad 39B
Discovery crew: Collins, Kelly, Noguchi, Robinson, Thomas, Lawrence and Camarda
"We are ready to get on with a mission that the station has been waiting to see for two-and-a-half years," said flight director Paul Hill.
Nevertheless, Nasa is having to grapple with the disappointment of seeing the foam issue raise its head again.
It was a suitcase-sized chunk of the material that led to the loss of Discovery's sister craft, Columbia, and its crew of seven in February 2003.
During Tuesday's launch, at least three pieces of foam came off the Discovery, including one about 80cm (31 inches) by 35cm (14 inches), slightly smaller than the piece which caused Columbia's destruction.
"We will simply never be able to get the amount of debris shed by the tank down to zero," Dr Griffin told NBC television. "We are trying to get it down to a level that cannot damage the orbiter."
Of more immediate concern will be apparent signs of small damage to tiling near Discovery's nose landing-gear doors and to a square "chine" tile further toward the aft (back) end of the ship.
Nasa will want to establish if these areas have been compromised in a way that might prohibit a safe return to Earth for Discovery. That landing is currently scheduled for 7 August.
Three spacewalks are planned for the mission.
The first on Saturday will test repair kits designed to deal with small damage areas on the shuttle's heatshield tiles.
The two other spacewalks will repair and install critical hardware outside the space station.