Final answer:
The surgical procedure to puncture the amniotic sac and collect amniotic fluid is called amniocentesis, which is used for genetic health analysis of the fetus.
Step-by-step explanation:
The procedure where the amniotic sac can be surgically punctured to obtain a sample of amniotic fluid is called amniocentesis. This medical process is performed to analyze aspects of the baby's genetic health, as the amniotic fluid contains fetal cells which can be studied for genetic information and abnormalities. Along with genetic screening, amniotic fluid is also a valuable source of non-embryonic stem cells, which have the potential to develop into various types of cells.