When you rescue the last of the three spies, you get Ultra Vision Goggles that can see the lasers, and then they appear to go on and off. You can slip by them.
In order to enter the control center, you will also need the Fingerprint form the BAD guy at the BAD Bistro, and the passcodes from the three rescued spies.
(see related questions)
The BAD control center is to the far right of Spy island, past Toupee Terrace. You can only enter the control center when you have rescued all 3 spies and have the Fingerprint from the BAD Bistro. (see the related question)
You will get a Laser Pen, a "Grappling Bowtie" and Ultra-Vision Goggles to get past the lasers in BAD control center.
Spy island
spy island
The satellite control center
Use the xray glasses
you need to get the goggles which you get after finding all the spies
it means that the hohokam were more heterogenous than we realized
you click it and move it
You Get the chameleon from The eye doctor place then put it on then use it in the headquarters.
You have to save the agent 3 then she'll give you x ray vision glasses to get past the lasers.
Find agent 3 and she'll give you x-ray goggles