You’ve probably moved on but I’ll offer my thoughts. If you go with offering an incentive, I would word it as:
Get a $20 Visa gift card by taking part in research about how you use Radar.
I guess it is dependent on what kind of incentive you can afford and how involved the research is. Also, if Radar is already on the market, I think you could consider something like a percentage discount off their next purchase. However, Radar might not work that way.
Underneath that, you can have an opt-in button (as well as one that says something like, “No, thanks.”) that says:
Yes, please email me more information.
I think people also may be turned off about not knowing what their information will be used for. I know that is the case for me. I think you might want to reassure users what the research will be used for. I think that if you aren’t sharing their information with other companies etc. that that should be prominent. Perhaps something like:
Get a $20 Visa gift card by taking part in research about how you use Radar. Read about how we use what we learn here.
I hope this helps.
ETA: I would also think about adding an explanation about what you do with email addresses. It might not be relevant though if you already have that information.
ETAA: Sorry this is my thinking from someone who is learning copywriting and is not a UX designer. I should have put that disclaimer at the start.