How to render a new texture image from scene I am working with a brick texture that looks like this:


(this is only a small section to illustrate)

For my project, I have UV-unwrapped a circle to have a concentric pattern of bricks using this texture, like this:


(this is a screenshot from rendered view)

My problem is that this UV-unwrapping takes a lot of time, and I don't want to have to do the same for other circles in my project that will have the same pattern. So I was thinking that I could render the existing circle from top view and in that way create a new circular texture that I can easy UV-unwrap other circles onto. But to do this, I need the render to look exactly like the original square brick texture. This means I need completely neutral, flat lighting without any influence from the world around or any other lights. 

Is there an easy way to render my circle object so that the result has the exact same values as the original texture? Do I need to use traditional rendering for this when I don't want any influence from the scene?

I appreciate any help, thanks!
You can render the diffuse color viewed from the top 
but the color won't exactly be the same unless you set the look in color management to none: 
Here is a more detailed answer: render albedo (color passe without shadow)