Lens Distortion Effect with Illustrator

Question

I'm trying to model a lens distortion to apply to a vector image. I originally tried to use the Warp > Inflate effect, and I was able to get close in some scenarios to what I was looking for, but the problem is the inflate effect's scale is uniform throughout the x/y axis. The effect I'm looking for is for the effect to be on a logarithmic scale based on distance from the center.

I've got an example of what I'm looking for:

The original image on the left, an approximation of what I'm looking for in the center, and what the inflate effect is doing on the right (note the consistent spacing in between each warped ring).

So I guess the main question is, does anyone know of an effect that can implement the effect I'm looking for? or am I stuck writing a custom plugin or something?

Answer 1

Goto Effect » Distort & Transform » Transform apply values which shown in below image

Answer 2

I know you're trying to do this to a vector image, but if you're willing to convert to bitmap then you can use Photoshops pucker tool to achieve this effect.

in PS filter > liquify > select pucker tool on the left

you can use the Freeze tool with a feather to prevent the center of the image from distorting too much, depending on what exactly you want.

It might be a bit messy, but you can convert back to Vector once you're done by using AIs image trace.

Hope this helps