What you’re seeing is mostly perspective, not barrel distortion. If the camera isn’t effectively very far away and perfectly centered, parts of a 3D object with some height will appear shifted or thicker.

For a true orthographic view, you’d need a telecentric lens, but those are specialty optics and impractical/expensive for large objects.

Practical options:

• Place the camera exactly centered above the subject.
• Increase camera-to-subject distance and use a longer focal length to reduce perspective effects.
• Keep the object as flat as possible.
• If you only need the outline, a flatbed scanner is often the best solution because it captures line-by-line with a constant viewing angle.

Another possible workaround is to capture the object’s shadow instead of the object itself, since a shadow on a flat surface is inherently 2D. This only works well if the light rays are close to parallel and the projection surface is perpendicular to the light.

So: no normal inexpensive lens will give perfect zero-perspective top views; scanner or specialty telecentric optics are the real solutions, while longer focal lengths and more distance help minimize the problem.