When does a lens go from 'linear' to 'fisheye' I recently ordered some lenses in an attempt to gather more light from an object being imaged in very low light conditions. I'm trying to use a converging lens with the object > 2f from the lens so it projects a smaller real image at the camera lens. Unfortunately I ordered some 75mm plano-convex lenses with a 75mm focal distance only to find they are very distorting like fish eye lenses.
Image quality is important, so I'm wondering at what d/f or other physical attribute starts to cause extreme image warping?
Below is a concept of what we are doing. As for how much distortion is tolerable, i don't know how to specify that, other then we are open to some, as a trade off for more light.
Also, this was a concept I had, I have yet to verify it will send more photons towards the camera... I believe it will, but no one has confirmed or denied it yet... So let me know if this is just a poor idea.

 A: You want a telescope. Even though people tend to think of them as gadget that makes distant objects appear bigger, one of the prime purposes is to make faint objects appear brighter. They work like you are thinking. They gather a lot of light with a big opening, and focus it onto a smaller area. 
Your first problem is you have one lens. You need two. 

I have drawn parallel rays in front of the telescope, as if the object was very far away. Usually you can adjust the focus of a telescope. This will make rays diverging from a nearby object focus properly.
If you focus the camera at infinity, parallel rays will focus on the sensor.

You might be able to use the camera lens as the smaller telescope lens. But as you found, the plano-convex lens and camera were not designed to work together like that. 

A telescope that is designed to work will parallel rays in and out might work better with a camera that is designed to work with parallel rays in (among other things.) 
But no promises. If you want a system you know will work, design one. 
