In an experiment I am trying to image a phosphor surface on a camera using a 3x zoom lens. The distance of phosphor surface to lens input surface is ~100 mm. The effective focal length of the zoom lens is ~20 mm and the magnification is ~1/5x. This is a C mount lens and have 6 elements. 3 element for condensor lens (front lens) and 3 elements for focusing lens (back lens). All the lenses have anti reflection coatings. In order to decrease the working distance have inserted a spacer (5 mm, to increase image distance) between the lens and camera.
Now the problem is that the collection efficiency of this setup is very poor. I have searched the internet but I only found this article. The article points out the problem description but do not provide any solution.
The problem here is that the condenser lens is of large focal length and do not divert all the incident light to the focusing lens. Only a part of incident light is intercepted by the focusing lens due to its small size. I have put the focusing lens at minimum distance from condenser lens, to increase the collection efficiency.
I have also tried to put a Short focal length plano convex Macro lens in front of condenser lens but It increases the distortions.
The question is how can I increase the collection efficiency of the system, by adding some additional optics without compromising with sharp focusing. If someone can suggest any other technique or any other lens arrangement or any other product which has large focusing lens that would be really helpful.
There are loads of lens combinations available in the market but I do not have clue how to select the right product.
I am searching for the answer from quite some time. Please help. This may not be a basic physics problem but related with experimental aspects.
One of the side queries is how can I estimate the effective collection efficiency of this lens (either experimentally or theoretically).