# How to choose the right lens for projecting a certain area to a fiber optic

I am looking for a lens to magnify a certain area so that it can be captured by a fiber optic. Specifically, I want the fiber optic to capture a certain object, which requires it to be at a distance 6cm from the object. The minimum distance from the object I am able to place it is 13cm away which means that the fiber will be capturing other objects alongside the one required. I guess, in order to capture just the intended object, I need to magnify the object first with a lens and then insert it in the fiber optic. How can it be done? hat kind of lens should I use? Below is a schematic diagram of the setup. If my question can't be answered directly could you at least guide me through some bibliography? (textbooks, terminology to look for).

• When you say captured by a fiber optic, do you mean just the light from the object, or an image of the object? If you mean an image, you should be aware you will need what is called a coherent fiber bundle. A coherent fiber bundle relays an image on it's front face to it's output plane. In contrast, a single fiber relays the light, but does not maintain a coherent image. Also, how big is the object and how big is the fiber? This is needed to find the lens that will do the imaging.
– JB2
Commented May 22, 2022 at 22:39

You can image the object on to the fiber facet by using the simple imaging relationship $$\frac{1}{f_{lens}}=\frac{1}{d_{object}}+\frac{1}{d_{image}}$$ along with $$Magnification = \frac{image\ size}{object\ size} = \frac{d_{image}}{d_{object}}$$ where $$d_{object}$$ is the object distance from the lens and $$d_{image}$$ is the image distance from the lens. Of course, this is assuming a 2D object and a 2D image. Depending on the depth of focus of your beam (which would depend on factors such as wavelength, beam size, beam spatial shape e.g. Gaussian, etc.), you will be capturing not only the 2D plane defined by the $$d_{object}$$ but some $$d_{object}\pm\Delta d$$. Of course these imaging formulas are assuming paraxial approximation is valid and the lens is a thin one. For most cases, these are okay assumptions to make. Some practical suggestions:
• The image size should match the core size of your fiber (assuming the core is what you are trying to couple the light into). I would just assume image size to be the same size as the core. The object size is also fixed since there is a real object to image. This means the magnification is fixed as well. If you also fix the distance between the object and the fiber ($$d_{object}+d_{image}$$=6 cm? based on the question) one can solve the equations above for fixed magnification and fixed $$d_{object}+d_{image}$$ and come up with specific $$d_{object}$$ and $$d_{image}$$ values based on your lens.
• You should select your lens such that the acceptance angle (or in extension the numerical aperture NA $$= n\ sin (\theta_{acc})$$) matches that of your fiber's. For most cases where I am trying to couple maximum amount of structured light (i/e/ light does not have the simple Gaussian spatial profile) into multimode fibers I use an 8 mm aspherical lens of 0.5 NA from Thorlabs. This may be an overkill though, picking a lens of the same or larger NA as the fiber is sufficient.