Beam Splitter ghosting I am trying to build a coaxial microscope with a camera as a college project but am having trouble with the beamsplitter.
My light source is beamed onto a 50/50 beam splitter behind which sits my camera but I cannot seems to eliminate ghosting from the surface of the beamsplitter. I am not getting a usable image and would hugely appreciate some help. 
I have tried placing pinholes in front of my light source to limit beam size but this did not remove the haze. I have also cross polarized my optical system but again, this did not help. 
Any tips would be really appreciated and I hope to hear from someone soon. 

Additional information in response to early answers:
I am currently using a plate beamsplitter set at 45 degrees.
The reason for using this set up is to align my imaging and illumination source.
Most of the reflection I am getting seems to be from the edge of the beamsplitter which is quite small, its only 12.5mm x 12.5m and is 1.1mm thick. The white LED I am using is a 5mm led.
The entire object of this experiment is to have my light source perfectly aligned with my camera to avoid any shadowing on my imaged object.
I have painted the edges with a matte black paint. That helped, to some extent to reduce the reflections.
Unfortunately, I can see the surface of the beam splitter when the light is on. Small specs of dust. I will try to completely clean the surface and see if that helps. 
If you have a better method of achieving this, please feel free to share. 
 A: I assume that you're building an infinity corrected microscope (because I don't see why else you would need a beam splitter)? 
If that is the case, I would immediately assume you're using a cube beam splitter? If so, replace it with a plate beam splitter, which would eliminate the ghosts, because there would be no optical surfaces perpendicular to the optical axis. Take into consideration that a plate will displace your optical axis laterally, so you'll have to compensate for that.
A: If the problem is due to scattering from the edges of your beamsplitter, you may be able to reduce the problem by painting the edges black.  A black enamel paint - like black fingernail paint - should work.
It's also possible that your beamsplitter may have a dirty surface, which could easily cause haze. If you can see anything on the surface when it's illuminated, then it is dirty or damaged.  
Edit 12/27/18: It's very difficult to get a perfectly clean surface on an optical element.  Your best bet is to use a good lens cleaner solution and lens cleaner paper which you can get from a camera store.  You are probably getting multiple internal reflections inside your plate beamsplitter, which might be contributing to your problem. An antireflection coating on the non-silvered side of your beamsplitter plate would help.  
Since your goal is to take a photograph with the light source perfectly aligned with the line of sight, I think your best bet is to use a beamsplitter cube this way:

Although using glossy black paint seems counter-intuitive, it works better than matte black.  Matte black scatters light, while gloss black on the back of a glass surface absorbs light very well.  But clean surfaces are crucial.
A: It might be worth trying to place a pinhole or aperture in front of your beam splitter (rather than just in front of your light source).
That way you should be able to eliminate more of the divergent part of the beam that won't hit your object anyway but will contribute to glare on the camera.
If you have an iris you could play around with different sizes of apertures to optimise for the best result.
As others have mentioned a beam splitter with an AR coating at the wavelength of your LED would reduce any unwanted glare/reflections onto the camera significantly, but that will be more expensive than a BS without AR coating.
Where is your unused beam going, i.e. the one transmitted by the BS? Any light reflected back from whatever surface that beam hits will also be reflected onto your camera by the BS.
A: 
When using a plate beamsplitter for visual optics the secondary beam is always a nuisance and difficult to minimise. The simplest solution for a camera or microscope as well visually observing the image, for example a retinoscope, is to employ cross polarisation.  Painting matte black or using soot surfaces or even felt fabric seldom achieve adequate cancellation.  This is partly due to the residual secondary image being reflected onto the back surface of the beamsplitter and down into camera etc forming veiling glare.
If the opposing piece of polaroid is lain against the back surface of the plate it serves two purposes. The first is to absorb over 90+% of the secondary beam but secondly and equally importantly it reflects the residual stray light forward.
