A plano-convex lens is supposed to make the light rays parallel along the optical axis of the lens. Does it ensure that the collimated beam falling on a surface gets uniformly illuminated?
I think the answer should be no.
This only works if you have a true point source that emits constant intensity in all directions and if there are no spherical abberations. In practice you will have a light source with finite dimensions and you will create an image of this source somewhere. This gives structure in the illumination.
You could avoid this by passing the light through pinholes etc. to create a better point source at the expense of intensity. If you want to have a large beam or a lot of light in the illumination you need to worry about spherical surfaces and lens errors.
This is a well-known problem in microscopy with a solution called Koehler illumination: http://zeiss-campus.magnet.fsu.edu/articles/basics/kohler.html
A related problem occurs in machine vision when you need to determine the size of an object. This is solved by using telecentric lenses. http://www.opto-engineering.com/resources/telecentric-lenses-tutorial
In both cases the solutions to creating a uniform illumination involves a multi-element lens system, so my answer would still be a 'no'.
Note that acceptable results can be achieved if you relax the requirements on how uniform the illumination should be and how much of the light should reach the object/sample. The way to do this is to combine a single lens and a couple of diaphragms. I would place the lens a focal distance away from the source and use a diaphragm at the position of the lens and a second one exactly one focal distance behind the lens.
I agree with Michiel.
Your lense can only convert a perfect spherical wave in a perfect plane wave. Pinholes filtering will give you the spherical wave but at the expense of intensity. Koehler integrators are a good solution to overcome this problem for many kind of sources.
An other option is the use of homogenization rods. The idea is to homogenize your source by multiple reflections inside the rod. You can then image the exit facet of the rod on the surface you want to be uniformly illuminated.
The focal length of your imaging lens and the size of the exit facet of the rod will give you the illumination field.
Sibasish, I agree with Dood and Poyet's commnets. I tested how small the light source should be to obtain substantially flat filed after actual plano convex lens. Test example is the focal lens of plano convex lens 50mm, radius of the stop aperture 6.25mm (F/4), and half size of light source 0.05mm. Please see ppt file attached, where 30,000 rays Monte Carlo simulation results is shown to demonstrate substantially falt field after the lens at z=1000mm, as predicted by Bob Boyd's serachlight analysis. Shigeo
what michiel said is correct - notice that you *can* achieve a mostly uniform illumination at the expense of power - if you have the system out of collimation.
arie
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