# How to produce a loss-free combination of two "identical" beams?

This is for anyone with experience in optics/imaging/photography as well as anyone who likes to puzzle over tricky physics problems.

As the title suggests, this is about combining two (for all practical purposes) identical light beams in an optical system to one beam of twice the intensity. Mind you, I'm not talking about monochromatic laser beams, although the underlying problem would be the same. As an example, imagine a fancy imaging system that you've constructed and with which you look at objects, which are fairly dim. Therefore, you'd like to enhance the image quality by collecting as much light as possible coming from that source by using not one, but multiple copies of your fancy device. You then project the beams from those device onto, let's say, a single CCD chip and thereby end up with a higher signal-to-noise ratio. You only have one camera available, so just buying a few extra cams and superposing the images on your PC is NOT an option.

Now, the crux of this problem is: How does one combine multiple identical beams into one, while keeping the intensity loss (that one can certainly expect) to a minimum?

In general, there seems to be two basic approaches to tackle this problem:

1. Don't bother with beam combining, instead, project the beams from different angles onto the CCD and somehow deal with the varying distortion/defocussing of the resulting images caused by the different angles of incident.

2. Try to combine the beams into one. You then won't have to deal with the troubles arising from different angles as in the first strategy.

Intuitively, I prefer option 2, but after pondering on it for a week, I found the problem of combining identical beams surprisingly non-trivial.

Maybe anyone of you guys here has had to deal with a similar problem or maybe you just happen to have a really nice idea how to solve it. Let me know what you think, I will also try to explain some of the (flawed) ideas I had a bit later!

• The time-reversibility of optics makes option 2 difficult. The obvious way to combine to beams is to send them into the same beam splitter, but that way you lose as much of each beam as you keep of the other. No win, and this is because of the time reversal symmetry of Maxwell's equations. Dec 26, 2013 at 19:20

## 2 Answers

If you merely want a sum of the input intensities and the final polarization of the output beam is not an issue, then you could use a 2-port polarization splitter/combiner (PBS/C) cube. This may suffice for example when the CCD chip is polarization insensitive.

Assuming the spatially-separated but identical beams posses horizontal polarization (H beam), you would need a half wave plate (HWP) to turn one of them into vertical polarization (V beam) and then combine each of them on the PBS/C cube. I guess this could be achieved with <5% total loss for each of the two beams. Good quality components with anti-reflection coatings etc. could probably result in even smaller losses (<1%).

Using a PBS/C + waveplate can be an elegant solution in many situations, but unfortunately, the beams considered here are randomly polarized (we're dealing with incoherent sources such as stars or fluorescent molecules).

Time-reversibility: Had the same thought! No matter how elaborate the setup, one always seems to end up with a severe trade-off between the transmittance and the efficiency of combination.

If one decided to go for option 1, the challenge would be to minimize the difference angle between the incident beams, while keeping optical path length to a minimum (e.g. the distance between the tube lens and CCD should not exceed a few tens of centimeters). Only...how??