What you have and what you want to have
During my experience in laser labs I encountered many different approaches of how to align a delay stage. Therefore I would like to explain how it is done easily and as accurate as possible. Not all stages have the necessary precision within their path to be used as optical delay stages. Long stages are not more difficult to align than short stages but they are more likely to be not accurate.
Figure 1: The stage as you would like to have it (left) and how you will initially find it (right)
Lets say you set up your stage on the optical table, put two mirrors (the blue rectangles in figure 1) on it and now you find yourself in a situation similar to figure 1 (right picture). Furthermore you don't now exactly how the beams propagate with respect to your stage but at least you know that its not like figure 1 (left picture) because when you move your stage the outgoing beam moves. So lets start figuring this out.
Step 1 - clarify the incoming beam
First of all don't worry too much about the stage orientation on the table. It helps if its roughly aligned with some edge or line of threaded holes (assuming you have an optical table). The alignment of the stage on the table does not matter as long as the beams will be aligned with respect to the driving axis of the stage.
To clarify the incoming beam with respect to that driving axis put a paper (orange in fig. 2 ) in front of the mirror on the incoming-beam side of the stage as shown in figure 2.
Figure 2: Stage at different positions with paper in front of the mirror to be able to see the beam
As you move the stage back and forth you will see that the beam moves on the paper left/right or up/down or both. For this process its good to have a stage that can be moved by hand back and forth the full travel distance. Doing this via a slow software is tedious but still possible. For me being able to move the stage by hand is one important criterion when buying a stage.
The paper in front of the mirror is just to see the beam because the mirror itself is the worst thing to see a beam on. Instead of a paper you can also use a camera, beam profiler or some other fancy device. I prefer the paper to keep things simple and trust me you will most likely be accurate enough with your eyes and the paper card. Furthermore if you do the alignemt procedure for the first time its highly recommended to use a paper not to confuse yourself with complicated technology.
So what do you see ? Have a look in figure 3 on the spots on the paper card for situation b) - stage in the front and situation c) - stage in the back.
Figure 3: Spots on the paper card for stage in front (b) and stage in the back (c)
In figure 3 b) you see the spot on the top right. When you move the stage further away from the incoming beam you see the beam moving down and left. In your case it might go in a different direction depending on your situation on the table.
Now concentrate because its easy to fool yourself in the lab. Just focus on the left-right movement of the beam first. By seeing the left right movement like in figure 3 you can in your mind reconstruct figure 2. You will find that you have to use the last mirror in front of the delay stage to tilt the beam to the right. This you can conclude only by looking at the spots on the paper card (figure 3) and knowing that b) is in front and c) is in the back.
The same reasoning has to be done with the up/down movement. The beam has to be moved up. The result of the tilt of the mirror in front of the stage can be seen in figure 4.
Figure 4: Aligned incoming beam
Some things have to be said here. Don't take the position of the beam drawn in figure 4 on the paper too serious. It does not mean that you should be one beam diameter outside the dotted circle. You have to find the position yourself. When you move the stage back and forth and the position of the beam on the paper does not change anymore, you found the correct position. This has to be done as perfect as possible !!!
Congratulation if you found that spot. This means your incoming beam is aligned to the driving axis of your stage. It does not necessarily mean that you hit the mirror behind the paper card as you can see in figure 4. There you would hit the corner of the mirror.
Instead of using the mirror in front of the stage you could have achieved that alignment by tilting the (driving axis of the) delay stage. By tilting the stage you can compensate for the left right but up/down is not possible. Therefore the mirror in front of the stage is usually the knob to turn.
You should not be too sloppy to center the beam on the mirror on the delay stage correctly. There are 3 ways to do this now (looking at figure 4):
- Move the mirror in front of the delay stage to the left by approx. half a mirror diameter (and do the process again!)
- Move the complete delay stage by half a mirror diameter to the right (and do the process again!)
- Move the first mirror on the stage to the right.
As you see option 3. has no "do the process again!" comment. So in this tutorial we go for this option although it might be inappropriate in the lab depending on the mirror position on the stage. Don't have mirrors hanging over the edge of your stage platform because you are lazy. The reduced stability will hurt you later in your experiments. For this tutorial its ok.
Step 2 - on the stage
Figure 5: Beams on the stage
As the incoming beam is aligned and hits the first mirror on the stage always at the same position (and hopefully in the center) all the other alignments on the stage don't matter. It could be that you are using dielectric mirrors that need a certain angle of incidence of 45 degrees or there is another reason for making things perfect on the stage but in terms of alignment of the stage itself these issues do not matter.
Because you hit the first mirror always at the same position you will hit the second mirror always at the same position independent of the stage platform being in the front or in the back. You might ask yourself why I am stressing that but believe my that I had several discussions about how to precisely align the mirrors on the stage and in the end makes no difference what you do on the stage platform
Step 3 - leaving the stage
Finally you want to align the last mirror on the stage such that the outgoing beam matches the driving axis of the stage. When you will be done with that it will automatically be parallel to the incoming beam.
To achieve that you place the paper card on the outgoing side of the stage (see figure 5). You might ask how far away from the stage you should place the card. I tell you that it does not matter. Let me illustrate what happens when you (figure 6).
Figure 6: Beams leaving the stage
The incoming beam is aligned therefore all the movements of the spot on the papercard result from the misalignment of the last mirror on the stage. In our case (figure 6) the beam moves from left to right while moving the stage closer to the card. Imagine that it does not matter how far away the paper card is from the stage because the beam will perform a parallel shift when you move the stage platform back and forth.
To align the outgoing beam you have to tilt the beam more in the direction where moves when you put the stage platform closer to the card. To tilt the beam you use only the last mirror on the stage. The result is seen in figure 7.
Figure 7: Perfectly aligned stage
As seen in figure 7 you would have to move the paper card while aligning the beam, otherwise it would miss the card but that should be clear. You found the perfectly aligned outgoing beam if the beam on the card does not move anymore when you move the stage back and forth. This also means that the stage is aligned perfectly. I have to stress here again that this only works if you have a perfectly aligned incoming beam. All of this does not ensure that your stage and beams are aligned with the table itself, meaning that the beam is parallel to the threaded holes etc. This is usually not so important.
I wish you success with the alignment of your optical delay stage. If anything is unclear or you find this text helpful, leave a comment.