Experimental setup

Generally speaking there are two possibilities one can consider for the setup: either one uses lenses or not. A lensless setup is interesting because of its simplicity but it is also limited in the sense that the size of the resulting interference patterns is only influenced by the size of the mask that is set on the SLM. Hence one might end up using only a small part of the SLM depending on the reproduction size of the amplitude pattern (photo sensors for example can be small compared to the size of the SLM). When using lenses one can on the other hand scale the pattern to an appropriate size (e.g. the size of the photo sensor) but this comes at the cost of a more complex setup.

For the above reasons we decided to use a setup involving lenses but we also provide code that allows to use a lensless setup. The setup is shown schematically in the figure below.

Final setup

Before going into the incremental steps that lead to the final setup we just want to present the final version.

And here a picture taking of it in the lab.

Focusing the optical system with the two lenses exactly on the photo sensor is a bit tricky. By experience it is easiest to fix the convex lens and then moving the concave lens and the camera in such a way that both scaling and focus are good. Additionally, one can compute the exact focus plane of the lenses once you found a configuration which is close to the scaling you are looking for. Consider the following diagram.

Hence, one can derive a formula for \(b\).

\[\begin{split}\begin{align} \frac{1}{-30}=\frac{1}{b}-\frac{1}{a} &\iff \frac{1}{b}=\frac{1}{a}-\frac{1}{30} \\ &\iff b=\left(\frac{1}{a}-\frac{1}{30}\right)^{-1} \\ &\iff b=\left(\frac{1}{200-c}-\frac{1}{30}\right)^{-1} \\ \end{align}\end{split}\]

with \(a=200-c\) and \(170 < c < 200\).

Measurements

Note that only the distances between the SLM, both lenses and the photo sensor do actually matter. Here rough measurements of the important distances are given.

• SLM to convex lens: 2.5cm

• Convex lens to concave lens (\(c\)): 18cm

• Concave lens to photo sensor (\(b\)): 7cm

Partial coverage of the SLM with the laser beam

Another element which is important to account for is the portion of the SLM that is actually hit by the laser beam. Ideally, the laser beam would cover the entire SLM and hence all the pixels could be effectively used. But as in our case the circular laser beam does only hit pixels in a circle of radius 1cm around the center of the SLM. This setup actually “disables” the pixels which are not hit by the laser beam for any phase retrieval algorithm. Alternatively one could enlarge the laser beam (which requires some optical gear). To keep the optics simple we decided to reflect our setup with only partial coverage of the SLM. This behavior can be changed at any point by changing the amp_mask variable in the mask_designer/experimental_setup.py script.

For illustrative purposes, here an image of the part of the SLM that is hit by laser.

Practical considerations

Now, some important details that can improve that quality of the setup. First, the Holoeye SLM has a preferred orientation.

Additionally, both the lenses we used in our setup have one planar side. Those should both face each other, i.e the curved side of the convex lens should face the SLM and the curved side of the concave lens should face the camera.

Incremental development of final setup

In this next section, we are going to walk through the different experimental setups we tested to finally converge to the final setup. As a general rule we found it to be way easier to use a camera with an exposed photo sensor i.e. with no optics at all. Otherwise perfect alignment was tricky to achieve and all the inconveniences of a bare bone senor could be resolved fairly easily. But you can also use a simply screen instead of camera to avoid those complications.

Version 1

This setup was the simplest setup that was proposed in the OptiXplorer manual that came with the Holoeye SLM. It’s a starting point and conceived to built upon. Note that both lenses and the SLM generally have a preferred orientation. Additionally, for best results the laser beam should be collimated (all it’s rays should be parallel). The camera should be placed at the focal distance of the convex lens.

Version 2

In the same manual it is suggested to place the SLM after the lens because this does not affect the resulting interference pattern but the relative position of the SLM in between the lens and the camera changes the scale of that pattern. Hence, by moving the the SLM closer to the camera the image size is reduced and makes it easy to scale the size of the interference pattern to perfectly match the photo sensor of the camera.

Version 3

Again, suggested by the manual, a polarizer (\(-45°\)) and an analyzer (\(15°\)) are added to the very front and the very back of the optical pipeline respectively. Those are the required settings according to Holoeye for the SLM to perform optimally as a phase SLM.

Version 4

A second lens, this time a concave one, is added to the optical setup which allows to change the scaling of the interference pattern. The relative position of the to lenses determines the scale (and the position of the SLM).

This setup was the final version suggested by Holoeye but we experienced several issues and problems with it. Firstly, having the SLM after the first lens creates a situation where the laser beam that enters the SLM actually is no longer collimated which goes against what was suggested earlier. Visually it seems to make not a big difference as the convex lens has a rather big focal distance the beam is still close to being collimated. Nonetheless, it is cleaner to put the SLM in front of any lens and handle the scaling of the interference pattern differently. And adding the concave lens gave us another way of manipulating the scale. Secondly, we experienced oversaturation of the photo sensor even with the shortest exposure times possible with Thorlabs software (ThorCam) that natively comes with the camera. A handy way of controlling the amount of light, i.e. its intensity, is to use two polarizers back to back and turning them relative to each other such that just the right amount of light passes through them. Instead of adding a third polarizer we simply moved the analyzer in between the polarizer and the SLM. The removal of the analyzer did not visually degrade the results. But it would be cleaner to follow Holoeye suggestions here.

Version 5

For simplicity, we first only used one lens to test if our changes to the setup where a step in the right direction. And indeed they where. Note that in order to stay as close to Holoeye’s setup the input polarization of the light hitting the SLM was not changed. We no longer had any issues with the light intensity as the back to back polarizers provide an efficient way of controlling the light intensity parameter. But, as expected, the resulting pattern was pretty small and hence we needed to address the scaling issue.

Version 6

Adding the concave lens back into the setup solved the scaling issue.

Final setup

As mentioned earlier, removing the analyzer and using it in the back to back polarizer pair didn’t harm the visual results but still is not what was suggested by Holoeye. Hence, either we should use 3 polarizers or find another solutions. Luckily, testing other software that allows to control the camera (IDS Peak) enabled even lower exposure times. So low that the intensity of the laser beam did not oversaturate the photo sensor, even without the back to back polarizer pair anymore. Hence, we could use the two polarizers as intended by Holoeye, leading to the final setup.