What SLM is suitable for correcting beam profile aberrations?

[Choisai]

Hi there! I have a couple of questions for you guys about Spatial Light Modulators and laser beam profile aberrations.

In the laboratory where I work we have a setup with which we can create a Bose-Einstein condensate and do all kinds of funky stuff with it. We have (as far as we know) the largest condensate in the world (~300 million atoms). This is achieved by using laser cooling of atoms and then trapping them in a Magnetic Optical Trap.

For the imaging of this we use a probe beam that shines on the condensate and thus casts a shadow on the detector behind it. The beam is currently Gaussian in terms of wavefront and we need to get it a top hat wavefront. Aside from that we also want to be able to adjust the beam so that in the future we can use different kinds of imaging.
And then there is the problem of small aberrations: our current setup has many aberrations due to the high amount of mirrors and lenses. In the end we have an unclean Gaussian beam that needs to be a clean top hat beam.

For this we decided to use a Spatial Light Modulator (SLM). Diffractive Optical Elements (DOEs) are unsuitable because they cannot be adjusted. You just put them there, they give you a top hat and that's it. We need something that we can 'play' with and adjust in the future.

So what kind of SLM can I use? I have been looking at primarily Liquid Crystal SLM's and am particulary interested in a Hamamatsu LCOS-SLM (a reflective type of SLM) but the LC type of SLM are said to have lots of static in the 60 Hz - 1 kHz area. Deformable Mirrors (DM) are said to be quite handy but also very expansive. A Thorlabs DM of 15000 euro's is around the maximum of our budget, but what are the limitations of DM? And has anyone experience in wavefront correction of imaging lasers through SLMs?
And what kind of SLM is most suitable for me?

 

[Cthugha]

Could you describe in detail what kind of performance you expect from the device?

First, there are amplitude and phase SLMs. Amplitude SLMs allow you to vary the intensity of the beam locally by changing the polarization locally. Phase SLMs can be used more or less as an adjustable DOE. If you need to focus your beam and have a certain shape at the sample position, phase SLMs have some edge as the focusing lens will perform a Fourier transform of your image. Using a phase SLM you can imprint the Fourier transform of the target image onto the beam and have the lens transform it back.

What spatial resolution do you need? The pixel size on the SLM is the quantity of interest here. Do you need to be able to vary the beam shape with time automatically? If so, on what timescale? What wavelength range will you operate in? How many grey levels do you need? Do you prefer a reflective or a transmissive SLM or is that question irrelevant? Is the total beam power an issue or can you afford to lose some intensity?

I used that guy:http://holoeye.com/spatial-light-modulators/slm-pluto-phase-only/ and it works quite well. Some basic games I played with it can be found here: http://prb.aps.org/abstract/PRB/v85/i15/e155320.

 

[Choisai]

Note that the SLM project itself is now running for two weeks and we have just started researching it. So the questions you ask (as good as they are) cannot all be answered.

The type of performence I expect is this: our 'dirty' laser with a Gaussian beam and several unknown aberrations in the profile of the beam to be turned into a laser beam with uniform intensity distribution over the cross section and all the aberrations filtered out. The Gaussian-flattop conversion is done (to my knowledge) only through phase modulation. But as I already said, due to the large amount of optical components there also many varying amplitude aberrations in the beam.

So we expect to be able to set up an algorithm that can be run every morning to make up for the distortions and whatnot of the entire setup in order to not only create a flattop wavefront, but one that is also 'clean' of any distortions. Perhaps a combination of DOEs and SLM's can be used here.

We use a 589 nm laser that shines upon a Na condensate. It is only a few microwatts and images for a just a few miliseconds. Sometimes longer recordings are made of around 80 ms, but around 60 ms the condensate loses most of it's useful properties and we can't do much with it anymore.

We don't want to vary the beam shape in the sense that while imaging the condensate we vary the beam shape. We want to use one in a feedback loop so we can me up for any aberrations. The pixel size is limited by the pixel size of the camera.

The atoms are imaged using an Apogee AP1E camera with a Kodak KAF-0401E chip camera with a pixel size of 9 X 9μm². At the magnification M = 3.0, the effective camera resolution of 3.0μm per pixel is comparable to the diffraction limit xres = 1.22lambda f1/(2r)= 3.6μm of the imaging lens L1 with radius r = 25mm for probe light with a wavelength lambda = 589 nm.

So we need something with higher resolution than the camera. How large exactly isn't something I can tell you (yet).

There are already several thesis's published on this project, so here is an excerpt of Robert Meppelinks work on the setup. It is about the imaging of the lens, and it explains how we image the condensate:

"The usual way to determine the number of condensed atoms is by taking a
series of absorption images in time-of-flight. Absorption imaging turns out to
become unreliable when the optical density exceeds 4 due to the limited dynamic
range of the CCD camera. If the cloud of atoms is a BEC, the typical optical
density is in the order of 500 when the probe is on-resonance. Imaging the atoms
off-resonance to take advantage of the reduced photon scattering cross section
turns out to be complicated since the cloud behaves as a gradient-index lens in
this regime. The optical density can be lowered by turning off the confinement
causing the atoms to expand during a certain time-of-flight, until the density
is low enough that the optical density is in the order of 4. However, expansion
complicates the interpretation of the measured density profiles, since it consists
of the convoluted momentum and spatial distribution of the atoms and the
expansion of the cloud cannot be described exactly.
Furthermore, the switching of the magnetic confinement complicates the retrieval
of the column density due to the finite time needed to switch the magnetic
fields. In the absence of the magnetic field, the quantization axis of the atoms is
no longer well defined causing the atoms to align along small residual magnetic
fields during time-of-flight. This changes the effective cross section of the atoms
for the applied polarized probe light. The magnitude and direction of the residual
magnetic fields are expected to be spatially dependent. Since the atoms fall
during time-of-flight due to gravity, the effective cross section is also expected to
depend on the time-of-flight duration. Furthermore, the imaging lenses have to
be repositioned for each time-of-flight duration. A final complication is that the
accuracy of detuning of the probe light is limited to 1MHz, corresponding to a
reduction of the absorption up to 4%. All these effects cause uncertainties in the
measured number of atoms up to 20 %."

- Robert Meppelink's thesis 'hydrodynamic excitations in a Bose-Einstein condensate'

Note: the 'time of flight' refers to the condensate being released from the magnetic field that holds it. When it is held together by the magnetical field (via quadrupole) no light will shine through the condensate. That makes measuring rather hard so the condensate is released and immediately light shines on the condensate. That 'releasing' of the atom is several miliseconds long.

Is the total beam power an issue or can we afford to lose some intensity?
Well, we can lose some. As I already said we image the condensate through the shadow it casts on the camera. But if we go lower, the amount of light reaching the camera will be less. So in order to make up for that we then need to release the condensate even longer. But doing that increases the uncertainty in shape of the condensate. So loss of power, if inevitable, should always be minimised. We can allow some loss though, as long as it doesn't exceed around 10%.

 

[Cthugha]

Ok, in that case a phase SLM should do the trick. You may need to write an adaptive algorithm which takes your measured wavefront and iteratively changes the phase mask on the SLM until the measured wavefront looks like you want it to, but that should not be much of a problem.

Things to keep in mind:

Have a look at the available SLM pixel sizes beforehand. I am not sure there are devices with pixels smaller than 8X8 micrometers.

The losses might be a problem, though. You may need to consider the filling factor of the SLM and the diffraction efficiency. Unfortunately the latter depends on your pattern. But getting less than 10% losses is a very optimistic approach. Are you already operating at the maximum intensity of your laser and cannot afford to lose more?

 

[Choisai]

I've been talking to the guys who built the laser setup so I've some new info. The current beam is about 1 cm (for absorption imaging that is) in diameter as it goes into the beam profile. We need to have about 2,5 micrometer per feature of the condensate. In what way can I translate this into needed SLM spatial resolution?

By the way, due to some fiddling with the optical fibers the power is no longer a problem. For absorption imaging we use a laser that is 5 mW and can even be lowered. For the phaseshift imaging we use a 2 mW laser. For both power is no longer an issue. Hamamatsu informed me that all of their SLM's which might even be remotely suited for our setup have damage thresholds of around 1 W up to 5 W. Boulder non-Linear systems has similar numbers (I expect more detailed responses this week) and I have yet to receive a reply from Holoeye.