HowTo: Spatial Light Modulators

About This Tech-Talk

Spatial light modulators (SLMs) are active optical components that can alter a light beam’s amplitude, phase, or polarization. For this tech-talk, I’ll focus on a specific subset: those that achieve this using a pixelated, two-dimensional array. While this doesn’t cover all types of SLMs, it’s a sufficiently large and interesting category to explore. Because this blog focuses on system integrators, I’ll also highlight key considerations if you decide to incorporate an SLM into your system.

Reflective or Tranmissive

To begin with, we have two major sub classes, reflective and transmissive. Most of the industrially interesting SLMs are reflective for the simple reason that high performing devices require a CMOS wafer to distribute the data and the simplest to arrange that is to put a MEMS of a metallic layer directly on top of the wafer. It is possible to arrange an optically transmissive surface that can distribute an electric signal but that implies free electrons and those tend to interact with the transmitted light. The trade-off that this implies typically affects device speed or optical transmission.

That said, you can still find many technically interesting products that use this principle in both consumer applications (such as LCD displays and some LCoS-based projects) and industrial settings.

Reflective Amplitude SLMs

This is a major class of spatial light modulators. Notably, we find the The Texas Instruments DLP in this class. Even if this type of SLMs alter the phase of the reflected light, they are not used as such. Let me explain. The DLP is a purely reflective micro-mirror device where each micro-mirror can have only two stable states altering between plus or minus 12 degrees along its diagonal, although the angle can differ between various types. Each point on the surface of this device alters the phase of the light by introducing an optical path difference, but since these phases are not independent, we can only observer the net effect of a small, tilted mirror.

There are other SLMs operating along the same optical principle, such as the IPMS analog tilt mirror SLM. Since the tilt-mirror devices are overall phase neutral, they rely on the imaging system to express their intended effect. Without it, they just look like a rough reflecting surface. With a properly designed projection system, they turn into high performing pattern generating systems that cannot be distinguished from high-quality binary masks.

The analog tilt-mirror devices are simple to calibrate and simple to use but require an Excimer laser to reach their true potential. There are, however, some properties that a tilted mirror in the image plane brings which are worth to keep in mind. The tilt of an isolated mirror can never hidden by the optical system even if the projection optics is not even close to resolving the micro-mirror. This can sometimes be used to properly set focus, possibly even the most sensitive way to do it without an interferometer or wavefront sensor but probably only useful at lower resolutions.

Fourier theory to the rescue

In order to use a tilt-mirror device of this type for high-end applications, the mirror tilt has to be alternating (as in the figure above). The projection optics will then cancel the phase. Generally speaking, these devices are best understood using Fourier theory.

Here’s an example: A device having flat mirrors has infinite contrast, one just has to tilt the mirrors to the correct angle. The tilted plate (or mirror) has a reflection pattern given by the sinc-function and the zero of that sinc is the correct angle for infinite contrast. What happens when we use partially coherent illumination. Then the SLM is then illuminated with a range of incident angles. Does that mean the contrast is degraded with partially coherent illumination? If we stick with the sinc-picture, we may be led to believe that it is impossible to arrange an optimal tilt angle since we cannot simultaneously adapt the one tilt angle to -range- of incident angles. If we go with the Fourier approach instead, the array illuminated at zero incidence reflects all light along the normal. The effect of the tilt is represented as a set of diffraction modes which are not going to be transmitted through the pupil. For any off-axis plane wave, the reflected light is just a shifted replica of the on-axis pattern. If the first one had infinite contrast (when viewed through the projection optics), so does the replica. The Fourier approach gives the right answer.

Common device defects

MEMS devices are never perfectly flat. When the polished surface they are made on top of is resolved, there is a mechanical release of forces which adds a short-range vertical displacement. This introduces a partially developed speckle and other effects. It sets the limit to image quality when using these devices. Not all manufacturers are forthcoming with a specification regarding these effects. For example, I have not been able to find it for the Ti DLP. However, some limits to this parameter are given by diffraction efficiency. Since the DLP must overlay many images in order to generate a grayscale, partially developed speckle should not contribute significantly to the degradation of image quality when using these devices.

With time, especially when using short wavelengths, the top surface can suffer some annealing and compactification that leads to some curling of the mirrors. For the DLP, this has an insignificant effect on image quality due to the large tilt. For the analogue devices, this is probably the property that sets the usable lifetime of the device. It is visible as a contrast degradation but affects other important imaging properties, like focus sensitivity.

Reflective Phase SLMs

Reflective phase SLMs create a path length difference mostly in two ways. Either by displacing the reflecting surface or by locally changing the refractive index in order to generate a path-length difference. The former would describe spatial light modulators like the RealHolo, the Texas Instruments PLM or Silicon Light Machines PLV. In terms of technical potential, the RealHolo clearly stands out in the MEMS crowd.

Liquid Crystal on Silicon – LCoS

Another popular phase SLM technology is Liquid Crystal on Silicon (LCoS). These micro-displays rely on a fairly complex stack of technologies, including a CMOS backplane, metallic pixel layer, top and bottom alignment layers for the liquid crystal, an Indium Tin Oxide (ITO) layer to generate the electric field across the liquid crystal, and a cover glass to hold the ITO. Despite this complexity, manufacturers can produce LCoS panels in large volumes with high yields and minimal pixel defects.

LCoS panels offer several advantages, including robustness. However, they also have drawbacks, such as polarization dependence. Additionally, the liquid crystal layer’s thickness, determined by the wavelength the SLM is designed for, limits the modulator’s effective resolution. This limitation arises from the nature of electric fields, which tend to diverge as they spread from their source. LCoS panels are essentially densely packed transparent capacitors, and when the lateral size of each capacitor is smaller than the distance between its plates, the electric field spills over into neighboring pixels, creating cross-talk. In the LCoS industry, this phenomenon is known as fringe-field effects. It causes both unwanted polarization effects and disclinations. Before we jump into MEMS SLMs, we have to mention one major advantage which is that you can buy them today from companies like Hamamatsu or Holoeye Photonics.

MEMS Piston Mirror Arrays

Even if the piston-MEMS devices are not as rare as unicorns, you will not easily spot one in the wild. That said, they do exist and if Texas Instruments eventually releases the PLM, they may in fact become quite common. Piston devices are really flexible from the optical point of view. There are no polarization effects to speak of. No wavelength dependence as long as we illuminate with one wavelength at the time. They are fast and the phase is stable. With LCoS, one has to frequently change the polarity of the driving voltage in order to prevent degradation of the liquid crystal. None of that stuff here. 360 degree phase modulation and no cross talk to talk about. Great. Can I have a bunch? There is one problem, which is equally valid for the LCoS panels, how to you decide which phase to set on each illuminated pixel?

Image generation with phase-only devices

Naturally, this is a “solved” problem, and as many of you know, it is solved—or at least solvable—using the Gerchberg-Saxton algorithm or numerous other phase retrieval algorithms. These algorithms are particularly useful in visual applications, where the brain renders the result more palatable. Perhaps this should have been said first of all, and this is true both for LCoS and piston devices, they do not need any optics. Illuminate with a beam, wide enough to cover most of the device, and the diffracted light can be controlled to generate any pattern. The wavelength divided by the pixel size limits its angular extent but if that is enough, we are done. Otherwise, we may use a Galilean telescope to provide the desired magnification.

For lithography, where image quality is everything, we have to control the reflected phase of the light. If we fail to do that over a long range, our objects move through focus. Failure to do that over a short range also adds speckle to our objects which, in addition, increase with the aberrations of our projection optics.

There is, however, one more thing to consider. How will we decide the phase to set for each pixel? Phase retrieval methods are iterative and, to my knowledge, return a random projected phase. The direct methods that I know use neural networks but I have not seen what image quality we can expect of them. I would expect that the neural network approach will at best reproduce the results of the phase-retrieval methods used to train it. Consequently, I would expect those methods to generate a random phase.

Some theory fundamentals

On the topic of generating high quality patterns with phase-only modulators, we must at least identify two cases, one which is the linear mapping case, and the other, a non-linear mapping. The linear mapping case corresponds to the linear mapping between modulator and image amplitude of coherent imaging, while the non-linear case applies to partially coherent imaging.

For coherent imaging, we know that the image amplitude is a linear “function” of the reflected amplitude,

And when P represents a discrete device, we can turn the integral to a sum by integrating over the “pixels”,

There are details to this that I think we can skip for the moment. However, we know that one way or another, we can inverse this relation,

Practically speaking, the inverse of H is probably a pseudo-inverse and so on. This is not the point. However, even for the simple case where the impulse response H is real (meaning zero imaginary part), and the amplitude we are looking to solve for is also real, the solution (p) is then real. Not exactly a great solution for a piston device.

So, then we need a way to transform a real vector p (having NxM elements, where NxM is the size of our SLM) into a vector,

where the vector h has the same size as p. We want the heights, h, to have the property that,

meaning, that we want the imaginary part of the mapping to be cancelled by the optical system. Now, it’s not my point to turn this blog into a math paper, but a well-designed image system intended for gray-scaling will leave a fair amount of room for solutions h that closely match the images generated by the mapping Hp.

There’s, obviously, more breadcrumbs than meat here, but driving a piston modulator is a big topic and this blog is about what you need to think of in case you decide to incorporate an SLM in your system so we leave that topic for another blog post.

When the Sky is Not the Limit SLM

The piston modulator applied to lithography is the ultimate modulator for those who want to push sub-wavelength resolution beyond its otherwise practical limits, but it does come at a cost. Here’s the point. A piston modulator can project any phase and amplitude (in relative terms) but for lithography, we actually do not want any amplitude. We want the image to have a constant phase over the entire image because a phase variation is a variation of feature dimensions or placement through focus, and we absolutely don’t want that. This means that we have to spend time in order to find a solution that constrains that particular degree of freedom of this modulator.

To both have the cake and eat it, Micronic invented a tilt-mirror design which included a quarter wavelength step over one half of the mirror. The result was an image amplitude that could reach a (relative) range of -1 to 1 and zero phase variation. All the good stuff that you needed the piston mirror for without the work. The downside was a reduction in reflectivity of the device, which for an application that included an Excimer laser was not an issue. Strictly speaking, there may be 2D topologies that this modulator cannot deal with in a single image. Nevertheless, ASML decided to use this solution for their direct-write behemoth. Unfortunately, it was never released as a product. To my knowledge, this is the largest SLM designed and fabricated to date. 11 million analogue-tilt 8 micron mirrors and 6 kHz image repetition rate. You can find a nice image SEM image of it here.

Want to Know More

If you want to know more, feel free to contact me through the contact page or simply drop and email to [email protected]. I like talking SLMs. You can also leave a comment right here.