Final Project Proposal Williams
Contents
Spatial Light Modulators Galore
Left and right pictures were taken from Spatial Light Modulators: Processing Light in Real Time and the center image was found using google images.
Introduction and Theoretical Framework
Spatial Light Modulators (SLMs) are essentially time varying mask. Their primary function is to spatially modulate a readout beam. They can do this electronically (EASLM) or optically(OASLMs). SLM Appliacations. Currently SLMS are being used to implement a variety of optical tasks from wavefront correction, optical correlation and filtering, to phase contrasts by modulating either the illuminating beam or the imagining beam.
EASLM are also known as Programmable spatial light modulators (PSLMs) and are two-dimensional electrically addressable devices that function as reusable transparencies on which spatially varying amplitude or phase patterns can be written electronically, often with an output signal from a computer1.
EASLMs are made from LC films which rotate when an electric field is applied. The rotation of the molecules causes a change in the refractive index seen by the incident beam. This is because the refractive index along the optic axis parallel to the long axis of the liquid crystal is significantly different from the index along a perpendicular short axis. The difference, also known as the birefringence, allows for the modulation of the phase of incoming light. With an appropriate choice of the rotation of the liquid crystal axis or the thickness of the material ,and the polarization of the readout light, the polarization of the light may be rotated and its phase modulated. Polarization rotation can be converted to intensity modulation by filtering through a polarizer.
The most powerful tool of the SLM is its ability to utilize the Fourier properties of light. Generally to utilize the Fourier Properties of a lens you need a coherent output. However, most imaging systems are incoherent. SLM allows you to perform powerful imaging techniques based on the Fourier transform without disrupting the coherence of your incident light. [1]
OASLM are optically activated and thus an optical signal is sent to the photo-detector which detects the “incoherent” light as an electrical distribution. This electrical distribution is applied to the LC crystals and causes them to rotate which leads to effects similar to those seen in the EASLMs. OASLM, although they have poorer resolution that SLM, can be used for optical correlation and filtering.[2]
Statement of Interest & Objectives
Explore the abilities of LC-SLM and OASLM. In exploration, to use applications of these microelectronic systems to improve mini-projects already in 20.345. A part of my final goal is to characterize a holographically generated Bessel beam and then use these beam and another holographically generated phase plate to improve the resolution on a fluorescent microscope and then to compare the performance of a images generated using PSF and deconvolution and the Bessel beam with axicon phase plate.
Literature Review
SLMs for phase mask and hologram generation
Analog multiplication of the complex amplitude of an optical wavefront by the complex reflectivity or transmissivityof the propagation medium is a fundamental property of electromagnetic waves. For example, a uniform plane wave passing through film will have it s amplitude spatially multiplied by the transmissivity of the film.SLMs offer a way of rapidly changing the reflectivity or transmissivity of a medium, thereby replacing the cumbersome mechanical action of advancing the film with an optically or electrically controlled framing rate that could well reach into the multi-kilohertz range. [3]
Optical Filtering and Spiral Phase Plate Mask
As a rule, if an object is illuminated with a spatially coherent light source, any imaging arrangement which – if one removed the sample – would produce a focus of the illumination light in a certain plane also performs a Fourier transform of the sample’s complex amplitude transmission function in this particular plane, except for a possible offset phase term. In this plane the spatial Fourier components which compose the amplitude image of the sample are separated and can thus be accessed individually.In particular, such a Fourier plane appears in the back focal plane of an infinity-corrected microscope objective if the sample is illuminated with a plane wave. There the Fourier components are arranged around the focused spot of the illumination light, which corresponds to the spatial carrier wave (namely the zeroth-order Fourier component, sometimes called the ‘DC component’) of the image and can be individually modulated with a filter mask. Some well-known contrast techniques, such as phase contrast, are based on the manipulation of the zeroth-order Fourier component. If it is just blocked, then the image details appear as highly contrasted bright structures against a dark background, a method which is called dark field microscopy. On the other hand, if the phase of the zeroth-order Fourier component is shifted (typically by ($ \frac{\pi}{2} $) with respect to the remaining wave, then this converts phase-contrasted into intensity-contrasted images, a method known as (central) phase contrast microscopy. [4].
Diffraction - free propagation
Durnin et al. [5] have shown that an optical beam with a Bessel function electric - field profile can propagate without diffraction. This diffraction free behavior can be created by illuminating an annular right or passing a beam through a axicon which is just a conical prism. The axicon and hologram are both equivalent to a transmission function4 of the form:
$ T(r) = exp^{i\phi(r)} = exp^{-2\pi r/r_{0}} $
This phase function creates a beam with an approximate Bessel function profile whose width stays constant over a distance of L = $ Dr_{0} /2λ $.
Proposed Project
- Spatial Light Modulation
- SLM Characteristics,Properties & Holography
- Calibration, pixels, crystals, diffraction to gray scale imaging
- Learn about algorithms for holography + set up weekly meetings with someone who can explain concepts I get stuck on
- Write script for simple lens
- Test script for simple lens and then perform mini experiment using a modified version of Young's double split experiment.
- Optical Filtering: Spiral Phase Plate Contrast & Edge Detection
- Write phase mask needed to create a spiral phase for isotropic edge detection
- Write script needed to create a spiral phase mask for relief detection
- Bright field imaging of red blood cells using spiral plate phase mask ( created by writing a hologram image onto the SLM)
- Measure lose of resolution due imaging with a spiral phase plate mask
- Bessel Beam and Optical Micromanipulation
- Write hologram script to create a Bessel beam from a Gaussian beam
- Measure the optical properties of the Bessel Beam with CCD
- Beam waist width
- Intensity Profile
- Attempt increase resolution for fluorescent microscopes
- Use Bessel beam passing through holographic "axicon"
- Compare PSF generated for 'normal' fluorescent microscope set up and 'bessel beam with axicon' fluorescent microscope set up
- Other Experiments if time permits
Design Methods and Procedures
As of today undetermined. The optical trap for the Bessel Beam configuration will probably be built in a similar fashion to the one outlined in the paper [6]. The fluorescence microscope will probably not be built, but will be a borrowed from someone who built the microscope for Lab 2.
Significance of Study
Proposed Timeline
Please see Timeline