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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
Chapters
Summary January 28th, 2019
We show how to encode the complex field of laser beams by using a single phase element. A common-path interferometer is employed to mix the phase information displayed into a phase-only spatial light modulator to finally retrieve the desired complex field pattern at the output of an optical imaging system.
Transcript
This protocol can be useful to perform beam shaping or spatial echo HALO laser beam by using just a defractic optical element and call it into the phase-only spatial eye modulate. The technique that's created it this protocol gives you a simple but high echo densital, able to spatially modify and micro minusculely, both have better than phase of laser beams, simultaneously. Encode the complex field using a spatial light modulator and computer.
Find the light modulator spatial resolution from its technical specifications. Next, move to a computer to define the amplitude and phase patterns. Define the desired amplitude pattern as a digital image in gray level format, with values ranging from 0 to 255.
For the desired phase pattern, define it in gray level format with values ranging from negative pi over two to pi over two. With the phase and amplitude defined, computer generate these two different phase patterns, using equations two and three. Note that A max is set to two.
Also define two, two dimensional binary gradings with spatial resolution equal to the spatial light modulator display. These appear as checkerboard patterns, shifted by one square vertically or horizontally so that when superposed they produce a uniform pattern with height one. To help reduce the effect of pixel crosstalk, generate other pairs of checkerboard patterns for the binary phase gradings with different pixel cells having an increased number of pixels.
The total number of pixels should be the same and equal to the spatial resolution of the spatial light modulator. To construct a single phase element, pair each binary grading with a different phase term. Then spatially multiplex each pair and add the results.
This is the phase element for the previously defined phases and gradings with pixel cell size one. Note that changing the pixel cell size does effect the spatial resolution of the final single phase element. This schematic provides an overview of the initial setup for the experiment.
Place a spatial light modulator to have its programmable surface face a CCD camera. Have a collimated linear polarized, spatially coherent laser beam go to a beam splitter that redirects the beam to the spatial light modulator. Light from the spatial light modulator passes through the beam splitter into a 44F optical image system.
Place the CCD at the output plane of the imaging system. This is the setup as it appears on the bench. The laser beam passes through a beam expander to adjust its size.
Two mirrors direct the output beam to the beam splitter. Here is the beam splitter in front of the spatial light modulator. Two lenses focus light from the spatial light modulator onto a CCD camera.
When setting up the optical system, send the computer generated phase pattern with the lowest pixel cell to the light modulator. Image the phase pattern with the CCD camera placed at several different positions along the optical axis. Identify the output plane by as the position with the best resolution.
Secure the camera at the position associated with the best resolution. Next place a circular iris at the focal plane of the first lens in the optical path, centered with the laser beam. Again, use the CCD camera to image the phase pattern from the spatial light modulator while varying the iris aperture.
Adjust the iris aperture to the position that has the best spatial resolution. Next, perform similar steps in order to minimize crosstalk. Experiment with different pixel cell sizes in the phase element on the spatial light modulator.
For each, select the aperture size that gives the highest resolution image on the CCD camera. To minimize crosstalk, choose the pixel cell size and iris aperture that allows the highest spatial resolution. For measurements use the polarization-based phase shifting technique.
Place an optical polarizer just before the spatial light modulator. Image the phase element on the camera, and set the polarizer's rotation angle, by visualizing search for the angles corresponding to the sharpest and most blurred images in the CCD camera. Fix the polarizer between the two angles.
Next, place the second polarizer after the back plane of the imagining system before the camera. Set its rotation angle by searching for the angles corresponding to the sharpest and most blurred images in the CCD camera. Fix the polarizer angle between these two angles.
Now, record interferograms while maintaining the camera at the output plane. At a matrix of zero radians to the phase element and send it to the spatial light modulator. Record the corresponding image with the CCD.
For the second interferogram, add a matrix of pi over two radians to the phase element and send it to the spatial light modulator. Record its image with the CCD camera. Add a matrix of pi radians to the phase element and send it to the spatial light modulator to record its interferogram with the CCD camera.
Finally, add a matrix of three pi over two radians to the phase element. Use it in the spatial light modulator to record the fourth interferogram with the camera. Once the interferograms are recorded, transfer the data to a computer.
Here, each of the interferograms is labeled by the order in which was recorded. From the one involving the zero matrix to the three pi over two matrix. This is the retrieved amplitude of the complex field.
To find it, implement this expression, which makes use of the interferogram data. To retrieve the phase of the complex field, implement the remaining code to evaluate this expression with the interferogram data. This image defines the amplitude of the complex field for an experiment.
This image defines its phase. The phase shifting technique requires measuring interferograms using phases shifted by zero, pi over two, pi, and three pi over two radians. These interferograms allow the retrieval of both the amplitude and the phase of the complex field using straightforward algorithms.
I recommend you to go step-by-step. Start with the simple amplitude and phase pattern, and pay attention to our protocol details, including complementary tasks, like the salient coloration. Please note that the iris side depend on the selective piece itself.
However increasing too much the pixel cell can significantly reduce the spatial resolution of the retrieved complex field. This single method in orders to get the particular application, but it can be Westbury used for any reshaping purposes, to enhance, for instance, micro processing move materials or Norlina microscopy.
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