# 0.2 Projector setup and issues  (Page 2/2)

In addition to difficulties with the light source and focusing lens, we also had trouble with speeding up image acquisition time. We originally were sending frames to the projector from a standard MATLAB script. This was very slow. Using the Psychtoolbox plugin allowed us to take advantage of frame buffering . This sped up the rate to between 15 and 50 frames per second (fps). The frames shown in the video below change at a rate in this range.

To further decrease capture time we tried exploring tighter control of the projector's image display capabilities.Although the video frame rate is 60 Hz, which is the maximum rate at which the projector can receive images, the mirrors on theprojector's digital micromirror array (DMD) flip at a rate of at least 1000 Hz. Possibly, the mirror flip rate may even be asfast as 9800 Hz . So, we wanted to use every mirror flip as a random frame for our CS measurements,rather than just using each video frame to take one measurement. The result would be such that for each video frame, we would obtain between 16 and 164 measurements. Ultimately, if for a 1-megapixel image we required 100,000 frames, then this could give an image capture time of 10 to 50 seconds.

In order to exploit each individual mirror flip, we needed to understand pulse width modulation (PWM). This is the scheme thatthe projector uses to determine mirror flipping. Under normal operation conditions, PWM is used to simulate grayscale values ofimage frames. For example, consider the image in the figure below. In this image, the grayscale of the right half is true while the grayscale of the left half is anillusion: the left half in fact contains only black and white dots, no grey. A projector creates the grayscale illusion in asimilar manner. By rapidly toggling its mirrors between "on" to "off" positions, it tricks the eye into perceiving a seriesof black and white squares as grey. The "on"/"off" pattern is determined according to PWM.

Our investigation of PWM schemes led us to understand thatbasic PWM works as illustrated in the example of the figure below. First, the time allotted for a video frame (1/60th of a second) is divided into blocks. There is one blockfor each bit of a pixel's grayscale value. If grayscale values can range between 0 and 31, then 6 blocks are created. For thelength of each block, the mirror will either be turned to its "on" position if the bit associated with the block is a 1, orits "off" position if the bit associated with the block is a 0. This is an acceptable method for creating a grayscale effectusing only black and white projections. However, the long duration of blocks associated with higher-order bits can produceeffects that are jarring to the eye.

A smoother version of PWM is used in most projectors, to reduce the jarring effects seen with basic PWM . The methodology of smooth PWM is illustrated in the example below. This modulation scheme devotes the same amountof time to each bit as basic PWM. However, instead of laying the blocks for each bit end-to-end, it breaks them up into smallerpackets and mixes them up. Each block from basic PWM becomes a series of blocks in smooth PWM. These smaller blocks are spreadout over the entire time for a frame, alternating with blocks that represent the other bits of the desired grayscale value.

After completing textbook research of PWM, we attempted to observe PWM patterns in the lab. We sent the projector frames with known grayscale values and captured themirror-flipping with a visible-range photodiode. However, the mirror-flipping patterns we observed with this approach did not resemble anything like what we had expected. They looked something like the plot shown in the figure below. At first we thought the problem must be on the photodiode end. Yet, the specification sheet for the photodiode listed its response time in the nanosecond range. So, we took another look at the documentation of PWM available on TI's website, and emailed some TI representatives to see if they could give us some insight on the problem. From these sources, we learned that the PWM scheme employed by current DLP projectors is very much more complex than that described in the examples of basic and smooth PWM above. Although smooth PWM may be a part of what current projectors use, the actual mirror flipping patterns are determined based on an algorithm that takes into account a large variety of projector settings. We were told that, in fact, TI considers their mirror-flipping algorithms proprietary, as these codes contribute to the projector's image quality.

Due to the multitude of dead ends we ran into trying to create a projector-based version of a compressive sensing NIR camera, we turned to working with a stand-alone DMD board for the last few months of our project.

#### Questions & Answers

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1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
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Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
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Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
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