500 lines
31 KiB
ReStructuredText
500 lines
31 KiB
ReStructuredText
---
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title: "LED Characterization"
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date: 2018-05-02T11:18:38+02:00
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---
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Preface
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-------
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Recently, I have been working on a `small driver`_ for ambient lighting using 12V LED strips like you can get
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inexpensively from China. I wanted to be able to just throw one of these somewhere, stick down some LED tape, hook it up
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to a small transformer and be able to control it through Wifi. When I was writing the firmware, I noticed that when
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fading between different colors, the colors look *all wrong*! This observation led me down a rabbit hole of color
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perception and LED peculiarities.
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The idea of the LED driver was that it can be used either with up to eight single-color LED tapes or, much more
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interesting, with up to two RGB or RGBW (red-green-blue-white) LED tapes. For ambient lighting high color resolution was
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really important so you could dim it down a lot without flickering. I ended up using the same driver stage I used in the
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`multichannel LED driver`_ project for its great color resolution and low hardware requirements.
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.. raw:: html
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<figure>
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<img src="images/rgb_cube.svg" alt="An illustration of the RGB color cube.">
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<figcaption>An illustration of the RGB color cube.
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<a href="https://commons.wikimedia.org/wiki/File:RGB_color_cube.svg">Picture</a> by
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<a href="https://commons.wikimedia.org/wiki/User:Maklaan">Maklaan from Wikimedia Commons</a>,
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<a href="https://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA 3.0</a>
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</figcaption>
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</figure>
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To make setting colors over Wifi more intuitive I implemented support for HSV colors. RGB is fine for communication
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between computers, but I think HSV is easier to work with when manually inputting colors from the command line. RGB is
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close to how most monitors, cameras and the human visual apparatus work on a very low level but doesn't match
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higher-level human color perception very well. When we describe a color we tend to think in terms of "hue" or
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"brightness", and computing a measure of those from RGB values is not easy.
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Colors and Color Spaces
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-----------------------
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`Color spaces`_ are a mathematical abstraction of the concept of color. When we say "RGB", most of the time we actually
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mean `sRGB`_, a standardized notion of how to map three numbers labelled "red", "green" and "blue" onto a perceived
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color. `HSV`_ is an early attempt to more closely align these numbers with our perception. After HSV, a number of other
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*perceptual* color spaces such as `XYZ (CIE 1931)`_ and `CIE Lab/LCh`_ were born, further improving this alignment. In
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this mathematical model, mapping a color from one color space into another color space is just a coordinate
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transformation.
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.. raw:: html
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<figure>
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<img src="images/hsv_cylinder.png" alt="An illustration of the HSV color space as a cylinder.">
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<figcaption>An illustration of the HSV color space as a cylinder.
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<a href="https://commons.wikimedia.org/wiki/File:HSV_color_solid_cylinder.png">Picture</a> by
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<a href="https://commons.wikimedia.org/wiki/User:SharkD">SharkD from Wikimedia Commons</a>,
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<a href="https://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA 3.0</a>
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</figcaption>
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</figure>
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CIE 1931 XYZ is much larger than any other color space, which is why it is a good basis to express other color spaces
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in. In XYZ there are many coordinates that are outside of what the human eye can perceive. Below is an illustration of
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the sRGB space within XYZ. The wireframe cube is (0,0,0) to (1,1,1) in XYZ. The colorful object in the middle is what
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of sRGB fits inside XYZ, and the lines extending out from it indicate the space that can be expressed in sRGB but not in
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XYZ. The fat white curve is a projection of the *monochromatic spectral locus*, that is the curve of points you get in
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XYZ for pure visible wavelengths.
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As you can see, sRGB is *much* smaller than XYZ or even the part within the monochromatic locus that we can perceive. In
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particular in the blues and greens we loose *a lot* of colors to sRGB.
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.. raw:: html
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<figure>
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<video controls loop>
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<source src="video/sRGB.mkv" type="video/h264">
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<source src="video/sRGB.webm" type="video/webm">
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Your browser does not support the HTML5 video tag.
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</video>
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<figcaption>Illustration of the measured sRGB color space within XYZ. The thick, white line is the spectral
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locus.
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<a href="video/sRGB.mkv">mkv/h264 download</a> /
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<a href="video/sRGB.webm">webm download</a>
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</figcaption>
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</figure>
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The wrong colors I got when fading between colors were caused by this coordinate transformation being askew. Thinking
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over the problem, there are several sources for imperfections:
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* The LED driver may not be entirely linear. For most modulations such as PWM the brightness will be linear starting
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from a certain value, but there is probably an offset caused by imperfect edges of the LED current. This offset can be
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compensated with software calibration. I built a calibration setup for driver linearity in the `multichannel LED
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driver`_ project. Below are pictures of ringing on the edges of an LED driver's waveform.
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* The red, green and blue channels of the LEDs used on the LED tape are not matched. This skews the RGB color space.
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In practice, the blue channel of my RGB tape to me *looks* much brighter than the red channel.
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* The precise colors of the red, green and blue channels of the LEDs are unknown. Though the red channel *looks* red, it
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may be of a slightly different hue compared to the reference red used in `sRGB`_ which would also skew the RGB color
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space.
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.. raw:: html
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<figure>
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<figure class="side-by-side">
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<img src="images/driver_ringing_strong.jpg" alt="Strong ringing on the LED voltage waveform edge at about
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100% overshoot during about 70% of the cycle time.">
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<figcaption>The LED strip being at the end of a couple meters of wire caused extremely bad ringing at high
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driving frequencies.</figcaption>
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</figure><figure class="side-by-side">
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<img src="images/driver_ringing_weak.jpg" alt="Weak ringing on the LED voltage waveform edge at about 30%
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overshoot during about 20% of the cycle time.">
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<figcaption>Adding a resistor in front of the MOSFET gate to slow the transition dampened the ringing
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somewhat, but ultimately it cannot be eliminated entirely.</figcaption>
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</figure>
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</figure>
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These last two errors are tricky to compensate. What I needed for that was basically a model of the *perceived* colors
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of the LED tape's color channels. A way of doing his is to record the spectra of all color channels and then evaluate
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their respective XYZ coordinates. If all three channels are measured in one go with the same setup the relative
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magnitudes of the channels in XYZ will be accurate.
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To map any color to the LEDs, the color's XYZ coordinates simply have to be mapped onto the linear coordinate system
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produced by these three points within XYZ. LEDs are mostly linear in their luminous flux vs. current characteristic so
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this model will be adequate. The spectral integrals mapping the channels' measured responses to XYZ need only be
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calculated once and their results can be used as scaling factors thereafter.
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Measuring the spectrum
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----------------------
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In order to compensate for the cheap LED tape's non-ideal performance I had to measure the LED's red, green and blue
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channels' spectra. The obvious thing would be to go out and buy a `spectrograph`_, or ask someone to borrow theirs. The
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former is kind of expensive, and I did not want to wait two weeks for the thing to arrive. The latter I could probably
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not do every time I got new LED tape. Thus the only choice was to build my own.
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Luckily, building your own spectrometer is really easy. The first thing you need is something that splits incident light
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into its constituent wavelengths. In professional devices this is called the *`monochromator`_*, since it allows extraction
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of small color bands from the spectrum. The second thing is some sort of optics that project the incident light onto a
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screen behind the monochromator. In professional devices lenses or curved mirrors are used. In a simple homebrew job a
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pinhole as you would use in a `camera obscura`_ does a remarkably nice job.
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For the monochromator component several things could be used. A prism would work, but I did not have any. The
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alternative is a `diffraction grating`_. Professional gratings are quite specialized pieces of equipment and thus
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rather expensive. Luckily, there is a common household item that works almost as well: A regular CD or DVD. The
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microscopic grooves that are used to record data in a CD or DVD work the same as the grooves in a professional
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diffraction grating.
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Household spectra
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-----------------
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From this starting point, a few seconds on my favorite search engine yielded an `article by two researchers from the
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National Science Museum in Tokyo`_ providing a nice blueprint for a simple cardboard-and-DVD construction for use in
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classrooms. I replicated their device using a DVD and it worked beautifully. Daylight and several types of small LEDs I
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had around did show the expected spectra. Small red, yellow, green, and blue LEDs showed narrow spectra, daylight one
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continuous broad one, and white LEDs a continuous broad one with a distinct bright spot in the blue part. The
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single-color LED spectra are quite narrow since they are determined by the LED's semiconductor's band gap, which is
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specific to the semiconductor used and is quite precise. White LEDs are in fact a blue LED chip covered with a so-called
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*phosphor*. This phosphor is not elementary phosphorus but an anorganic compound that absorbs the LED chip's blue light
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and re-emits a broader spectrum of more yellow-ish wavelengths instead. The final LED spectrum is a superposition of
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both spectra, with some of the original blue light leaking through the phosphor mixing with the broadband yellow
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spectrum of the phosphor.
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.. raw:: html
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<figure>
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<figure class="side-by-side">
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<img src="images/spectrograph_step1_parts.jpg">
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<figcaption>The ingredients. The cup of coffee and Madoka Magica DVD set are essential to the eventual
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function of the appartus.</figcaption>
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</figure><figure class="side-by-side">
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<img src="images/spectrograph_step2.jpg">
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<figcaption>Step 1: Cut to size and mark down all holes as described in <a
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href="http://www.candac.ca/candacweb/sites/default/files/BuildaSpectroscope.pdf">the manual</a></figcaption>
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</figure>
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<figure class="side-by-side">
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<img src="images/spectrograph_step3.jpg">
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<figcaption>Step 2: Cut out all holes</figcaption>
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</figure><figure class="side-by-side">
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<img src="images/spectrograph_step4_complete.jpg">
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<figcaption>The finished result with the back side showing. The viewing window is on the bottom of the other
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side.</figcaption>
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</figure>
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</figure>
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Now that I had a spectrograph, I needed a somewhat predictable way of measuring the spectrum it gave me.
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Measuring a spectrum
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--------------------
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Pointing a camera at the spectrograph would be the obvious thing to do. This produces pretty images but has one critical
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flaw: I wanted to acquire quantitative measurements of brightness across the spectrum. Since I don't have a precise
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technical datasheet specifying the spectral response of any of my cameras I can't compare the absolute brightness of
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different colors on their pictures. Some other sensor was needed.
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.. raw:: html
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<figure>
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<img src="images/daylight_spectrum_dvd.jpg">
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<figcaption>The daylight spectrum as seen using a DVD as a grating.
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<a href="https://commons.wikimedia.org/wiki/File:SpectresSolaires-DVD.jpg">Picture</a> by
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<a href="https://commons.wikimedia.org/wiki/User:Xofc">Xofc from Wikimedia Commons</a>,
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<a href="https://creativecommons.org/licenses/by-sa/4.0/">CC-BY-SA 4.0</a>
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</figcaption>
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</figure>
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Measuring light intensity
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~~~~~~~~~~~~~~~~~~~~~~~~~
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Looking around my lab, I found a bag of `SFH2701`_ visible-light photodiodes. Their
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datasheet includes their spectral response so I can compensate for that, allowing precise-ish absolute intensity
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measurements. Just like LEDs, photodiodes are extremely linear across several orders of magnitude. The datasheet of the
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classic `BPW34`_ photodiode shows that this photodiode's light current is exactly proportional to illuminance over at
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least three orders of magnitude. The `SFH2701`_ datasheet does not include a similar graph but its performance will be
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similar. The `SFH2701`_ photodiodes I had at hand were perfect for the job compared to the vintage `BPW34`_ since their
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active sensing area is really small (0.6mm by 0.6mm) compared to the BPW34 (a whopping 3mm by 3mm). If I were to use a
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`BPW34`_ I would have to insert some small apterture in front of it so it does not catch too broad a part of the
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spectrum at once. The `SFH2701`_ is small enough that if I just point it at the projected spectrum directly I will
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already get only a small part of the spectrum inside its 0.6mm active area.
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To convert the photodiode's tiny photocurrent into a measurable voltage I built another copy of the `transimpedance
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amplifier`_ circuit I already used in the `multichannel LED driver`_. A `transimpedance amplifier`_ is an
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amplifiert that produces a large voltage from a small current. The weird name comes from the fact that it works kind of
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like an amplified resistor (which can be generalized as an *impedance* electrically). Apply a current to a resistor and
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you get a voltage. A transimpedance amplifiert does the same with the difference that its input always stays at 0V,
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making it look like an ideal current sink to the connected current source.
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Transimpedance amplifiers are common in optoelectronics to convert small photocurrents to voltages. In this instance I
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built a very simple circuit with a dampened transimpedance amplifier stage followed by a simple RC filter for noise
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rejection and a regular non-inverting amplifier using another op-amp from the same chip to further boost the filtered
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transimpedance amplifier output. I put all the passives setting amplifier response (the gain-setting resistors and the
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filter resistor and capacitors) on a small removable adapter so I could easily change them if necessary. I put a small
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trimpot on the virtual ground both amplifers use as a reference so I could trim that if necessary.
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.. raw:: html
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<figure>
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<img src="images/preamp_schematic.jpg" alt="A drawing of the photodiode preamplifier's schematic">
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<figcaption>The photodiode preamplifier schematic. Schematic drawn with an unlicensed copy of
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DaveCAD.</figcaption>
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</figure>
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Following are pictures of the preamplifier board. The connectors on the top-left side are two copies of the analog
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signal for the ADC and a small panel meter. The SMA connector is used as the photodiode input since coax cables are
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generally low-leakage and have built-in shielding. The circuit is powered via the micro-USB connector and the analog
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ground bias voltage can be adjusted using the trimpot.
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For easy replacement, all passives setting gain and frequency response are on a small, pluggable carrier PCB made from a
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SMD-to-DIP adapter.
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Flying-wire construction is just fine for this low-frequency circuit. In a high-speed photodiode preamp, the
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transimpedance amplifier circuit would be highly sensitive to stray capacitance, but we're not aiming at high speed
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here.
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.. raw:: html
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<figure>
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<figure class="side-by-side">
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<img src="images/preamp_front.jpg">
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<figcaption>The front side of the preamplifier board.</figcaption>
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</figure><figure class="side-by-side">
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<img src="images/preamp_back.jpg">
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<figcaption>The wiring of the photodiode preamp.</figcaption>
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</figure>
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</figure>
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Given a way to measure intensity what remains missing is a way to scan a single photodiode across the spectrum.
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Scanning the projection
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~~~~~~~~~~~~~~~~~~~~~~~
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A cheap linear stage can be found in any old CD or DVD drive. These drives use a small linear stage based on a
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stepper-driven screw to move the laser unit radially. Removing the laser unit and connecting a leftover stepper driver
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module I was left with a small linear stage with about 45 steps per cm without microstepping enabled. The driver I used
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was an `A4988`_ module that required at least 8V motor drive voltage. I used a small micro USB-input boost converter
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module to generate a stable 10V supply for the motor driver, with the USB's 5V rail used as a logic supply for the motor
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driver.
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The `SFH2701`_ can easily be mounted to the linear stage using a small SMD breakout board glued in place with thin wires
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connecting it to the transimpedance amplifier. The DVD drive linear stage is not very strong so it is important that
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this wire does not put too much strain on it.
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Above the photodiode, I mounted a small piece of paper on the linear stage to be used as a projection screen to align
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the linear stage in front of the spectrometer viewing window. A line on the screen paper points to the photodiode die in
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parallel to the linear stage allowing precise alignment.
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The whole unit with photodiode preamplifier, linear stage, photodiode and stepper motor driver finally looks like this:
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.. raw:: html
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<figure>
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<img src="images/electronics_whole.jpg" alt="The complete electronics setup of the spectrograph. In the back
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there is the DVD drive stepper stage. In front of it, mounted on a piece of wood are a small USB-to-12V
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switching-regulator module to power the stepper motor in the top left, below on the bottom left is the
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photodiode preamp and on the right is a breadboard with the stepper driver module and lots of jumper wires
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interconnecting everything. On the right of the breadboard, a buspirate is attached to interface everything to a
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computer. On the bottom edge of the piece of wood, two LED panel meters are mounted for readout of the preamp
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output and the stepper supply voltages.">
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<figcaption>The complete electronics setup. The buspirate on the right interfaces to a computer and controls the
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stepper driver and ADC'es the preamp output. The two panel meters show the preamp output and stepper voltage for
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setup.</figcaption>
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</figure>
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The projection of the spectrum can be adjusted by moving the light source relative to the entry slot and by moving
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around the grating DVD.
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The capture process
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~~~~~~~~~~~~~~~~~~~
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To capture a spectrum, first the light source has to be mounted near the spectrograph's entry slot. The LED tape I
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tested I just taped face-down directly into it. Next, the grating DVD has to be adjusted to make sure the spectrum
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covers a sensible part of the photodiode's path. Mostly, this boils down to adjusting the photodiode distance and height
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to match the vertical extent and wiggling the grating DVD to adjust the projection's horizontal position.
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After the optics are set-up, the photodiode preamplifier has to be adjusted. In my experiments, most LED tape at 5GΩ
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required a high-ish amplification. The goal in this step is to maximize the peak response of the preamp to be just
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shy of its VCC rail to make best use of its dynamic range. To adjust the pre-amp, I took several very coarsely-spaced
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measurements to give me an estimate of the peak while I did not yet know its precise location.
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Since stray daylight totally swamped out the weak projection of the LED's spectrum I shielded the entire setup with a
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small box made of black cardboard and two black t-shirts on top. This shielding proved adequate for all my measurements
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but I had to be careful not to accidentially move the DVD that was stuck into the spectrograph with the shielding
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t-shirts.
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For capturing a single spectrum I wrote a small python script that will automatically move the stepper in adjustable
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intervals and take two measurements at each point, one with the LED tape off that can be used for offset calibration and
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one with the LED tape on. All measurements are stored in a sqlite database that can then be accesssed from other
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scripts.
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I built a small script that shows the progress of the current run and an jupyter notebook for data analysis. The jupyter
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notebook is capable of live-updating a graph with the in-progress spectrum's data. This was quite useful as a sanity
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check for when I made some mistake easy to spot in the resulting data.
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After one color channel is captured, the LED tape has to be manually set to the next color and the next measurement can
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begin.
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.. raw:: html
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<figure>
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<img src="images/raw_plot_cheap_rgb.svg" alt="A plot with three wide peaks, two large peaks on both sides and
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one smaller one in the middle. The middle one overlaps the two on the sides. The large ones are about 2.5V in
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amplitude. Overall, the plot is about 300 stepper steps wide with each peak being around 130 steps wide.">
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<figcaption>A plot of the raw preamp output voltage versus stepper position. From left to right, the three peaks
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are blue, green and red. Step 0 corresponds to the bottommost stepper position and the shortest wavelength.
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</figcaption>
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</figure>
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Data analysis
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~~~~~~~~~~~~~
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Data analysis consists of three major steps: Offset- and stray light removal, wavelength and amplitude calibration and
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color space mapping.
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Offset removal
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**************
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The first task is to remove the offset caused by dark current as well as stray light of the LED's bright primary
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reflection on the DVD. The LED is very bright and only a small part of its light gets reflected by the grating towards
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the photodiode screen. The remaining part of the light is reflected onto the table in front of the DVD spectrograph.
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Though I covered all of this with black cardboard, some of that light ultimately gets reflected onto the photodiode.
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This causes a large offset, in particular in the blue part of the spectrum since in this part the photodiode is closest
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to the spectrograph's opening.
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The composite offset can be approximated with a second-order polynomial that is fitted to all the data outside of the
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main peak's area. Since at this point the wavelength of each data point is still unknown this is done with a rough first
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estimate of the three colors' peaks' locations and widths.
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Wavelength- and amplitude calibration
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*************************************
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The photodiode's response is strongly wavelength-dependent. In particular in the blue band, the photodiode's sensitivity
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gets very poor down to about 20% at the edge to ultraviolet. This effect is strong enough to move the apparent location
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of the blue peak towards red.
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.. raw:: html
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<figure>
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<img src="images/photodiode_sensitivity.svg" alt="A plot of photodiode sensitivity against wavelength relative
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to peak sensitivity at 820nm. The sensitivity rises from 20% at 380nm approximately linearly to 80% at 620nm,
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then the rise rolls off.">
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<figcaption>A plot of the photodiode's relative sensitivity in the visible spectrum. The sensitivity is
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normalized against its peak at 820nm.
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</figcaption>
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</figure>
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The problem is that in order to remove this non-linearity, we would already have to know the wavelength of the measured
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light. Since I don't, I settled for a two-step process. First, a coarse wavelength calibration is done relative to the
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red peak and the short-wavelength edge of the blue peak. The photodiode measurements are then sensitivity-corrected
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using this coarse measurement. Then all three channel peaks are measured in the resulting data and a fine wavelength
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estimate is produced by a least-squares fit of a linear function. This fine estimate is then used for a second
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sensitivity correction of all original measurements and the scale is changed from stepper motor step count to
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wavelength in nanometers.
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.. raw:: html
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|
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<figure>
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<img src="images/processed_plot_cheap_rgb.svg" alt="A plot with three wide peaks, all three of different
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heights. The leftmost peak is highest at 6nA, the middle peak lowest at 1.6nA and the rightmost peak in between
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at 4nA. The middle one overlaps the two on the sides. Overall, the plot spans about 300nm on its x axis with
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each peak being around 100nm wide.">
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<figcaption>A plot of the processed measurements. From left to right, the three peaks are blue, green and red.
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</figcaption>
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</figure>
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.. FIXME re-do these measurements, avoiding clipping
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.. FIXME re-do calibration using CCFL
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.. FIXME calibration for brightness imbalance due to wedge-shaped projection of spectrum
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Color space mapping
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|
*******************
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Finally, to achieve the objective of measuring the LED tape's channels' precise color coordinates the measured spetra
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|
have to be matched against the color spaces' *color matching functions*. The color matching functions describe how
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strong the color space's idealized *standard observer* would react to light at a particular wavelength. Going from a
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|
measured spectrum to color coordinates XYZ works by integrating over the product of the measurement and each color
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coordinate's color matching function.
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|
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|
The result are three color coordinates X, Y and Z for each channel R, G and B yielding nine coordinates in total. When
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|
written as a matrix conversion between XYZ color space and LED-RGB color space is as simple as multiplying that matrix
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|
(or its inverse) and a vector from one of the color spaces.
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|
|
|
In XYZ space, the set of colors that can be produced with this LED tape is described by the `parallelepiped`_ spanned by
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|
the three channel's XYZ vectors. In the following figures, you can see a three-dimensional model of the RGB LED's color
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|
space (colorful) as well as sRGB (white) for comparison plotted within CIE 1931 XYZ. There is no natural map to scale
|
|
both so for this illustration the LED color space has been scaled to fit. These figures were made with blender and a few
|
|
lines of python. The blender project file including all settings and the python script to generate the color space
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|
models can be found in the `project repo`_.
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|
|
|
.. raw:: html
|
|
|
|
<figure>
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|
<video controls loop>
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<source src="video/led_within_srgb_scale=1.0.mkv" type="video/h264">
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|
<source src="video/led_within_srgb_scale=1.0.webm" type="video/webm">
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|
Your browser does not support the HTML5 video tag.
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|
</video>
|
|
<figcaption>Illustration of the measured LED color space scaled to fit within XYZ with sRGB (light gray) for
|
|
comparison. The thick, white line is the spectral locus.
|
|
|
|
<a href="video/led_within_srgb_scale=1.0.mkv">mkv/h264 download</a> /
|
|
<a href="video/led_within_srgb_scale=1.0.webm">webm download</a>
|
|
</figcaption>
|
|
</figure>
|
|
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|
As you can see, the result is pretty disappointing. The LED's color space parallepiped is very narrow, which is because
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the blue channel is much brighter than the other two channels. An easy fix for this is to scale-up the RGB space and
|
|
drop any values outside XYZ. The scaling factor is a trade-off between color space coverage and brightness. You can
|
|
produce the most colors when you clip all channels to brightness of the weakest channel (green in this case), but that
|
|
will make the result very dim. Scaling brightness like that stretches the RGB parallelepiped along its major axis. Up to
|
|
a point the number of possible colors (the gamut) increases at expense of maximum brightness. When the parallelepiped is
|
|
stretched far enought for all three channel vectors to be outside the 1,1,1 XYZ-cube, maximum brightness continues to
|
|
decrease but the gamut stays constant. I don't know a simple scientific way to solve this problem, so I just played
|
|
around with a couple of factors and settled on 2.5 as a reasonable compromise. Below is an illustration.
|
|
|
|
.. raw:: html
|
|
|
|
<figure>
|
|
<video controls loop>
|
|
<source src="video/led_within_srgb_fancy_camera_path_scale=2.5.mkv" type="video/h264">
|
|
<source src="video/led_within_srgb_fancy_camera_path_scale=2.5.webm" type="video/webm">
|
|
Your browser does not support the HTML5 video tag.
|
|
</video>
|
|
<figcaption>Illustration of the measured LED color space at scale factor 2.5 within XYZ with sRGB (light gray)
|
|
for comparison. The thick, white line is the spectral locus.
|
|
|
|
<a href="video/led_within_srgb_fancy_camera_path_scale=2.5.mkv">mkv/h264 download</a> /
|
|
<a href="video/led_within_srgb_fancy_camera_path_scale=2.5.webm">webm download</a>
|
|
</figcaption>
|
|
</figure>
|
|
|
|
Firmware implementation
|
|
-----------------------
|
|
In the end, the above measurements yield two matrices: One for mapping XYZ to RGB, and one for mapping RGB to XYZ. Of
|
|
the several versions of CIE XYZ I chose the CIE 1931 XYZ color space as a basis for the firmware because it is most
|
|
popular. Mapping a color coordinate in one color space to the other is as simple as performing nine floating-point
|
|
multiplications and six additions. Mapping Lab or Lch to RGB is done by first mapping Lab/Lch to XYZ, then XYZ to RGB.
|
|
Lab to XYZ is somewhat complex since it requires a floating-point power for gamma correction, but any self-respecting
|
|
libc will have one of those so this is still no problem. Lch also requires floating-point sine and cosine functions, but
|
|
these should still be no problem on most hardware.
|
|
|
|
My implementation of these conversions in the ESP8266 firmware of my `Wifi LED driver`_ can be found `on Github`_. You
|
|
can view the Jupyter notebook most of the analysis above `here <http://nbviewer.jupyter.org/github/jaseg/led_drv/blob/master/doc/Spectrum%20Measurement.ipynb>`__.
|
|
|
|
.. _`on Github`: https://github.com/jaseg/esp_led_drv/blob/master/user/led_controller.c
|
|
.. _`project repo`: https://github.com/jaseg/led_drv
|
|
.. _`Wifi LED driver`: {{<ref "posts/wifi-led-driver/index.rst">}}
|
|
.. _`small driver`: {{<ref "posts/wifi-led-driver/index.rst">}}
|
|
.. _`multichannel LED driver`: {{<ref "posts/multichannel-led-driver/index.rst">}}
|
|
.. _`sRGB`: https://en.wikipedia.org/wiki/SRGB
|
|
.. _`CC BY-SA 3.0`: https://creativecommons.org/licenses/by-sa/3.0
|
|
.. _`Color spaces`: https://en.wikipedia.org/wiki/Color_space
|
|
.. _`HSV`: https://en.wikipedia.org/wiki/HSL_and_HSV
|
|
.. _`CIE Lab/LCh`: https://en.wikipedia.org/wiki/Lab_color_space
|
|
.. _`XYZ (CIE 1931)`: https://en.wikipedia.org/wiki/CIE_1931_color_space
|
|
.. _`camera obscura`: https://en.wikipedia.org/wiki/Pinhole_camera
|
|
.. _`article by two researchers from the National Science Museum in Tokyo`: http://www.candac.ca/candacweb/sites/default/files/BuildaSpectroscope.pdf
|
|
.. _`spectrograph`: https://en.wikipedia.org/wiki/Ultraviolet%E2%80%93visible_spectroscopy
|
|
.. _`monochromator`: https://en.wikipedia.org/wiki/Monochromator
|
|
.. _`diffraction grating`: https://en.wikipedia.org/wiki/Diffraction_grating
|
|
.. _`SFH2701`: https://dammedia.osram.info/media/resource/hires/osram-dam-2495903/SFH%202701.pdf
|
|
.. _`BPW34`: http://www.vishay.com/docs/81521/bpw34.pdf
|
|
.. _`transimpedance amplifier`: https://en.wikipedia.org/wiki/Transimpedance_amplifier
|
|
.. _`A4988`: https://www.pololu.com/file/0J450/A4988.pdf
|
|
.. _`parallelepiped`: https://en.wikipedia.org/wiki/Parallelepiped
|