Initial commit

4 files changed, 359 insertions, 0 deletions

diff --git a/content/posts/led-characterization.rst b/content/posts/led-characterization.rst
new file mode 100644
index 0000000..e856a09
--- /dev/null
+++ b/content/posts/led-characterization.rst
@@ -0,0 +1,304 @@
+---
+title: "Led Characterization"
+date: 2018-05-02T11:18:38+02:00
+draft: true
+---
+
+Preface
+-------
+
+Recently, I have been working on a `small driver`_ for ambient lighting using 12V LED strips like you can get
+inexpensively from China. I wanted to be able to just throw one of these somewhere, stick down some LED tape, hook it up
+to a small transformer and be able to control it through Wifi. When I was writing the firmware, I noticed that when
+fading between different colors, the colors look *all wrong*! This observation led me down a rabbit hole of color
+perception and LED peculiarities.
+
+The idea of the LED driver was that it can be used either with up to eight single-color LED tapes or, much more
+interesting, with up to two RGB or RGBW (red-green-blue-white) LED tapes. For ambient lighting high color resolution was
+really important so you could dim it down a lot without flickering. I ended up using the same driver stage I used in the
+`multichannel LED driver`_ project for its great color resolution and low hardware requirements.
+
+.. figure:: https://upload.wikimedia.org/wikipedia/commons/d/d6/RGB_color_cube.svg
+   :width: 100%
+   :alt: An illustration of the RGB color cube
+
+   An illustration of the RGB color cube. `Picture by Maklaan
+   <https://commons.wikimedia.org/wiki/File:RGB_color_cube.svg>`_ (`CC BY-SA 3.0`_), from Wikimedia Commons.
+
+To make setting colors over Wifi more intuitive I implemented support for HSV colors. RGB is fine for communication
+between computers, but I think HSV is easier to work with when manually inputting colors from the command line. RGB  is
+close to how most monitors, cameras and the human visual apparatus work on a very low level but doesn't match
+higher-level human color perception very well. When we describe a color we tend to think in terms of "hue" or
+"brightness", and computing a measure of those from RGB values is not easy.
+
+Colors and Color Spaces
+-----------------------
+
+`Color spaces`_ are a mathematical abstraction of the concept of color. When we say "RGB", most of the time we actually
+mean `sRGB`_, a standardized notion of how to map three numbers labelled "red", "green" and "blue" onto a perceived
+color. `HSV`_ is an early attempt to more closely align these numbers with our perception. After HSV, a number of other
+*perceptual* color spaces such as `XYZ (CIE 1931)`_ and `CIE Lab/LCh`_ were born, further improving this alignment.  In
+this mathematical model, mapping a color from one color space into another color space is just a coordinate
+transformation.
+
+.. figure:: https://upload.wikimedia.org/wikipedia/commons/4/4e/HSV_color_solid_cylinder.png
+   :width: 50%
+   :align: center
+   :alt: An illustration of the HSV color space as a cylinder
+   
+   An illustration of the HSV color space as a cylinder. `Picture by SharkD
+   <https://commons.wikimedia.org/wiki/File:HSV_color_solid_cylinder.png>`_ (`CC BY-SA 3.0`_), from Wikimedia Commons.
+
+The wrong colors I got when fading between colors were caused by this coordinate transformation being askew. Thinking
+over the problem, there are several sources for imperfections:
+
+* The LED driver may not be entirely linear. For most modulations such as PWM the brightness will be linear starting
+  from a certain value, but there is probably an offset caused by imperfect edges of the LED current. This offset can be
+  compensated with software calibration. I built a calibration setup for driver linearity in the `multichannel LED
+  driver`_ project.
+  .. FIXME picture with ringing on edges
+
+* The red, green and blue channels of the LEDs used on the LED tape are not matched.  This skews the RGB color space.
+  In practice, the blue channel of my RGB tape to me *looks* much brighter than the red channel.
+
+* The precise colors of the red, green and blue channels of the LEDs are unknown. Though the red channel *looks* red, it
+  may be of a slightly different hue compared to the reference red used in `sRGB`_ which would also skew the RGB color
+  space.
+
+These last two errors are tricky to compensate. What I needed for that was basically a model of the *perceived* colors
+of the LED tape's color channels. A way of doing his is to record the spectra of all color channels and then evaluate
+their respective XYZ coordinates. If all three channels are measured in one go with the same setup the relative
+magnitudes of the channels in XYZ will be accurate.
+
+To map any color to the LEDs, the color's XYZ coordinates simply have to be mapped onto the linear coordinate system
+produced by these three points within XYZ. LEDs are extremely linear in their luminous flux vs. current characteristic
+so this model will be adequate. The spectral integrals mapping the channels' measured responses to XYZ need only be
+calculated once and their results can be used as scaling factors thereafter.
+.. FIXME: Add led/current graph here
+
+Measuring the spectrum
+----------------------
+
+In order to compensate for the cheap LED tape's non-ideal performance I had to measure the LED's red, green and blue
+channels' spectra. The obvious thing would be to go out and buy a `spectrograph`_, or ask someone to borrow theirs. The
+former is kind of expensive, and I did not want to wait two weeks for the thing to arrive. The latter I could probably
+not do every time I got new LED tape. Thus the only choice was to build my own.
+
+Luckily, building your own spectrometer is really easy. The first thing you need is something that splits incident light
+into its constituent wavelengths. In professional devices this is called the *`monochromator`_*, since it allows extraction
+of small color bands from the spectrum. The second thing is some sort of optics that project the incident light onto a
+screen behind the monochromator. In professional devices lenses or curved mirrors are used. In a simple homebrew job a
+pinhole as you would use in a `camera obscura`_ does a remarkably nice job.
+
+For the monochromator component several things could be used. A prism would work, but I did not have any. The
+alternative is a `diffraction grating`_. Professional gratings are quite specialized pieces of equipment and thus
+rather expensive. Luckily, there is a common household item that works almost as well: A regular CD or DVD. The
+microscopic grooves that are used to record data in a CD or DVD work the same as the grooves in a professional
+diffraction grating.
+
+Household spectra
+-----------------
+
+From this starting point, a few seconds on my favorite search engine yielded an `article by two researchers from the
+National Science Museum in Tokyo`_ providing a nice blueprint for a simple cardboard-and-DVD construction for use in
+classrooms. I replicated their device using a DVD and it worked beautifully. Daylight and several types of small LEDs I
+had around did show the expected spectra. Small red, yellow, green, and blue LEDs showed narrow spectra, daylight one
+continuous broad one, and white LEDs a continuous broad one with a distinct bright spot in the blue part. The
+single-color LED spectra are quite narrow since they are determined by the LED's semiconductor's band gap, which is
+specific to the semiconductor used and is quite precise. White LEDs are in fact a blue LED chip covered with a so-called
+*phosphor*. This phosphor is not elementary phosphorus but an anorganic compound that absorbs the LED chip's blue light
+and re-emits a broader spectrum of more yellow-ish wavelengths instead. The final LED spectrum is a superposition of
+both spectra, with some of the original blue light leaking through the phosphor mixing with the broadband yellow
+spectrum of the phosphor.
+.. FIXME: Cardboard spectrograph pictures
+
+Now that I had a spectrograph, I needed a somewhat predictable way of measuring the spectrum it gave me.
+
+Measuring a spectrum
+--------------------
+
+Pointing a camera at the spectrograph would be the obvious thing to do. This produces pretty images but has one critical
+flaw: I wanted to acquire quantitative measurements of brightness across the spectrum. Since I don't have a precise
+technical datasheet specifying the spectral response of any of my cameras I can't compare the absolute brightness of
+different colors on their pictures. Some other sensor was needed.
+.. FIXME: Spectrum picture
+
+Measuring light intensity
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Looking around my lab, I found a bag of `SFH2701`_ visible-light photodiodes. Their
+datasheet includes their spectral response so I can compensate for that, allowing precise-ish absolute intensity
+measurements. Just like LEDs, photodiodes are extremely linear across several orders of magnitude. The datasheet of the
+classic `BPW34`_ photodiode shows that this photodiode's light current is exactly proportional to illuminance over at
+least three orders of magnitude. The `SFH2701`_ datasheet does not include a similar graph but its performance will be
+similar. The `SFH2701`_ photodiodes I had at hand were perfect for the job compared to the vintage `BPW34`_ since their
+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
+`BPW34`_ I would have to insert some small apterture in front of it so it does not catch too broad a part of the
+spectrum at once. The `SFH2701`_ is small enough that if I just point it at the projected spectrum directly I will
+already get only a small part of the spectrum inside its 0.6mm active area.
+
+To convert the photodiode's tiny photocurrent into a measurable voltage I built another copy of the `transimpedance
+amplifier`_ circuit I already used in the `multichannel LED driver`_. A `transimpedance amplifier`_ is an
+amplifiert that produces a large voltage from a small current. The weird name comes from the fact that it works kind of
+like an amplified resistor (which can be generalized as an *impedance* electrically). Apply a current to a resistor and
+you get a voltage. A transimpedance amplifiert does the same with the difference that its input always stays at 0V,
+making it look like an ideal current sink to the connected current source.
+
+Transimpedance amplifiers are common in optoelectronics to convert small photocurrents to voltages. In this instance I
+built a very simple circuit with a dampened transimpedance amplifier stage followed by a simple RC filter for noise
+rejection and a regular non-inverting amplifier using another op-amp from the same chip to further boost the filtered
+transimpedance amplifier output. I put all the passives setting amplifier response (the gain-setting resistors and the
+filter resistor and capacitors) on a small removable adapter so I could easily change them if necessary. I put a small
+trimpot on the virtual ground both amplifers use as a reference so I could trim that if necessary.
+.. FIXME: Add transimp amp schematic and build pics
+
+Given a way to measure intensity what remains missing is a way to scan a single photodiode across the spectrum.
+
+Scanning the projection
+~~~~~~~~~~~~~~~~~~~~~~~
+
+A cheap linear stage can be found in any old CD or DVD drive. These drives use a small linear stage based on a
+stepper-driven screw to move the laser unit radially. Removing the laser unit and connecting a leftover stepper driver
+module I was left with a small linear stage with about 45 steps per cm without microstepping enabled. The driver I used
+was an `A4988`_ module that required at least 8V motor drive voltage. I used a small micro USB-input boost converter
+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
+driver.
+
+.. FIXME: Add picture of photodiode stage here
+
+The `SFH2701`_ can easily be mounted to the linear stage using a small SMD breakout board glued in place with thin wires
+connecting it to the transimpedance amplifier. The DVD drive linear stage is not very strong so it is important that
+this wire does not put too much strain on it.
+
+Above the photodiode, I mounted a small piece of paper on the linear stage to be used as a projection screen to align
+the linear stage in front of the spectrometer viewing window. A line on the screen paper points to the photodiode die in
+parallel to the linear stage allowing precise alignment.
+
+The whole unit with photodiode preamplifier, linear stage, photodiode and stepper motor driver finally looks like this:
+
+.. FIXME: pics of linear stage unit electronics
+
+The projection of the spectrum can be adjusted by moving the light source relative to the entry slot and by moving
+around the grating DVD.
+
+The capture process
+~~~~~~~~~~~~~~~~~~~
+
+To capture a spectrum, first the light source has to be mounted near the spectrograph's entry slot. The LED tape I
+tested I just taped face-down directly into it. Next, the grating DVD has to be adjusted to make sure the spectrum
+covers a sensible part of the photodiode's path. Mostly, this boils down to adjusting the photodiode distance and height
+to match the vertical extent and wiggling the grating DVD to adjust the projection's horizontal position.
+
+After the optics are set-up, the photodiode preamplifier has to be adjusted. In my experiments, most LED tape at 5GΩ
+required a high-ish amplification. The goal in this step is to maximize the peak response of the preamp  to be just
+shy of its VCC rail to make best use of its dynamic range. To adjust the pre-amp, I took several very coarsely-spaced
+measurements to give me an estimate of the peak while I did not yet know its precise location.
+
+Since stray daylight totally swamped out the weak projection of the LED's spectrum I shielded the entire setup with a
+small box made of black cardboard and two black t-shirts on top. This shielding proved adequate for all my measurements
+but I had to be careful not to accidentially move the DVD that was stuck into the spectrograph with the shielding
+t-shirts.
+
+For capturing a single spectrum I wrote a small python script that will automatically move the stepper in adjustable
+intervals and take two measurements at each point, one with the LED tape off that can be used for offset calibration and
+one with the LED tape on. All measurements are stored in a sqlite database that can then be accesssed from other
+scripts.
+
+I built a small script that shows the progress of the current run and an jupyter notebook for data analysis. The jupyter
+notebook is capable of live-updating a graph with the in-progress spectrum's data. This was quite useful as a sanity
+check for when I made some mistake easy to spot in the resulting data.
+
+After one color channel is captured, the LED tape has to be manually set to the next color and the next measurement can
+begin.
+
+Data analysis
+~~~~~~~~~~~~~
+
+Data analysis consists of three major steps: Offset- and stray light removal, wavelength and amplitude calibration and
+color space mapping.
+
+Offset removal
+**************
+The first task is to remove the offset caused by dark current as well as stray light of the LED's bright primary
+reflection on the DVD. The LED is very bright and only a small part of its light gets reflected by the grating towards
+the photodiode screen. The remaining part of the light is reflected onto the table in front of the DVD spectrograph.
+Though I covered all of this with black cardboard, some of that light ultimately gets reflected onto the photodiode.
+This causes a large offset, in particular in the blue part of the spectrum since in this part the photodiode is closest
+to the spectrograph's opening.
+
+The composite offset can be approximated with a second-order polynomial that is fitted to all the data outside of the
+main peak's area. Since at this point the wavelength of each data point is still unknown this is done with a rough first
+estimate of the three colors' peaks' locations and widths.
+
+Wavelength- and amplitude calibration
+*************************************
+The photodiode's response is strongly wavelength-dependent. In particular in the blue band, the photodiode's sensitivity
+gets very poor down to about 20% at the edge to ultraviolet. This effect is strong enough to move the apparent location
+of the blue peak towards red.
+
+The problem is that in order to remove this non-linearity, we would already have to know the wavelength of the measured
+light. Since I don't, I settled for a two-step process. First, a coarse wavelength calibration is done relative to the
+red peak and the short-wavelength edge of the blue peak. The photodiode measurements are then sensitivity-corrected
+using this coarse measurement. Then all three channel peaks are measured in the resulting data and a fine wavelength
+estimate is produced by a least-squares fit of a linear function. This fine estimate is then used for a second
+sensitivity correction of all original measurements and the scale is changed from stepper motor step count to
+wavelength in nanometers.
+
+.. FIXME: calibration for brightness imbalance due to wedge-shaped projection of spectrum
+
+Color space mapping
+*******************
+Finally, to achieve the objective of measuring the LED tape's channels' precise color coordinates the measured spetra
+have to be matched against the color spaces' *color matching functions*. The color matching functions describe how
+strong the color space's idealized *standard observer* would react to light at a particular wavelength. Going from a
+measured spectrum to color coordinates XYZ works by integrating over the product of the measurement and each color
+coordinate's color matching function.
+
+The result are three color coordinates X, Y and Z for each channel R, G and B yielding nine coordinates in total. When
+written as a matrix conversion between XYZ color space and LED-RGB color space is as simple as multiplying that matrix
+(or its inverse) and a vector from one of the color spaces.
+
+If you view the three channels' color coordinates as vectors in XYZ space, the set of colors that can be produced with
+this LED tape is described by the `parallelepiped`_ spanned by the three channel vectors.
+
+The last task is to decide on a scaling factor to map XYZ space to RGB space. Both are limited to values between 0.0 and
+1.0. The LEDs cannot go below off or above fully on. For any LED tape there will be a set of colors that are outside
+the range that this tape can produce.
+
+A scaling factor can be used to increase the number of XYZ coordinates that can be mapped to RGB colors the tape *can*
+produce by stretching 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.
+
+Firmware implementation
+-----------------------
+In the end, the above measurements yield two matrices: One for mapping XYZ to RGB, and one for mapping RGB to 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`_.
+
+.. _`on Github`: https://github.com/jaseg/esp_led_drv/blob/master/user/led_controller.c
+.. _`Wifi LED driver`: {{<ref "posts/wifi-led-driver.rst">}}
+.. _`small driver`: {{<ref "posts/wifi-led-driver.rst">}}
+.. _`multichannel LED driver`: {{<ref "posts/multichannel-led-driver.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
diff --git a/content/posts/multichannel-led-driver.rst b/content/posts/multichannel-led-driver.rst
new file mode 100644
index 0000000..181fb63
--- /dev/null
+++ b/content/posts/multichannel-led-driver.rst
@@ -0,0 +1,6 @@
+---
+title: "Multichannel Led Driver"
+date: 2018-05-02T11:31:14+02:00
+draft: true
+---
+
diff --git a/content/posts/wifi-led-driver.rst b/content/posts/wifi-led-driver.rst
new file mode 100644
index 0000000..1c83de5
--- /dev/null
+++ b/content/posts/wifi-led-driver.rst
@@ -0,0 +1,6 @@
+---
+title: "Wifi Led Driver"
+date: 2018-05-02T11:31:03+02:00
+draft: true
+---
+
diff --git a/content/posts/zeus-hammer.rst b/content/posts/zeus-hammer.rst
new file mode 100644
index 0000000..d2a2eec
--- /dev/null
+++ b/content/posts/zeus-hammer.rst
@@ -0,0 +1,43 @@
+---
+title: "Zeus Hammer"
+date: 2018-05-03T11:59:37+02:00
+draft: true
+---
+
+In case you were having an inferiority complex because your friends' IBM Model M keyboards are so much louder than the
+shitty rubber dome freebie you got with your pc... Here's the solution: Zeus Hammer, a simple typing cadence enhancer
+for `PS/2`_ keyboards.
+
+.. FIXME: add demo video
+
+The connects to the keyboard's PS/2 clock line and briefly actuates a large solenoid on each key press. An interesting
+fact about PS/2 is that the clock line is only active as long as either the host computer or the input device actually
+want to send data. In case of a keyboard that's the case when a key is pressed or when the host changes the keyboard's
+LED state, otherwise the clock line is silent. We ignore the LED activity for now as it's generally coupled to key
+presses. By just triggering an NE555 configured as astable flipflop we can stretch each train of clock pulses to a
+pulse a few tens of milliseconds long that is enough to actuate the solenoid.
+
+.. image:: /images/zeus_hammer_schematic.jpg
+
+Since PS/2 sends each key press and key release separately this circuit will pulse twice per keystroke. It would be
+possible to ignore one of them but I figure the added noise just adds to the experience.
+
+Built on a breadboard, the circuit looks like this.
+
+.. image:: /images/zeus_hammer_breadboard.jpg
+
+The completed system looks like this.
+
+.. FIXME: add image of completed system
+
+Since my solenoid did not have a tensioning spring I used a rubber band and some vinyl tape to make an adjustable
+tensioner. The small orange USB hub serves as an end-stop because I had nothing else of the right shape. The sound and
+resonance of the thing can be adjusted to taste by moving the end stop, adjusting the tensioning rubber and tuning the
+excitation duration using the potentiometer. My particular solenoid was a bit slow so I added some pieces of circuit
+board as shims between the plunger and the case to limit the plunger's travel inside the solenoid core. Here is another
+video of the thing in action in which I tune and de-tune the mechanical resonance using the potentiometer.
+
+.. FIXME: add video w/ tune/detune
+
+.. _`PS/2`: https://en.wikipedia.org/wiki/PS/2_port
+