Estimating Oculus Rift pixel density


A few months ago I bought an Oculus Rift DK2. Although these are designed for VR gaming, they’re actually pretty reasonable stereo displays. They have several desirable features, particularly that the OLED display is pulsed stroboscopically each frame to reduce motion blur. However, this also means that each pixel is updated at the same time, unlike on most LCD panels, meaning they can be used for timing sensitive applications. As of a recent update they are also supported by Psychtoolbox, which we use to run the majority of experiments in the lab. Lastly, they’re reasonably cheap, at about £300.

In starting to set up an experiment using the goggles I thought to check what their effective pixel resolution was in degrees of visual angle. Because the screens are a fixed distance from the wearer’s eye, I (foolishly) assumed that this would be a widely available value. Quite a few people simply took the monocular resolution (1080 x 1200) and divided this by the nominal field of view (110° vertically), producing an estimate of about 10.9 pixels per degree. As it turns out, this is pretty much bang on, but that wasn’t necessarily the case, because the lenses produce increasing levels of geometric distortion (bowing) at more eccentric locations. This might have the effect of concentrating more pixels in the centre of the display, increasing the number of pixels per degree.

Anyway, I decided it was worth verifying these figures myself. Taking a cue from methods we use to calibrate mirror stereoscopes, here’s what I did…

First I created two calibration images, consisting of a black background, and either one central square, or two lateralised squares. All the squares were 200 pixels wide (though this isn’t crucial), and the one with two squares was generated at the native resolution of the Oculus Rift (2160×1200). Here’s how the first one looks:


And here’s how the other one, with only one square looked:


These images were created with a few lines of Matlab code:

ORw = 2160; % full width of the oculus rift in pixels
ORh = 1200; % height of the oculus rift in pixels
CSw = 1440; % height of other computer's display in pixels
CSh = 900;  % width of other computer's display in pixels
ORs = 200;  % width of the squares shown on the rift
CSs = 200;  % width of the square shown on the computer's display

a = zeros(ORh,ORw);
a((1+ORh/2-ORs/2):(ORh/2+ORs/2),(1+ORw/4-ORs/2):(ORw/4+ORs/2)) = 1;
a((1+ORh/2-ORs/2):(ORh/2+ORs/2),(1+3*ORw/4-ORs/2):(3*ORw/4+ORs/2)) = 1;

a = zeros(CSh,CSw);
a((1+CSh/2-CSs/2):(CSh/2+CSs/2),(1+CSw/2-CSs/2):(CSw/2+CSs/2)) = 1;

I then plugged in the Rift, and displayed the two-square image on it, and the one-square image on an iPad (though in principle this could be any screen, or even a printout). Viewed through the Rift, each square goes to only one eye, and the binocular percept is of a single central square.

Now comes the clever bit. The rationale behind this method is that we match the perceived size of a square shown on the Rift with one shown on the iPad. We do this by holding the goggles up to one eye, with the other eye looking at the iPad. It’s necessary to do this at a bit of an angle, so the square gets rotated to be a diamond, but we can rotate the iPad too to match the orientation. I found it pretty straightforward to get the sizes equal by moving the iPad forwards and backwards, and using the pinch-to-zoom operation.

Once the squares appeared equal in size I put the Rift down, but kept the iPad position fixed. I then measured two things: the distance from the iPad to my eye, and the width of the square on the iPad screen. The rest is just basic maths:

The iPad square was 7.5cm wide, and matched the Rift square at 24cm from the eye. At that distance an object 1cm wide subtends 2.4° of visual angle (because at 57cm, 1cm=1°). [Note, for the uninitiated, the idea of degrees of visual angle is that you imagine a circle that goes all the way around your head, parallel to your eyes. You can divide this circle into 360 degrees, and each individual degree will be about the size of a thumbnail held at arm’s length. The reason people use this unit is that it can be calculated for a display at any distance, allowing straightforward comparison of experimental conditions across labs.] That means the square is 2.4*7.5=18° wide. Because this is matched with the square on the Rift, the Rift square is also 18° wide. We know the square on the Rift is 200 pixels wide, so that means 18° = 200 pix, and 1° = 11 pixels. So, the original estimates were correct, and the pixel density at the centre of the screen is indeed 11 pixels/deg.

This is actually quite a low resolution, which isn’t surprising since the screen is close to the eye, individual pixels are easily visible, and the whole point of the Rift is to provide a wide field of view rather than a high central resolution. But it’s sufficient for some applications, and its small size makes it a much more portable stereo display than either a 3D monitor or a stereoscope. I’m also pleased I was able to independently verify other people’s resolution estimates, and have developed a neat method for checking the resolution of displays that aren’t as physically accessible as normal monitors.

Aesthetically pleasing, publication quality plots in R


I spend a lot of my time making graphs. For a long time I used a Unix package called Grace. This had several advantages, including the ability to create grids of plots very easily. However it also had plenty of limitations, and because it is GUI-based, one had to create each plot from scratch. Although I use Matlab for most data analysis, I’ve always found its plotting capabilities disappointing, so a couple of years ago I bit the bullet and started learning R, using the RStudio interface.

There are several plotting packages for R, including things like ggplot2, which can automate the creation of some plots. Provided your data are in the correct format, this can make plotting really quick, and tends to produce decent results. However, for publication purposes I usually want to have more control over the precise appearance of a graph. So, I’ve found it most useful to construct graphs using the ‘plot’ command, but customising almost every aspect of the graph. There were several things that took me a while to work out, as many functions aren’t as well documented as they could be. So I thought it would be helpful to share my efforts. Below is some code (which you can also download here) that demonstrates several useful techniques for plotting, and should create something resembling the following plot when executed.

Example plot created by the script.

Example plot created by the script.

My intention is to use this script myself as a reminder of how to do different things (at the moment I always have to search through dozens of old scripts to find the last time I did something), and copy and paste chunks of code into new scripts each time I need to make a graph. Please feel free to use parts of it yourself, to help make the world a more beautiful place!

# this script contains examples of the following:
# outputting plots as pdf and eps files
# creating plots with custom tick mark positioning
# drawing points, bars, lines, errorbars, polygons, legends and text (including symbols)
# colour ramps, transparency, random numbers and density plots

# Code to output figures as either an eps or pdf file. Note that R’s eps files appear not to cope well with transparency, whereas pdfs are fine
outputplot <- 0
if(outputplot==1){postscript(“filename.eps”, horizontal = FALSE, onefile = FALSE, paper = “special”, height = 4.5, width = 4.5)}
if(outputplot==2){pdf(“filename.pdf”, bg=”transparent”, height = 5.5, width = 5.5)}
# all the code to create the plot goes here
if(outputplot>0){dev.off()}  # this line goes after you’ve finished plotting (to output the example below, move it to the bottom of the script)

# set up an empty plot with user-specified axis labels and tick marks
plotlims <- c(0,1,0,1)  # define the x and y limits of the plot (minx,maxx,miny,maxy)
ticklocsx <- (0:4)/4    # locations of tick marks on x axis
ticklocsy <- (0:5)/5    # locations of tick marks on y axis
ticklabelsx <- c(“0″,”0.25″,”0.5″,”0.75″,”1”)        # set labels for x ticks
ticklabelsy <- c(“0″,”0.2″,”0.4″,”0.6″,”0.8″,”1”)    # set labels for y ticks

par(pty=”s”)  # make axis square
plot(x=NULL,y=NULL,axes=FALSE, ann=FALSE, xlim=plotlims[1:2], ylim=plotlims[3:4])   # create an empty axis of the correct dimensions
axis(1, at=ticklocsx, tck=0.01, lab=F, lwd=2)     # plot tick marks (no labels)
axis(2, at=ticklocsy, tck=0.01, lab=F, lwd=2)
axis(3, at=ticklocsx, tck=0.01, lab=F, lwd=2)
axis(4, at=ticklocsy, tck=0.01, lab=F, lwd=2)
mtext(text = ticklabelsx, side = 1, at=ticklocsx)     # add the tick labels
mtext(text = ticklabelsy, side = 2, at=ticklocsy, line=0.2, las=1)  # the ‘line’ command moves away from the axis, the ‘las’ command rotates to vertical
box(lwd=2)      # draw a box around the graph
title(xlab=”X axis title”, col.lab=rgb(0,0,0), line=1.2, cex.lab=1.5)    # titles for axes
title(ylab=”Y axis title”, col.lab=rgb(0,0,0), line=1.5, cex.lab=1.5)

# create some synthetic data to plot as points and lines
datax <- sort(runif(10,min=0,max=1))
datay <- sort(runif(10,min=0.2,max=0.8))
SEdata <- runif(10,min=0,max=0.1)
lines(datax,datay, col=’red’, lwd=3, cex=0.5)     # draw a line connecting the points
arrows(datax,datay,x1=datax, y1=datay-SEdata, length=0.015, angle=90, lwd=2, col=’black’)  # add lower error bar
arrows(datax,datay,x1=datax, y1=datay+SEdata, length=0.015, angle=90, lwd=2, col=’black’)  # add upper error bar
points(datax,datay, pch = 21, col=’black’, bg=’cornflowerblue’, cex=1.6, lwd=3)   # draw the data points themselves

# create some more synthetic data to plot as bars
datax <- 0.1*(1:10)
datay <- runif(10,min=0,max=0.2)
SEdata <- runif(10,min=0,max=0.05)
ramp <- colorRamp(c(“indianred2”, “cornflowerblue”))  # create a ramp from one colour to another
colmatrix <- rgb(ramp(seq(0, 1, length = 10)), max = 255)   # index the ramp at ten points
barplot(datay, width=0.1, col=colmatrix, space=0, xlim=1, add=TRUE, axes=FALSE, ann=FALSE)  # add some bars to an existing plot
arrows(datax-0.05,datay,x1=datax-0.05, y1=datay-SEdata, length=0.015, angle=90, lwd=2, col=’black’)  # add lower error bar
arrows(datax-0.05,datay,x1=datax-0.05, y1=datay+SEdata, length=0.015, angle=90, lwd=2, col=’black’)  # add upper error bar

coltrans=rgb(1,0.5,0,alpha=0.3)             # create a semi-transparent colour (transparency is the alpha parameter, from 0-1)
a <- density(rnorm(100,mean=0.75,sd=0.1))   # make a density distribution from some random numbers
a$y <- 0.2*(a$y/max(a$y))                   # rescale the y values for plotting
polygon(a$x, 1-a$y, col=coltrans,border=NA) # plot upside down hanging from the top axis with our transparent colour

# create a legend that can contain lines, points, or both
legend(0, 1, c(“Lines”,”Points”,”Both”), cex=1, col=c(“darkgrey”,”black”,”black”), pt.cex=c(0,1.8,1.8), pt.bg=c(“black”,”violet”,”darkgreen”),lty=c(1,0,1), lwd=c(5,3,3), pch=21, pt.lwd=3, box.lwd=2)
# add text somewhere, featuring symbols and formatting
text(0.8,0.95,substitute(paste(italic(alpha), ” = 1″ )),cex=1.2,adj=0)

In Rainbows


Our department recently obtained a custom-made Psychology logo rainbow flag to celebrate pride month.


This matches the rainbow seating in our staff room!


Vision in amblyopia


In recent years there have been a number of treatments proposed for amblyopia in adults. These treatments (reviewed in this paper) often involve balancing the inputs to the two eyes – down-weighting the input to the stronger eye to allow the weaker eye to contribute. The treatments improve visual function in the amblyopic eye, and some patients have even recovered stereo vision (e.g. see this TEDx video by ‘stereo’ Sue Barry). However we know very little about the mechanisms by which these improvements occur, or indeed what the nature of the neural deficits in amblyopia actually are.

Today a new paper came out online in the journal Investigative Ophthalmology & Vision Science. In it, we show that neural responses in amblyopia are reduced in the affected eye. We used a steady-state visual evoked potential technique to measure responses in each eye. The reductions are large enough that they could potentially be used to monitor improvements in visual function during treatment.

These data served as the pilot results for a grant proposal that was recently funded by the Centre for Chronic Diseases and Disorders (and part-funded by the Wellcome Trust). The plan is to use both fMRI and EEG to understand the architecture of the amblyopic binocular visual system, and to monitor improvements in visual function during a course of therapy. A postdoc job is available for 18 months to work on this project, and I’d be very interested in hearing from qualified applicants before the deadline (27th February 2015).

Welcome to new PhD students


Our term started last week. Returning to the lab is Greta Vilidaitė. Greta completed a summer project last year, and now returns as a PhD student. Her project will investigate abnormalities of neural noise in autism spectrum disorders. She is pictured here drinking some very strong mead from her native Lithuania.


Another new addition is Dave Coggan. Dave completed our Cognitive Neuroscience masters course last year, and now returns to start a PhD supervised by Tim Andrews and myself. He will study processes of mid-level vision using fMRI. He is pictured here singing at the annual ECR karaoke night.


Conferences and various things


I’ve just finished a very busy term. It was my first term of proper teaching, which took up a lot more time than I was expecting. It seemed to go well though – I got some very positive feedback from the students, as well as some hilarious comments (“Iron your shirts!!!” being my favourite…).

I’ve also been planning two conferences that we’re holding at York this year. The AVA meeting is in a few weeks time on the 11th April. We’ve got some excellent talks lined up, and have just finalised the program. Also, the BACN meeting is taking place in September, so still plenty of time to submit abstracts for that.

Last week I was up in Glasgow, where I gave a talk in the optometry department at Glasgow Caledonian. I also went to an excellent gig at King Tut’s Wah Wah Hut, where my old band played a few times about 15 years ago. We saw two bands from the 90s: Republica and Space. It looked like this:

Space at King Tut's

Space at King Tut’s

Other than that, I’ve had a couple of papers out this year, and am working on some more. I’m also anxiously awaiting news of a BBSRC grant proposal I put in back in September. I got some very positive reviews in January, and should hear next month whether it’s been funded. Fingers crossed!

Arduino sound to TTL trigger for EEG





Arduino trigger





PsychPortAudio(‘Start’, tr);





#define DEBUG 0 // change to 1 to debug 
 int prev_voltage = 0; // must be initialized to something
 void setup() {
  if(DEBUG) {
  // set output pin
  pinMode(outPin, OUTPUT);
 void loop() {
   // read input on analog pin 0
  float voltage = sensorValue * (5.0 / 1023.0);
 if(DEBUG) {
    Serial.println(voltage); // This delays the trigger by
                             // about 6ms so remove before using
                             // during experiments
    // Simplest algorithm ever.  
    if (voltage > prev_voltage + THRESHOLD)
      digitalWrite(outPin, HIGH);
     digitalWrite(outPin, LOW); 
   prev_voltage = voltage;