Although we perceive movies, TV shows, and lights as continuous displays, they're made up of discrete sequences of images and flashes of light. This circuit allows you to measure the frequency at which you start perceiving a flickering light as stable. It will allow you to replicate classic psychophysical experiments on visual perception.

You might find it useful if you're a professor of biology or psychology and want to demonstrate flicker fusion to your students, or if you're curious about visual perception and want to understand how the brain turns discrete images into coherent percepts.

Step 1: Build the Circuit

The circuit uses an Arduino to control an RGB LED. Follow the Fritzing diagram above to build it.

The frequency of the blinking is controlled by a quad encoder. The flicker frequency is displayed using an LCD display. One potentiometer controls the brightness of the LCD display, and the other the brightness of the LED. A push button cycles the color of the LED from red to green to blue.

Almost all of the elements needed to build this circuit were part of the Sunfounder Super Kit for Arduino (except the Arduino Uno itself). I had to buy an extra potentiometer (a 10k Philips potentiometer that you can find online for 0.20$). All the resistors are 10k. The three transistors are standard PNPs.

Step 2: Upload the Software

Use the Arduino IDE to upload the sketch below.

Some background: the tricky part was to get the LED to both blink and dim. Usually, dimming on an LED is implemented using high-frequency PWM (pulse width modulation). Low-frequency blinking is implemented using... low-frequency PWM. So how do you get both low-frequency blinking and high-frequency dimming?

Easy: you multiply the two! One master pin is modulated at a low frequency controlled by the TimerOne library. 3 pins output standard high-frequency PWM signals. I then use three transistors to multiply the three pairs of signals to separately control red, green and blue pins. The rest is pretty standard stuff.

/* Critical flicker fusion frequency circuit controller

Flashes an LED at a frequency controlled by a rotary encoder, displays
the frequency on a LCD, controls the brightness of the LED with a pot,
controls the color of the LED with a button.

Uses three transistors to multiply a low-frequency PWM pin (the one that does 
the visible low-frequency blinking) controlled with the TimerOne library with
three regular high-frequency PWM pins controlled by the usual digitalOutput.

Author: Patrick Mineault
http://xcorr.net
*/

#include <TimerOne.h>

// These two correspond to interrupts, so only work
// with pins 2 & 3 on the Uno.
// Button that controls the color of the LED.
const int buttonPin = 3;

// Quad encoder pin A
const int encoder0PinA = 2;

// For the other part of the quad encoder.
const int encoder0PinB = 12;  

// The slow modulation pin.
const int slowPin = 9;

// The fast modulation pins.
const int redPin = 11;
const int greenPin = 6;
const int bluePin = 5;

// The potentiometer has to be on an analog pin to be read.
const int potInput = A5;

// Move .5 Hz per rotation.
const int rotaryMultiplier = 2; 

volatile unsigned int encoder0Pos = 2; // Start at encoder0Pos / rotaryMultiplier (= 1) Hz
volatile unsigned int oldLedLum = 128; // Start at 50% luminance.
volatile unsigned int colorState = 0; // Start in the red state.

// Include the library code for the LCD.
#include <LiquidCrystal.h>

// initialize the library with the numbers of the interface pins.
LiquidCrystal lcd(7, 4, A0, A1, A2, A3);

void setup() { 
  // Display a friendly message on the LCD.
  lcd.begin(16, 2);
  lcd.print("Fusion freq circ");
  lcd.setCursor(0, 1);
  lcd.print("Ready");

  // Prepare the quad encoder.
  pinMode(encoder0PinA, INPUT); 
  digitalWrite(encoder0PinA, HIGH);
  pinMode(encoder0PinB, INPUT); 
  digitalWrite(encoder0PinB, HIGH);
  // Note: we use an interrupt to catch the quad encoder event.
  attachInterrupt(digitalPinToInterrupt(encoder0PinA), quadEncoderCallback, CHANGE);
  
  // Initialize the timer on the special low frequency modulator pin.
  Timer1.initialize(rotaryMultiplier * 1000000 / encoder0Pos);
  
  // initialize the pushbutton pin as an input:
  pinMode(buttonPin, INPUT);
  
  // Attach an interrupt to the push button callback
  attachInterrupt(digitalPinToInterrupt(buttonPin), pushButtonCallback, CHANGE);

  // Initialize the pins for the RGB LED.
  pinMode(redPin, OUTPUT);
  pinMode(greenPin, OUTPUT);
  pinMode(bluePin, OUTPUT);
} 

const int nstates = 4;
void loop(){
  // Always set the slow pin so that it has a 50% duty cycle.
  // 512 / 1024 == 50% duty cycle.
  Timer1.pwm(slowPin, 512);
  
  // Read the luminance of the LED from the potentiometer.
  int ledLum = map(analogRead(potInput), 0, 1023, 0, 255);
  if(ledLum != oldLedLum) {
    oldLedLum = ledLum;
  }
  
  // Set it so that there are 4 states, with the first being red, the second 
  // green, the third blue, and the fourth off.
  if(colorState % nstates == 0) {
      analogWrite(redPin, ledLum);
      analogWrite(greenPin, 0);
      analogWrite(bluePin, 0);
  } else if(colorState % nstates == 1) {
      analogWrite(redPin, 0);
      analogWrite(greenPin, ledLum);
      analogWrite(bluePin, 0);
  } else if(colorState % nstates == 2) {
      analogWrite(redPin, 0);
      analogWrite(greenPin, 0);
      analogWrite(bluePin, ledLum);
  } else {
      analogWrite(redPin, 0);
      analogWrite(greenPin, 0);
      analogWrite(bluePin, 0);
  }
}

void quadEncoderCallback() {
  /* If pinA and pinB are both high or both low, it is spinning
   * forward. If they're different, it's going backward.
   *
   * For more information on speeding up this process, see
   * [Reference/PortManipulation], specifically the PIND register.
   */
  if (digitalRead(encoder0PinA) == digitalRead(encoder0PinB)) {
    encoder0Pos++;
  } else {
    // Don't let it roll over.
    if(encoder0Pos != 0) {
      encoder0Pos--;
    }
  }
  
  // Set the frequency of the slow pin.
  Timer1.initialize( rotaryMultiplier * 1000000 / encoder0Pos); // in microseconds

  // And update the LCD display so it shows some nice feedback.
  lcd.setCursor(0, 0);
  lcd.clear();
  
  // Ideally you'd want a sprintf here to display a float here, but in the 
  // absence of this, print the integer part first, then multiply by 10, 
  //mod 10 to get the first decimal, and print that.
  float freq = float(encoder0Pos) / float(rotaryMultiplier);
  lcd.print(int(freq));
  lcd.print('.');
  lcd.print((int(freq * 10) % 10));
  lcd.print(" Hz");
}

void pushButtonCallback() {
  // Cycle through the color states.
  int buttonState = digitalRead(buttonPin);
  if(buttonState == 0) {
    colorState++;
  }
}

Step 3: Try It!

One interesting thing you'll notice is that the flicker fusion frequency changes depending on how you look at the light. In the center of the eye (the fovea), the flicker fusion frequency is around 40Hz. However, if move your eyes a bit, so the LED falls in the near visual periphery, you will notice the light flickering.

The flicker fusion frequency is quite a bit higher in the periphery; we're also much more sensitive to motion in the periphery than in the fovea. The higher flicker and motion sensitivity in the periphery is explained by the larger proportion of magnocellular retinal ganglion cells, which are sensitive to high temporal frequency. The higher sensitivity to motion and flicker means that when something changes in the periphery - where you don't have high spatial resolution - you can reflexively, and very rapidly turn your eye towards it. This is called a reflexive or stimulus-evoked saccade, and it's very important to rapidly detect foe or pray.

You can also try measuring differences in flicker fusion frequency as a function of brightness. The brighter the light, the easier it is to notice flicker. There's some interesting nonlinearities in the retina which make this happen.

Finally, you can try to detect differences in flicker fusion frequency with color. In theory, there shouldn't be much difference, unless the light is very very dim -- in the scotopic, or night vision range. That's because in that case, it's the rods, not the cones that are causing the response, and they have different visual sensitivities -- they don't see red, in particular. Try it in a dim room!