(This article is a supporting part of our ongoing testing of low-light camera metering reliability)
Exposure Values (EVs) are units that photographers use to measure the brightness of a subject or environment. In the days before electronic cameras, photographers used hand-held light meters that reported the light level in EVs and equivalent camera settings. Eventually, light meters shrank enough to fit inside cameras, and this made automatic exposure possible. EVs are usually quoted for ISO 100 images–if the ISO is not specified, this can be assumed. The formal definition of EV is:
where N is the f-number, t is the exposure time, and S is the ISO. EV0 corresponds to a 1-second exposure with a f/1.0 lens at ISO 100. A change in EV of 1 indicates that the light has doubled or halved.
You may notice that this definition of EV does not include any information about the scene. Some assumptions must be made about how a scene of a given brightness should be mapped to the film’s or detector’s dynamic range. The next step is
where L (denoted Lv in many physics texts) is the luminance of the scene in units of cd/m2, and K is the reflected-light meter calibration constant. 1 cd (candela) = 1 lm/sr (lumen per steradian) = 1 lx m2 / sr (lux square meter per steradian). Canon, Nikon, and Sekonic use K = 12.5 cd ISO / m2 for their metering systems, so my calculations do too. Therefore 0 EVISO100 corresponds to a luminance of L = 0.125 cd/m2. However, there is no wavelength information in these units. Luminance is the total spectrum of the subject’s light multiplied against the human eye’s response. Mathematically,
where L is the luminance of the earlier equation, is a dimensionless luminosity function described shortly, and Le,Ω(λ) is radiance and has units of W / (sr m2 nm), and λ is wavelength. The luminosity function gives the normalized response of human vision to light of different wavelengths. As shown in the plot below, is 0 below 400 nm and above 700 nm, and it peaks at 1.0 at 555 nm.
In other words, we can’t see light outside the 400-700 nm range, and our peak sensitivity is to 555 nm (yellow-green) light. I used the Judd/Voss 1978 luminosity function because it seems to be fairly standard, though I could not find any reference to it in the light meter literature I reviewed.
I borrowed a spectrophotometer and pointed it into my illuminated integrating sphere. I commanded the Arduino to power the LEDs at maximum brightness. The resulting spectrum is plotted in red above and is the Le,Ω(λ) in the third equation above.
By inserting the measured spectrum and Judd/Voss luminosity function the third equation, I calculated the luminance L. This was then inserted into the second equation to calculate the brightness of the sphere in EVs. Finally, I adjusted the current to the LEDs using a variable resistor and collected new spectra until the sphere was EV0. At that point, I glued the variable resistor so it couldn’t be bumped.
At this point, the maximum brightness of the sphere was EV0. Next, I pulsed the LEDs at 240 Hz with various duty cycles to achieve dimmer lighting conditions. EV-1 was achieved by turning on for 1/480 of a second and then off for 1/480 of a second (i.e. a 50% duty cycle). EV-2 was achieved by turning on the LED for 1/960 of a second and off for 3/960 of a second (i.e. a 25% duty cycle). And so on, until EV-10 was 4 microseconds on followed by 4163 microseconds off (0.1% duty cycle). This technique is called pulse width modulation.
The Arduino struggles with microsecond-precision timings, so some adjustments to the above scheme were made. Finally, to check that the PWM response was as commanded, I put a camera in the integrating sphere and doubled the sensitivity (ISO and/or shutter speed) with every 1 stop decrease in light. The result was this plot:
In an ideal world, the result would be perfectly flat. In reality, this is a 9% peak-to-valley nonlinearity. The quasi–EV-10 lighting level is log21.0949 = 0.13 stops brighter than it should be. Since camera meters have 0.33-stop increments, and most cameras have no metering sensitivity at EV-10 anyway, I consider this nonlinearity acceptable.
In summary, light is a function of many quantities: wavelength, flux, directionality, polarization, phase, coherence, and so on. A photographic light meter simplifies these parameterizations of light into a single number: EVs (or, equivalently, ISO, shutter speed, and aperture). I measured the internal radiance of the integrating sphere using a spectrophotometer and adjusted its LEDs to achieve EV0. The conversion from radiance (i.e. actual physics units) to EVs (photographer units) involved three assumptions in the math: 1) the metering calibration constant of K=12.5, which is the value used by Canon, Nikon, and Seikonic; 2) the Judd/Voss 1978 luminosity function for the human eye’s response to color; and 3) the radiance reported by the spectrophotometer. The spectrophotometer had been calibrated in the previous year, and these assumptions are reasonable, but any change in them would affect the calibration from LED output to EVs of ambient brightness. Finally, I confirmed that the pulse width modulation of the LEDs creates lighting conditions as expected.
Integrating Sphere & Camera Metering Test Project