What Are EVs, The Technical Explanation, and Calibration of the Integrating Sphere

(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 (PWM).

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

Main Project Page – Test Results

Project Overview – What Is An Integrating Sphere, and How We Used One to Measure Cameras’ Low-Light Metering Capability

Frequently Asked Questions / FAQ

What are EVs, and What do They Mean for Different Cameras? (Non-Technical Explanation)

The Technical Explanation of EVs, and Calibration of the Integrating Sphere
(YOU ARE HERE)

So, How Did You Build an Integrating Sphere, Anyway?

Timelapse Methods Compared: Aperture Priority VS Holy Grail Method


 

Happy 7th birthday, Canon 6D. You’re still one of the best values in astrophotography!

Today, in 2012, the Canon 6D was announced. It only had a single SD card slot and Canon Rebel-style focus point layout, (so I didn’t count it as a top choice for my day job as a wedding photographer) …but its sensor was, and still is, a huge milestone in high ISO image quality. So, happy birthday, Canon 6D! (Also known as the 6D mk1 or 6D classic, now)

Canon 6D – Astrophotography Legend

The 6D sensor was shockingly good in its day. It forfeited just two megapixels compared to its bigger brother, the Canon 5D mk3, but it was actually significantly better than its predecessor at high ISO image quality, particularly 3200-6400 where many nightscape photographers will likely spend a lot of time.

Smart photographers who needed incredible image quality more than they needed the flagship AF and dual card slots that the 5D3 offered, opted for the 6D as soon as its image quality was extensively tested and nightscape, landscape, and adventure photographers, in general, realized that not only did it have great image quality at high ISOs, it had better dynamic range at its base ISO than all previous Canons ever, including all flagships.

Though, admittedly, that base ISO dynamic range was still 2-3 stops behind Nikon and Sony, so if you also do a ton of shooting at ISO 100, then I must stop praising the 6D for a second and suggest that you consider the similarly priced (used) Nikon D750, which recently had its 5th birthday, I  might add. The D750’s high ISO image quality is not as good as the 6D’s, (though it’s close!) but its dynamic range at ISO 100 is still considered “insane” *1 by today’s standards. (Just like the D600 and D610, BTW.)

*1 “insane” is a scientific measurement that means “way better than most photographers will ever need. In fact, you’re more likely to see a bigger difference in image quality by just making sure you use perfect technique, than switching from this camera to anything better.”

Although the Canon 6D lacks a lot of pro features, it wins big in one way- that “magnify” button can be programmed to offer 1-click 100% zooming, unlike the Nikon D600 and D610. It even plays back the zoomed-in image if the LCD is off!

Indeed, when shopping used, you can easily find a good condition 6D for $700-800, making it one of the best values on the market today for anyone who needs a hard-working full-frame sensor in a very affordable package.

Why buy a Canon 6D instead of a newer camera?

By the way, if you’re curious: why wouldn’t you buy a newer camera instead, let alone a camera for a newer, more future-proof mount? There’s the 6D mk2 and the 5D mk4 for Canon’s EF DSLR mount, both which are old enough to be found for decently good deals on the used market. Plus, there’s the Canon EOS RP which is the newest mirrorless camera body in their RF lineup, yet it debuted at a mere $1300 and can be found for under $1000 used, if you’re patient…

Glen Canyon, Utah | Canon EOS RP, Irix 15mm f/2.4

The answer is, yes, all these newer cameras are good, great even. BUT, they’re all not as “clean” at ISO 3200+ as the 6D sensor, as per photonstophotos.net. Shocking, but true.

Oh, and what about the Sony A7-series cameras that are also starting to get old, the 1st-gen and 2nd-gen A7, A7S, and A7R series cameras? You can definitely find them for under $1K, that’s for sure! But, this is because as underwhelming as the 6D’s other specs are, (autofocus, card slots, etc.) …the early Sonys are worse. Also, most of their oldest sensors are far worse at high ISO image quality.

The only old Sony A7-series cameras that have equal or better high ISO performance versus the Canon 6D are the A7R2, A7S, and A7S2. (As well as the A7R3, if you count it among the now-replaced cameras since the mk4 is here, but the R3 is still a $2500 camera, and remember, we’re shopping for a ~$700 full-frame body.)

So, if you’re just breaking into astrophotography now, if you’re on an extreme budget, and especially if you’re at all familiar with Canon cameras already, then the 6D is still your best value, despite being 7 years old. Whether or not it’s actually the right choice for you depends on your total budget for both lenses and bodies, and of course the other features you are likely looking for beyond image quality. Last, but the polar opposite of least, remember: it’s not about the gear, it’s about getting out there and shooting.

Search for a used Canon 6D on B&H (Latest price check: $689.95-$879.95, depending on the condition)