Since the dawn of photography, man has attempted to push the limits of speed. Never content with that f/11 meniscus lens, he pushed on to bigger and bigger glass, wider and wider apertures, whatever the cost in equipment and image quality. I predict that by the year 1961, man will have designed a lens with a shockingly fast aperture of 0.95.

1. Can a cool new lens...

"the FASTEST 35 standard production lens ever made for 35mm rangefinder cameras,"

"The previous 35 RF speed king lens was the Leica 35/1.4 ASPH.  Will an half a stop really make any difference to you?  Most of the time certainly not, but if you are a pro and that extra half a stop even brings you just one extra printable pic a year, it could make a big difference in your pocketbook if the other shooters at the event missed the shot in the low light."

or so the pitch goes for the new Cosina Voigtlander 35/1.2 Nokton (wow, that's a pretty cool name). I am not setting out to pick on Cosina specifically; the quest for speed (and the marketing) began with Ernemann in the early 1900s and continued with Zeiss, Nikon, Zunow, Fuji, Konica, Canon, and Leica rangefinder lenses through the 1960s - and even up to the present. Arguably until the 1970s, superspeed lenses were mainly a show-off type of exercise. Maybe they still are.

2. ...rewrite the laws of physics?

For fifty years, lenses have been increasing in speed, or so we have been told. Manufacturing statements that describe lens speeds are are largely true as they relate to the aperture (opening at the lens node divided by focal length). Where they fall somewhat short is in describing the amount of light a lens of a given aperture can actually transmit.

Apertures (f-stops) are largely derived by simple division. T-stops (t=transmission) is a measure used in cinema applications, where screwing up exposure is a much bigger issue. T-stops are derived by measuring light transmission through an optic and converting that measurement into a logarithmic scale similar to f/stops. Unlike the maximum f/stop of a lens, which is invariable no matter how complex the lens, maximum T-stop (transmission) of a lens can diminish considerably if it has a lot of elements. Given even modern coatings, light loss per surface can make lenses considerably slower in real life than they are in advertising fantasy.

The transmission dropoff was something I discovered in practice when comparing a 50/1.5 Canon to a 50/1.2 Canon. There was about a 1/3 stop difference in f/stops, but the light transmission difference was really a lot smaller in practice (as in imperceptible on film or in scans). Then I did some research on light loss and learned that the entire difference could be swallowed by light transmission loss in a single-coated system. I surmised that this was because the 50/1.5 had 6 air-glass surfaces, and the 50/1.2 had something like 10. This is why you almost have to chuckle at the prices that 85/1.5 Summarexes and Canons get; they could not be nearly as fast in reality as they seem to be on paper. But read on; the fun doesn't end with lens coatings.

3. Air-Surface Loss

We will start with the coatings, which are the first thing you see when you look at a lens. These have an effect on light transmission. Many people work from the assumption that the biggest advance in lens technology was the invention of the coating. So first we will come up with a way of validating or disproving that idea.  According to Schneider, the light loss for each air-glass interface is

– 4% for uncoated glass

– 2% for single-coated glass

– 0.5% for MRC glass

Hoya (an equally reputable source, since they make Leica elements) claims that it is

– 4-4.5% for uncoated glass

– 2-2.5% for single-coated glass

– 0.5-1% for HMC glass

"But wait! you protest. My Pentax SMC materials/Osterloh book/etc. say(s) that the multicoating on my Pentax lens lose only 0.2% at each surface." Maybe yes, maybe no. To be effective, coatings must be a uniform thickness of 1/4 wavelength of the light they are designed to protect. The wavelength of yellow-green light, the reference for antireflection coatings, is 589 nanometers. You can do the math and figure out just how thin (and precise the coating must be).

As one optical engineer who read this article in its first draft told me, the antireflective effect falls off quickly on either side of the target wavelength. As my further research has revealed, coating efficiency is highly on the incident angle of the light. So maybe there 0.2% at each surface, on a bright, clear day, with no lateral illumination. You might have wondered how it is possible for multicoated lenses to flare.

If it were my call, I would probably take the Schneider (Schott) or Hoya numbers as a more realistic estimate of the real-world performance of coatings. The Pentax number may only be valid for collimated, coherernt light sources.

4. Fun with Magnesium Flouride and Math?

As Kingslake advocated, it is possible to estimate transmission loss by reference to the number of air-glass surfaces. The first step is to first figure out what percentage proportion of the light is lost at glass-air interfaces.

T(ransmission %)= (1-S)^N

Where S is the transmission loss (the percentage expressed as a decimal) per surface, N is the number of air-glass surfaces in the lens (generally, twice the number of single elements and cemented groups). Note that published "groups" in modern convention can also mean airspaced groups. It is true that there is some loss associated with the cemented interface, but it is so small compared to glass and air that it is insignificant.

Next, we will take that percentage to compute the loss in light (as a percentage) to f/stops.

ABS (Log₂ T) = L(oss in f/stops)

Example (a really bad f/2.8 lens): ABS (Log₂ 50%) = 1 stop loss

Then the math gets tougher. We now need to add L to A, the geometric aperture, to reach a corrected value for the lens. The easiest way to do this is in two parts. The first is to create a multiplier for the geometric f/stop.

2^0.5L = M

Example:= 2^0.5•1 = 1.41

If you don't have your scientific calculator handy, this is a table correlating light loss in stops to the multiplier for the numerical aperture.

(So, for example, you can see that 1 stop less transmission than f/2.8 is f/4).  Then you do the last step: multiply M by the geometric aperture (what is written on the lens, if you believe that).

AM = T_est.

f/2 • 1.41 = f/2.8

This will give you an estimated T-stop (or more accurately, a corrected f/stop) based on the glass-air surfaces.

5. So where does it get you?

Depends on what you are doing with the numbers.

Coated vs. Uncoated. When you wade through the math, you find that the light loss from glass-air contact is not as big a factor as you might imagine in comparing coated and uncoated lenses. Using the formula, the best an uncoated 50/1.5 Xenon could do is 1.89 (@4.5%); if you could drop the loss to even 2% per surface, you can get 1.66, so you are in the neighborhood of 1/2 a stop. This was not a small deal in the 1950s, when color film was pushing a blistering 25 ASA. Today, most people consider ISO 400 a normal color film, and color films today are built with huge latitude (at a minimum one stop underexposure). Just as an FYI, the much maligned 50mm f/2 Leica Summar (6 elements in 4 single and cemented groups) would rate a 2.12.

Sonnar vs. Planar. Conventional wisdom is that the Planar-style 50mm lenses could never be as good as triplets (and their derivatives like Tessars and Sonnars) until coatings were developed. But this explains precious little of of the difference between Planars and triplets. An f/1.5 Sonnar has a 7/3 construction (6 interfaces). Assuming 4.5% loss per interface, a "perfect" uncoated f/1.5 Sonnar would have TE=1.72 (in other words still better than a theoretically-perfect f/2 multicoated lens). After the war (with coated lenses losing 2% per surface), the Sonnar would rate a TE of 1.59; the Summilux 50/1.4 (7/5) would hit 1.58. The difference is that the Summilux could have superior correction through a greater number of elements.

Superspeed Japanese lenses of the 1950s. Here's where it gets weird. In the late 1950s and early 1960s, they made bigger and heavier and allegedly-faster lenses. Corrected for their air-glass interfaces, they are, in (likely) descending speed order:

1.Canon 50/0.95 - f/1.05 (10 surfaces)

2. Zunow 5cm f/1.1 - f/1.22 (12 surfaces)

3. Canon 50mm f/1.2 - f/1.22 (10 surfaces)

4. Nikkor 5cm f/1.1 - f/1.24 (12 surfaces)

5. Fuji 5cm f/1.2 - f/1.30 (8 surfaces)

6. Konishiroku Hexanon 60mm f/1.2 - f/1.33 (12 surfaces)

So even here, not everything as it seems.

6. The Devil is in the Darkening

So it looks like coatings and air-glass surfaces are a dead end even for figuring out why coated lenses seem so much better. Coatings are no good as a definitive measure of lens speed due to a number of factors which don't fit neatly into a formula.

Glass improvements and reduction of light absorption by the glass itself. Through the 1950s, the refractive index of glass was on the rise. This led to thinner lens elements and less loss in the actual glass of the element. The same went for the development of lower-dispersion glass. These, arguably, had more of an effect on performance than even coatings did.

Off-Axis Flare. If multicoating could truly knock down light loss to 0.2% per surface, then your lens would never flare. Flare likes to come in when the light is not perpendicular to the coating surface it is hitting. This deflects part of the light through the glass sideways.

Lens mount flare. Many lenses are painted black inside to kill internal reflections. If a lens barrel is too reflective, light can skate in sideways, bounce off the inside of the lens barrel and hit the next element off-axis. One thing to remember is that light never travels straight into a lens along the optical axis. Unless it's a laser.

Overstating the maximum aperture of a product (see any Pop Photo test for the measured aperture) can make a lens sound much faster than it really is.

So there is no way it can approach the accuracy of measured T-stops, but it should at least provide a method for comparing the effective speeds of two lenses made with the same types of glass. As a benchmark, many cine lenses have T-stops that are, by the numbers, 10% smaller than the f/stop of the lens (i.e., f/2.2 instead of f/2).

7. Some things they don't tell you about superspeed lenses

While you may be excited to rush out and replace all of your normal-speed lenses with superspeed lenses, you may be in for some nasty shocks.

Size and weight. All superspeed lenses are B-I-G and H-E-A-V-Y. For example, 50mm f/2 rangefinder lenses generally have 39mm or 40.5mm filter threads. A 50/1.2 Canon RF lens has a 55mm front thread. It gets worse with SLR lenses, where 62mm is not unknown. For example, the 35/1.2 Cosina Voigtlander lens is approaching the size of a Coke can (95mm projection vs. 120mm for the coke can). Weight can also more than double as the apertures get bigger. The weight does not go away on sunny days.

Cost. Superspeed lenses are much more expensive than normal lenses. This is because they are low-volume items and because it costs a lot more to grind bigger glass to high tolerances.

Contrast. Universally, superspeed lenses are less contrasty than, say, f/2 lenses. They are allegely designed this way because situations where you actually need the speed involve hight-contrast lighting.

Illumination. Superspeed lenses tend to have high light falloff in the corners, meaning that evenly-illuminated surfaces (sky, for example) will darken in the corners.

Depth of field. Faster lenses mean less depth of field. This means that close-up, you may get someone's eyes and the bridge of the nose in focus. While this may be fun for effect when it works, it shows up your focusing errors in grand fashion. Superspeed lenses have no realistic hope of minimizing depth of field outside during the day; try to shoot any lens at f/1.2 during daylight on a camera with a 1/1000 sec maximum speed. You're actually better off moving to a fast medium telephoto.

When you are looking at say, an f/1.4 vs. an f/1.2, you are looking at a half-stop difference. This is practically insignificant with black and white film and even 100-speed color neg film. For that extra half-stop, you are trading a lot of contrast and optical correction.

With a straight-line film like Plus-X or T400CN, you have little to lose by using a slightly-slower lens and underexposing by that half-stop. Unlike digital, film does not get really noisy when it is underexposed (in fact, what gets noisy are the bright parts of negatives when you scan them), so you might lose shadow detail but not much else.

8. Upshot

The moral of the story is that stated numerical aperture of a lens and even the types of coatings it has can be a red herring, especially when you are comparing two lenses of a like vintage and close maximum aperture (f/1.4 vs 1.5).

But admit it, superspeed lenses are cool.