Why does Rosco's filter page show that 33% transmission is 1 stop rather than 50%?

Question

I was taught that each stop halves/doubles the light throughput. So one stop up is double as much light, one stop down is half as much light.

Now, according to this Rosco table: https://www.rosco.com/filters/ecolour.cfm Filter #207 has a throughput of 33%, that equals a 1 stop light loss.

Why? If one stop is half the light, then 50% throughput should equal 1 stop, and 33% should equal about 1 and 2/3 stops.

In the same way, according to the table, filter #208 has a throughput of 16%, that according to the table equals 2 stops. Isn't 2 stops supposed to be 1/4th of light, so 25%?

Where is my mistake?

Answer 1

If you look at filter #209 you'll see "Reduces light 1 stop (Transmission = 51%)". That is what you expect to see. Filter #210 reduces light 2 stops and has transmission of 24%. Again, what you expect. So what is the matter with filters 207 and 208? They are COLOR filters not neutral. They a) reduce light, and b) reduce it differently in different wavelength. See the datasheet of #207

So it makes 1 stop down (50%) and blocks blue wavelengthes which adds another 17%. Altogether you have ca. 67% loss.

Answer 2

This is because the filters you are looking at on that page are color filters in addition to neutral density filters. The ND portion is as described at How to read ND filter description? and as you expect: 0.3 has (around) 50% transmission, 0.6 25%, and 0.9 12.5%. From further down that table:

• #209: .3 Neutral Density — Reduces light 1 stop (Transmission = 51%)
• #210: .6 Neutral Density — Reduces light 2 stops (Transmission = 24%)
• #211: .9 Neutral Density — Reduces light 3 stops (Transmission = 13%)

The filters you are looking at are

• #207: CT Orange + .3 Neutral Density — Daylight to Tungsten 3200K and reduces light one stop. (Transmission = 33%)
• #208: CT Orange + .6 Neutral Density — Daylight to Tungsten and reduces light 2 stops. (Transmission = 16%)

... emphasis added on the "and".

Answer 3

About the notations used for filters: Notations based on tradition of 19th century scientist.

T = Transmission (always as a percent) O = Opacity (always as decimal fraction) D = Density (always as logarithmic value)

T as percentage O as decimal fraction (avoids confusion). D as log base 10 (because scientists of that era had no computers or calculators). They used slide rule and log tables. This technique simplified calculations. Many things like pH and star magnitude and human vision response light levels and earthquake and sound dB are based on log notation. The blackening of film due to exposure and developing is measured in Density.

ND 1 stop = T = 50% ---- O = 2.0 ---- D = 0.30

ND 2 stops = T = 25% ---- O = 3.98 ---- D = 0.60

ND 3 stops = T = 12.6% --- O = 7.94 ---- D = 0.90

ND 4 stops = T = 6.3% ---- O = 15.85 ---- D = 1.20

ND 5 stops = T = 3.2% ---- O = 31.62 ---- D = 1.50

ND 6 stops = T = 1.6% ---- O = 63.10 ---- D = 1.80

ND 7 stops = T = 8% ---- O = 125.9 ---- D = 2.10

ND 8 stops = T = 4% ---- O = 251.2 ---- D = 2.40

ND 9 stops = T = 1% ---- O = 501.2 ---- D = 2.70

ND10 stops = T = 0.1% ---- O = 1000 ---- D = 3.00