What is the Relationship Between Candelas, Watts, and Brightness?

[guyburns]

The SMPTE 196M standard specifies screen brightness for cinemas, as 55 candela per square meter, open gate (no film in the projector, just white light). It used to be specified in terms of foot-lamberts, but let's stick to SI.

I ultimately want to compare the brightness I see in a cinema, with what I see at home and in the local auditorium. But before we get there, I want to go back to basics. With assistance here, I'm hoping to obtain a pretty good understanding of brightness and how it is measured. I'll make certain statements to test my understanding as I go along. Feel free to tell me if I'm right or wrong.

So, just like in Sound of Music, let's start at the very beginning: candelas:

A source that emits monochromatic radiation of frequency 540×10^12 hertz and that has a radiant intensity in that direction of 1/683 Watts per steradian, has an intensity of 1 candela.​

Statement 1
An ordinary candle has a luminous intensity of about 1 candela.

Statement 2
Candelas, and therefore all related light measurements, at the most fundamental level are measuring Watts – the power of the light. Our eyes interpret that power as brightness, but really, it's Watts.

Statements 3

• On the surface of an imaginary sphere, 1 metre from a candle, the power arriving at each square metre will be about 1/683 Watts.
• Let's say the power arriving on the Earth's surface from the Sun is 1kW per square metre. Therefore, compared to a surface 1 metre from a candle, the Sun provides 683,000 times more power at the surface of the Earth.
• But the Earth is 1.5 x 10^8 metres from the sun.
• So the Sun is approximately (6.83 x 10^5) x (1.5 x 10^8)^2 = 1.5 x 10^22 candlepower.

If my understanding of candelas is correct, I can move onto lumens.

Please bear with me. This is going to take some time as I work my way through lumens, lux, candela per square metre, and finally to EV.

 

[olgerm]

Earth is 1.5 x 10^8 metres from the sun.

it is approximately $1.5 \cdot 10^{11}\cdot m$ .

Candelas, and therefore all related light measurements, at the most fundamental level are measuring Watts

Candelas and watts are related, but ratio depends of wavelenght and is called luminous efficacy. (https://en.wikipedia.org/wiki/Luminous_efficacy)

${\displaystyle K={\frac {\Phi _{\mathrm {v} }}{\Phi _{\mathrm {e} }}}={\frac {\int _{0}^{\infty }K(\lambda )\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda }{\int _{0}^{\infty }\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda }},}$

• Φv is the luminous flux;
• Φe is the radiant flux;
• Φe,λ is the spectral radiant flux;
• K(λ) = KmV(λ) is the spectral luminous efficacy.

 

[guyburns]

I forgot to convert km to metres. Make the sun about 1.5 x 10^28 candle power.

Ques: Is there an instrument that measures candelas?

 

[Andy Resnick]

The SMPTE 196M standard specifies screen brightness for cinemas, as 55 candela per square meter, open gate (no film in the projector, just white light). It used to be specified in terms of foot-lamberts, but let's stick to SI.

I ultimately want to compare the brightness I see in a cinema, with what I see at home and in the local auditorium.

Let's correct a few things. 'Candela' is a photometric unit, not a radiometric unit. A candela is a measure of luminous intensity, but a foot-lambert is a unit of luminance (cd/m^2) and so they are not equivalent. In order to determine luminous intensity, you need to specify either the angular distribution of light emission or the collection optics for the detector.

Candela does not refer to Watts- 1 cd = 1 lm/sr.

 

[guyburns]

Thanks for the response, Andy – but you've confused me when you said "they are not equivalent".

The statement about the SMPTE standard came from https://en.wikipedia.org/wiki/Foot-lambert, and it says that a standard measured in foot-lamberts has been replaced with a standard measured in candelas per square meter. Aren't they the same unit?

I'm here to learn about brightness, and I'd like responses to be kept very simple and basic if possible.

I'm trying to get a grip on candelas and I need convincing that candelas, as defined in my original post, are not simply a measure of the Watts crossing a surface. i.e. that there is a direct correlation: double the Watts, double the candelas – under the conditions of the definition. If there is a better way of understanding candelas, please let me know. Just saying it is luminous intensity or brightness doesn't satisfy me. What is brightness? What is luminous intensity? How do you measure it? With what instrument?

I may be wrong, but I have the idea that candelas can't be measured directly. So if you can't measure them directly, what are they? To put it another way, I can measure distance, weight, pressure with simple instruments – directly. I may not get an accurate meaasurement, but anyone can understand what's being measured. What's being measured when a candela is measured?

 

[Andy Resnick]

Thanks for the response, Andy – but you've confused me when you said "they are not equivalent".

The statement about the SMPTE standard came from https://en.wikipedia.org/wiki/Foot-lambert, and it says that a standard measured in foot-lamberts has been replaced with a standard measured in candelas per square meter. Aren't they the same unit?

A foot-lambert and cd/m^2 are the same unit; a foot-lambert and cd are not the same unit. I may have mis-read the OP.

I'm trying to get a grip on candelas and I need convincing that candelas, as defined in my original post, are not simply a measure of the Watts crossing a surface. i.e. that there is a direct correlation: double the Watts, double the candelas – under the conditions of the definition. If there is a better way of understanding candelas, please let me know. Just saying it is luminous intensity or brightness doesn't satisfy me. What is brightness? What is luminous intensity? How do you measure it? With what instrument?

I may be wrong, but I have the idea that candelas can't be measured directly. So if you can't measure them directly, what are they? To put it another way, I can measure distance, weight, pressure with simple instruments – directly. I may not get an accurate meaasurement, but anyone can understand what's being measured. What's being measured when a candela is measured?

A picture is worth 1000 words:

http://www.dfisica.ubi.pt/~hgil/Fotometria/HandBook/ch07.html

Does this help? Isotropic sources make a lot of the above seem needlessly complicated. Things are more interesting for directional sources.

 

[f95toli]

Ques: Is there an instrument that measures candelas?

Yes, a radiometer (for precise calibration work a cryogenic radiometer).

 

[Andy Resnick]

Yes, a radiometer (for precise calibration work a cryogenic radiometer).

Not exactly- a radiometer will measure power (flux). If you know the area of the aperture, you can measure incidance (flux density). If the radiometer is calibrated with a point source, you can measure radiant intensity and if it is calibrated with an extended source, you can measure radiance. If you know the spectral response of the detector, you can then normalize the radiometer and compute the corresponding photometric quantities (or other normalization schemes, such as finsens).

A candela corresponds to luminous intensity.

 

[f95toli]

Sorry, you are right; I meant photometer; not radiometer.
(photometers are calibrated with the help of cryogenic radiometers, but it is not the same instrument)