Lumen Candela Lux Nits

 1. Understand Steradian

You know how exactly 2PI of a circle's radius makes up the the circumference of a circle

Fact: this also means the angle subtended at the center of the circle by an arc of length 1 radius is exactly 1 radian ~ 57.3 degrees

Now, in the 3D case, the surface area of a sphere is 4 * PI * r^2

and if we use the same logic, and analogous to using r as our base unit in the 2D case, we use r^2, we can say that 1 steradian the angle subtended by the surface areas of exactly is exactly 1 r^2

meaning the entire sphere has solid angle of 4*PI steradians

Quick Recap: 

1 radius (r) subtends an angle of 1 radian

1 surface patch (r^2) subtends a solid angle of 1 steradian

(solid angle = angle but 3D, steradian = radian but 3D, surface patch = radius but 2D) (yes, 2D)

2. Candela (cd)

Just note, that 1 common candle emits roughly 1 candela (cd) of luminous intensity (that's the actual term)

If you think of light as tangible, and flying in all directions

then if you collect all the light flying in one steradian, then for a common candle, you get 1 cd of light

or 1 cd of luminous intensity

3. Lumen (lm)

A 25W compact fluorescent light bulb puts out 1700 lumens

What does that mean?

Well, if you collect all the light flying in all directions (not just 1 steradian, but all 4*PI steradians),

then you get the luminous flux of the light source. 

So if you have 1 common candle, which we know is 1 cd of luminous intensity (aka, 1 cd of light in 1 steradian), now we collect light from all angles, thus 4*PI steradians, getting us 4*PI*1 lm = 12.57 lm from 1 candle

that's the aggregate amount of 'light', aka, the luminous flux, of a common candle

similarly, back to our 25W light bulb example, if you collect the light from just 1 steradian of that light bulb, you get 1700/(4*PI) ~ 135 cd of luminous intensity. 

4. Radiant Flux (what is this doing here?)

Well, one remark

lumen, aka luminous flux, is weighted towards em wave frequencies that the human eye is sensitive to (using a Luminous efficiency function). AKA, the total amount of visible light emitted per unit time. 

The more comprehensive term is Radiant Flux.

Radiant Flux is the amount of radiant energy emitted per unit time. Thus units in Watts (W). This includes waves visible and invisible to human eye (all waves). 

BTW. Spectral flux is the radiant flux per unit frequency (or wavelength, same thing). Units (W/Hz) or (W/nm)

5. 

Remember this logical chain -> Lumens, Candela, Lux, Nits

Why? Because they each are useful in different settings, and they all add upon each other

Lumens (lm) (aka luminous flux) measures the total amount of visible (note, visible, not total) light emitted

- useful in designing light bulbs, you know how much light is produced, in total

Candela (cd) measure the luminous flux PER SOLID ANGLE [measured in steradians, a 3D angle] (called luminous intensity), 

- for industrial lighting, lights are focused in a beam, so useful to know how bright that beam is

Lux (lm/m^2) (lx) measures the luminous flux PER UNIT AREA [m^2] (called Illuminance)

- means how much of that light (whether beam or bulb) actually falls on a certain surface area (e.g. the face of a subject), at a PARTICULAR DISTANCE. Note, since Lux changes with distance (due to spreading of light), you must report Lux with the distance that measurement was taken.)

- useful for photography, since you want to know how much light actually falls on someone's face when buying a studio light. You don't just wanna know how bright the whole light is (you're not trying to light up an entire room) (you're also not looking for how strong a beam is, although that could be useful) 

Nits (cd/m^2) (nt) measure the amount of luminous intensity PER UNIT AREA (called Luminance)

- suppose you shine a light source onto a face, as a camera/viewer, how much light do you actually see after the light bounces off the face?

- well that means what is the measurement

- this is why screens use nits, since you want to know how much light is actually hitting your eye. 

- still not sure why we can' just use Lux for this, but oh well. that's for next time. 

- one explanation is that, since monitors have a viewing angle, you want to know how much light hit you from a specific angle. still not sure how this works. 

Bascially, depending on your use, you only care about a certain characteristic of the light source

Luminous Flux (lm) = Total light output everywhere

Luminous intensity (cd) = Total light output in a specific beam (beam of 1 steradian to be exact)

Illuminance (lx) = Total light falling on a specific area at a specific distance from light source (photographer)

It's pretty funny how this chain works actually. 

If I point LED panel at wall. 

How much an LED panel lights up a section of a wall is measured in Lux

How much light bounded off that wall is measured in Nits. 

How much of that bounded off light illuminates my face again is measured in Lux. 

How much light someone else perceives that bounded off my face is measured in Nits. 

Basically, when we examine the light source, we use Lux.

When we talk about perceived brightness, we use Nits. 

Fun fact:

cloudy overcast sky at midday is about 2000 nits to your eyes

that same sky would have an illumination power of 1000-2000 lux. 

and a sun on a clear sky on midday would be about 1.6 billion nits. Your eyes can't stand that. 

Side note: 

Foot-candle (lm/ft^2) (fc) is Illuminance at exactly 1 foot distance from light source.

It's lux, but standardized to 1 feet, and measured in ft^2 instead of m^2

conversion: 1 fc = 10.7639 lux (at 1 feet distance)

guess it's sorta nice since you don't have to worry about reporting the distance from light source like in lux, since it's standardized to 1 foot away from light source.