Ed, post 57
Attempts to clarify things is never offense, so do not worry, I sleep well. The term "brightness" obviously is a matter of definition and language. When you consult different textbooks, you will see that in quite a few "brightness" in the sense of light current/lumens is not the only way to understand the term brightness.
I will try to simplify it as much as possible:
Suppose our eye receives a photo current of 1000 photons of violet light per square centimeter and also of 1000 photons of yellow light per square centimeter (I know that you have to define the wavelenght with much more precision, but let us not look at that for a moment). In that case our eye-brain system interprets the yellow signal as brighter than the violet signal, that is what a number of textbooks say when they make a definition of brightness. Others tell us: no brightness is fully determined by the photonflux, so 10000 photons per square centimeter is brighter then 1000 photons per square centimeter regardless of the color and that is their definition of brightness.
Gijs
Hi Gijs,
First let me say we are not disagreeing, or even defining the word "brightness" differently (in this case), — but a critical concept is missing. So, I'll give it another try and hope we can tie this together.
Referring to what you said earlier,
..."Brightness is not only determined by the light intensity the eye is exposed to (this is the combination of exit pupil and transmitted light). The color hue also plays a role in our perception of brightness..."
by "light intensity" I'm reasonably sure you meant the photons the eye is exposed to. Then you went on to say the "color hue also plays a role in our perception of brightness." I agree completely. But this begs the question: "How
much of a role does color play, and how is that measured and incorporated into a mathematical expression for estimating total instrument brightness? What are the units of measure?
Fortunately for us, the the solution lies in the fact that visual scientists already consolidated the perceived brightness differences between individual frequencies into a standard formulation called the
Human Luminosity Function. [Actually several, but we'll limit this to the photopic adapted eye, i.e, daylight.] This conveniently allows us to transition from the physical domain of photons to the psychological domain of perceptions. Such devices are commonly referred to as
psycho-physical functions.
Returning to your example, then, if one wants to express numerically the brightness difference between violet and yellow light having the same number of photons, or any other colors for that matter, one simply compares their values on the luminosity function.
Which leads us to evaluating overall brightness numerically. This is important because the light entering the eye through binoculars is typically of mixed frequencies. Since each frequency makes its own contribution to brightness, a
frequency-independent overall measure is obtained by cross multiplying the physical energies and the luminosity values, and then adding them up. Mathematically, this is simply the 'dot-product' of the energy and luminosity vectors over the visual range. The units are called lumens.
I wouldn't be so confident in making this statement were it not for the fact that nowadays every other product involving light, be they light bulbs, computer screens, TVs, or whatever, uses
lumens to express overall brightness. It's an international standard. Why isn't it used for evaluating optical instruments?
Ed