Dj Joofa
05-07-2008, 10:23 PM
The recent debate between Glazarus and Peter Majtan prompted me to scribble down a few facts that I am sure are known to most people, but still for the record.
Glazarus: t-stop is a measure of transmission loss by the lenses.
Peter Majtan: t-stop > f-stop is a number that limits f-stop.
And, we shall see that, as I mentioned before, both are saying the same things, but in different words.
The exposure equation for a camera can get quite involved as given below:
E = I * B * F^2 * (cos theta)^4 * H * T * time / (4 * v^2 * f^2) ---------------------- (I)
where, the symbols have the usual meaning and I shall not go into them except those that interest us: H is transmission at off-axis points as limited by barrel vignetting, T is the transmission as limited by losses due to reflection and absorption by glass, F is the focal length, and f is the f-stop, time is of course time.
Equation (I) neglects one minor factor, which being the slight decrement of image brightness due to the fact that under some unusual conditions the illumination arising from an object point and incident upon the first surface of the photographic lens is not perfectly uniform.
The interesting thing to note here is the factor F^2 * T / f^2, lets drop the factor F^2, and concentrate on T / f^2. But, before that, I want to mention in passing that the factor (time / f^2) is an important one as it can be used as a measure of the exposure / exposure value.
Now coming back to the factor, T / f^2, it can also be derived in a simpler and a more instructive way. Lets assume that the light passing through the lens is proportional to area of the aperture, A,
A = pi * d^2 / 4, ------------------------------ (II)
where d is the diameter. Lets discount the constant factor pi / 4, and absorb that into the already existing proportionality constant, we can say that the light is proportional to d^2. Now, the f-stop, f, is
f = F / d,
and using equation (II), we see that light is proportional to F^2 / f^2, the same factor we saw in equation (I).
Okay, Glazarus says that t-stop is a measure of transmission loss, which ignoring H, would mean T < 1 in the equation (I). Now consider the factor again:
T / f^2 = 1 / (f^2 / T) = 1 / (f / R)^2,
where I have used R = sqrt (T), and of course if T < 1, then T < R < 1.
Consider the factor f / R, where R < 1, we see that f is multiplied by a factor > 1, (because R < 1, so 1 / R > 1), and then you may consider your t-stop as
t-stop = f-stop * (a number greater than 1),
which essentially boils down to what Peter Majtan was saying:
that t-stop > f-stop is a number that limits f-stop.
Glazarus: t-stop is a measure of transmission loss by the lenses.
Peter Majtan: t-stop > f-stop is a number that limits f-stop.
And, we shall see that, as I mentioned before, both are saying the same things, but in different words.
The exposure equation for a camera can get quite involved as given below:
E = I * B * F^2 * (cos theta)^4 * H * T * time / (4 * v^2 * f^2) ---------------------- (I)
where, the symbols have the usual meaning and I shall not go into them except those that interest us: H is transmission at off-axis points as limited by barrel vignetting, T is the transmission as limited by losses due to reflection and absorption by glass, F is the focal length, and f is the f-stop, time is of course time.
Equation (I) neglects one minor factor, which being the slight decrement of image brightness due to the fact that under some unusual conditions the illumination arising from an object point and incident upon the first surface of the photographic lens is not perfectly uniform.
The interesting thing to note here is the factor F^2 * T / f^2, lets drop the factor F^2, and concentrate on T / f^2. But, before that, I want to mention in passing that the factor (time / f^2) is an important one as it can be used as a measure of the exposure / exposure value.
Now coming back to the factor, T / f^2, it can also be derived in a simpler and a more instructive way. Lets assume that the light passing through the lens is proportional to area of the aperture, A,
A = pi * d^2 / 4, ------------------------------ (II)
where d is the diameter. Lets discount the constant factor pi / 4, and absorb that into the already existing proportionality constant, we can say that the light is proportional to d^2. Now, the f-stop, f, is
f = F / d,
and using equation (II), we see that light is proportional to F^2 / f^2, the same factor we saw in equation (I).
Okay, Glazarus says that t-stop is a measure of transmission loss, which ignoring H, would mean T < 1 in the equation (I). Now consider the factor again:
T / f^2 = 1 / (f^2 / T) = 1 / (f / R)^2,
where I have used R = sqrt (T), and of course if T < 1, then T < R < 1.
Consider the factor f / R, where R < 1, we see that f is multiplied by a factor > 1, (because R < 1, so 1 / R > 1), and then you may consider your t-stop as
t-stop = f-stop * (a number greater than 1),
which essentially boils down to what Peter Majtan was saying:
that t-stop > f-stop is a number that limits f-stop.