> You raise some interesting points. I've long known that the
> actual apertures of lenses is often somewhat different from the
> "published" ones. But I have 3 questions.
> 1. How would an individual, without any formal technical
> training, actually test this with a particular lens?
have had a few too many to cogently eplain this ...
> 2. How did you arrive at the values "f/37 to f/45" minimum
> aperture from an actual f/6.3 maximum aperture?
let's see ... the lens was f/3.5 at 24mm and f/6.3 at 70mm. so that is a drop
of - I can't think half stops so let me deal with whole ones to begin with, OK?
so f/2.8 to f/5.6. That is 2.8 - 4 - 5.6 or three stops ... so what is three
stops less than f/5.6 - OK .... 5.6 - 8 - 11 - at maximum aperture. But iof
lens has a minumum aperture of f/16 then 3 stops less is: 16 - 22 - 32 or f/32.
If the minimum aperture on the lens is f/22 then in reality at 70mm this
becomes 3 stops less than that or 22 - 32 - 45 or f/45!
so what did we do above? first found out how many stops "drop" there was with
the lens wide open and then applied the difference to the smallest stop with
the lens at 24mm.
but wait! there has to be a logarithmic solution to the problem or a solution
that involves logs ... I am afraid that is beyond me tonight!
> 3. How would one "calculate for diffraction"?
hmmmm ... theoretically speaking of course ... the maximum resolution
capability of an optical system depends to a rough approximation on the f
number ... well, inversely so I believe. Meaning simply that the smaller the f
number the higher the theoretical resolving power capability of an optical
system. Problem is that large apertures (small f numbers) are adversely
affected by aberrations ... so there is an optimum aperture for any lens where
it achieves the highest resolving power and where opening it up any wider
causes a degradation of resolving power due to various optical construcion
limitations and defects while stopping it down causes a loss of resolution due
to diffraction.
OK - so you probably will ask "what is this relationship?" To a rough
approximation the theoretical resolving power of any lens was worked out by
veritable luminaries in the field of optics such as Rayleigh, Abbe, Newton and
others I can't at this specific time remember and when I just trtied to look it
up on the web I got confused. These guys were alive, of course, BTV - before
TV.
Anyway, let's see if we can make things sort of work out with some assumptions.
We expect a resolution capability from our lenses of something like 100 line
pairs per millimeter. Note that the resolving power of a lens is also affected
by the wavelength of the light. The shorter the higher the resolving power. So
how do we get something like this?
Let's see: If we take 2 lenses, one of f/4 and the other of f/16 aperture we
expect the f/16 one to have less capability in terms of resoving power than the
one of f/4 according to diffraction limits worked out by those guys mentioned
above. Hmmmmm ...
So, let's take a number like 1000 and divide it by the f number we would see
that an f/2 lens might have a resolving power of 500 line paris per mm while
one of f/16 would only achieve 62.5 lpm. I think we are on to something. Now if
we take the 1000 (some constant) and divide by the f# multiplied by a number
like 2 we would see that the number we get is smaller than if we don't do that
... so if we take the f# and massage it somehow taking into account the
wavelength of the color of light we might get somewhere.
OK. So let us use instead of 1000 the number 1 and this would of course give
resolving powers that are much less than what we expect. But if we use
something like 1,000,000 and divide this by the f# multiplied by the wavelength
of the light expressed in nanometers something interesting happens.
Assuming we are photographing with 1000 nm light, at f2 a lens would
theoretically be able to resolve 500 lpm while at f/16 it would only be 62.5
lpm. Because 1,000,000 / 2x1000 = 500 and 1,000 / 16x1000 = 62.5
But if we used 500 nm light then the situation would improve and we could
expect higher resolving powers such that at f2 it would be 1,000,000 divided by
2x500 or 1,000 lpm and at f/16 it would be 1,000,000 divided by 16x500 or 125.
Meaning that by using shorter wavelength light we have increased the
theoretical resolving power of a lens. We seem to be on the right track.
Please note that the above numbers are only assumptions and besides the whole
thing is nothing more than ramblings in a state of semi awareness ... but
anyway, this is what I believe or think I believe that happens.
So, if we stop the lens down beyond its optimum aperture resolving power drops.
Now suppose that my assumptions are valid ... then if we assume that we will
use green light (about 500 nm) then at f/16 a lens has a theoretical limit of
1,000,000 / (16 x 500) or 125 lpm while at f/45 the lens would only be able to
reach a maximum of 1,000,000 / (45 x 500) or 44 lpm ... not good!
> Math is not my strong suit but I'll try to absorb any
> explanation you care to offer. This subject (variable f/stops)
> has long intrigued me.
hey -- I am in the same boat with you methinks.
hic ergo sum,
andy
