Re: f-stop calculations and reciprocity failure numbers

If the question is "what's the formula for f stops and what's the difference
between them?", each F stop is the diameter of the opening compared to the
focal length of the lens, focussed at infinity. Each f stop admits twice as
much or half as much light per unit of time as the next F stop above or
below it. F stops are convenient when using a lens, but with a fixed
diameter pinhole I just divide the area of the pinhole (pi times radius
squared) into the area (ditto)of the F22 aperture (diameter that is 1/22 of
the distance from pinhole to negative) and multiply the result times the
metered exposure at F22, then correct for reciprocity failure. Someday I'll
find someone else who has also turned away from the altar of F stop.
----- Original Message -----
From: Murray <uptown@uptowngallery.org>
To: <pinhole-discussion@pinhole.com>
Sent: Friday, July 20, 2001 6:58 PM
Subject: [pinhole-discussion] f-stop calculations and reciprocity failure
numbers

> Time for some geek-speak...
>
> I had read the discussion of f-stop increments and rounding pinhole
> calculated f-stops to the 'standard' ones in a chart, in part because
> pinhole exposures tend toward (and I can't remember over or under) being
one
> side of exposed.
>
> This intrigued and bothered me. It made me curious what was the origin of
> the f-stop increments and also wonder why one's pinhole f-stop number
> couldn't be exactly what it's supposed to be.
>
> If focal length and aperture define f-stop, rounding to a standard
f-number
> equates to rounding off one's f.l. or aperture diameter...they're all
> interrelated.
>
> I haven't completely satisfied myself with regard to answering all my
> questions (like some "why's?"), but this is what I have thought up.
>
> if f 1.0 is the theoretical 100% light getting in, (although I did see a
> Canon rangefinder supposedly with an f 0.95 lens...must have had some kind
> of amplification), the f-stop increments appear to come from an
exponential
> relationship based on powers of the square root of two. I haven't derived
> where that comes from, but I figured out how to calculate the 'standard'
> table numbers and how many factors of exposure multiplication result from
> using higher f-stops.
>
> The camera I am converting to pinhole has a continuously adjustable f-stop
> range (which of course doesn't get used in this application), despite
> 'standard' f-numbers. The aperture can be placed in-between the 'standard'
> stops.
>
> Since reciprocity failure has to be factored in and detemining exposure is
> pretty variable, all this boiling down to a time multiplier, I question
the
> necessity of choosing an f-number that 'fits' the chart.
>
> How many conformists do we have here, anyway (anybody with me on this?).
>
> Anyway, the f-numbers appear to appear as follows. This is getting too
wordy
> already and I can't explain it in other-than-math language so just look at
> the results...I see it but don't know what to call it
>
> exponent 0 1 2 3 4 5 6 7
> 8 9
> f-stop 1 1.414 2 2.828 4 5.656 8 11.313 16
> 22.63
>
> These look familiar? I think f11 looks better on a lens than f11.3.
>
> Anyway, I am trying to figure out how to put my variation of a calculator
on
> the web...maybe one of you cats (oops, that would be the jazz discussion
> group)music that knows Java or Javascript can help me
>
> What it figures out is, what number to multiply exposure time by when
> using a f-stop off the chart, with respect to another f-stop, say f-16, or
> any other.
>
> I have tried to simplify my logarithm algebra but some subconscious error
> keeps creeping in when I try to simplify it and I'm sick of trying to
polish
> any further.
>
> basically, take natural logarithm (call it "ln", apologies to followers of
> European notation) of the larger f-stop number and divide it by ln(2^0.5).
>
> Now do the same with the smaller f-number and subtract the result from the
> first resulting number, and multiply by two.
>
> This is the factor by which exposure time has to be multiplied when
shifting
> from one fstop to another.
>
> If you use the 'accurate' f-numbers as shown in my chart (which may get
> butchered by email programs everywhere), this is exactly accurate. If you
> use 'convenient' numbers like 4,5.6,8,11,16,22, 32 there is error.
>
> I have it in a MS Works spreadsheet right now, and could put it on Excel
if
> desired. If anyone wants it , email me.
>
> Oh, almost forgot my question -
>
> Does anyone have reciprocity failure multipliers for common 35 mm films?
> Kodak wouldn't address my question unless I gave them a specific product,
> and I didn't know what to use yet. Fujii is mailing me datasheets, but who
> knows how long that will take.
>
> Thanks
>
> Murray
>
> Murray
> Murray
>
>
>
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Received on Sat Jul 21 06:48:14 2001