Filter Factor Math

[jeroldharter]

I need some help with arithmetic. I am trying to develop a table for the required exposure compensation for bellows extension to the 1/3 stop. I can find the formula for the exposure factor, extension squared over focal length squared. But how do I convert that to 1/3 stops?

So I need help filling in this table:

Factor 1 = 0 stops
. = + 1/3 stop
. = +2/3 stop
factor 2 = + 1 stop
. = + 1 1/3 stop
. = + 1 2/3 stop
Factor 4 = 2 stops
. = 2 1/3 stop
. = 2 2/3 stop
Factor 8 = 3 stop
. = 3 1/3 stop
. = 3 2/3 stop
Factor 16 = 4 stop

Thanks.

[Jim Michael]

You can use logs. One stop is .3 and 1/3 stop is .1.

Factor 1 = 0
+1/3 .1
+2/3 .2
Factor 2 = .3
2 + 1/3 = .4
2 + 2/3 = .5
Factor 4 = .6
etc.

Whole stop correction = (integer part of (Factor/.3))^2
fractional stop = Factor modulo .3

[Emmanuel BIGLER]

hello from France

I have in my files the following table, I'm happy that it could serve our LF friends !

By 1/third of f-stop


-6 ____> 0,0156X = 1/64
-5-2/3 > 0,0197X
-5-1/3 > 0,0248X
-5 ____> 0,0313X = 1/32
-4-2/3 > 0,0394X
-4-1/3 > 0,0496X
-4 ____> 0,0625X = 1/16
-3-2/3 > 0,0787X
-3-1/3 > 0,0992X
-3 ____> 0,125X _= 1/8
-2-2/3 > 0,158X
-2-1/3 > 0,198X
-2 ____> 0,25X __= 1/4
-1-2/3 > 0,315X
-1-1/3 > 0,397X
-1 ____> 0,5X ___= 1/2
-2/3 __> 0,63X
-1/3 __> 0,794X

0 _____> 1X

1/3 ___> 1,26X
2/3 ___> 1,59X
1 _____> 2X
1+1/3 _> 2,52X
1+2/3 _> 3,17X
2 _____> 4X
2+1/3 _> 5,04X
2+2/3 _> 6,35X
3 _____> 8X
3+1/3 _> 10,1X
3+2/3 _> 12,7X
4 _____> 16X
4+1/3 _> 20,2X
4+2/3 _> 25,4X
5 _____> 32X
5+1/3 _> 40,3X
5+2/3 _> 50,8X
6 _____> 64X

--------------

by half-stops

-6 ___> 0,0156 = 1/64
-5,5 _> 0,022
-5 ___> 0,031X = 1/32
-4,5 _> 0,044X
-4 ___> 0,0625X= 1/16
-3,5 _> 0,088X
-3 ___> 0,125X = 1/8
-2,5 _> 0,177X
-2 ___> 0,25X _= 1/4
-1,5 _> 0,353X
-1 ___> 0,5X __= 1/2
-0,5 _> 0,707X
0 ____> 1X
0 ____> 1X
0,5 __> 1,41X
1 ____> 2X
1,5 __> 2,83X
2 ____> 4X
2,5 __> 5,66X
3 ____> 8X
3,5 __> 11,3X
4 ____> 16X
4,5 __> 22,6X
5 ____> 32X
5,5 __> 45,2X
6 ____> 64X

[Emmanuel BIGLER]

I have attached a pdf graph which is probably easier to use than a list of numbers.

[jeroldharter]

You guys are great. That is just what I needed. Thanks.

[evan clarke]

BUT, Don't cut yourself short trying to add the minimum possible exposure adjustment. Make the calculation and then give it a little, the biggest danger is selling out the shadows..Evan

[Drew Bedo]

I most frequently use either a 250mm (6 inch) or a 210mm 8 1/4 inch).

In the field, I know that for the 150mm lens, 3 inches of extension is one stop, so each inch equals 1/3 stop.

For the 210mm inch lens, 4 inches equals one stop and each inch of extension equals 1/4 stop.

May not be too cerebral but it works for me.