Hi,
A while ago I asked the following question:
>> 1-Is there any easy way of recalculating the TTL OTF (Normal Auto) mode
>> and Super FP mode tables in such a way that a specific amount of
extension
>> is taken into account? In other words, does anyone know the correlation
>> between the amount of milimeters added in extension and the loss of light
>> (in stops)? If this correlation is known, it should be possible to
>> recalculate these tables rather than creating them by means of test
shots.
>> This information would be handy for determining the minimum working
>> distance between the F280 and the subject.
Now, when I obtained the Olympus "Manual for macrophoto group" booklet, I
finally seem to have found the right formulas to do the math. The answer to
my questio seems to be: No, there is no _easy_ way of recalculating these
distances (at least, I think there isn't). However, it's not impossible
either. Down below follow the results of my quest for creating a table of
working distances, as I thought it might be illustrative to list the various
steps for deducing the table, this message is quite long. I hope someone can
verify my calculations and correct me if I went wrong somewhere. I typed the
below information in a regular text editor, so if your mail reader doesn't
use fixed size fonts, you might be best off copying this text into a plain
text file, so the tables and formulas have the proper spacings. Enjoy:
My goal was to obtain a formula or table to determine the working distances
when using the OM-4Ti + 50/3.5 Macro + Hama (13mm, 21mm, and 31mm) auto
extension tubes + F280.
I tried using some of the formulas given in the Macro manual to work out a
table, that can be used as a guideline, so here are the results:
First, I calculated the magnification ranges for the various extension tubes
I have.
Doing so yields table 1:
Table 1: Magnification ranges with the 50/3.5 Macro + 13mm, 21mm, and 31mm
extension rings:
Tubes: Infinity Close
-------------------------------
13 : 0,26x <-> 0,76x
21 : 0,42x <-> 0,92x
31 : 0,62x <-> 1,12x
13 + 21 : 0,68x <-> 1,18x
13 + 31 : 0,88x <-> 1,38x
21 + 31 : 1,04x <-> 1,54x
13 + 21 + 31 : 1,30x <-> 1,80x
Note: for determining the "close" numbers an internal 25mm of extension of
the
lens itself has been taken into account. The above table has been derived
using
calculations such as:
(13+21+31)/50 = 1,30 (focused to infinity)
(25+13+21+31)/50 = 1,80 (focused to minimum close)
Next, two functions were taken from the Macro manual.
The first one is for determining flash to subject distances without taking
magnification into account (Dcm = flash to subject distance in CM).
The second one is a correction factor that is applied to the values obtained
from the first function.
The functions are:
(1): Dcm = GN/f-stop x 100cm
(2): D'cm = Dcm x DC
For the distance correlatives DC a partial table is given, this is
the following table (table 2):
Table 2: Distance correlatives (DC) at various magnifications (Magn.):
Magn. DC
------------
0,2x 0,82
0,3x 0,75
0,5x 0,65
1,0x 0,50
1,5x 0,40
2,0x 0,33
3,0x 0,25
4,0x 0,20
I haven't tried to deduce a formula for calculating the DCs at different
magnifications (any volunteers?), but rather since the numbers were pretty
close
to one another, I decided to use linear interpolation between the closest
lower and
upper boundaries of the given magnifications.
To do this, I used the following formula for the calculations:
/ DC(lower) - DC(upper)
\
(3): DC(actual) = DC(lower) - ( ------------------------- * (Magn(actual) -
Magn(lower)) )
\ Magn(upper) - Magn(lower)
/
An example for an actual magnification of 0,42x:
/ 0,75 - 0,65 \
0,75 - ( ----------- * (0,42 - 0,3) ) = 0,75 - 0,06 = 0,69
\ 0,5 - 0,3 /
Applying this formula to the actual magnification ranges' extremes yields
table 3:
Table 3: Actual distance correlatives at various magnifications of table 1:
Magnifications: DC extremes:
-------------------------------------
0,26x <-> 0,76x 0,78 <-> 0,57
0,42x <-> 0,92x 0,69 <-> 0,52
0,62x <-> 1,12x 0,61 <-> 0,48
0,68x <-> 1,18x 0,60 <-> 0,46
0,88x <-> 1,38x 0,54 <-> 0,42
1,04x <-> 1,54x 0,49 <-> 0,39
1,30x <-> 1,80x 0,44 <-> 0,36
Now, using formula 1 with the apertures of the 50/3.5 Macro yields table 4:
Table 4: Uncorrected flash to subject distances for the F280 + 50/3.5 Macro:
f Dcm
---------------
3.5 800
5.6 500
8 350
11 255
16 175
22 127
For example @ 3.5: Dcm = 28/3.5 x 100cm = 800cm
Then, using formula 2, calculating the working distances (in cm) for all the
different apertures yields
table 5:
Table 5: Flash to subject distances for the F280 + 50/3.5 Macro,
semi-corrected:
Tubes: Magnifications: f3.5 f5.6 f8
f11 f16 f22
----------------------------------------------------------------------------
---------------------------
13 : 0,26x <-> 0,76x 624 - 456 390 - 285 273
- 200 199 - 145 137 - 100 99 - 72
21 : 0,42x <-> 0,92x 552 - 416 345 - 260 242
- 182 176 - 133 121 - 91 88 - 66
31 : 0,62x <-> 1,12x 488 - 384 305 - 240 214
- 168 156 - 122 107 - 84 77 - 61
13 + 21 : 0,68x <-> 1,18x 480 - 368 300 - 230 210
- 161 153 - 117 105 - 81 76 - 58
13 + 31 : 0,88x <-> 1,38x 432 - 336 270 - 210 189
- 147 138 - 107 95 - 74 69 - 53
21 + 31 : 1,04x <-> 1,54x 392 - 312 245 - 195 172
- 137 125 - 100 86 - 68 62 - 50
13 + 21 + 31 : 1,30x <-> 1,80x 352 - 288 220 - 180 154
- 126 112 - 92 77 - 63 56 - 46
Looks cool, right?
Wrong, a simple glance at the values tells that these distances are probably
way too optimistic.
Re-reading part of the Macro manual shows that when the manification rate
increases,
the aperture increases.
This is rather uncool, as I assume this means that I need to take these
aperture increases
into account for all the different magnifications.
According to the Macro manual, the following formula can be used to
calculate the effective f-stop:
(4): EF-Stop = F-Stop x (Magnification + 1)
For example:
f3.5 with a 0,42x magnification yields an EF of: EF = 3.5 x (1,42) = 4.97
In order to successfully correct the values from table 5, an additional
multiplication with
1
--------- is needed (i.e. a division by (1 + Magn.)).
1 + Magn.
For example, the corrected value for a 0,26x magnification at f3.5 is:
1
---- x 624 = 495,24
1,26
This has been verified by first calculating the EF-Stop for this
combination, and then
applying the formulas 1 and 2, this yields the same result.
Applying the correction to all the magnifications of table 1, at all the
various apertures,
then finally gives the table of effective F-stops.
Table 6: Flash to subject distances (in cm) for the F280 + 50/3.5 Macro,
fully (?) corrected:
Tubes: Magnifications: f3.5 f5.6 f8
f11 f16 f22
----------------------------------------------------------------------------
---------------------------
13 : 0,26x <-> 0,76x 495 - 259 310 - 162 217
- 114 158 - 82 109 - 57 79 - 41
21 : 0,42x <-> 0,92x 389 - 217 243 - 135 170
- 95 124 - 69 85 - 47 62 - 34
31 : 0,62x <-> 1,12x 301 - 181 188 - 113 132
- 79 96 - 58 66 - 40 48 - 29
13 + 21 : 0,68x <-> 1,18x 286 - 169 179 - 106 125
- 74 91 - 54 63 - 37 45 - 27
13 + 31 : 0,88x <-> 1,38x 230 - 141 144 - 88 101
- 62 73 - 45 51 - 31 37 - 22
21 + 31 : 1,04x <-> 1,54x 192 - 123 120 - 77 84
- 54 61 - 39 42 - 27 30 - 20
13 + 21 + 31 : 1,30x <-> 1,80x 153 - 103 96 - 64 67
- 45 49 - 33 33 - 23 24 - 16
So, this should be the proper working distances according to the
guidelines (unless I've made a mistake somewhere), in reality
matters will of course also depend on how much light the subject
reflects, etc. but at least it seems to be a guide...
Any opinions? Anyone?
Cheers!
Olaf
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