Bellows Compensation Table - Check My Math?

Todd Barlow · Jun 15, 2019

Hello all:
I have made a small table to give the bellows compensation for various lens and bellows extension - would anyone like to check a couple of the numbers I have come up with to check my math?

Thanks in advance for the help.

Todd

BradS · Jun 15, 2019

well, first one I checked is incorrect.

bellows factor = [(image distance) / (focal length)] ^2
and to convert an exposure factor to stops...
stops = log(exposure factor) / log(2)

so, for image distance of 120mm and focal length of 90mm,
bellows factor = (120/ 90) ^2 = (4/3)^2 =1.77777 and log(1.7777) / log(2) = 0.83 stops

but the next is ok....
for 180mm of extension and a 90mm lens,
bellows factor = (180 / 90) ^2 = 4 which is exactly 2 stops. .

note that when...
bellows extension = sqrt(2) * focal length
then bellows factor = 2 which is one stop
for a 90mm focal length, when bellows extension is about 127mm then the bellows factor is 2 which is one stop.

Todd Barlow · Jun 16, 2019

Thanks Brad.
I also came up with 0.83 stops but I rounded for the final table.
I think I will build an additional table by adding the Bellows Factors based on BE=SqRoot of 2 * Focal Length.

I appreciate you taking the time.
Best regards
Todd

removed account4 · Jun 16, 2019

Hi Todd

Have you poked around in this thread yet : https://www.photrio.com/forum/threads/bellows-extension.43275/page-2
post 27 is a lot easier than doing the math ...

BradS · Jun 16, 2019

Todd Barlow said:
Thanks Brad.
I also came up with 0.83 stops but I rounded for the final table.
I think I will build an additional table by adding the Bellows Factors based on BE=SqRoot of 2 * Focal Length.

I appreciate you taking the time.
Best regards
Todd

Hi Todd,

After I posted, I realized that 120mm and 127mm are not so different....especially in the context of photography.

For what it's worth, I just measure the bellows and do the calculations in the field as needed.
It's not really that difficult if you have a decent scientific calculator....

1. measure the bellows extension
2. divide by the focal length and
3. square the result
...that gives you the bellows factor. You can use this directly or convert it to stops.

stops = log(factor) / log(2)

I think you're probably fine.

Peter Schrager · Jun 16, 2019

sorry but total overthink....just use a tape measure

Doremus Scudder · Jun 16, 2019

I think making a table with bellows-extension factors for the lenses one has is a great idea. Print it out and carry it with you in the field along with your tape measure. No math needed; simply measure the bellows and consult the table. That's what I've done for years.

Best,

Doremus

Peter Schrager · Jun 16, 2019

Doremus Scudder said:
I think making a table with bellows-extension factors for the lenses one has is a great idea. Print it out and carry it with you in the field along with your tape measure. No math needed; simply measure the bellows and consult the table. That's what I've done for years.

Best,

Doremus

..why make it so complicated? An 8 inch lens extended to 10 inches is one stop ..to 12 inches is 2 stops..or fractions of. Always give extra exposure if in doubt. I've been using foma 100 and have no problems with reciprocity...whatever times ivr used for trix or fp4 are just extended a little
I like to make photographs not spend time doing calculations

BradS · Jun 16, 2019

Peter Schrager said:
..why make it so complicated? An 8 inch lens extended to 10 inches is one stop ..to 12 inches is 2 stops..or fractions of. Always give extra exposure if in doubt. I've been using foma 100 and have no problems with reciprocity...whatever times ivr used for trix or fp4 are just extended a little
I like to make photographs not spend time doing calculations

My memory is not so good and tends to be full of other stuff. I could never remember all the table entries for each of my lenses...so, I do the math. Its really very easy and only need remember the two equations (which I have written down in my field notebook).

incidently, 10 inches of bellows extension with an 8 inch lens needs only about 2/3 stops of additional exposure and 12 inches of bellows needs only about 1 stop.

silveror0 · Jun 16, 2019

Doremus Scudder said:
I think making a table with bellows-extension factors for the lenses one has is a great idea. Print it out and carry it with you in the field along with your tape measure. No math needed; simply measure the bellows and consult the table. That's what I've done for years.

+1

This method allows calculations to be done in advance when image-making isn't an option. It allows improved precision (instead of just splashing around in generalities), and it expedites the flow of image-making in the field. To me, it makes no sense to do all the zone system film testing to define exposures and EIs within 1/3-stop and then loosely deal with other factors (such as bellows extension).

Peter Schrager · Jun 16, 2019

BradS said:
My memory is not so good and tends to be full of other stuff. I could never remember all the table entries for each of my lenses...so, I do the math. Its really very easy and only need remember the two equations (which I have written down in my field notebook).

incidently, 10 inches of bellows extension with an 8 inch lens needs only about 2/3 stops of additional exposure and 12 inches of bellows needs only about 1 stop.

And incidentally it works just fine...

Peter Schrager · Jun 16, 2019

silveror0 said:
+1

This method allows calculations to be done in advance when image-making isn't an option. It allows improved precision (instead of just splashing around in generalities), and it expedites the flow of image-making in the field. To me, it makes no sense to do all the zone system film testing to define exposures and EIs within 1/3-stop and then loosely deal with other factors (such as bellows extension).

Show me your negatives and I'll show you mine

silveror0 · Jun 16, 2019

Peter Schrager said:
Show me your negatives and I'll show you mine

Apparently your method meets YOUR standards for an acceptable negative, and that's great for YOU. I choose mine and it works for me. I see no problem here.

removed account4 · Jun 16, 2019

Peter Schrager said:
..why make it so complicated? An 8 inch lens extended to 10 inches is one stop ..to 12 inches is 2 stops..or fractions of. Always give extra exposure if in doubt. I've been using foma 100 and have no problems with reciprocity...whatever times ivr used for trix or fp4 are just extended a little
I like to make photographs not spend time doing calculations

Hi Peter
Your method is pretty much the same one that Mateo suggests in post #27 in the "sticky'd bellows extension thread".
But I can see why people might want exact rather than a little over exposed. I over expose a little (or a lot ) because i like beefy negatives
but if someone is exposing IDK chromes, or has their technique dialed into whatever paper they use ... our carefree attitude might monkey wrench the machine ..

awty · Jun 16, 2019

I just use the app. https://play.google.com/store/apps/details?id=uk.co.monochrome.reciprocity&hl=en_AU
calculates bellows, filter factors and film reciprocity even has a timer.

Ian Grant · Jun 17, 2019

Doremus Scudder said:
I think making a table with bellows-extension factors for the lenses one has is a great idea. Print it out and carry it with you in the field along with your tape measure. No math needed; simply measure the bellows and consult the table. That's what I've done for years.

Best,

Doremus

The Kodak Specialist 2 has a table on its side and metric scales on the baseboard and the extension rail, I don't think the model was made/sold in the US. Essentially it's an upgraded Kodak 2D which was made in the UK.

Ian

Ian C · Jun 17, 2019

Bellows compensation b in f-stops is

b = 2*ln(E/f)/ln(2)

where E is the bellows extension (distance from the 2nd nodal point of the lens to the image plane). E is also called the image distance.

Since the factor 2/ln(2) has the constant value of 2.8854, the above can be written more simply as

b = 2.8854*ln(E/f)

making the calculation a bit less tedious.

Note: Due to the laws of logarithms,

(1) b = 2*ln(E/f)/ln(2) and

(2) b = ln(E/f)^2/ln(2)

have exactly the same value. Version (1) avoids exponentiation and allows combining the 2 in the numerator with ln(2) in the denominator to form the single factor 2.8854.

jeffreyg · Jun 17, 2019

I have three lenses for my 4x5. I did the math backwards using stops Ie 1, 1 1/2 etc and found the bellows extension in inches and marked a small retractable ruler that is attached to my light meter strap. The settings for each lens was marked with a different color Sharpie. I compose, focus and measure from the lens board to the film plane and set accordingly. No math needed.

http://www.jeffreyglasser.com/

http://www.sculpturandphotography.com/

Bellows Compensation Table - Check My Math?

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