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Thread: Missing exposure equation

  1. #1

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    Missing exposure equation

    I'm checking some calculations and on-camera indicators I made a while back and need help with a calculation. Before recommending that I go to the home page or other other sites, please understand that that's what I did to get what I am about to present. I struggle with math and am asking, not for a way to calculate bellows extension compensation factors easily in the field, which I understand, but simply for the missing equation for the Excel sheet I already have, which looks like this (click to enlarge):
    Click image for larger version. 

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    I have rechecked my formulas at Ken Lee's valuable site; they are fine as far as I can tell. What I would like, is a formula to fill in the last column, giving, e.g. 1/3, 1/2, 3/4, being the increase in stops that I need for that extension, not a multiplier for the time. I realize that it may include fractions like 2/7; I can deal with that.

    For any who really wish to know, I use a little stick-on label on my Tachihara bed, which indicates how many stops of exposure increase I need when the end of the front standard baseboard lines up with a number on the mysteriously designed ruler. (I realized today that my sticker's off; I erred previously in my calculations.) This is a quick technique recommended here and elsewhere, which suits my work well; I only need a few values and can interpolate between them. I have only two lenses, so one sticker goes by the left ruler, the other by the right.

    Thank you.
    Philip U.

    Sine scientia ars nihil est. (Without science/knowledge, art is nothing.)
    https://www.flickr.com/photos/156933346@N07/

  2. #2

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    Re: Missing exposure equation

    Philip,

    The calculation you want is how to find "stops to open the aperture" from the exposure factor, which is log2 of the exposure factor.

    However, I don't know how to write the formula for Excel... Maybe you do, or someone can chime in with the proper formula.

    FWIW, here's a rough guide:

    Exp. factor --- Stops to Open
    1.5 ---------------- ⅔
    2 ------------------ 1
    3 ------------------ 1 ⅔
    4 ------------------ 2
    6 ----------------- 2 ⅔


    Best,

    Doremus

  3. #3

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    Re: Missing exposure equation

    I still have some of those old Calumet compensation rulers in my bags or cases... I was missing some of the "targets" you put into the scene to measure off of, but found a bag of 35mm 2×2 slide mounts to replace them, and leave a piece of paper tape on them to stick them to stuff... (I just have to remember to pull them before shooting...)

    Some day I intend to scan one to duplicate, print, and lanimate so I have many to leave laying around while doing tabletop sets...

    Steve K

  4. #4

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  5. #5

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    Re: Missing exposure equation

    Use full apertures to get a very close estimate of needed aperture.
    Lets say you are using an 8" lens. You measure the bellows extension and find it to be just under 11". from 8 to 11 is one stop. Open our lens one stop and forget the complicated math.

  6. #6

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    Re: Missing exposure equation

    Quote Originally Posted by Doremus Scudder View Post
    Philip,

    The calculation you want is how to find "stops to open the aperture" from the exposure factor, which is log2 of the exposure factor.

    However, I don't know how to write the formula for Excel... Maybe you do, or someone can chime in with the proper formula.

    FWIW, here's a rough guide:

    Exp. factor --- Stops to Open
    1.5 ---------------- ⅔
    2 ------------------ 1
    3 ------------------ 1 ⅔
    4 ------------------ 2
    6 ----------------- 2 ⅔


    Best,

    Doremus


    The general equation in Excel is:

    =log(X,b)

    where X is the value to be logged, and b is the log's base

    in this case, X is the Exposure factor, b = 2 is the log's base

    The calculated value is in f-stops


    For example, =log(2,2) = 1

    You can use a cell address within the formula rather than typing in the exposure value there. If the table (as above) already has the exposure value, this saves time, as the equation can be copied and pasted into the cells below and the addresses will automatically adjust.

    The cell address is column letter, row number (e.g., A2) Excel has instructions on how to do this, but they are not very accessible. An internet search of "relative address excel" will bring up some good instructions.

  7. #7
    Louie Powell's Avatar
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    Re: Missing exposure equation

    This formula will allow Excel to calculate an exposure compensation with whatever degree of precision you want. You can specify the precision either by formatting the cell in the spreadsheet, or by modifying the formula to round the answer to a desired number of decimal places.

    There are actually two ways to compensate exposure - by adjusting the aperture, and by adjusting the exposure time. It's easy to compensate by adjusting exposure time - you just multiply the 'indicated time' by the calculated factor, and expose accordingly. However, most people won't do it that way because that introduces the complication of reciprocity failure, and the need for a further adjustment that is harder to determine.

    Instead, most people compensate by adjusting the aperture. But in that case, depending on the lens in use, you will either have a rather coarse selection of detented intermediate stops to choose from, or else a continuous adjustment but with an undefined calibration settings between the markings on the lens. I suspect that most people take this approach, and practically, this is functionally the same as the stick-on label that Phillip mentioned. And if you are concerned that this is not sufficiently precise, you can always bracket exposures.

    Another approach to doing this calculation in Excel is to embed the rough selection of adjustment factors that Doremus listed within the Excel spreadsheet, and then use the table lookup function (either @vlookup or @hlookup) to select the rough adjustment as a function of exposure factor.

  8. #8

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    Re: Missing exposure equation

    Thanks, all.
    mmerig, that's exactly what I need. Thanks for the full instructions! I know about the cell location entry, but wouldn't have gotten the log formula construction right.
    Brian, I have the quick disc. Great for close up, but most of my work is portraits; see next line.
    Jim, the reason for my one-bed guide is to avoid the need in the middle of a portrait session to pull out a tape measure. Were I still a working pro, I would have it all memorized, but I don't get nearly as much opportunity as I would like. C'est la vie.

    The way I have my Excel calculations set up, I can change the focal length in the far-left cell and have all the numbers instantly recalculated for it. I also have (not shown) a conversion from mm to inches to get the required number for that.

    Anyone who would like a copy, please send me a private message with your email.
    Philip U.

    Sine scientia ars nihil est. (Without science/knowledge, art is nothing.)
    https://www.flickr.com/photos/156933346@N07/

  9. #9

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    Re: Missing exposure equation

    Hello from France!

    I have always found, for this kind of "photographic" calculations where a 4-digit precision is useless, that a good ol' dedicated analogue slide rule is more useful than any computer system, be it an expensive mobile phone

    Free to download! Electricity-free! Environmentally-friendly! No monthly subscription of any kind!
    Can serve as an exposure meter, based on the legendary "sunny-16" rule!

  10. #10

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    Re: Missing exposure equation

    Unless your subject is moving, and unless reciprocity issues might be a problem, I typically opt to do any necessary exposure compensation by using exposure time as my variable, as it is the specifics of whatever optic I'm using (characteristics at certain f-stops, etc.) that is most important to me to control, as this will have way more influence on actual results than exposure time...again (broken record) as long as there would be no significant issues by a change in exposure time. I hate to generalize for others here but I think my approach has some merit.

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