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Thread: Image Circle Coverage and Angle of View - how to calculate?

  1. #1

    Image Circle Coverage and Angle of View - how to calculate?

    Please can someone explain how the Angle of View (in degrees) relates to the Image Circle Coverage (in mm) as quoted in View Camera Magazine lens tables etc?
    I realise that the term 'angle of view' has different meaning when used by view camera users compared with 35mm users, and understand the 35mm users version (2*arctan (format diameter/focal length).
    However I am struggling with the relationship for view cameras where I see 72 degrees coverage etc quoted.
    Thanks for any help on this.

  2. #2

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    Re: Image Circle Coverage and Angle of View - how to calculate?

    Use focal length f as your adjacent leg, and half the coverage degrees as the adjacent angle phi, then image circle c = 2 f tan(phi).

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    Resident Heretic Bruce Watson's Avatar
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    Re: Image Circle Coverage and Angle of View - how to calculate?

    Quote Originally Posted by newmoon2night View Post
    Please can someone explain how the Angle of View (in degrees) relates to the Image Circle Coverage (in mm) as quoted in View Camera Magazine lens tables etc?
    They hardly relate at all. The coverage circle is determined by the design of the lens itself. Angle of view is a completely different thing; it's a function of focal length and format size.

    BTW, that's not "format diameter" in your equation, it's "d" which is the length of film in the direction you want to calculate angle of view. This is required because most film formats are rectangular and therefore have a different angle of view for the long side vs. the short side. The correct equation is alpha = 2arctan (d/2f), and it works for all formats. Don't forget to use consistent units of measure for "d" and "f."

    Bruce Watson

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    Re: Image Circle Coverage and Angle of View - how to calculate?

    Hello !
    In large format (LF) only a part of the total image circle is used for a given setting of shift+tilts.
    When all movements are set to zero there is not difference with the situation encountered with smaller formats with no movements.

    However the angle of coverage listed in LF lens specs is the total possible angle of view either with the biggest film surface with no movements that can be illuminated by the lens, or when exploring the total image circle with a smaller format by shifting/tilting the front or the rear standard for perpective and depth of field control.

    the formulae are the same, namely

    image circle diameter = 2 * f * tan((total angle of view) /2)
    image circle radius = f * tan((total angle of view) /2)

    total angle of view = 2 * atan( (image circle diameter) / (2 * f))
    total angle of view = 2 * atan( (image circle radius) / f)

    The actual angle of view like for 35 mm and MF cameras with no movements is limited by the film format diameter and not by the total image circle delivered by the lens. In fact even in 35mm and MF, the actual image circle is slightly bigger than the format diameter. For example when Hasseblad introduced the FlexBody, they had to disclose the total image circle of their Zeiss lens products, something that had nevered been presented before

    I do not know if there is a precise terminology for total angle of view and the actual (film format limited) angle of view, I hope this is clear.

    Example : for 90° of total angle of view, plus or minus 45° with respect to the optical axis, the image circle diameter is equal to twice the focal length.
    There was a 75mm Biogon lens covering actually 165mm, i.e. slightly more than 152mm, the diameter pf the 4x5" image format (94x120 mm actually). Hence the total image circle of the 75mm biogon was not 90° but 95°

    A lens with 72° of image circle will cover in diameter its focal length plus 45%, a 70° covers the focal length plus 40%, a 75° covers the focal length plus 50%.

    Summary
    total angle | example | image diameter in f units

    60° tessar@f/22 1.15 f

    70 old symmar 1.40 f

    72° apo sironar N 1.45 f
    apo-symmar

    75° apo-symmar-L 1.50 f
    apo-sironar-S

    80° old-angulon 1.68 f

    90° Biogon 2.0 f
    95° Biogon (actual) 2.18 f

    100° super-angulon F/8 2.38 f

    102° grandagon-N F/6.8 2.47 f

    105° super symmar XL 2.6 f
    super angulon F/5.6
    grandagon-N F/4.5

    110° super angulon XL 2.85 f
    apo-grandagon 45/55

    120° apo grandagon 35 3.46 f
    super angulon xl 38

    135° old Goerz hypergon 4.8 f !!!!!

  5. #5

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    Re: Image Circle Coverage and Angle of View - how to calculate?

    One additional comment.

    The above formulas apply when focused at infinity. When focused close-up, the angle of coverage or angle of view doesn't change, but the diameters of the corresponding circles are larger. You must multiply by the ratio of the bellows extension to the focal length.

  6. #6

    Re: Image Circle Coverage and Angle of View - how to calculate?

    Quote Originally Posted by Bruce Watson View Post
    They hardly relate at all. The coverage circle is determined by the design of the lens itself. Angle of view is a completely different thing; it's a function of focal length and format size.

    BTW, that's not "format diameter" in your equation, it's "d" which is the length of film in the direction you want to calculate angle of view. This is required because most film formats are rectangular and therefore have a different angle of view for the long side vs. the short side. The correct equation is alpha = 2arctan (d/2f), and it works for all formats. Don't forget to use consistent units of measure for "d" and "f."
    Thanks for your advice and putting me right on this formula. I had been using 76.5 as D in my calculation, which is half the 4x5 diagonal (I think). If I use half of 127mm I will get the angle horizontally then?

    If I'm not mistaken this angle of view, as quoted by most 35mm format lens manufacturers, is calculated on the diagonal measurement, but most illustrations are on the basis that one is looking down from above (i.e. at the long side) which isn't the same ° measurement.

    Having seen the explanations I realise now that image circle coverage and angle of coverage don't relate, and this is where I was getting completely confused ... I just couldn't see the connection!

    Thanks again.

  7. #7

    Thanks Jim, Emanuel and Leonard

    Thanks Jim for the formula, Emanuel for the extensive workings, and for Leonard for explaining why lens manufacturers generally give two measurements, of which one is at ∞

    However my calculation skills are lacking, and when I enter the formula in Google to use their calculator I am getting meaningless results. I was using the following data as an example:

    It’s the Schneider 120mm F/5.6 Apo Symmar L, which is quoted as having 75° angle of coverage at ∞, and 189mm image circle at F/22.

    So presumably it should be 2*120*tan(75/2) should give an answer of 183mm? The answer I am getting is -48.12. Where am I going wrong anyone?!

    Reading Emanuel’s post, am I right in understanding that a 120mm lens needs a bigger angle of coverage to provide movements than say a 210mm lens, in order to provide reasonable movements for 4x5?

    Is there a minimum practical image circle one should look for with a lens for 4x5 if one doesn't want to run out of movements for landcapes? Looking at the 120mm Schneider Apo Symmar L again – is a 189mm image circle considered sufficient or restrictive?

    Finally I want to make a composing frame for a 180mm lens (and possibly a second one for a 120mm lens), out of 2" x 1" wood - basically a simple small piece of wood with a hole cut in it in proportion to 4x5 and with the hole cut at an angle fanning out (the angle needs to be 46° I think!), which I can hold up about an inch away (a little more than a thumb's width!) from my eye. Do I need to adjust this angle because of the one inch distance from my eye, or will the difference be minimal?

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    Re: Image Circle Coverage and Angle of View - how to calculate?

    newmoon, you forgot to convert degrees to radians.

  9. #9

    Re: Image Circle Coverage and Angle of View - how to calculate?

    Quote Originally Posted by Dan Fromm View Post
    newmoon, you forgot to convert degrees to radians.
    Thank you
    Answer 184.158! That's what I was expecting!
    I hadn't picked up on anyone mentioning radians in previous posts, but presumably the post referring to Phi was the clue?
    Unfortunately I'm not an engineer, my school days are long gone, and my work does not involve radians or degrees!

  10. #10

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    Re: Image Circle Coverage and Angle of View - how to calculate?

    Is there a minimum practical image circle one should look for with a lens for 4x5 if one doesn't want to run out of movements for landcapes? Looking at the 120mm Schneider Apo Symmar L again – is a 189mm image circle considered sufficient or restrictive?

    In fact, my understanding is that for decades photographers were happy with tessar-type lenses which cover in diameter their focal length plus 15%, not more.

    For example I have offered to my brother-in-law a vintage Voigtländer 9x12 cm (84x114, diagonal = 141 mm) Avus plate camera, the lens is a 135mm skopar, a tessar-type, the camera has a vertical shift, the amount of shift actually permitted was quite small, with respect to modern standards, may be 10mm only !

    However imagine that you want to shoot a conventional landscape with 1/3 of ground and 2/3 of skies or vice versa from a LF camera with a perfectly horizontal setup.
    From this starting point where the horizon is just located in the middle of the image, since you are a proud owner of a brand-new LF camera with all possible movements, you do not want to tilt the whole camera up or down for framing 1/3 - 2/3 (this is what your photographically ignorant brother-in-law does routinely with his point 'n shoot camera, shame on him ;-) )

    Hence you have to shift the standards of the camera, the amount of required shift is 1/6th of the vertical side of the image. And for a 150mm tessar in 4x5", in landscape orientation, 1/6th of the small side = about 16 mm this is already off-limits with respect to what the tessar lens can achieve without running out of image circle : a tessar-type covering 60°, with a f.l. of 150mm, the lens can be shifted by + or - 12.6 mm on the long side of the 4x5" film and 15.3 mm along the short side.

    The consequence is that modern lens manufacturers consider "standard' view camera lenses with a minimum of 70°-75° of angle, covering their focal length + 40% to 50%. With such a standard 150 mm lens covering 70°, no problem for a perfect 1/3-2/3 composition by shifting only, an image including of course some vertical buildings you would not like to "see falling on you" ;-)

    Regarding a lens with 189mm of image circle, this is 150 plus 26%, so you are ready for making a perfectly "vertically-correct" 1/3-2/3 landscape composition in 4x5" !
    precisely, an image circle of 189 mm allows you, in theory on 4x5", to shift by + or -22 mm on the long side and + or - 26 on the short side, i.e. about one inch.

    Now if you find that your excellent 120mm lens does not cover enough, you'll just have to switch to the smaller 9x12cm European film format : film holders are totally compatible with 4x5 holders !

    Have fun ! Once you've started to use the vertical shift, you'll wonder how you could have lived so long with a camera offering no movements at all ;-)

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