Lens view angle

Discussion in 'Lens Lust' started by Pa, Jul 19, 2005.

  1. Not sure if this belongs here or in the Technical Discussion forum, but I'll start here.

    I'm trying to compare field of view between different lenses at their widest, specifically the Nikkor 18-70 and the 28-200. The Nikon web page says for the 18-70 the field of view (FOV) at 18mm is 76 degrees, but for the 28-200 at 28mm, they give a FOV of 74 degrees, 20 minutes. This is a negligible difference, and I suspect it is not correct.

    Since the 18-70 was designed specifically for digital cameras, are they including the 1.5 crop factor for it and not for the 28-200?
     
  2. Chris101

    Chris101

    Feb 2, 2005
    Arizona
    Yes Pa, you have it correct. The DX lenses have the angle of view for a DX sensor given on Nikon's page, while the lenses designed to cover a film frame show the '135' format angle.
     
  3. O.K. so how do I figure out the "true" FOV for the 28-200 at 28mm on my D70? Divide 74 degrees 20 minutes by 1.5 ? That, of course, would get me down to about 50 degrees.
     
  4. Apparently it's a bit more complicated than dividing by 1.5.

    Nikon gives a FOV for an 18mm non-DX lens as 100 degrees, and 76 degrees for the DX. That gives a multiplier of 0.76, which says the FOV for 28 mm non-DX should be about 55 degrees on a D70.

    Agree?
     
  5. Chris101

    Chris101

    Feb 2, 2005
    Arizona
    The dimensions of the DX sensor are about 16mm X 24mm, so the diagonal is 28mm by the pythagorean theorem. Use half the diagonal to make a right triangle with the normal line from the center of the sensor to the center of the theoretical lens. The distance to the center of the theoretical lens is it's focal length. So now you have a right triangle with the side opposite (half) the angle in question equal to 14 (half the diagonal) and the adjacent side is the focal length of the lens. Now find the angle with the arcsin: arcsin (opposite/adjacent) = half angle, then multiply by two.

    So for 28mm, it's 60 degrees.

    Bet ya didn't think you'd need trig for this hobby... ;)
     
  6. ckdamascus

    ckdamascus

    928
    May 14, 2005
    New Jersey
    I am on the road now so I don't have my formulas with me.

    It is something like this

    2*(inverse tangent(2*(sensor size)/(focal length)))

    Width of sensor is one of the sensor lengths, widths, or diagonals. Focal length is the Focal Length of the lens. Inverse Tangent is the arctan function. I think Nikon's spec guys use the diagonal all the time.

    Presuming my memory is correct, this is the proper way to calculate the angle of view.

    You can find out sensor sizes pretty easily since the 35mm sensor is
    36 x 24 mm, D70 is 1.5X multiplier so divide by 1.5 and you get
    23.7 x 15.6 mm

    You can calculate the diagonal using Pythagoreum's theorem

    (23.7^2+15.6^2)^.5 == diag or about 28.37
     
  7. Chris101

    Chris101

    Feb 2, 2005
    Arizona
    Doh! You are right Carroll, make that arctan, not arcsin! So it's 53 degrees.
     
  8. Thanks guys. It's been a long time since I studied optics; guess I need a refresher course!
     
  9. Chris101

    Chris101

    Feb 2, 2005
    Arizona
    [img=right:442b667615]http://homepage.mac.com/cheilman1/images/cameras/lensangles.gif[/img:442b667615]A couple of weeks ago, I calculated the horizontal, vertical and diagonal angles of view for all the popular focal lengths on DX sensors. Here's my data:
     
  10. Ken-L

    Ken-L Guest

    It's clear as mud, but it covers the ground.... :lol:

    After studying all your data and comments, interpolating, exptrapolating, deducing, and figuring, I now see that if my zoom lens can't give a wide enough view I need to step back..... I'm getting a headache :oops:

    Seriously, how is this info used in it's application for you in the "field"?
     
  11. I was only interested in determining how much FOV I would lose at the widest end if I switched from the 18-70 to the 28-200 as my standard "walk-around" lens.

    I.e. it is input to a purchase decision, not something I would use while taking pictures.
     
  12. ckdamascus

    ckdamascus

    928
    May 14, 2005
    New Jersey
    Also, if you look at Chris101's data, you will find that the formula is very sensitive at the low focal length range.

    So, a few millimeters at the low end from say 18mm to 12 mm is a HUGE difference in FoV compared to say 200mm to 180mm.

    Also, with the generic formula you can calculate for any sensor/format size with unerringly accuracy vs just following some random photographic "truism" that "medium format lens have a bigger Field of View than 35 mm format".

    It's not supposed to be directly useful in the field. It's supposed to be useful for debunking common misconceptions and/or buying decisions to decide economic cost benefits. i.e. "how much wider is that 12 mm vs my 18mm" lens.
     
  13. Not to be outdone, I put these calculations into a spreadsheet to produce the following table:

    29000400-M.

    PM me if you'd like the spreadsheet (.xls).

    p.s. It's apparently the diagonal FOV that Nikon posts in their data sheets.

    p.p.s In the table, "f" is the focal length in mm, and the various FOV's are in degrees of angle.
     
  14. Chris101

    Chris101

    Feb 2, 2005
    Arizona
    Ken, some of the work I do is to copy flat art. By calculating the angle needed from a particular distance, I can put the right lens on the first time and not be fooling around with lenses in front of the client. It makes me look more professional so I can charge more than the kid next door who doesn't even use a spirit level.
     
  15. nfoto

    nfoto Guest

    Angle of view for any lens is *always* given by the diagonal. Nothing particular for Nikon.
     
  16. Chris101

    Chris101

    Feb 2, 2005
    Arizona
    Nice. It's obvious that you are an engineer while I am a scientist (and people think there is a Nikon/Canon dichotomy!) ;) ;)

    The pencil scratchings down the left side of my notebook page, by the way, is an HP48 program to do these calcs with one button.
     
  17. Sorry, I'm new at this game. To me, the horizontal angle of view seems most useful.
     
  18. Chris101

    Chris101

    Feb 2, 2005
    Arizona
    Most useful to the photographer and most useful to lens marketing are two different things. Using the diagonal makes wide angles look oh, so wider.

    Plus it's convention.
     
  19. nfoto

    nfoto Guest

    The lens projects an image circle. How wide view is encompassed by this circle? Given by the diagonal FOV.

    Formats can differ in aspect from the 3:2 ratio we're used to in 35 mm and suchlike derivates. Think of 4:3 (olympus) or the venerable 4x5" (which I've used for years).
     
  20. ckdamascus

    ckdamascus

    928
    May 14, 2005
    New Jersey
    Well, <cough> another vendor Whose Name Shall Not Be Spoken (Written) had a full chart of all of it's lens with Horizontal, Vertical, and Diagonal. Of course it had a typo in one of the entries, so using that formula I helped someone recover the correct value.

    :)

    You could argue that one could derive the Horizonal and Vertical values easily from the Diagonal given a sensor. It's just more work.

    So, perhaps it was for brevity. Or just marketing. hmmm... Perhaps both but leaning towards marketing.
     
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