Just how wide is the Samyang/Rokinon 7.5mm fisheye? Lets do the maths...

Discussion in 'Native Lenses' started by Andym72, Sep 1, 2013.

  1. Andym72

    Andym72 Mu-43 Veteran

    330
    Mar 4, 2013
    Reading, UK
    OK, beware, there is a fair amount of trigonometry in this post!

    Based on the info here:

    Fisheye Projection - PanoTools.org Wiki

    first we need to work out exactly the focal length of this lens, because 7.5mm is bound to be a rounding.

    The Samyang is meant to be an equisolid (equal-area) fisheye lens, so the lens equation is:

    R = 2f * sin (Θ/2)

    Θ (theta) is 90 degree in this case, the angle from the corners to the centre, R is 10.83333mm, half the sensor diagonal.

    What we get for f, the focal length, is 7.66mm. This is the smallest focal length without vignetting.

    Now, if we defish this to rectilinear, just how wide is it, and what focal length would we need to get an rectilinear lens that is as wide? This is a little more tricky. If you've run any fisheye images through tools to defish, you will have noticed that the result becomes a much wider aspect ratio than the 4:3 you started with.

    Horizontal angle of view is R = 8.666, f = 7.66 as we just found out, gives us 2Θ (the full aov from left to right) of 138 degrees. Do it again for the vertical angle of view, R = 6.5, and you get an angle of view of 100 degrees. Just for comparison, the 7-14mm at 7mm gives a horizontal angle of view of 102 degrees, so a fisheye is crazy wide in comparison!

    Now we need to change equation, to the rectilinear one. That page on the Panotools wiki handily gives this too:

    R = f * tan (Θ)

    So we know the focal length (7.66) and the angles, so how large a "pretend" sensor do we get when we defish? Horziontally we get about 40mm, and vertically we get 18.3mm. So the aspect ratio is about 2.2:1 which seems about right.

    How about if we had an m43 rectilinear lens, that we shot at 4:3 ratio then cropped to 2.2:1, what focal length would it have? R = 8.666, Θ = 69... and the focal length is 3.3mm!

    Very, very VERY wide.
     
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  2. RevBob

    RevBob Super Moderator

    Jun 4, 2011
    NorthWestern PA
    Bob
    My eyes just glazed over - but I think you're saying that the fisheye at 7.66 is wider than the rectilinear at 7. Interesting! :cool:
     
  3. ALMANST

    ALMANST Mu-43 Regular

    42
    Jan 20, 2013
    ON, Canada
    So.... its wide then.
     
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  4. Andym72

    Andym72 Mu-43 Veteran

    330
    Mar 4, 2013
    Reading, UK
    :clapping:
     
  5. inkista

    inkista Mu-43 Veteran

    332
    Jan 13, 2012
    San Diego, CA
    ... except when we defish the 7.5mm, we do tend to crop off the smeary edges as unusable, so it would probably come out to be a little longer than that.

    But I like the math! It's interesting to think of the lens (ideally) being a 3.3mm rectilinear when defished.

    OTOH, that's still not wide enough for me, so I'm building virtual 360º lenses when I do stereographic little planets of 360x180 panos I shoot with the 7.5mm. So I guess it's all relative. :)

    And for those who think this was speaking in tongues—you really don't want to see what happens when mathy types start playing with fisheye lenses and imaginary numbers...

    4529295991_d758c2a994_z.
    Peirce's Quincuncial remap with drostify in Mathmap Gimp plugin of equirectangular 360x180 "spherical" pano of Scripps Pier.
     

    Attached Files:

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  6. Andym72

    Andym72 Mu-43 Veteran

    330
    Mar 4, 2013
    Reading, UK
  7. Andym72

    Andym72 Mu-43 Veteran

    330
    Mar 4, 2013
    Reading, UK
    The exclamation was about the image, and how its screwing with my head. Thankfully mention of imaginary numbers and the Droste effect didn't fly totally over my head (it's been a while since I had to do any such maths, but I still remember the basics).

    And I found out that MathMap exists, which I didn't know about, so thank you.
     
  8. inkista

    inkista Mu-43 Veteran

    332
    Jan 13, 2012
    San Diego, CA
    BTW, there's an entire Mathmap group on Flickr.

    And, hey, no worries. I just didn't wanna hijack your thread with a huge long expositional interpretation of all my funny words. :) And yeah. The droste remapping alone can really screw with your head, let alone the Peirce's quincuncial/spherical pano thing.

    Most Droste-effect mappings, though, are done more simply, starting with more normal images.

    Like turning this:
    2219765984_8134c6079f_z.

    Into this:
    2219807540_78124b6d94_z.

    It started with some folks messing about in Mathmap with the Escher/Droste equations. Someone then ported it into Pixelbender for Photoshop/Premiere folks (although I believe Pixelbender's no longer supported in the current versions of the software). And it's gotten to the point where there are now smartphone apps that can do the same thing.
     

    Attached Files:

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  9. RoadTraveler

    RoadTraveler Mu-43 All-Pro

    Nov 23, 2012
    Your abilities to perform calculations are in another galaxy than mine (which don't exist)... but I'm happy to take your word for it = Very wide/3.3 mm rectilinear!

    Makes me even happier I have a 7.5 mm fisheye lens on the way.

    Thanks describing the width of a fisheye. :thumbup:
     
  10. ArchSaturn

    ArchSaturn Mu-43 Rookie

    19
    May 23, 2012
    Just received mine on Friday before the long weekend... I can tell you how wide it is...

    Wide enough to catch my fingers in the corners of shots, going to have to be careful about that. Imagine this must be an even bigger problem for those who have the grip.
     
  11. zap

    zap Mu-43 Veteran

    215
    Jul 23, 2012
    uk


    LOL!! :biglaugh:
     
  12. arch stanton

    arch stanton Mu-43 Veteran

    415
    Feb 25, 2012
    London
    Malc
    I've done this about a dozen times so far - it's insanely wide.
    I'm waiting for my own gurning face to appear in a shot ;)
     
  13. MiguelATF

    MiguelATF Mu-43 Veteran

    Just how wide is it? Well....seeing is believing

    Just how wide is the Rokinon 7.5mm? Good question. I was wondering the same myself. Just purchased a lightly used one from a fellow Forum member, it arrived today, so I checked it out. This picture was slightly modified in Lightroom with a custom lens profile to give a 'stereographic' image -

    10434366026_9cd4acbb0a_b.
    Home by La Chachalaca Fotografía, on Flickr

    But....yes! it's wiiiiide!
     
  14. tjdean01

    tjdean01 Mu-43 Top Veteran

    842
    Feb 20, 2013
    I work in real estate and bought the $100 10.5mm converter for my 14/2.5. It's wide, sure, and I even was able to use those as a tax write off as I use it taking photos of rooms for work. This is low-light, handheld work so the f2.5 helps. I always wanted wider but even the 9-18 is a lot so what could I buy for cheap...?

    Enter the fish! I shoot it f4 and up, but even there, I can handhold it better than the 14 + converter. Plus, these pics are meant for web resolution so IBIS on and ISO 6400 is useable for me (but with the windows open I can get away with f5.6 ISO 800 on the fish). The 14 is a nice lens but I hate the converter and how it attaches so it's going up for sale because....I finally learned how to defish! I'm really happy with the results. I didn't adjust colors or anything because this is a quick job, but I like it!

    I've discovered, however, that with some photos, I prefer the original image because there is no stretching, only the distortion. And I think the brain automatically compensates for that because the normal fished images look fine to me in many situations and gives the correct size of things from that particular angle of view. The fished image is the true image and IMO, the way I look at it, distortion is 0 because that's how the light passes through the lens. For the below shot, however, defishing is the way to go....for the edges at least:

    [​IMG]
     
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  15. Geoff3DMN

    Geoff3DMN Mu-43 Veteran

    This is a really interesting thread and whilst it's a long time since I had any exposure to maps or projections I did manage (after some slow and careful reading) to understand what was happening. I wasn't in the least aware that there were practical photography applications for this sort of thing let alone available plugins!

    I continue to be amazed at where digital photography editing is heading and thank you for allowing this old dog a chance to learn a new trick :)
     
  16. Zee

    Zee Mu-43 Top Veteran

    I do this a lot.

    I find myself looking at the bottom right hand corner all the time now...

    Z...
     
  17. wjiang

    wjiang Mu-43 Hall of Famer

    I find this to be true as well. When mapping a spherical view to a 2-D projection, there will always be distortion - it just depends on what you prefer. When thinking about it this way, a rectilinear projection is no more 'correct' than any other. I find myself 'de-fishing' quite a bit in Hugin, but have never re-projected to rectilinear. I've found cylindrical, stereographic (this is actually a bit more 'accurate' with proportions than a fish eye), trans mercator, and Panini general to be the most useful. Panini general, in particular, allows quite a bit of adjustment when you want a more rectilinear look for vertical lines without going full rectilinear.
     
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  18. datagov

    datagov Mu-43 All-Pro

    Dec 2, 2012
    New York
    It's pretty darned wide

    PA163523_01.
     
  19. SeanKelleher

    SeanKelleher Mu-43 Regular

    106
    Sep 24, 2014
    Melbourne
    Sean Kelleher
    All this makes me want one to play with.