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I need to work out the vertical FOV for the pocket.. ?? my brain can't cope

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  • I need to work out the vertical FOV for the pocket.. ?? my brain can't cope

    Good morning world.

    I'm in the midst of building up a mixed reality filming rig (Where by you can film someone inside a VR experience and composite the VR computer world with the user shot on a green screen).

    We're 90% of the way to having the perfect setup but have hit the final and in my mind trickiest hurdle.

    I need to tell the computer the exact Field of View (FOV) we're shooting with on our Black Magic Pocket Cinema Camera.

    The FOV needs to be the vertical FOV as well which I'm told is not the standard measurement.

    Any ideas to get this right without having to slowly eyeball it via a time consuming approach would be great.

    Our filming rig, is:

    A Black Magic Pocket : Metabones Speedbooster to Nikon Mount : Sigma 18 -35mm (*fully zoomed out.).


    Any help on the math for this would be amazing.

    for those interested here's an early mixed reality film. The FOV was way off and the footage was scaled to crudely match in post. Plus the green screen was a quick pop up with no lighting.. please don't judge me :-)

    https://www.youtube.com/watch?v=maODJkAwqMI

    Here's our filming setup..
    A professional 2D / 3D animator with a passion for film.
    www.stormystudio.com

  • #2
    With the BMPCC Specific MB Speedbooster (.58) the sensor size becomes: 21.52mm x 12.1mm.
    So mix that with an 18mm lens and I think we at least have the makings of the right equation.
    You do mean 18mm when you say "fully zoomed out", right? (Your picture shows the lens set the opposite way, to 35mm.)

    And of course there are many sources for finding the horizontal field of view..... as you pointed out.

    So what IS the vertical field of view?

    Geniuses?

    Anyone?
    Cameras: Blackmagic Cinema Camera, Blackmagic Pocket Camera (x2), Panasonic GH2 (x2), Sony RX100 ii, Canon 6D, Canon T2i,
    Mics: Sennheiser, AKG, Shure, Sanken, Audio-Technica, Audix
    Lights: Every Chinese clone you can imagine

    Comment


    • #3
      Yep 18m on the lens...

      Geniuses (Genie-eye)... please....
      A professional 2D / 3D animator with a passion for film.
      www.stormystudio.com

      Comment


      • #4
        FOV = 2 * (atan (sensor_size/(2*focal_length)))

        both sensor_size and focal_length need to be in millimeters.

        sensor_size can be any dimension horizontal, vertical or diagonal and the formula will calulate the corrosponding angular FOV.

        Comment


        • #5
          its a fairly simple geometric relationship

          if you know the horizontal FOV (this is what is usually used in CG apps like Maya BTW) of a lens/sensor combo then the the vertical FOV on a spherical lens is just a simple ratio identical to the ratio of the height of the sensor to to its width

          in the case of the BMPCC the sensor is 12.48mm x 7.02mm so the ratio is 1.78 (ie exactly 16:9)

          so if a given lens gave you say a 60 degree horizontal FOV then the vertical FOV is given by 60 / 1.78 = 33.7 degrees

          of course working out the Horizontal FOV precisely is the hard bit - especially with odd crop factors, zoom lenses and speed boosters in the mix I suspect any paper exercise would only ever give an approximate value that isn't going to be accurate enough (so I definitely would find a way to measure that really)
          doing so isn't that hard - its simple trigonometry if you can measure some distances accurately

          eg:

          mount a large bit of mdf or similar on a couple of C stands (make sure its plumb vertically and square)
          mark the center line vertically
          mount a tape measure or similar from the center line of the board to the edge on one side (make sure its straight, flat and fixed down)
          measure an exact known distance from the center line of the board (eg 1m) outwards from the board surface (ie normal to it) and mount the camera there on a tripod so its level with the board - you wanna put the camera sensor plane at that exact distance you measured and make sure the center line you marked is bang on in the middle of the frame (use a center cross mark in the camera)
          record some footage

          if you look at what you shot the furthest distance you can read on the tape measure gives you the 'opposite side' and the distance the camera is from the board is the 'adjacent side' of a virtual right angled triangle that you can use to compute the angle of view using trig (TAN)
          note that conventionally the lens FOV is 2 * the angle you are computing (we compute the "half angle" using the above measurements)
          you get this angle in degrees by using the inverse TAN function on the ratio between the two distances

          the final equations are thus:

          H FOV = 2 * ( inverse TAN ( distance seen on filmed tape measure at extreme edge of frame / distance between camera sensor and board ) )
          V FOV = H FOV / 1.78

          see here for a trig refresh:

          http://www.mathopenref.com/trigtangent.html

          Comment


          • #6
            dhessel's method is easier of course but the speed booster kind of complicates things

            for AR I think measuring what you are actually getting is probably a good idea (I'm a CG/VFX sup by trade and most methods of FX interacting with real world footage comes down to measuring whats in frame accurately)

            BTW you also want to shoot a lens grid as the sigma at the wide end will definitely show enough distortion that the perfectly rectilinear world of the rendered CG stuff will need reverse-warped to compensate for it

            Comment


            • #7
              a web page that demonstrates a similar method to the one I proposed:

              http://www.panohelp.com/lensfov.html

              fovsetup.jpg

              this may be pertinent: "It is a little known fact that telephoto lenses can have a radically different actual focal length depending upon focus distance"

              so just because the sigma says 18mm don't assume it is (not only is it being speed-boosted by 0.58 so its now 10.45mm - the exact focal length will likely be affected by the focal distance the lens is set to due to lens breathing between near and far - this means the FOV actually subtly changes dependent on focus point

              Comment


              • #8
                Originally posted by Stelvis View Post
                its a fairly simple geometric relationship

                if you know the horizontal FOV (this is what is usually used in CG apps like Maya BTW) of a lens/sensor combo then the the vertical FOV on a spherical lens is just a simple ratio identical to the ratio of the height of the sensor to to its width

                in the case of the BMPCC the sensor is 12.48mm x 7.02mm so the ratio is 1.78 (ie exactly 16:9)

                so if a given lens gave you say a 60 degree horizontal FOV then the vertical FOV is given by 60 / 1.78 = 33.7 degrees

                of course working out the Horizontal FOV precisely is the hard bit - especially with odd crop factors, zoom lenses and speed boosters in the mix I suspect any paper exercise would only ever give an approximate value that isn't going to be accurate enough (so I definitely would find a way to measure that really)
                doing so isn't that hard - its simple trigonometry if you can measure some distances accurately

                eg:

                mount a large bit of mdf or similar on a couple of C stands (make sure its plumb vertically and square)
                mark the center line vertically
                mount a tape measure or similar from the center line of the board to the edge on one side (make sure its straight, flat and fixed down)
                measure an exact known distance from the center line of the board (eg 1m) outwards from the board surface (ie normal to it) and mount the camera there on a tripod so its level with the board - you wanna put the camera sensor plane at that exact distance you measured and make sure the center line you marked is bang on in the middle of the frame (use a center cross mark in the camera)
                record some footage

                if you look at what you shot the furthest distance you can read on the tape measure gives you the 'opposite side' and the distance the camera is from the board is the 'adjacent side' of a virtual right angled triangle that you can use to compute the angle of view using trig (TAN)
                note that conventionally the lens FOV is 2 * the angle you are computing (we compute the "half angle" using the above measurements)
                you get this angle in degrees by using the inverse TAN function on the ratio between the two distances

                the final equations are thus:

                H FOV = 2 * ( inverse TAN ( distance seen on filmed tape measure at extreme edge of frame / distance between camera sensor and board ) )
                V FOV = H FOV / 1.78

                see here for a trig refresh:

                http://www.mathopenref.com/trigtangent.html
                A few things and a word of caution. Firstly, sorry but this is not correct. Angular field of view has a non-linear relationship to focal length and sensor size. You cannot multiply the ratio of sensor width and sensor height by the horizontal field of view to get the vertical fov. While the results may be close it will not be correct.

                Second, in my experience over the years I have found that while a lens may claim to a certain focal length often it is not actually exactly that focal length. It may be off by a fraction of a millimeter or even in some cases more than a millimeter. Lens distortion and breathing can both affect the actually focal length of the lens along with variations in manufacturing.

                On the tele end it doesn't matter as much but the fov calculations are far more sensitive on the wide end which is were lenses for the pocket will normally be. Go ahead and use the formula I posted but if you find it is still not quite working you may have to measure it manually.

                I also just noticed that a speed booster is involved. That being the case I would also recommend you measure it manually using a method like Stelvis posted.

                Comment


                • #9
                  pCam iOS application will give vertical angle of view in degrees, for a given camera format/sensor, and show how many feet covered at a given distance.
                  DS

                  Comment


                  • #10
                    Wow... many thanks for everyones input... I'll give this a proper attempt tomorrow based on the above directions. I'll try the formula route and see how close that is. Today (whilst waiting for input) I tried a very manual approach, with the camera mounted on a tripod, then kept adjusting the X, Y and Z offset values to align the 'virtual cameras' point with the pockets sensor...done crudely by a mixture of eye (and touch when wearing the headset). I then measured the distances with a tape measure based on a known point on the tracked controller and the numbers were very similar. Though once adjusted based on the actual measurements it all clicked into place very nicely... This however had nothing to do with the FOV... so two of use kept adjusting a scripted FOV value, launched a virtual test scene that I built so I can see the controllers you hold 100% to scale in both the VR and real world camera.. We then kept trying to find the sweet spot where the controllers were at the very edge of the frame in both the real and virtual cameras... Needless to say it took a lot of takes to little down to a roughly accurate FOV setting...After about an hour of too and frowing.. we get close... not yet perfect... somewhere between 30 and 36 seems to be about right... but as we change position in between each test (+controllers have attendance to change their order which breaks the whole test) I then ran out of time to keep fine tuning...
                    A professional 2D / 3D animator with a passion for film.
                    www.stormystudio.com

                    Comment


                    • #11
                      It's 34.65 degrees vFoV, with wiggle room for the specifics of the lens.

                      This is pulling from my giant spreadsheet of lens calculations.

                      Comment


                      • #12
                        I am getting around 36/37-degrees vertical FOV with pCAam, on Micro in 1.85

                        Comment


                        • #13
                          I remember having an Android App that calculated all this (FOV etx...) and showed you the frame (if it fit) on your phones camera. It also accounted for Speed Boosters and the like as well.

                          Is that an Vive motion controller attached to the camera? You gotta let us know if it gives you a usable camera track! They should build one of those things into a BM camera, with a gyro and ... oh wait ... yeah ... ummm ...

                          Comment


                          • #14
                            Originally posted by dhessel View Post
                            A few things and a word of caution. Firstly, sorry but this is not correct. Angular field of view has a non-linear relationship to focal length and sensor size. You cannot multiply the ratio of sensor width and sensor height by the horizontal field of view to get the vertical fov.
                            actually you are correct on this - my bad - I just did some calculations in my CAD software to make sure
                            the relationship will be given by some sort of equation by might require some effort to work out - none of the online trig references I could find looked at this relationship specifically. (ie how the angle varies vs the relative length of the opposite side alone. nice homework for somebody though

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