Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!swrinde!ucsd!dog.ee.lbl.gov!pasteur!miro.Berkeley.EDU!ph From: ph@miro.Berkeley.EDU (Paul Heckbert) Newsgroups: comp.graphics Subject: Re: Lunar Distortions Keywords: projection, perspective, distortion Message-ID: <9287@pasteur.Berkeley.EDU> Date: 28 Nov 90 21:07:33 GMT References: <27332@cs.yale.edu> <1097@shakti.ncst.ernet.in> <9236@pasteur.Berkeley.EDU> Sender: news@pasteur.Berkeley.EDU Reply-To: ph@miro.Berkeley.EDU (Paul Heckbert) Organization: University of California at Berkeley Lines: 145 In response to the question I asked earlier: | Is there a formula relating camera lens | focal length and angle of view? (I would guess that such a relationship | would not be theoretical, but would be based on praticalities, | and would vary from manufacturer to manufacturer) I've received several lucid replies: ------------------------------------------------------------ From greg@hobbes.lbl.gov Mon Nov 26 22:46:43 1990 From: greg@hobbes.lbl.gov (Gregory J. Ward) Subject: Re: lens angles The relationship is fairly straightforward as I understand it. Think pyramid where the width and length of the base are defined by the image dimensions and the height is given by the focal length. The formula for the angle is simply: angle = 2 * atan(film_size/2 / focal_length) For 35mm film, whose image dimensions are 34mm by 23mm (approx.), the view angles for a standard 50mm lens are 37.6 by 25.9 degrees. -Greg ------------------------------------------------------------ From grant%delvalle.llnl.gov@lll-lcc.llnl.gov Tue Nov 27 03:20:22 1990 From: grant%delvalle.llnl.gov@lll-lcc.llnl.gov (Chuck Grant) If Ken is rendering an outdoor picture at night with the moon in it, then it is probably a very wide angle picture, and you are absolutely correct that the answer is "stick you face closer to the screen and it will look ok." You state: >there is only one point in a movie theater from which a viewer will see the >same image as that seen by the camera (i.e. same angle of view). Theater >geometry and the lenses used for shooting and projection are usually >chosen to put that "ideal viewer position" near the middle of the >theater, I imagine. You don't have to imagine. You are exactly right. I remember this from filmmaking books I read in high school. A 35mm movie camera uses 50mm lenses as the "normal" lens. A 35mm film projector uses a 100mm lens so the picture looks right when you are seated half way between the projector and the screen. (I don't remember the numbers for "Panavision" or other wide screen systems.) Use of telephoto or wide angle lenses in the camera produces some distortion to the viewer at the center of the theater. This is something very important to film directors. All films are done this way. They understand it. I have never heard this issue mentioned in the context of computer graphics. Maybe no one knows this? As to your question: >is there a formula relating camera lens focal length and angle of view? Such a formula is simple, if the lens has no distortion, and the size and shape of the film is known. Where distortion is distortion in the strict optical aberration sense. Any optical system is subject to several aberrations to varying degrees. These are: spherical aberation coma astigmatism curvature of field distortion longitudinal chromatic aberration lateral chromatic aberration Distortion is non-uniform magnification across the field of view. Magnification usually varies slightly as the angle off the optical axis varies. This gives rise to "barrel" (negative) or "pincushion" (positive) distortion. Named, for what the image of a square looks like when subjected to said distortion. For camera lenses, you can safely assume the distortion is very small except for wide angle lenses (which is probably the case you were interested in). I expect that lens manufacturers would be relectant to release the actual numbers describing their lens's performance, since most people couldn't tell the difference anyway. For a lens focused at infinity and flat film, fov = 2 * atan ( film_width / ( 2 * focal_length ) ) The only difference between a distortionless lens and an ideal pinhole camera with respect to field of view is that if the lens is focused at a finite distance, replace focal_length in the above formula with: 1/(1/focal_length - 1/object_distance) which is the lens to image (film) distance. Chuck ------------------------------------------------------------ From awpaeth@watcgl.waterloo.edu Tue Nov 27 18:46:56 1990 From: Alan Wm Paeth Subject: Fields of View >Related question: is there a formula relating camera lens >focal length and angle of view? The way this is done for a rectilinear lens (everything one ever encounters short of optics with high distortions or a fisheye) is based on the size of the image formed. In an "ideal" lens -- a pin-hole is a nice first approximation -- the field is as large as you want -- the negative or film holder or other physical limitation defines the "field stop". In a more complex lens the diameter of some internal element might serve to define the field stop -- a 50mm lens for a 35mm SLR would probably not be able to produce a ~250 mm image circle if mounted on a large format camera's lens board. If if could it would make a tremendous wide angle! If the linear field F is given, then you can use the dimensionless relation: 2 tan(A/2) = F/EFL to solve for angular field A or effective focal length. This says (for instance) that a conventional SLR with 43 mm film diagonal (35 mm film is 24 mm x 36 mm; hypot(24,36)~=43) will cover a reasonable, mildly wide-angle 53 degree (diagonally) angular field with a 43 mm lens installed. /Alan ------------------------------------------------------------ So using the (theoretical! yay!) relation angle = 2 * atan(film_size/2 / focal_length) with 35mm film format, which I'm taking to be 34mm wide by 24mm high (Greg Ward's numbers; Alan Paeth's numbers differ slightly: 24x36), we get the following correspondence for some common lens focal lengths: focal length (mm) 24 35 50 80 200 horizontal angle (deg) 70.6 51.8 37.6 24.0 9.72 vertical angle (deg) 51.2 36.4 25.9 16.4 6.58 -Paul Paul Heckbert, Computer Science Dept. 570 Evans Hall, UC Berkeley INTERNET: ph@miro.berkeley.edu Berkeley, CA 94720 UUCP: ucbvax!miro.berkeley.edu!ph