Archived posting to the Leica Users Group, 1998/02/02
[Author Prev] [Author Next] [Thread Prev] [Thread Next] [Author Index] [Topic Index] [Home] [Search]Henning, 'Wide angle effect' distortion is dependant upon two factors: the first is 'correct' viewing distance and the second is the nature of the curved , natural perspective rendition of any lens being forced to render to a flat field object; the film. When the latter is corrected, oblique projection dictates image shape. Remember what happens to the circular globe, when it's laid out flat to a map? The center looms large, but the top, bottom and both sides recede due to the effect of correct perspective being what it is. Two solutions are made in lens design: the first is the fisheye lens, which renders that circular perspective directly 'as is' to the film and the second, the wide angle lens, varies the magnification towards the edge, top and bottom, to correct this to a more 'normal' perspective (when an image is changed from three to two dimensions). 'Oblique projection' is fully dependant, via imaging angle, on the co-relation of flange back length vs. focal length. A 20mm lens, with a symmetrical cell in the rear (identical to the front), has a nodal point at 20mm's from film. If you draw a triangle from the conjugate, "image distance" or nodal point of the lens, to the corners of the image, the coverage angle required is large with far travelling rays forming the image edges and corners; making a squat triangle. Besides stronger convergance, the 'extra' distance travelled makes light falloff more acute as well (hence center filter requirements) . A retrofocus 20mm, while having identical image size centrally, doesn't require as 'squat' a triangle (obviously, as the lenses rear element sits at least 40mm away from the film plane), and so, doesn't require the image magnification at frame edge that the RF version would. Because the angular distance to image edge is shorter, vignetting is also easier to correct. This also has a noticable effect on the manner in which the lens renders perspective. As you wrote: "the only factor governing perspective distortion is the angular distance of the object/image from the lens axis." The axis is the central point of the projected image and does meet the lens at its rear element, where the projection angle of corner-bound rays is determined. This is described as the "Image distance". In an RF 20, this is far closer to film center than it is with an SLR equivalent. The 'wide angle effect' (as per the Focal Encyclopedia of Photography) is present when "the image stretching occurs because the rays of light reach the film at oblique angles, rather than at the right angle that occurs in the center of the film". (pg 553, 'Wide angle effect' under heading 'Perspective') The description continues: "If the subject consists of balls or other spherical objects, the amount of stretching can be calculated in relation to the angle formed by the light rays that form the image and the lens axis. Thus, at an off axis angle of 25 degrees, the image is streched about 10%, and at 45 degrees, the image is stretched about 42%. The image size of off-axis subjects changes in proportion to the secant angle of the angle formed by the central image forming ray of light and the lens axis. The reciprocal of the cosine of the angle can be substituted for the secant." On the subject of viewing distance, the description reads (pg. 552, same book): " The so-called 'correct' viewing distance is equal to the focal length of the camera (or, more precisely, the **** _the image distance_***) for contact prints, and the focal length multiplied by the magnification for enlarged prints. This position is identified as the _center of perspective_. The correct viewing distance for an 8x10 inch negative, exposed with a 12 inch lens is 12 inches". (italic-like *'s mine) The * above relates to this description from pg. 374 of the book, Heading 'Image Distance: I quote: "The distance between the rear nodal (principal) plane of a lens and the plane of maximum sharpness of the image. When a lens is focussed on infinty, this distance has its minimum value and corresponds to the focal length of the lens ". The same physical law occurs via the projected image. An image formed, regardless of size, farther to the film plane, will also require a different eye view distance to match 'correct' perspective. Focal length is "the distance of the rear principal focus, that is, when the lens is focussed on infinty, so that parallel light is entering the lens. Image size is directly proportional to focal length" Obviously, were working to image size, central within the projected image. Proof that oblique projection changes the rendered shape of the image is simple to understand if you consider how a building is rendered when the lens is shifted up, to cover the building top, while the camera stays lower to the ground (a common architectural correction tehnique). The corners of the image show spectacular 'wide angle effect' stretching, no matter what the focal length. Of course, the shape changes are most dramatic with wide angle lenses, because of their more acute obliquely projected rays. Here is where the difference between an SLR lens and an RF lens will show their biggest differences: Because the corner-most rays of a retrofocus lens sit farther away from the film plane, in relation to the field angle required for full film coverage, their oblique projection is lessened, as compared to a true, symmetrical wide angle. Because the edge/corner image magnification is dependant on this coverage angle (remember, via the architectural example), a true RF lens will have a different edge rendition (with more wide ange distortion) than the SLR version, even though they have identical, central image size. Remember that "the image stretching occurs because the rays of light reach the film at oblique angles, rather than at the right angle that occurs in the center of the film". It absolutely follows that changing the severity of the 'oblique angles', produces a corresponding (and dramatically noticable) change in shape rendition, and apparant perspective. Regards, Danny Gonzalez