----- Original Message ----- From: "Tom Miller" <tomwmil...@attbi.com> To: <pinhole-discussion@p at ???????> > > This put two questions in head. First, would a concave film plane reduce > the fall off ratio? Optimally, the film plane could be curved in a way that > makes the entire film plane equally distant from the pinhole. I looked at > the 6x22 camera's photo on the silver-whatever web site and it looked like > it could possibly have a curved film plane, although I couldn't tell if > would be hemisperical like the Mottweiler Pinoramic.
Disclaimer, none of the these is needed to be known to practice extreme wide angle pinholing, but if somebody ask this questions, I am happy to oblige. Tom, The camera in question looks very thin, so I am pretty sure it is a flat film plane camera. Yes, a concave film plane would reduce the fall off ratio. Using a film plane conforming to a half circle and positioning the pinhole at the center of the circle would reduce the fall off by a very substantial amount. In math terms, it is reduced from being cosine^4, to just cosine of the off axis angle. There is a catch, tho, in the case of this camera (6x22), the focal length has to be increased to allow the width of the film to fits in the semi-circle. > Second, what is the formula that you used to calculate the fall off? I'm > curious because I've been doing a fair bit of extreme wide-angle stuff > lately and it doesn't seem like the light falls off as much as one would > think. I think that we expect pinhole images to have severe fall off, therefore the actual fall off we get doesn't look to be that severe (am I making any sense?), it is almost magical and even seemingly defying physic laws! but I am pretty sure is just subjective perception. > It is a flat film plane camera with a 1:3.7 ratio. I've read a rule > of thumb that at 30 degrees the fall of is one stop and that at 45 degrees > it is two stops. It seems like there is a possibly handy formula in there. There is a law in optics called Cosine^4 law, all lenses, including glass lenses are subjected to it. It says that the intensity of light at a off axis point will be reduced by a factor equal to cosine to the power of four of the off axis angle. In your camera with ratio 1:3.7 (I'll assume this ratio is focal length : width of format), which BTW has very similar ratio than the one we've been discussing 60mm/22cm, the sides of the film are 61.6 degrees off axis, hence, as per Cosine^4 law, the intensity of light at the sides will be just: Cosine(61.6) x Cosine(61.6) x Cosine(61.6) x Cosine(61.6) = 0.051174 In other words, if at the center we have an intensity of 100 units (whatever units), at the sides, it'll be just 5.1174 units. To find how many stops that correspond to, we just multiply 0.05117 by 2 as many times as needed to reach 1 , the number of times you multiply by 2 is the number of stops of fall off. A faster and precise way is using this formula: Stops of fall off = 3.322 x Log ( 1 / 0.051174 ) = 4.29 stops If W = width of camera in mm and F = focal length of the camera in mm, a single formula to find the fall off at the sides of the film would be: http://members.rogers.com/gpenate/stopsW.gif If instead we want to find the fall off at the corners of the film, when H = height of film, the formula becomes: http://members.rogers.com/gpenate/stopsWH.gif Correction welcomed. Guillermo
