Genie Nano-CL Series™ Additional Reference Information • 99Lens ModelingAny lens surrounded by air can be modeled for camera purposes using three primary points: thefirst and second principal points and the second focal point. The primary points for a lens should beavailable from the lens data sheet or from the lens manufacturer. Primed quantities denotecharacteristics of the image side of the lens. That is, h is the object height and h′ is the imageheight.The focal point is the point at which the image of an infinitely distant object is brought to focus.The effective focal length (f′) is the distance from the second principal point to the second focalpoint. The back focal length (BFL) is the distance from the image side of the lens surface to thesecond focal point. The object distance (OD) is the distance from the first principal point to theobject.Primary Points in a Lens SystemMagnification and ResolutionThe magnification of a lens is the ratio of the image size to the object size:hhm '= Where m is the magnification, h’ is the image height (pixelsize) and h is the object height (desired object resolutionsize).By similar triangles, the magnification is alternatively given by:ODfm '=These equations can be combined to give their most useful form:ODfhh '' = This is the governing equation for many object and imageplane parameters.Example: An acquisition system has a 512 x 512 element, 10m pixel pitch area scan camera, alens with an effective focal length of 45mm, and requires that 100mm in the object spacecorrespond to each pixel in the image sensor. Using the preceding equation, the object distancemust be 450mm (0.450m).ODmmmm 4510010 =mm 450mmOD =
