Close-Range Camera Calibration

For highest accuracies i t i s necessary in close range photogrammetry to account for the variation of lens distortion wi th in the photographic Jield. A theory to accomplish this i s developed along wi th a practical method for calibrating radial and decenfering distortion of close-range cameras. T h i s method, the analytical plumb line method, i s applied in a n experimental investigation leading to confirmation of the validity of the theoretical development accounting for variation of distortion wi th object distance. issue. Our concern in the present paper is with EXTENSION OF MAGILL'S MODEL one specific of close-range photoMagill (1955) derived and experimentally grammetry, t h a t of camera calibration. I n verified a formula which accounts for the particular, we shall be concerned with t h e of distortion with changing focus. variation of distortion within the photoMagill's result can be expressed as follows. grammetric model. This becomes a consideraLet: tion of increasing importance a s magnification increases. T h e essence of the problem as f =focal length of lens, s=distance of object plane for which lens is pointed ou t in Brown (1962) is a s follows: focussed, ~ ~ d i ~ l distortion is normally calibrated at 8ro=distortion function for focus on object infinity focus. Accuracies of zk2 microns rms plane at distance s, or better for the distortion function are not Gr,=distortion function of lens for infinity difficult to obtain from a rigorous stellar calibrafocus, tion. . H ~ ~ ~ ~ ~ ~ , optical ray tracing theory tells =distortion function of lens for inverted us that Gaussian radial distortion is a function infinity focus (i.e., distortion, if the lens is of object distance. Thus when the focal plane is reversed so that front element becomes set for a sensibly finite object distance, it is rear element and vice versa). necessary to employ the distortion function appropriate to that distance. Actually, i t is Then the magnificati0n the lens for the ject plane a t s is * Presented a t the Symposium on Close-Range Photogrammetry, Urbana, Illinois, January 1971. ma = f / ( s f )