Determination of Transverse Magnifications by Distortion Analysis

Abstract

A method to determine the transverse magnification (TM) of an imaging system is discussed. This method is different in that TM can be determined accurately by using distortion analysis. We demonstrate the validity of the method via numerical simulation with accompanying experimental data for a thick bi-convex lens.

Alternative Description for Gaussian Image Plane

“…(6) shows that the TM at the GIP does not depend on anything but the elements described above, as expected. In contrast, when the IP is not on the GIP, the TM is no longer a constant but a function of various parameters, as shown in Eq.…”

“…2 was utilized for a series of measurements to be conducted. We used our previous work on distortion analysis to obtain accurate and precise measurements of the transverse magnification [6,7]. Briefly, a 15" LCD monitor (pixel pitch = 0.294 × 0.294 mm 2 ) was used as an object plane to display a number of bright pixels in a square grid (55 × 55) as point sources, and a circular AS of diameter 3 mm was placed in front of a bi-convex testing lens (BICX-25.4-23.9-C, CVI Melles Griot, f = 24.8 mm at λ = 546 nm).…”

“…6. The tip/tilt angles were minimized and the distortion center was aligned to the optical axis as far as possible.…”

“…Note that the TM measurements require a set of off-axis [6,7], which can estimate an average error of 0.09% in the distortion for smartphone cameras over a full range of conjugation [8]. Therefore, a set of experimental data for a thick bi-convex lens system is presented to validate the description.…”

Accurate determination of distortion for smartphone cameras

“…Thus, the tested half-field angle was kept equal within 2% uncertainty. Figure 4 shows the object distances versus the transverse magnifications that were calculated as ratios of the paraxial spot spacing obtained from the regression to the spacing between the bright pixels on display [10]. The solid line was calculated with the focal length of the camera, whose value was one of properties of the image file, and the pixel size of the camera detector was assumed to be 2.38 μm which is another parameter not confirmed yet.…”