Nishi KAZUKI (西 一樹)

The Scheimpflug principle specifies the relationship between the object, lens, and image planes, providing conditions for focusing the entire image plane even for tilted objects. This classical principle is confined to unidirectional tilting and has not been extended to camera systems with two-axis tilts. Herein, we present an extension of the Scheimpflug principle to three dimensions, demonstrating that images can be decomposed and focused independently in the vertical and horizontal directions. This simplifies focusing on the overall image, which requires a two-dimensional search, into a combination of one-dimensional searches. The proposed theory was validated through practical experimentation using cameras.

The modulation transfer function (MTF) is essential for assessing the spatial frequency characteristics of optical imaging systems. This study presents an innovative sinewave-based methodology for measuring the MTF, which demonstrates robustness against noise and applies to images exhibiting distortion. Slanted-sinusoidal fringe charts were utilized as test objects to simplify contrast calculations. The MTF for each frequency is determined by optimally fitting a sinusoidal function to unequally spaced pixel data using nonlinear least-squares estimation, enabling the derivation of optimal solutions that comply with Cramér–Rao bounds. This methodology enables MTF measurements in small-sized images with minimal distortion and at frequencies beyond the Nyquist limit. Numerical simulations and empirical camera experiments revealed that our proposed approach outperformed traditional edge-based methods.

The slanted-edge method is commonly used for measuring the spatial frequency response (SFR) of digital imaging systems. To investigate the intrinsic capability of the slanted-edge method, this study formulated a procedure for calculating the SFR and proposed a numerical method for evaluating the accuracy of the estimated SFR relative to the theoretical value. It is shown that the slanted-edge method yields an accurate value of the SFR under ideal conditions and is a rational and consistent tool for determining the true resolution characteristics. However, under practical conditions, this includes some estimation errors. Based on this analysis, it is possible to identify the parameter that influences the estimation accuracy in the SFR computation.