TECHNICAL PAPER Measurement and analysis of modulation transfer function of digital image sensors Yi-chin Fang 1 • Yih-fong Tzeng 1 • Kuo-Ying Wu 1 • Ho-Lin Tsay 1 • Po-Ming Lin 1 Received: 28 March 2019 / Accepted: 16 May 2019 Ó Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract With the ceaseless development of technology, optical imaging systems have been extensively used in numerous different fields. As a result, verifying the performance of such systems has taken on significant importance. To test these systems, a commonly used metric is the modulation transfer function (MTF) because it reflects the spatial-frequency response of optical systems. To determine how best to measure the MTF of an image sensor, we use the slanted-knife-edge method to measure optical patterns and a black-and-white face sensor to receive patterns, following which we numerically calculate the MTF. We use the MTF of the Nyquist frequency (50 lp/mm) of an image sensor as the measured value, and the slanting angle for the slanted-knife-edge method ranges from 2° to 10°, which is known to provide accurate results. We then compare and analyze the experimental data and explore how inaccurate slanting angles affect the measured MTF. Finally, we propose a ‘‘program correction method’’ in which we input a corrected slanting angle into the region-of-interest program to correct for errors in the measurement of the MTF. The corrected parameters provide a more accurate mea- surement of the MTF of the given pattern. 1 Introduction Currently, instruments for measuring the modulation transfer function (MTF) of optical systems are procured primarily from professional manufacturers. Although such equipment provides highly accurate results, it is relatively expensive. Thus, home-built optical testing equipment is an attractive alternative, provided it meets the testing requirements at reasonable cost. Reaching this goal, how- ever, requires extensive study and development of MTF measurement technology. The present study thus investigates techniques to mea- sure the MTF of image sensors and develops the frame- work of an optical measurement system. The main result of this work is the development of a ‘‘program correction method’’ that corrects the measurement error, thereby improving the measurement accuracy. The main method to measure the MTF is based on the following three functions: the point spread function, the line spread function (LSF), and the edge spread function (ESF). In the present work, we use the ESF method to measure MTF. To analyze the results, we use the interac- tive data language to convert the MTF data from the image. 2 Methods 2.1 Knife-edge measurement pattern from edge spread function Acquiring insufficient samples from an optical sensor leads to an aliasing effect. To overcome this problem, the sam- pling frequency should be raised, which is most directly achieved by decreasing the sampling interval of the image sensor. For example, decreasing the sampling interval from 10 to 5 lm increases the sampling frequency from 50 to 100 lp/mm. One example of decreasing the sampling interval is the microscanning method, which is imple- mented by moving over and sampling sub-pixels, followed by interpolation of sub-pixels through image regrouping. & Kuo-Ying Wu jason.kh@msa.hinet.net Yi-chin Fang yfang@nkust.edu.tw Yih-fong Tzeng franktzeng@nkust.edu.tw 1 National Kaohsiung University of Science and Technology, Kaohsiung, Taiwan 123 Microsystem Technologies https://doi.org/10.1007/s00542-019-04493-1