ISSN 0030-400X, Optics and Spectroscopy, 2014, Vol. 117, No. 1, pp. 121–131. © Pleiades Publishing, Ltd., 2014. 121 1 INTRODUCTION The characteristic quality of an optical system is usually considered by a function of its ability to discern the smallest object from the farthest distance. The modular transfer function (MTF) is a measure of sys- tem response in terms of spatial frequency [1, 2]. MTF data can be used to determine the feasibility of overall system expectations [3]. The MTF is a quantitative measure of image qual- ity [4]. MTF of an optical system is a measure of its ability to transfer contrast at a particular resolution level from the object to the image. In other words, MTF is a way to incorporate resolution and contrast into a single specification. From a visual standpoint, high values of MTF correspond to good visibility, and low values to poor visibility. But this quality of visibility depends on frequency. Perhaps an easy way to inter- pret MTF is by thinking of imaging a target with black and white lines, i.e. a target with 100% contrast. It is a known fact that no optical system at any resolution can fully transfer this contrast to the image due to the diffraction limit. In fact, as the line spacing on the tar- get is decreased, i.e., the frequency increases, it becomes increasingly difficult for the optical system to efficiently transfer this contrast. Therefore, as the fre- 1 The article is published in the original. quency increases, contrast of the image decreases and an MTF graph, which relates the fraction of trans- ferred contrast as a function of the line frequency, is the best way to observe such performance degradation [5–7]. However, while the MTF is such an important resource to objective evaluation of the image-forming capability of optical systems, it is usually obtained experimentally, thus, leaving researchers without an analytical (mathematical) solution in terms of mea- suring the performance [8, 9]. Although there are many analytical MTF expressions proposed for optical systems, they usually do not completely fit experimen- tally obtained data [10–12]. However there are a lot of approaches and codes, including the ZEMAX code, which provides rather accurate estimations of MTF by numerical methods, based, first of all, on ray tracing techniques. Accuracy of commercial MTF measure- ment systems ranges from 5% to 10% in absolute MTF, however obtaining accuracy to within 1% is also possible. Thus, existence of an analytical expression that better fits the experimentally obtained MTF, would help researcher to achieve better determination of the image quality of the optical system at the design phase [13–15]. This is rather important as analytical expressions are employed at the modeling stage of sys- tems and modeling is a powerful tool to gain insight Modulation Transfer Function Estimation of Optical Lens System by Adaptive Neuro-Fuzzy Methodology 1 Dalibor Petkovi a , Shahaboddin Shamshirband b, *, Nenad T. Pavlovi a , Nor Badrul Anuar c , and Miss Laiha Mat Kiah c a University of Niš, Faculty of Mechanical Engineering, Deparment for Mechatronics and Control, 18000 Niš, Serbia b Department of Computer Science, Chalous Branch, Islamic Azad University (IAU), 46615-397 Chalous, Mazandaran, Iran c Department of Computer System and Technology, Faculty of Computer Science and Information Technology, University of Malaya, Kuala Lumpur, Malaysia *e-mail: shamshirband1396@gmail.com Received September 23, 2013 Abstract—The quantitative assessment of image quality is an important consideration in any type of imaging system. The modulation transfer function (MTF) is a graphical description of the sharpness and contrast of an imaging system or of its individual components. The MTF is also known and spatial frequency response. The MTF curve has different meanings according to the corresponding frequency. The MTF of an optical system specifies the contrast transmitted by the system as a function of image size, and is determined by the inherent optical properties of the system. In this study, the adaptive neuro-fuzzy (ANFIS) estimator is designed and adapted to estimate MTF value of the actual optical system. Neural network in ANFIS adjusts parameters of membership function in the fuzzy logic of the fuzzy inference system. The back propagation learning algorithm is used for training this network. This intelligent estimator is implemented using Mat- lab/Simulink and the performances are investigated. The simulation results presented in this paper show the effectiveness of the developed method. DOI: 10.1134/S0030400X14070042 c c PHYSICAL OPTICS