Abstract

The optical transfer function (OTF) and its modulus, the modulation transfer function (MTF), are widely accepted measurements of the quality of optical systems. There are different ways of estimating both OTF and MTF. Random-dot-pattern methods have some advantages when computing MTFs, especially those which present the pattern on a liquid crystal-display (LCD) screen because no additional light source is needed. Nevertheless spatial information is not usually available in the image plane because MTFs are computed for the whole image in a finite number of directions only. We propose a way of providing spatial information by measuring a number of point-spread functions (PSFs). Created by a white-dot pattern on a LCD screen, white pixels operate as point sources and PSFs are calculated to eventually result in the OTF of the system. MTFs in the main directions are computed to compare with reference values obtained by the random-dot method. Sensor and LCD resolutions define the achievable MTF range. Our proposed method is used to characterize a liquid-crystal tunable filter (LCTF) attached to a monochrome camera at different wavelengths. This method, which is both easy to install and to use, achieves results with errors of less than 3%, and has advantages over classical OTF estimation methods: spatial information provided in the image plane, all frequencies and directions covered in a single capture, no additional light source needed and derivative-dependent noise avoided.

Highlights

  • A widely accepted measurement of image quality, the optical transfer function (OTF) [1]–[3], and its modulus, the modulation transfer function (MTF), are used to characterize some optical systems [1]–[6]

  • Previous studies have proposed several methods for measuring the MTF of optical systems based on detector arrays of charge-coupled devices (CCDs) [8] and most of them differ essentially in the type of target or pattern used as the object pattern [9]

  • In the edge-gradient method, the object intensity has a knife-edge-like variation and the image data are described by an edge-spread function, whereby the MTF of the optical system is obtained as the Fourier transform of the derivative of the edge-spread function, which usually implies dealing with noise [2, 7]

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Summary

Introduction

A widely accepted measurement of image quality, the optical transfer function (OTF) [1]–[3], and its modulus, the modulation transfer function (MTF), are used to characterize some optical systems [1]–[6]. Previous studies have proposed several methods for measuring the MTF of optical systems based on detector arrays of charge-coupled devices (CCDs) [8] and most of them differ essentially in the type of target or pattern used as the object pattern [9] These techniques can be broadly classified into five categories: the sine-wave method, the bar-target method, the edge-gradient method, the series-expansion method and the random-pattern method [4]. The bar-target method calculates the MTF by imaging bar-target patterns and determining the reduction in amplitude of the fundamental frequency component [6, 10, 11] This approach requires a different target and a different set of measurements for each of the spatial frequencies sampled. There is no need to use an additional light source to illuminate the pattern, and second, using a laptop to present

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