Abstract
Numerous methods are available to measure the spatial frequency response (SFR) of an optical system. A recent change to the ISO 12233 photography resolution standard includes a sinusoidal Siemens star test target. We take the sinusoidal Siemens star proposed by the ISO 12233 standard, measure system SFR, and perform an analysis of errors induced by incorrectly identifying the center of a test target. We show a closed-form solution for the radial profile intensity measurement given an incorrectly determined center and describe how this error reduces the measured SFR of the system. Using the closed-form solution, we propose a two-step process by which test target centers are corrected and the measured SFR is restored to the nominal, correctly centered values.
Highlights
Measuring the spatial frequency response (SFR) of an optical system remains an intricate task, with several test methodologies available to the optical scientist and engineer, including slanted edge tests and measurements from known noise targets
We propose a two-step method whereby an initial coarse estimate is made of the center of the target, a low-frequency single circular profile is extracted from the image of the sinusoidal Siemens star, fit to Eq (3), and constants Cx and Cy are solved for and used to correct the initial guess
Determining the center of a sinusoidal Siemens star test target image can have significant impact on the SFR extracted from the image
Summary
Measuring the spatial frequency response (SFR) of an optical system remains an intricate task, with several test methodologies available to the optical scientist and engineer, including slanted edge tests and measurements from known noise targets. The mathematical function for the measured intensity of a sinusoidal Siemens star target with an incorrectly determined center location is derived and shown to cause effective changes to the sampled spatial frequency of the sinusoidal Siemens star target. Mitigation of the errors introduced by incorrectly determined centers through increasing angular segmentation of the star target is discussed, and it is shown that imagers with a better resolution performance (i.e., higher SFR) suffer more from incorrectly determined centers than an equivalent system with a worse performance. This document begins by discussing the generalized process for measuring the SFR of an optical system from the image of a sinusoidal Siemens star target. A mathematical analysis of measured intensity values given a sinusoidal Siemens star target with an incorrectly determined center is discussed. The results are summarized and future areas of investigation are proposed
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