J. Eur. Opt. Society-Rapid Publ. 2025, 21, 20 Ó The Author( s), published by EDP Sciences, 2025 https:// doi. org / 10.1051 / jeos / 2025012 Available online at: https:// jeos. edpsciences. org
EOSAM 2024 Guest editors: Luca De Stefano and Raffaele Velotta
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Influence of ambient temperature changes on the focus point for measurements of the modulation transfer function MTF
Hanno Dierke * and Markus Schake Physikalisch-Technische Bundesanstalt PTB, Bundesallee 100, 38116 Braunschweig, Germany
Received 24 January 2025 / Accepted 19 March 2025
Abstract. At Physikalisch-Technische Bundesanstalt( PTB), a multi camera measurement setup is developed for the traceable determination of the modulation transfer function( MTF) of objectives. In recent works the MTF of a reference objective is determined within the image field in an angular range of up to ± 20 ° to the optical axis. For the investigation of angular dependence of the transfer function, the MTF for a given spatial frequency is evaluated at a datum point. A common choice of the datum point is the focus point P f. There are different methods to obtain the focus point from the measurement data. In this contribution several approaches for the determination of the focus point are investigated and compared. In addition, owing to the temperature dependent extension of the measurement setup the position of the focus point strongly depends on the ambient temperature. We also present some results of investigations on the influence of temperature changes on the position of the focus point.
Keywords: Modulation Transfer Function, MTF, Focus point, Ambient temperature.
1 Introduction
The modulation transfer function( MTF) is a parameter commonly used to characterize the imaging properties of optical elements [ 1, 2 ]. The MTF contains information about the resolution as well as the ability of the optical element to transfer the object contrast into the image space. In addition, the MTF can be calculated on the basis of the design parameters, so that deviations from the calculated MTF provide an indication of existing imaging errors. At the Physikalisch-Technische Bundesanstalt( PTB), a measuring device for the traceable determination of the MTF in the image field( field angle currently h =± 20 °) is being set up based on a method proposed in ISO9335 [ 3 – 5 ]( Fig. 1). The following measurement modes can be used:
Measurement of the MTF in a fixed position for a range of spatial frequencies.
Measurement of the MTF for a selected spatial frequency in a range of positions along the optical axis z.
This mode will be referred to as“( through) focus scan”, as the measurement range usually includes the
* Corresponding author: hanno. dierke @ ptb. de so called focus point P f, which characterizes the position at which the MTF reaches its maximum value for a certain spatial frequency and when measuring along the optical axis( field angle h R = 0 °).
Measurement of the MTF in a range of positions along a rotated axis z 0 leading to several focus scans in the image field of the sample under test(“ field scan”).
A reference position is required in particular to determine the angular dependence of the MTF and to compare measurements. Usually, the focus point P f mentioned above is used. After assessing different approaches on the reliable determination of the focus point from the measurement data [ 6, 7 ] andtheinfluence of the employed camera [ 5, 8 ] this contribution is about the influence of changes in the ambient temperature on the measured position of the focus point P f owing to the thermal expansion of the measurement setup components.
2 Determination of the focus point P f
Previously, the focus point was determined by simply using the z coordinate of the data point with the highest MTF
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