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Deflectometric flatness metrology

Industry’s need for high-precision flatness measurements on large surfaces under test (SUTs) with uncertainties in the nanometer range is constantly growing. A measurement system for the high-precision absolute topography measurement of plane surfaces has therefore been set up at PTB [Ehr09a, Ehr09b, Ehr10, Schu10a, Schu10b]. The so-called deflectometric flatness reference (DFR) system is based on deflectometric measurement principles. It allows circular SUTs of up to 700 mm in diameter and longitudinal SUTs of up to 900 mm in length to be measured horizontally. The uncertainties aimed at with flatness measurement systems may reach, depending on the individual SUT, the subnanometer range for an individual section.

In the case of the DFR system at PTB, different deflectometric procedures are used. Among those are direct differential deflectometry and the so-called null method (EADS) [Ehr12a]. A common feature of all the methods is that the topography of the specimen is reconstructed by means of a high-precision angle measurement with the aid of an autocollimator. These are gradient methods, since the slopes of the SUT are measured, and these slopes are subsequently integrated to obtain the SUT’s topography.

In the case of the direct deflectometric method (see Fig. 1), the gradient angles σ(xk) are measured with a high-precision autocollimator (accuracies less than 0.01 arcsec). The autocollimator is permanently connected to the granite base while the SUT is being scanned by means of the beam deflector


Fig. 1: The principle of direct deflectometry

The topography h(xk) is obtained directly by summing up the measured gradient anglesl σ(xk):

The advantage of the direct deflectometry method lies in its short measuring times. Its disadvantage is that the optical path lengths of the autocollimator beam vary. This makes the calibration of the autocollimator more demanding and time-consuming. With these methods, it makes no sense to use apertures smaller than 3 mm, since commercially available autocollimators then have a very poor signal-to-noise ratio.

Differential deflectometry is a measurement principle that consists in measuring angle differences between positions with fixed distances – the so-called shears si – (see Fig. 2). This method is also called the extended shear angle difference (ESAD) procedure. It was invented at PTB [Els02, Gec02].


Fig. 2: The principle of differential deflectometry

Here, two shears (s1 and s2), which are coprime, are usually required to obtain an unambiguous solution [Els02]. The measurement yields the following angle differences:

Based on this, the gradient angles σ(xk) can be calculated using the so-called natural extension and by means of transfer functions [Els02]. From the reconstructed gradient angles, the sought topography h(xk) is calculated in accordance with formula (*). The advantage of difference deflectometry is the almost constant optical length of the autocollimator beam.

Another method, which was developed at PTB, is the so-called exact autocollimation deflectometric scanning (EADS) method [Schu10a, Ehr12a] (see Fig. 3). This method consists in orienting the SUT vertically to the beam by means of a piezo actuator; this procedure is repeated at each scanning position. In doing so, the autocollimator AC1 fulfils the task of a null indicator. The autocollimator AC2 measures the slope of the SUT σ(xk). The global topography is obtained by summing up the measured slopes. The advantage of this method is that AC1 works as a null indicator, so that a specifically adjusted null indicator with a higher lateral resolution can also be used. The optical path length of AC2 is nearly constant. This allows measurements with a larger aperture, which, in turn, leads to an improved signal-to-noise ratio.


Fig. 3: The principle of the EADS method

Figure 4 shows photos of the DFR system.


Fig. 4:
Photos of the DFR system (left: without casing; right: with casing)


Models have been developed in collaboration with  WG 8.42, Data Analysis and Measurement Uncertainty. This has been done to quantify parameters such as the influences of guidance accuracies, autocollimator errors and non-ideal lens systems on the measurement uncertainty and thus to compute the measurement uncertainty [Ehr12a].

This system allows calibrations to be performed for individual sections. The system is currently being enhanced so that measurements with lateral resolutions in the submillimeter range can be offered [Ehr17a]. The EADS method will be used for this purpose (see Fig. 3).

Selected publications

[Ehr19a] G. Ehret, H. Reinsch, M. Schulz: “Interferometric and deflectometric flatness metrology with nanometre measurement uncertainties for optics up to 1 metre at PTB“, Optical Metrology and Inspection for Industrial Applications VI , Proceedings of SPIE 11189  (2019), doi.org/10.1117/12.2538872

[Ehr17a] G. Ehret, S. Laubach, M. Schulz: „Flatness metrology based on small-angle deflectometric procedures with electronic tiltmeters“, Fouth European Seminar on Precision Optics Manufacturing ; Proceedings of SPIE: 10326, pp. 1032604-1 - 1032604-6  (2017) doi.org/10.1117/12.2268288

[Ehr12a] G. Ehret, M. Schulz, M. Stavridis, C. Elster, “Deflectometric systems for absolute flatness measurements at PTB,” Meas. Sci. Technol. 23 (2012) 094007 (8pp) doi.org/10.1088/0957-0233/23/9/094007

 [Schu10b] M. Schulz, G. Ehret, M. Stavridis, C. Elster: “Concept, design and capability analysis of the new Deflectometric Flatness Reference at PTB,” International Workshop on x-ray mirror design, fabrication and metrology, Osaka, Japan, Nucl. Instr. and Methods in Phys. Res. A616, pp. 134-139, (2010), doi.org/10.1016/j.nima.2009.10.108

[Ehr10a] G. Ehret, M. Schulz, M. Baier, A. Fitzenreiter, M. Stavridis, C. Elster: “Vergleich von hochgenauen deflektometrischen Verfahren für die Ebenheitsmetrologie,” 111. Jahrestagung der Deutschen Gesellschaft für angewandte Optik (DGaO), Wetzlar, 25-29, Mai, 2010, [Online only], (2010), www.dgao-proceedings.de/download/111/111_a20.pdf

[Schu10a] M. Schulz, G. Ehret, A. Fitzenreiter: „Scanning deflectometric form measurement avoiding path-dependent angle measurement errors,,”  Journal of the European Optical Society: Rapid Publications (2010), www.jeos.org/index.php/jeos_rp/article/view/10026/596

[Ehr09a] G. Ehret, M. Schulz, M. Baier, A. Fitzenreiter: “A new optical flatness reference measurement system,” DGaO-Proceedings, 110. Jahrestagung der Deutschen Gesellschaft für angewandte Optik (DGaO), Brescia, 02-05, Juni, 2009, (2009),  www.dgao-proceedings.de/download/110/110_p22.pdf

[Ehr09b] G. Ehret, M. Schulz, M. Stavridis, C. Elster: “A new flatness reference measurement system based on deflectometry and difference deflectometry“, Fringe: 6th International Workshop on Advanced Optical Metrology: pp. 318-323, (2009), doi.org/10.1007/978-3-642-03051-2_52

[Els02] C. Elster, I. Weingärtner:  Solution  to  the  Shearing  problem,  Applied Optics 38 (23):5024-5031, 1999.  [2] R. D. Geckeler, I. Weingärtner: „Sub-nm Topography Measurement by Deflectometry: Flatness Standard  and  Wafer  Nanotopography“,  in  Proc. of SPIE 4779:1-12, (2002), doi.org/10.1364/AO.38.005024

[Gec02] R. D. Geckeler, I. Weingärtner: Sub-nm Topography Measurement by Deflectometry:  Flatness  Standard  and  Wafer  Nanotopography,  in  Proc. of SPIE 4779:1-12, (2002), doi.org/10.1117/12.451723


Dr.-Ing. Gerd Ehret

Phone: +49 531 592-4220
E-Mail: gerd.ehret(at)ptb.de