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Form and Wavefront Metrology

Working Group 4.21

New Deflectometric Flatness Measuring Systems

In industry, the demand for high-precision flatness measurements with both smaller uncertainties and larger specimens is constantly increasing. This is why new measuring systems [1-4] for absolute high-precision topography measurements of plane surfaces were installed at PTB.The so-called DFR systems (Deflectometric Flatness Reference) are based on deflectometric measurement principles. It allows both circular specimens up to 700 mm and elongate specimens up to 1 m to be measured in horizontal as well as in vertical position. With the flatness measuring system, an uncertainty down to 0.1 nm (depending on the specimen) is being aimed at for the 95% confidence interval.

In the case of the new systems, two different deflectometry methods are applied which will, in the following, be referred to as "direct deflectometry" and "difference deflectometry". A common feature of these two methods is that the topography of the specimen is reconstructed by means of a high-precision angle measurement, which is realized by an autocollimator.

In the case of the direct deflectometry method (see Fig. 1), the slopes σ(xk) are measured with a high-precision autocollimator (accuracies less than 0.01 arcsec). The autocollimator is thereby firmly connected with the granite base, while the specimen is scanned with the beam deflector.

Fig. 1: Principle of the direct deflectometry

The topography  h(xk) is obtained "directly“ by summation of the measured slope angles σ(xk):



An advantage of the direct deflectometry method are the short measuring times. A disadvantage are the changing optical lengths of the autocollimator beam. This makes the calibration of the autocollimator more demanding and time-consuming.

In the case of the difference deflectometry, angle differences between positions with fixed distances - the so-called shears si - are measured (see Fig. 2). This method is also called the "Extended Shear Angle Difference (ESAD) procedure". It has been invented in the working group and realized in the so-called ESAD measurig system.


Fig. 2: Principle of the difference deflectometry

To obtain an unambiguous solution here, usually two shears s1 and s2, which are prime to each other, are required. The measurement results in the following angle differences:

Δ σ ( xk , si ) = σ ( xk + si ) - σ ( x) with i = 1,2 for k = 1,2, ...n

From this, the slope angles σ(xk ) can be calculated by the so-called natural extension and by means of transfer functions [4]. From these slope angles, the topography h(xk) is calculated in accordance to equation (*) . An advantage of difference deflectometry is the almost constant optical length of the autocollimator light.

Fig. 3 shows a photo of the system for horizontal orientated specimens and Fig. 4 shows a photo for vertical orientated specimens. The DFR system for the horizontal orientated specimens can be measured with the direct and the difference deflectometry procedure. The DFR system for vertical orientated specimens uses the difference deflectometry procedure.

Fig. 3: Constructional sketch of the set-up for lying specimens (AC: autocollimator, PP: pentaprism)

In cooperation with WG 8.42 "Data Analysis and Measurement Uncertainty", models are developed in order to quantify, for example, the influences of guidance errors, autocollimator errors or non ideal optics and in order to be able to calculate the measurement uncertainty.

The new flatness measuring systems are currently evaluated and subsequently used both for customer and for comparison measurements. In addition, the systems were used for  investigation of new flatness measuring method with higher lateral resolution, for example  the so-called Exact Auto Collimation Deflectometric scanning (EADS) [5].