**7. Thermal stability**

### **7.1 Temperature stability requirement of ±0.01°C to ensure the 0.1µrad rms accuracy**

After much experience with LTP stability scan measurements, we have seen that thermal variation has a significant impact on the ability to achieve 0.1 µrad rms slope error measurements. One can clearly see that slope error variations follow temperature fluctuations. Some precision profiler measurements require averaging of several tens of repeated measurements in order to achieve 0.1µrad accuracy, and 2-D testing also requires much longer scanning time for multiple lines measurements in X and Y directions. In addition, the thermal drift effects are always delayed for one hour or more. So we use a 15 hour stability scan test as the standard procedure to verify measurement stability.

Fig. 25 is a stability comparison measurement between the LTP II and the PTLTP made at NSRRC in Taiwan (Qian & Wang, 2005). Test beams are sent from both LTP II and PTLTP to the same test point on the mirror through comparison unit, and then each reflected beam is divided into two beams back to two LTPs individually.

Fig. 25. Stability comparison test between the LTP II and the PTLTP made at NSRRC in Taiwan

Four files of stability scan are obtained simultaneously. Each LTP receives two reflected beams sent from itself and from the other. Fig.26 a) is the temperature oscillation during the test. Fig. 26 b) is the slope errors of 4 stability scans. 2 large slope error curves are: beam is sent from LTP II; and 2 small slope error curves are: beam is sent from PTLTP no matter it is accepted by which LTP. These indicate: a) Slope error exactly follows temperature fluctuation period but with some delay; b) The LTP II has large stability error due to adopting unstable non-monolithic beam splitting structure; c) When temperature oscillation

Another versatile at-wavelength technique has been developed by Souvorov (Souvorov et al., 2002) and by Yumoto(Yumoto et al., 2006) and their coworkers, based upon the phase retrieval algorithms of Fienup (Fienup, 1982). By measuring the intensity variations in propagating x-ray beams downstream from a reflection or transmission element, the phase of the wave-front can be computed and projected back to the surface of the optical element. Yumoto has shown that surface figure errors measured by visible light interferometric means and by the phase retrieval methods agree to better than 1.5 nm on an 80mm long mirror. This method has the advantage over visible light interferometry in that it is sensitive to errors in the multilayer coatings on the optics, resulting in a measurement of the actual

performance of the optic rather than just the profile of the top-most surface layer.

hour stability scan test as the standard procedure to verify measurement stability.

divided into two beams back to two LTPs individually.

Fig. 25 is a stability comparison measurement between the LTP II and the PTLTP made at NSRRC in Taiwan (Qian & Wang, 2005). Test beams are sent from both LTP II and PTLTP to the same test point on the mirror through comparison unit, and then each reflected beam is

Fig. 25. Stability comparison test between the LTP II and the PTLTP made at NSRRC in

Four files of stability scan are obtained simultaneously. Each LTP receives two reflected beams sent from itself and from the other. Fig.26 a) is the temperature oscillation during the test. Fig. 26 b) is the slope errors of 4 stability scans. 2 large slope error curves are: beam is sent from LTP II; and 2 small slope error curves are: beam is sent from PTLTP no matter it is accepted by which LTP. These indicate: a) Slope error exactly follows temperature fluctuation period but with some delay; b) The LTP II has large stability error due to adopting unstable non-monolithic beam splitting structure; c) When temperature oscillation

**7.1 Temperature stability requirement of ±0.01°C to ensure the 0.1µrad rms accuracy**  After much experience with LTP stability scan measurements, we have seen that thermal variation has a significant impact on the ability to achieve 0.1 µrad rms slope error measurements. One can clearly see that slope error variations follow temperature fluctuations. Some precision profiler measurements require averaging of several tens of repeated measurements in order to achieve 0.1µrad accuracy, and 2-D testing also requires much longer scanning time for multiple lines measurements in X and Y directions. In addition, the thermal drift effects are always delayed for one hour or more. So we use a 15

**7. Thermal stability** 

Taiwan

dropped to ±0.01°C (flat section of the temperature curve), the stability over 15 hours was below 0.1rad rms.

Fig. 26. a) LTPs temperature during the stability scan (without enclosure); b) Stability comparison test: 1) 2 large slope error curves: beam is sent from LTP II; 2) 2 small slope error curves: beam is sent from PTLTP

Another stability measurement with an f=150mm LTP had a larger slope of 0.17rad rms due to larger temperature variation of 0.07°C (Fig. 27 a). The Fig. 27 b) shows the 0.156 rad rms stability test of 15 hours in X-direction with an improved 2D CCD system (f'=400 mm) while temperature variation of 0.2 °C (P-V). These stability measurements verify that the ±0.01°C temperature stability is necessary to ensure much less stability slope error than 0.1rad rms.

Fig. 27. a) Stability tested over 15 hours on f=150mm LTP with temperature variation of 0.07°C; b) The 15 hours stability test in X-direction with an improved 2D system (f'=400 mm) while temperature variation of 0.2 °C (P-V)

#### **7.2 Error reduction caused by thermal or mechanical drift**

Recently, Yashchuk has developed measurement techniques that correct for slow thermal and mechanical drift errors that are inherent in typical LTP measurements (Yashchuk, 2009). His methods involve making a series of measurements on a surface in the forward and reverse directions with the mirror rotated to the 180 and 0 orientations. Correcting these slow drift effects greatly improves the accuracy of the measurement. A project is underway to design a next-generation optical profiler that will incorporate an automated mirror rotation mechanism into the system so as to avoid operator intervention between scans (Yashchuk, 2011).
