Length Stability

Reiner Haug, Wilfried Heimerl, Burkhard Speit 4.5.1 Length Stability 

Originally developed as a mirror blank for large astronomical telescopes, Zerodur is today also used in X-ray telescopes and in a number of high-precision optical applications, such as laser gyroscopes, reflective optics for microlithography, or distance-defining parts in laser resonators. 

For all these applications Zerodur has to be used because its coefficient of thermal expansion (CTE) is practically zero within a large temperature range. This very low CTE is achieved by the special microstructure of the glass ceramic Zerodur which comprises two phases  

Both phases can be adjusted in such a way that the overall CTE nearly vanishes. 

As the requirements for the stability of high-precision instruments in which Zerodur has to be used because of its benefits are increasing progressively, it has become apparent that there is a limit to dimensional stability if the relative length changes Al/l of a Zerodur part are required to remain of the order of 10 or less, certain temperature cycles such as 

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Figure 2 Schematic diagram of the time-resolved IR spectrometer. CLS, cavity length stabilizer SHG, second harmonic generator IS, intensity stabilizer BPS, beam pointing stabilizer CS, coherent seeder PR, polarization rotator.

The long-wave-length stability expressed in eq. (10.23) also states quite interestingly that for m= 1, i.e., a Newtonian viscous bar,... 

In general, a DRO is overconstrained this makes smooth tuning of these devices difficult. Specifically, to maintain a single output frequency, the length stability of the resonator length normally has to be of the lenght order of, or better than, 1 nm. In contrast, for an SRO device. Equation (4.5) implies a required length stability of only a few hundred nanometres. 

Interferometric measurements lead to even higher degrees of accuracy on the other hand, these measurements are distinguished by very expensive sample preparation procedures and very long measuring times. Interferometrical measurements were performed with Zerodur , investigating its length stability by the above-mentioned standardization institutes [4.44,45,49,50]. 

There are three temperature ranges where length stability may be diminished by changes of expansion or GTE ... 

Scales and gauges from the glass ceramic Zerodur are also in widespread use, since they are the temperature-independent standard for length measurement (see Fig. 4.73). This usage takes advantage of another property of Zerodur - the length stability over time. 

O. Lindig, W. Pannhorst Thermal expansion and length stability of Zerodur in dependence on temperature and time , Appl. Opt. 24, 3330-3334 (1985)... 

O. Lindig, W. Pannhorst Thermal expansion and length stability of Zerodur in dependence on temperature and time , Appl. Opt. 24, 3330 3334 (1985) W. Pannhorst, R. Haug, E. Rodek, K. Stetter Hysteresis effects in low expansion glass-ceramics , J. Non-Cryst. Solids 131—133, 488-491 (1991)... 

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