Related Experiment Video
Updated: Jun 12, 2026

11:11
Experimental Methods for Investigation of Shape Memory Based Elastocaloric Cooling Processes and Model Validation
Published on: May 2, 2016
Surface figure changes due to thermal cycling hysteresis
Applied Optics
|June 5, 2010
Summary
Thermal cycling hysteresis can distort mirror surfaces, especially with nonuniform heating. Standard Zerodur showed distortions, but a new experimental Zerodur and other materials like ULE and Cer-Vit did not exhibit this hysteresis effect.
Area of Science:
- Materials Science
- Optical Engineering
- Thermal Analysis
Background:
- Low expansivity mirror substrates are critical for high-precision optics.
- Thermal cycling can induce stresses and affect the surface figure of optical components.
- Understanding material behavior under thermal stress is essential for mirror substrate selection.
Purpose of the Study:
- To investigate the impact of thermal cycling hysteresis on the surface figure of low expansivity mirror substrates.
- To identify which materials exhibit hysteresis and under what heating conditions.
- To evaluate potential solutions for mitigating hysteresis-induced distortions.
Main Methods:
- Thermally cycled 20.3-cm (8-in.) diameter mirrors and dilatometer samples made of Zerodur, ULE, and Cer-Vit.
- Applied thermal cycling rates of 6 K/h and 60 K/h.
- Utilized both uniform and nonuniform heating methods.
Main Results:
- Figure distortions up to lambda/10 were observed exclusively with nonuniform heating of standard Zerodur.
- Standard Zerodur was the only material exhibiting measurable thermal hysteresis.
- A new experimental formulation of Zerodur demonstrated no thermal hysteresis.
Conclusions:
- Nonuniform heating during thermal cycling is the primary cause of surface figure distortion in standard Zerodur substrates due to thermal hysteresis.
- ULE and Cer-Vit materials, along with the new experimental Zerodur, are more robust against thermal cycling hysteresis.
- Material selection and controlled heating are crucial for maintaining surface figure integrity in precision optics.
Related Concept Videos
Heating and Cooling Curves
When a substance—isolated from its environment—is subjected to heat changes, corresponding changes in temperature and phase of the substance is observed; this is graphically represented by heating and cooling curves.
For instance, the addition of heat raises the temperature of a solid; the amount of heat absorbed depends on the heat capacity of the solid (q = mcsolidΔT). According to thermochemistry, the relation between the amount of heat absorbed or released by a substance, q, and its...
For instance, the addition of heat raises the temperature of a solid; the amount of heat absorbed depends on the heat capacity of the solid (q = mcsolidΔT). According to thermochemistry, the relation between the amount of heat absorbed or released by a substance, q, and its...
Thermal expansion and Thermal stress: Problem Solving
San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55 °C.
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55 °C.
Thermal Stress
If the temperature of an object is changed while it is prevented from expanding or contracting, the object is subjected to stress. The stress is compressive if the object expands in the absence of constraint and tensile if it contracts. This stress resulting from temperature change is known as thermal stress. It can be quite large and can cause damage. To avoid this stress, engineers may design components so they can expand and contract freely. For instance, on highways, gaps are deliberately...
Temperature Dependent Deformation
In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...
Thermal Strain
Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
Fatigue
Fatigue occurs when materials rupture under repeated or fluctuating loads, even at stress levels far below their static breaking strength. It typically results in brittle failure, even for ductile materials. It is a critical consideration in designing machines and structural components subjected to repetitive or varying loads. The nature of these loadings can range from fluctuating loads like unbalanced pump impellers causing vibrations to repeatedly bending a thin steel rod wire back and forth...

