Optics - The Series
Performance Losses From Thermal Issues Of Mirrors
Shane Santi – President
Dream Telescopes & Accessories, Inc.
Copyright 2017 – v4
In 1928 George Willis Ritchey wrote, "We shall look back and see how inefficient, how primitive it was to work with thick, solid mirrors, obsolete mirror-curves, ..."1 He was talking about the performance loss that is associated with front-surface solid mirrors. The vast majority of applications that use mirrors have been dealing with these thermal issues since the first use of solid glass mirrors 166 years ago. Solid metal mirrors started 349 years ago.
More recently optical surface quality has increased dramatically. This has come about due to;
· Accuracy & reliability of optical metrology
o Global, mid-spatial and high-spatial frequency errors can now be quantified to lower thresholds than ever before
o Radius, conic and other optical parameters that also affect the performance of the system can now be quantified to a lower threshold than ever before
· Performance improvements in optical finishing
o Brought on by the above improvements in optical metrology
o More recent scientific studies into every aspect of optical finishing
o More recent methods of finishing, like deterministic polishing
· Greatly improved capabilities for optical and mechanical analysis using modern software and the powerful modern computer.
Improvements in the optical surface have drawn more attention to the remaining errors in the system. If far tighter tolerances for conic and radius, to name two of many, have reduced errors attributed to them at the focal plane down to the 0.1 to 0.01 arc-second (“) range, then ignoring errors that are two or more magnitudes larger means the previous “gains” are buried in the noise and therefore are not benefiting the system.
Optimal performance of a mirror (or lens) will occur when it is within +0.1°C/-0.2°C of the ambient temperature. When a mirror is within this tolerance it can be considered at equalization with the ambient temperature.
Thermal issues caused by a given mirror can be from;
· boundary layer issues; “at” and directly above the optical surface and
· internal temperature gradients within non-zero-expansion mirrors.
Performance loss at the boundary layer is caused by the thermal mass of the mirror. Although the degradation is occurring outside the mirror and is considered external, the source of the thermals is the mirror itself. Thermal mass, and therefore performance loss at the boundary layer, is driven by the below four factors. Note that Coefficient of Thermal Expansion (CTE) is not one of them.
· thickness of the mirror (mirror disk or similar) or its features (ribs, etc.),
· thermal conductivity of the mirror material,
· specific heat capacity of the mirror material and
· density of the mirror material.
Internal temperature gradients within non-zero-expansion mirrors will cause thermo-elastic distortions, changing the figure of the optical surface. These are driven by CTE, as well as the four factors listed above. Other typically much more dynamic factors will influence the real-world performance of the mirror, like the starting delta between the mirror and ambient air temperature, insulating factors (mirror mounts, telescope tubes, etc., which slow equalization even further), air flow, etc. Because those factors can vary by such large amounts, they are typically not considered when evaluating the performance of a mirror and/or system initially.
For a borosilicate-based 400mm solid mirror that is 2" thick (8:1 aspect ratio), a 1°C internal gradient will distort the figure of that optic by roughly 1/3rd wave (~183nm of physical distortion). Like boundary layer issues, distortions caused by internal temperature gradients will continue long after visual cues disappear. Out of sight, out of mind is unfortunately not a good optical metrology tool in this instance. Over-reaching claims regarding the quality of such surface’s can contradict the mechanical, thermal and environmental realities inherent to the given mirror. The importance of basic material science and mechanical knowledge is vital in cutting through common promotional statements.
G.W. Ritchey2 found that the 60” Mt. Wilson & 100” Hooker primary mirrors both experienced an “edge effect.” The outer portion of the solid glass mirror would cool faster than the interior portion of the mirror, thus creating thermo-elastic (figure) distortion in those outer zones. In the case of the 60” & 100” mirrors the zones extended in 5” and 15” in radius respectively. If we assume both telescopes have a 30% central obscuration, then;
60” primary 2827.4 square inches (in²) 100” primary 7854.0 in²
20” secondary 314.2 in² 30” secondary 706.9 in²
Total Area 2513.2 in² Total Area 7147.1 in²
60” primary* 1963.5 square inches (in²) 100” primary* 3848.5 in²
20” secondary 314.2 in² 30” secondary 706.9 in²
Total Area 1649.3 in² Total Area 3141.6 in²
* 60” masked down to 50” and 100” masked down to 70”.
The 60” unmasked telescope has 1.52 times (2513.2/1649.3 or 52.4%) more total surface area than the masked version. The 100” unmasked telescope has 2.28 times (7147.1/3141.6 or 127.5%) more total surface area than the masked version.
The equalization range (+0.1°C/-0.2°C of the ambient temperature) is an extremely small window and it applies to all mirror materials, including zero-expansion mirrors. Although a zero-expansion mirror (alone) will show little to no detectable figure distortion as temperature changes, it will continue to have boundary layer issues because the optic still has thermal mass.
If a mirror mount made from a zero-expansion material supports the zero-expansion mirror, then whatever distortion the mirror mount is causing at one temperature and static angle will remain the same as temperature changes. More often than not inexpensive and high CTE aluminum is used with zero-expansion mirrors. As temperature changes, the zero-expansion mirror itself changes little but is being distorted mechanically because the aluminum mirror mount is changing shape at a rate more than 400 times greater than the mirror.
When a zero-expansion mirror material is supported by an aluminum mirror mount, then figure distortion (due to internal temperature gradients within a non-zero-expansion mirror) has been traded for thermo-mechanically induced figure distortion due to the wildly mismatched mirror and mirror mount materials. Which one is larger depends on numerous factors and should be evaluated using modern engineering tools because the zero-expansion mirror does not always show the smallest (physical) error. Although this sounds like a mechanical issue outside this discussion, it would not exist if temperature were not changing (thermal).
Many statements made by manufacturers are based on a static temperature. The use of aluminum with a zero-expansion mirror material is perfectly fine when used in one or both conditions; a very temperature-controlled environment or flexures are designed into the mirror mount, to compensate for the differential CTE between the mirror and mirror mount materials.
The views shown in Fig. 1 through Fig. 3 look no different between plate glass, borosilicate and zero-expansion glass-ceramic mirror materials. So although a zero-expansion mirror will have extremely small thermo-elastic distortion internally, it will still have performance-robbing boundary layer issues, since CTE has nothing to do with the thermal mass of the mirror.
Fig. 1 shows a 220mm diameter solid mirror that is 25mm thick. Note how the double to triple set of lines around the mirror are disturbed. The thermals are coming from the mirror itself and are therefore passing directly through the hypersensitive boundary layer.
Fig. 1: Heat coming off a 220mm diameter solid mirror that is 25mm thick; zenith-angle..
You can see the thermals moving above the mirror in Fig. 1, from left to right in the series of three photos. The three photos were taken within 20 seconds. The exact behavior of these thermals cannot be stated in an all-encompassing rule that works for all mirrors, all assemblies, all instruments and all angles. The exact movement, scale of performance loss, time to equalization, etc., will be influenced by the mirror material’s thermal properties, mirror thickness, geometry and the nature of structures around the mirror, like the mirror support, telescope tube, air flow and numerous other factors mentioned earlier. Structures directly behind and around the mirror will act as insulators, making these degrading thermals even more prolonged than the mirror alone. Even at this initial glance it is clear that thermals, like optics, are complex.
In the case of an astronomical application a zenith-pointing (Fig. 1) primary mirror is looking through the thinnest section of atmosphere and will typically have the lowest performance loss due to atmospheric-based seeing. Fig. 1 shows that this position can be the worst for mirror-seeing.
Lowne (1979)3 examined performance loss for a 100mm solid mirror in a laboratory. He found performance loss had a linear relationship between the mirror’s bulk temperature and the ambient air temperature. He also found that zenith-pointing performance loss was ~0.8 arc-seconds (“)/°C and ~0.13”/°C when the mirror had a 50° zenith-angle. Because it is a linear relationship a 2°C delta between the mirror and the ambient temperature will produce 1.6” and 0.26” of degradation for each respective mirror angle.
Guillot4, et al, concluded that primary mirror seeing was 0.23”/°C for the 400mm f4.9 Antarctica telescope, which used a 405mm diameter solid Zerodur primary mirror that was 45mm thick (9:1). Other than the equalization temperature tolerance, which appears fairly universal, degradation numbers are far more subjective and specific to the particular mirror, instrument, observatory, local site conditions, etc.
Fig. 2: Heat coming off a 220mm diameter solid mirror that is 25mm thick; 45° zenith-angle..
Fig. 2 shows the same 220mm diameter mirror as shown in Fig. 1 but now at a 45° zenith-angle. Go here to gain access to videos: http://www.dreamscopes.com/BLvideos/ . Visually the bottom third to half of the mirror experiences fewer thermals. However, in all angles the author witnessed thermals emanating from regions that in most images appear to have far fewer thermals than others. This is logical since the thermals are originating from the entire mirror.
Fig. 3: Heat coming off a 220mm diameter solid mirror that is 25mm thick; 90° zenith-angle.
Fig. 3 shows the same 220mm diameter mirror but now at a 90° zenith-angle; optical axis pointing at the horizon. The first one or two images appear to relate well to Lowne’s work. But as previously stated thermals during this author’s work could be seen coming from other areas, illustrated in the far right image of Fig. 3. This also illustrates why performance loss is dynamic and complex. The distortions shown here could be considered anisoplanatic, much like differential atmospheric seeing produces different degrees of distortion within large fields.
It should be noted that these visually observed thermals would disappear well before the mirror was within 1.0°C of ambient temperature. Fairly large losses, regardless of the mirror material, are therefore still occurring. Always keep the scale of the optical surface errors and the scale of the equalization range in mind. Detailed studies over the decades have shown time and time again that performance loss is almost always occurring and can be quite large when no effort is made to minimize those losses.
All glass and glass-ceramic mirror materials want to hold onto their temperature (heat capacity) and are slow to conduct it away (thermal conductivity). This is the opposite of what we desire in a mirror. Thermals are driven by seven main factors;
· Heat Capacity of the mirror material
· Thermal Conductivity of the mirror material
· Density of the mirror material
· Thickness of the mirror substrate
· Temperature difference between mirror and ambient air
· Surface area of the mirror substrate
· Air flow around the mirror substrate
Using the formula for Thermal Time Constant (TTC), a measure of thermal responsiveness, we can compare different materials to each other. The formula accounts for the thickness of the material, heat capacity, thermal conductivity, and density, which are the same factors mentioned for thermal mass.
If we evaluate the same thickness material in Zerodur, Borofloat and aluminum we see that Zerodur will equalize 1.1x faster than Borofloat. Although aluminum is denser than both Zerodur and Borofloat, as well as being quite close to both in heat capacity, it has far superior thermal conductivity. Aluminum will equalize 95.7x faster than Zerodur and 106.5x faster than Borofloat. This puts the modest 10% difference between Borofloat and Zerodur into perspective. In the real world a 10% difference would be difficult to detect.
Combating Mirror Seeing -
One way to combat mirror seeing is to use thinner aspect ratio solid mirrors, since thickness is a key factor in how quickly a material will equalize. If we compare the same mirror material, we find that a solid mirror that is half as thick will equalize 4x faster. Unfortunately the stiffness of the thinner mirror is also 4x lower. Therefore we have improved one parameter but degraded another by the same amount.
If we double the diameter while also doubling the aspect ratio of a mirror (half the thickness), the larger, thinner mirror will cool 4x faster but it will be 16x lower in stiffness. This is equivalent to comparing a solid mirror that is 100mm with a 6:1 aspect ratio, to a 200mm mirror that has a 12:1 aspect ratio.
As the stiffness of the mirror itself drops it becomes more difficult to process and is more difficult to support in the instrument. Issues that didn’t show themselves in a thicker mirror now start to show more easily because it takes less errand force around and behind the mirror to bend it to noticeable levels. Astigmatism, one of the most common errors remaining in mirrors, becomes a greater hurdle as diameter and aspect ratio are increased. The use of highly accurate actuators and wavefront sensors, to control the figure of the thin mirror, is possible, but complex, expensive and itself adds thermal mass behind the mirror. Like most things in optics, there are no free lunches.
For a detailed discussion about stiffness and the 6:1 aspect ratio, please read the following; http://www.dreamscopes.com/images%26graphics/2017/DreamArticle_AspectRatio%26Stiffness_v4_043017.doc
There is an important distinction that should be made. An improvement does not imply that the optic is then operating at an optimal level. Most of the solutions listed here can make improvements but they are rarely, if ever, optimal. Performance loss is almost always still occurring when the underlying cause of the problem is not addressed directly.