Download Combating Mirror Seeing

Optics - The Series
Solid Mirror Performance Loss From Thermal Mass
Shane Santi – President
Dream Telescopes & Accessories, Inc.
Copyright 2017 – v3
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.
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 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 parameters, 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 up to two or more magnitudes larger means the previous “gains” are
buried in the noise and therefore pointless. Adding excess costs to the optic(s).
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.
Mirror seeing is the performance loss at the boundary layer that is caused by the thermal mass of
the mirror. Internal temperature gradients within non-zero-expansion mirrors will cause thermoelastic distortions, changing the overall figure of the optical surface. Like boundary layer issues
distortions caused by internal temperature gradients can occur far longer than most are aware.
Over-reaching claims regarding the quality of such surface’s can fly in the face of the
mechanical, thermal and environmental realities inherent to a non-zero-expansion solid mirror.
The importance of material science in optics cannot be overstated.
As G.W. Ritchey2 found with 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 distortion in those outer zones. In
the case of the 60” & 100” mirrors the zones extended in 5” and 15” in radius respectively. At
times Ritchey would mask off the 60” to a 50” aperture. That’s an areal loss of 30.6% for the
mirror.
The general rule of thumb is that no noticeable degradation will occur when a mirror is within
+0.1°C/-0.2°C of the ambient temperature. When a mirror is within this tolerance it could be
considered at equalization with ambient temperature. This is a very small window and it applies
to all mirror materials, including zero-expansion mirrors. 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, it will still have performance-robbing mirror seeing, at the boundary layer.
Fig. 1: Heat coming off a 220mm diameter solid mirror that is 25mm thick; zenith-angle..
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.
You can see the thermals moving above the mirror in Fig. 1, from left to right in the series of
three photos. All three of these 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 and all instruments. The exact movement, 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. 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. If mirror seeing is not addressed, 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 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, according to Lowne.
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 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.
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 in Fig. 3. It also illustrates why performance loss is dynamic
and complex in nature. The distortions shown here could be considered anisoplanatic, much like
differential atmospheric seeing produces different levels of distortion within large fields.
It should be noted that although the visual signs of thermals will disappear from a person’s view
before the mirror is within +0.1°C to –0.2°C of the ambient temperature, performance loss is still
occurring. Like viruses and bacteria, out of (visual) sight, out of mind does not mean the
problems are eliminated. Performance loss is still occurring.
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
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



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 of the material.
Zerodur will equalize 1.1x faster than Borofloat when both are the same thickness, say 25mm.
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. In the same thickness aluminum
will equalize 95.7x faster than Zerodur and 106.5x faster than Borofloat. This should put the
modest difference between Borofloat and Zerodur into perspective, as well as shed light on the
importance of material science; understanding materials and their properties.
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 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 in the mirror drops it becomes more difficult to process and is
more difficult to support in the instrument. Astigmatism, one of the most common errors
remaining in moderate to large 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.
There is an important distinction here. Improvements rarely mean the optic is 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.
Another way to combat mirror seeing is the use of air flow. Lowne1 and others have shown that
knocking down the boundary layer can provide improved results. However, thermals and air
flow are complex, leading solutions to be inconsistent and less than optimal. The best air flow is
laminar and across the entire mirror’s surface. In the case of a Cassegrain with a M1 baffle tube,
producing a constant and laminar air flow that can move across the entire mirror is impossible,
because of the obstruction of the baffle, which will cause disruption in the air flow.
Laminar air flow is difficult to achieve in reality because even if no structures were in the way,
air flow would have to coincide with any natural flow, like wind. Observatory enclosures that
have modern design features allow the exchange of air between the interior and exterior,
otherwise observatory-seeing will become a large performance loss itself. Both active, forced
ventilation through the use of fans/blowers, and passive, natural wind flowing through opened
louvers, etc., will have a directional component to that air flow. For passive systems that air
flow direction can change dynamically, since it is controlled by local weather patterns. All of
these create additional complexity because the telescope is dynamically changing angles as well.
This means performance loss will change due to varying alignment or misalignment of air flow
patterns, telescope angles, wind speeds at any given time, etc. This is far from controlled and
consistent performance. It is not addressing the source of the thermal problem(s).
Some modern facilities have insulated the observatory and condition (control) the interior
temperature during the day. An attempt is made to have the interior temperature at the nighttime,
opening temperature. This way there is “no” delta because all components inside the
observatory are at the opening, ambient temperature already. This can make a dramatic
improvement in performance. However, the opening temperature estimates have to be accurate
to +0.1°C to –0.2°C of ambient temperature. This small temperature tolerance is not an easy
temperature accuracy to achieve inside an observatory. If a person can estimate temperatures to
this level of accuracy, astronomy/optics is not their calling, meteorology is.
Even if the opening interior temperature very closely matches the outside ambient temperature,
optimal performance is only maintained if interior and exterior temperatures remain static. This
points to the next problem, which is that most locations will see temperature changes during the
night. During the night a 5°C change over six hours might be too much for a given diameter,
thickness, etc., mirror to stay within the tight thermal window. Remember, everything
surrounding the mirror will also influence the total TTC.
The most efficient way to beat mirror seeing is to greatly reduce the amount of mirror material,
while simultaneously increasing mirror surface area. This addresses the problem directly and is
done through the use of lightweight mirror technology; cast, fused, frit-bonded or pocket-milled
from a solid. G.W. Ritchey was a strong proponent of cellular mirrors and first started creating
and using them in 1912; 105 years ago.5
Using our 220mm diameter example we will compare a lightweight Borofloat mirror, which has
features no greater than 3.175mm thick, to a solid Zerodur mirror that has a 6:1 aspect ratio
(36.67mm thick). TTC shows that the lightweight Borofloat mirror will equalize 119.9x faster
than the solid Zerodur mirror. If we compare a 400mm lightweight Borofloat mirror (3.175mm
features) to a 400mm Zerodur solid mirror that has a 6:1 aspect ratio, the lightweight mirror will
equalize more than 400x faster. If the solid Zerodur mirror took six hours to equal, then the
lightweight mirror mentioned would equalize in less than one minute. Clearly this is a way to
deal directly with the issue, providing a substantial improvement.
This author has seen just such behavior in person. It not only improves the final use performance
of the mirror but it also eliminates any traditional delays required to bring the optic to
equilibrium while testing the mirror during processing. This means far more test, then
polish/figure iterations can be done. This greatly reduces fatigue in the optician.
TTC is not accounting for surface area or forced air, so the lightweight mirror will equalize faster
than just mentioned. It is also not accounting for the lower mass mirror mount and surrounding
structures, since the lightweight mirror is 3-6x lower in mass, which does not require such heavy
support and main structures around it, thereby decreasing the insulative affect normally
associated with those structures.
Although a 12:1 aspect ratio Zerodur solid mirror will cool 4x faster than its 6:1 solid Zerodur
counterpart, 4x doesn’t compare to the 119.9 and ~400x thermal performance improvements of
the Borofloat lightweight mirror mentioned above. The thin solid mirror will still have quite
large thermal performance loss and, because stiffness was sacrificed (by doubling the aspect
ratio), it now has additional problems.
Fig. 4: Charting different types and thickness mirrors – 0.7m in diameter.
Fig. 4 shows the performance of 700mm diameter mirrors of different types and thickness. One
of the important details to notice is the heel of the cellular mirror temperature line, since the
heals of the other mirrors are literally off the chart. All mirrors will exponentially slow as they
approach ambient temperature. This is why it can literally take all night for a 400-500mm fullthickness (6:1) solid mirror to equalize to ambient temperature. If no forced air is used and the
solid mirror is buried in a solid telescope tube, it may not reach equalization over a given night.
Thin-featured borosilicate-based lightweight mirrors not only equalize extremely fast to a static,
different temperature but are also extremely nimble, able to quickly follow ever-changing
ambient temperatures, which are typical in astronomical and other applitcations. This means the
internal temperature gradients, which cause thermo-elastic distortions in solid and even thickfeatured lightweight mirrors, will not show distortion of the optical surface1.
Thermal issues with a mirror have no relationship to atmospheric seeing. In other words, good
atmospheric seeing will not improve or change the inherent thermal properties and
characteristics of the mirror. No amount of polishing to perfection by the optician will change
this fact either. Mirror-seeing is a loss of performance, due to the mirror’s own thermal issues.
Thermals from sources other than the mirror(s) can get into the light path and cause performance
losses. In order to minimize mirror and instrument seeing both mirrors and the telescope
structures need to be equalized. Ever-changing ambient temperature makes achieving the tiny
thermal equilibrium window even more difficult; a tiny, moving target. Understanding through
education can help in making the right choices, choices that allow the utmost in performance.
1: Journal Of RASC 1928 VolXXIII, Part II, New Astrophotography, p376 G.W. Ritchey
http://adsabs.harvard.edu/full/1928JRASC..22..359R
2: Journal Of RASC 1928 VolXXIII, Part II, New Astrophotography, p374 G.W. Ritchey
http://adsabs.harvard.edu/full/1928JRASC..22..359R
3: Reducing Mirror Seeing Problems In Mensicus Mirrors. Barr, et al., pg. 596:
http://articles.adsabs.harvard.edu/cgi-bin/nphiarticle_query?bibcode=1988ESOC...30..595B&db_key=AST&page_ind=0&plate_select=NO&
data_type=GIF&type=SCREEN_GIF&classic=YES
4: Thermalizing a telescope in Antarctica - Analysis of ASTEP observations - T. Guillot, et al. 2015
The bottom left of page 17 shows that for every 1°K temperature difference between M1 and the ambient air
temperature, there is a 0.23 arc-second degradation at the focal plane. This correlates well with other papers I’ve
read over the last 20 years that state 0.25” degradation per 1°C.
https://arxiv.org/pdf/1506.06009.pdf
5: Journal Of RASC 1929 VolXXIII, Part V, New Astrophotography. Footnote 2 on page 17 (pg 8 of pdf).
http://adsabs.harvard.edu/full/1928JRASC..23..15R
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